Seminars: Mathematics@IISc

Seminars

By Year

Title: APRG Seminar: Macdonald's conjecture on hypergeometric functions associated to Jack polynomials

Speaker: Siddhartha Sahi (Rutgers University, USA)

Date: Thu, 06 Jun 2019

Time: 3:30 pm

Venue: LH-1, Mathematics Department

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Title: Algebra & Combinatorics Seminar: Metaplectic Representations of Hecke algebras

Speaker: Siddhartha Sahi (Rutgers University, USA)

Date: Tue, 04 Jun 2019

Time: 3:30 pm

Venue: LH-1, Mathematics Department

We construct certain representations of affine Hecke algebras and Weyl groups, which depend on several auxiliary parameters. We refer to these as “metaplectic” representations, and as a direct consequence we obtain a family of “metaplectic” polynomials, which generalizes the well-known Macdonald polynomials.

Our terminology is motivated by the fact that if the parameters are specialized to certain Gauss sums, then our construction recovers the Kazhdan-Patterson action on metaplectic forms for GL(n); more generally it recovers the Chinta-Gunnells action on p-parts of Weyl group multiple Dirichlet series.

Venue: LH-5, Mathematics Department

Consider the tensor product of two irreducible finite dimensional representations of a simple Lie algebra. The submodules generated by a tensor product of extremal vectors of the two components are called Kostant-Kumar submodules. These are parametrized by a double coset space of the Weyl group.

Littelmann’s path model is a very general combinatorial model for representations, which encompasses many classical constructs such as Young tableaux and Lakshmibai-Seshadri chains. The path model for the full tensor product is simply the set of concatenations of paths of the individual components. We describe a way to associate a Weyl group element (rather, a double coset) to each such concatenated path and thereby obtain a path model for Kostant-Kumar submodules.

Finally, we recall the many descriptions of Demazure modules, which may be viewed as the analog of the above picture for single paths (rather than concatenations). In this case, the Weyl group element associated to a path admits different descriptions in different path models in terms of statistics such as initial direction, minimal standard lifts and Kogan faces of Gelfand-Tsetlin polytopes. Along the way, we mention some relations to jeu-de-taquin and the Schutzenberger involution.

This is based on joint work with Mrigendra Singh Kushwaha and KN Raghavan.

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Title: Algebra & Combinatorics Seminar: The Brylinski filtration and W-algebras

Speaker: Sankaran Viswanath (IMSc, Chennai)

Date: Fri, 03 May 2019

Time: 3 pm

Venue: LH-1, Mathematics Department

Each finite dimensional irreducible representation V of a simple Lie algebra L admits a filtration induced by a principal nilpotent element of L. This, so-called, Brylinski or Brylinski-Kostant filtration, can be restricted to the dominant weight spaces of V, and the resulting Hilbert series is very interesting q-analogs of weight multiplicity, first defined by Lusztig.

This picture can be extended to certain infinite-dimensional Lie algebras L and to irreducible highest weight, integrable representations V. We focus on the level 1 vacuum modules of special linear affine Lie algebras. In this case, we show how to produce a basis of the dominant weight spaces that is compatible with the Brylinski filtration. Our construction uses the so-called W-algebra, a natural vertex algebra associated to L.

This is joint work with Sachin Sharma (IIT Kanpur) and Suresh Govindarajan (IIT Madras).

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Title: Algebra & Combinatorics Seminar: Suslin Matrices vs Clifford Algebras

Speaker: Vineeth Chintala (IIT, Bombay)

Date: Wed, 01 May 2019

Time: 3 pm

Venue: LH-1, Mathematics Department

In this talk, we will introduce the notion of an embedding of a quadratic space (in an associative algebra). Familiar examples of embeddings are given by Complex Numbers, Quaternions, Octonions, Clifford Algebras, and Suslin Matrices.

When there are two embeddings of the same quadratic space, then we can gather information about one embedding using the other. This is the main theme of the talk. To illustrate this, we will see the connection between Suslin Matrices and Clifford Algebras. In one direction, we are able to give a simple description of Clifford Algebras using matrices. Conversely, we can now explain some (seemingly) accidental properties of Suslin matrices in a conceptual way.

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Title: Determinantal processes and stochastic domination

Speaker: Raghavendra Tripathi (IISc Mathematics)

Date: Tue, 30 Apr 2019

Time: 11:30 am

Venue: LH-1, Mathematics Department

The systematic study of determinantal processes began with the work of Macchi (1975), and since then they have appeared in different contexts like random matrix theory (eigenvalues of random matrices), combinatorics (random spanning tree, non-intersecting paths, measures on Young diagrams), and physics (fermions). A particularly interesting and well-known example of a discrete determinantal process is the Uniform spanning tree (UST) on finite graphs. We shall describe UST on complete graphs and complete bipartite graphs—in these cases it is possible to make explicit computations that yield some special cases of Aldous’ result on CRT.

Time: 3 – 5 pm (with a 15 minute break at 3:45)

Venue: LH-1, Mathematics Department

According to Wikipedia, a continued fraction is “an expression obtained through an iterative process of representing a number as the sum of its integer part and the reciprocal of another number, then writing this other number as the sum of its integer part and another reciprocal, and so on.” It has connections to various areas of mathematics including analysis, number theory, dynamical systems and probability theory.

Continued fractions of numbers in the open interval (0,1) naturally gives rise to a dynamical system that dates back to Gauss and raises many interesting questions. We will concentrate on the extreme value theoretic aspects of this dynamical system. The first work in this direction was carried out by the famous French-German mathematician Doeblin (1940), who rightly observed that exceedances of this dynamical system have Poissonian asymptotics. However, his proof had a subtle error, which was corrected much later by Iosifescu (1977). Meanwhile, Galambos (1972) had established that the scaled maxima of this dynamical system converges to the Frechet distribution.

After a detailed review of these results, we will discuss a powerful Stein-Chen method (due to Arratia, Goldstein and Gordon (1989)) of establishing Poisson approximation for dependent Bernoulli random variables. The final part of the talk will be about the application of this Stein-Chen technique to give upper bounds on the rate of convergence in the Doeblin-Iosifescu asymptotics. We will also discuss consequences of our result and its connections to other important dynamical systems. This portion of the talk will be based on a joint work with Maxim Sølund Kirsebom and Anish Ghosh.

Familiarity with standard (discrete and absolutely continuous) probability distributions will be sufficient for this talk.

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Title: Counting nodal components of ‘boundary-adapted arithmetic random waves’

Speaker: James Cann (University College London, UK)

Date: Thu, 28 Feb 2019

Time: 2:15 pm

Venue: LH-1, Mathematics Department

The ‘nodal sets’ (zero sets) of Dirichlet Laplace eigenfunctions for the two-dimensional unit square have raised many questions over the past century. The nodal domain theorems of Courant (1924), Stern (1926) and Pleijel (1956), give deterministic (upper, liminf, and limsup resp.) bounds for the number of nodal domains which can be exhibited by an n-th eigenfunction, assuming the eigenvalues are ordered increasingly and with multiplicities listed. Prominent amongst contemporary research is the closely related question of the number of ‘nodal components’ (connected components of the zero set) of a ‘typical’ eigenfunction.

The spectral degeneracy for the square means that the nodal count of an n-th eigenfunction could take a wide range of values, and to understand the ‘typical’ behaviour of this number we attribute Gaussian random coefficients to a standard basis of eigenfunctions for each eigenspace, to form the ensemble of ‘boundary-adapted arithmetic random waves’. The number of nodal components —now a random variable— can then be studied, and this talk will draw together tools from various areas of mathematics (random fields, integral geometry, number theory, mathematical physics, …) in order to say a few things about its asymptotic properties.

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Title: Spectral asymptotics for a singularly perturbed periodic elliptic operator

Speaker: Klas Pettersson (University of Tromsø – The Arctic University of Norway)

Date: Tue, 26 Feb 2019

Time: 3 pm

Venue: LH-1, Mathematics Department

We consider a singularly perturbed Dirichlet spectral problem for an elliptic operator of second order. The coefficients of the operator are assumed to be locally periodic and oscillating in the scale ε. We describe the leading terms of the asymptotics of the eigenvalues and the eigenfunctions to the problem, as the parameter ε tends to zero, under structural assumptions on the potential. More precisely, we assume that the local average of the potential has a unique global minimum point in the interior of the domain and its Hessian is non-degenerate at this point.

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Title: Geometry & Topology Seminar: A compactness theorem for Einstein metrics on the four-sphere

Speaker: Harish Seshadri (IISc Mathematics)

Date: Mon, 25 Feb 2019

Time: 4 pm

Venue: LH-1, Mathematics Department

It is open question if the standard round metric on S^4 is the unique positive Einstein metric, up to isometry and scaling. In this talk, I will discuss a compactness theorem which rules out nonstandard unit-volume Einstein metrics whose scalar curvatures lie within a certain range.

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Title: Algebra & Combinatorics Seminar: Cohomology of modules over H-categories and co-H-categories

Speaker: Samarpita Ray (IISc Mathematics)

Date: Fri, 22 Feb 2019

Time: 3 pm

Venue: LH-1, Mathematics Department

An ordinary ring may be expressed as a preadditive category with a single object. Accordingly, as introduced by B. Mitchel, an arbitrary small preadditive category may be understood as a “ring with several objects”. In this respect, for a Hopf algebra H, an H-category will denote an “H-module algebra with several objects” and a co-H-category will denote an “H-comodule algebra with several objects”. Modules over such Hopf categories were first considered by Cibils and Solotar. In this talk, we present a study of cohomology in such module categories.

In particular, we consider H-equivariant modules over a Hopf module category C as modules over the smash extension C#H. We construct Grothendieck spectral sequences for the cohomologies as well as the H-locally finite cohomologies of these objects. We also introduce relative (D,H)-Hopf modules over a Hopf comodule category D. These generalize relative (A,H)-Hopf modules over an H-comodule algebra A. We construct Grothendieck spectral sequences for their cohomologies by using their rational Hom objects and higher derived functors of coinvariants.

Valiant (1979) showed that unless P = N P, there is no polynomial-time algorithm to compute the number of perfect matchings of a given graph – even if the input graph is bipartite. Earlier, the physicist Kasteleyn (1963) introduced the notion of a special type of orientation of a graph, and we refer to graphs that admit such an orientation as Pfaffian graphs. Kasteleyn showed that the number of perfect matchings is easy to compute if the input graph is Pfaffian, and he also proved that every planar graph is Pfaffian. The complete bipartite graph $K_{3,3}$ is the smallest graph that is not Pfaffian. In general, the problem of deciding whether a given graph is Pfaffian is not known to be in N P.

Special types of minors, known as conformal minors, play a key role in the theory of Pfaffian orientations. In particular, a graph is Pfaffian if and only if each of its conformal minors is Pfaffian. It was shown by Little (1975) that a bipartite graph $G$ is Pfaffian if and only if $G$ does not contain $K_{3,3}$ as a conformal minor (or, in other words, if and only if $G$ is $K_{3,3}$-free); this places the problem of deciding whether a bipartite graph is Pfaffian in co – N P. Several years later, a structural characterization of $K_{3,3}$-free bipartite graphs was obtained by Robertson, Seymour and Thomas (1999), and independently by McCuaig (2004), and this led to a polynomial-time algorithm for deciding whether a given bipartite graph is Pfaffian.

Norine and Thomas (2008) showed that, unlike the bipartite case, it is not possible to characterize all Pfaffian graphs by excluding a finite number of graphs as conformal minors. In light of everything that has been done so far, it would be interesting to even identify rich classes of Pfaffian graphs (that are nonplanar and nonbipartite).

Inspired by a theorem of Lovasz (1983), we took on the task of characterizing graphs that do not contain $K_4$ as a conformal minor – that is, $K_4$-free graphs. In a joint work with U. S. R. Murty (2016), we provided a structural characterization of planar $K_4$-free graphs. The problem of characterizing nonplanar $K_4$-free graphs is much harder, and we have evidence to believe that it is related to the problem of recognizing Pfaffian graphs. In particular, we conjecture that every graph that is $K_4$-free and $K_{3,3}$-free is also Pfaffian. The talk will be mostly self-contained. I will assume only basic knowledge of graph theory. For more details, see: https://onlinelibrary.wiley.com/doi/full/10.1002/jgt.21882.

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Title: A study of some conformal metrics and conformal invariants on planar domains

Speaker: Amar Deep Sarkar (IISc Mathematics)

Date: Wed, 13 Feb 2019

Time: 11 am

Venue: LH-1, Mathematics Department

The main aim of this thesis is to explain the of some conformal metrics and invariants near a smooth boundary point of a domain in the complex plane. We will be interested in the invariants associated the Carathéodory metric such as its higher order curvatures that were introduced by Burbea and the Aumann-Carathéodory rigidity constant, the Sugawa metric and the Hurwitz metric. The basic technical step in all these is the method of scaling the domain near a smooth boundary point.

To estimate the higher order curvatures using scaling, we generalize an old theorem of Suita on the real analyticity of the Caratheodory metric on planar domains and in the process, we show the convergence of the Szego and Garabedian kernels as well. By using similar ideas we also show that the Aumann-Caratheodory rigidity constant converges to 1 near smooth boundary points.

Next on the line is a conformal metric defined using holomorphic quadratic differentials. This was done by T. Sugawa and we will refer to this as the Sugawa metric. It is shown that this metric is uniformly comparable to the quasi-hyperbolic metric on a smoothly bounded domain.

We also study the Hurwitz metric that was introduced by D. Minda. Its construction is similar to the Kobayashi metric but the essential difference lies in the class of holomorphic maps that are considered in its definition. We show that this metric is continuous and also strengthen Minda’s theorem about its comparability with the quasi-hyperbolic metric by estimating the constants in a more natural manner.

Finally, we get some weak estimates on the generalized upper and lower curvatures of the Sugawa and Hurwitz metrics.

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Title: Universal models in ergodic theory

Speaker: Nishant Chandgotia (Hebrew University of Jerusalem, Israel)

Date: Tue, 12 Feb 2019

Time: 3:30 pm

Venue: LH-1, Mathematics Department

A topological dynamical system is a pair $(X,T)$ where $T$ is a homeomorphism of a compact space $X$. A measure preserving action is a triple $(Y, \mu, S)$ where $Y$ is a standard Borel space, $\mu$ is a probability measure on $X$ and $S$ is a measurable automorphism of $Y$ which preserves the measure $\mu$. We say that $(X,T)$ is universal if it can embed any measure preserving action (under some suitable restrictions).

Krieger’s generator theorem shows that if $X$ is $A^{\mathbb{Z}}$ (bi-infinite sequences in elements of $A$) and $T$ is the transformation on $X$ which shifts its elements one unit to the left then $(X,T)$ is universal. Along with Tom Meyerovitch, we establish very general conditions under which $\mathbb{Z}^d$ (where now we have $d$ commuting transformations on $X$)-dynamical systems are universal. These conditions are general enough to prove that the following models are universal:

A self-homeomorphism with non uniform specification on a compact metric space (answering a question by Quas and Soo and recovering recent results by David Burguet).
A generic (in the sense of dense $G_\delta$) self-homeomorphism of the 2-torus preserving Lebesgue measure (extending result by Lind and Thouvenot to infinite entropy).
Proper colourings of the $\mathbb{Z}^d$ lattice with more than two colours and the domino tilings of the $\mathbb{Z}^2$ lattice (answering a question by Şahin and Robinson).

Venue: LH-1, Mathematics Department

As a natural generalization of the classical uniformization theorem, one could ask if every conformal class of Riemannian metrics contains a metric with constant scalar curvature. In 1960, Yamabe attempted to solve the problem, and gave an incorrect “proof” of an affirmative answer to the above question. Yamabe’s idea was to to use techniques from calculus of variations and partial differential equations to minimize a certain functional, now named after him. Building on some work of Trudger, Aubin solved the Yamabe problem under an additional analytic condition, namely that the Yamabe invariant of the manifold is strictly smaller than the corresponding for the n-dimensional sphere. Aubin was able to verify this analytic condition for all manifolds of dimension strictly greater than 5 that are not locally conformally flat. Most remarkably, the problem was finally solved by Schoen in 1984 using the newly proven positive mass theorem of Schoen and Yau, which in turn has origins in general theory of relativity. A curious feature of Schoen’s proof is that it works precisely in the cases left out by Aubin’s result.

In the first part of the talk, I will provide some background in Riemannian geometry, and then describe the developments surrounding the Yamabe problem until Aubin’s work in 1976. A recurring theme will be the role played by the n-dimensional sphere and its conformal transformations, in all aspects of the problem. In the second part of the talk, I will describe the positive mass theorem, and outline Schoen’s proof of the Yamabe problem in low dimensions and for locally conformally flat manifolds. Most of the Riemannian geometric quantities (including scalar curvature, gradients, Laplacians etc.) will be be defined in the talk, and so the hope is that both the talks will be accessible to everyone.

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Title: Algebra & Combinatorics Seminar: Bisections and bicolorings of hypergraphs

Speaker: Niranjan Balachandran (IIT, Bombay)

Date: Wed, 30 Jan 2019

Time: 4 pm

Venue: LH-1, Mathematics Department

Given a hypergraph $\mathcal{H}$ with vertex set $[n]:={1,\ldots,n}$, a bisecting family is a family $\mathcal{A}\subseteq\mathcal{P}([n])$ such that for every $B\in\mathcal{H}$, there exists $A\in\mathcal{A}$ with the property $|A\cap B|-|A\cap\overline{B}|\in{-1,0,1}$. Similarly, for a family of bicolorings $\mathcal{B}\subseteq {-1,1}^{[n]}$ of $[n]$ a family $\mathcal{A}\subseteq\mathcal{P}([n])$ is called a System of Unbiased Representatives for $\mathcal{B}$ if for every $b\in\mathcal{B}$ there exists $A\in\mathcal{A}$ such that $\sum_{x\in A} b(x) =0$.

Venue: LH-1, Mathematics Department

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Title: Hermitian Vector Bundles over Jordan Manifolds

Speaker: Harald Upmeier (Universität Marburg, Germany; InfoSys Chair Professor, IISc)

Date: Wed, 23 Jan 2019

Time: 4 pm

Venue: LH-1, Mathematics Department

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Title: Symmetric Spaces and Jordan Triples

Speaker: Harald Upmeier (Universität Marburg, Germany; InfoSys Chair Professor, IISc)

Date: Tue, 22 Jan 2019

Time: 4 pm

Venue: LH-1, Mathematics Department

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Title: Geometry & Topology Seminar: Holomorphic differentials and stability in Fukaya categories

Speaker: Pranav Pandit (ICTS, Bangalore)

Date: Mon, 21 Jan 2019

Time: 4 pm

Venue: LH-1, Mathematics Department

Spectral networks are certain decorated graphs drawn on a Riemann surface. I will describe a conjectural picture in which spectral networks can be viewed as analogues of Hermitian-Einstein metrics on vector bundles, and in which holomorphic differentials on the Riemann surface arise as stability conditions on certain Fukaya-type categories. This talk is based on various joint projects with Fabian Haiden, Ludmil Katzarkov, Maxim Kontsevich, and Carlos Simpson.

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Title: Algebra & Combinatorics Seminar: Extensions of partial cyclic orders, boustrophedons and polytopes

Speaker: Sanjay Ramassamy (Ecole Normale Superiure, Paris, France)

Date: Fri, 18 Jan 2019

Time: 11 am

Venue: LH-1, Mathematics Department

While the enumeration of linear extensions of a given poset is a well-studied question, its cyclic counterpart (enumerating extensions to total cyclic orders of a given partial cyclic order) has been subject to very little investigation. In this talk I will introduce some classes of partial cyclic orders for which this enumeration problem is tractable. Some cases require the use of a multidimensional version of the classical boustrophedon construction (a.k.a. Seidel-Entringer-Arnold triangle). The integers arising from these enumerative questions also appear as the normalized volumes of certain polytopes.

This is partly joint work with Arvind Ayyer (Indian Institute of Science) and Matthieu Josuat-Verges (Laboratoire d’Informatique Gaspard Monge / CNRS).

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Title: Eigenfunctions Seminar: Some unpublished work of Harish-Chandra

Speaker: Ramesh Gangolli (University of Washington, Seattle, USA)

Date: Fri, 18 Jan 2019

Time: 3 – 5 pm (with a 15 minute break at 3:45)

Venue: LH-1, Mathematics Department

When Harish-Chandra died in 1983, he left behind a voluminous pile of handwritten manuscripts on harmonic analysis on semisimple Lie groups over real/complex and p-adic fields. The manuscripts were turned over to the archives of the Institute for Advanced Study at Princeton, and are archived there.

Robert Langlands is the Trustee of the Harish-Chandra archive, and has always been interested in finding a way of salvaging whatever might be valuable in these manuscripts. Some years ago, at a conference in UCLA, he encouraged V. S. Varadarajan and me to look at these manuscripts.

The results of our efforts have resulted in the publication of the Volume 5 (Posthumous) of the Collected works of Harish-Chandra by Springer Verlag, which appeared in July this year. This volume covers only those manuscripts that deal with Real or Complex groups. The manuscripts dealing with p-adic groups remain in the archive.

My talk will be devoted to an outline of the results in this volume, without much detail. However, I will try to describe the main ingredient of the methods that cut across most of this work.

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Title: Totally nonnegative GCD matrices and kernels

Speaker: Dominique Guillot (University of Delaware, Newark, USA)

Date: Wed, 16 Jan 2019

Time: 3 pm

Venue: LH-1, Mathematics Department

Let $X=(x_1, … ,x_n)$ be a vector of distinct positive integers. The $n \times n$ matrix with $(i,j)$ entry equal to gcd$(x_i,x_j)$, the greatest common divisor of $x_i$ and $x_j$, is called the GCD matrix on $X$. By a surprising result of Beslin and Ligh (1989), all GCD matrices are positive definite. In this talk, we will discuss new characterizations of the GCD matrices satisfying the stronger property of being totally nonnegative (i.e., all their minors are nonnegative).

Joint work with Lucas Wu (U. Delaware).

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Title: Algebra & Combinatorics Seminar: From word games to a Polymath project

Speaker: Apoorva Khare (IISc Mathematics)

Date: Fri, 11 Jan 2019

Time: 3 pm

Venue: LH-1, Mathematics Department

Consider the following three properties of a general group $G$:

Algebra: $G$ is abelian and torsion-free.
Analysis: $G$ is a metric space that admits a “norm”, namely, a translation-invariant metric $d(.,.)$ satisfying: $d(1,g^n) = |n| d(1,g)$ for all $g \in G$ and integers $n$.
Geometry: $G$ admits a length function with “saturated” subadditivity for equal arguments: $\ell(g^2) = 2 \; \ell(g)$ for all $g \in G$.

While these properties may a priori seem different, in fact they turn out to be equivalent. The nontrivial implication amounts to saying that there does not exist a non-abelian group with a “norm”.

We will discuss motivations from analysis, probability, and geometry; then the proof of the above equivalences; and if time permits, the logistics of how the problem was solved, via a PolyMath project that began on a blogpost of Terence Tao.

(Joint - as D.H.J. PolyMath - with Tobias Fritz, Siddhartha Gadgil, Pace Nielsen, Lior Silberman, and Terence Tao.)

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Title: Dynamics of Schwarz reflections: mating rational maps with groups

Speaker: Sabyasachi Mukherjee (State University of New York, Stony Brook, USA)

Date: Mon, 07 Jan 2019

Time: 4:30 pm

Venue: LH-1, Mathematics Department (Skype talk)

A domain in the complex plane is called a quadrature domain if it admits a global Schwarz reflection map. Topology of quadrature domains has important applications to physics, and is intimately related to iteration of Schwarz reflection maps. As dynamical systems, Schwarz reflection maps produce various instances of “matings” of rational maps and groups.

We will introduce this new class of dynamical systems, and illustrate the above-mentioned mating phenomenon with a few concrete examples. We will then describe a specific one-parameter family of Schwarz reflection maps such that “typical” maps in this family arise as unique conformal matings of a quadratic anti-holomorphic polynomial and the ideal triangle group.

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Title: Algebra & Combinatorics Seminar: Tensor product decomposition for the general linear supergroup $GL(m|n)$

Speaker: Thorsten Heidersdorf (Max-Planck-Institut fur Mathematik, Bonn, Germany)

Date: Thu, 20 Dec 2018

Time: 11 am

Venue: LH-1, Mathematics Department

Let $\mathfrak{gl}(n)$ denote the Lie algebra of the general linear group $GL(n)$. Given two finite dimensional irreducible representations $L(\lambda), L(\mu)$ of $\mathfrak{gl}(n)$, its tensor product decomposition $L(\lambda) \otimes L(\mu)$ is given by the Littlewood-Richardson rule.

The situation becomes much more complicated when one replaces $\mathfrak{gl}(n)$ by the general linear Lie superalgebra $\mathfrak{gl}(m|n)$. The analogous decomposition $L(\lambda) \otimes L(\mu)$ is largely unknown. Indeed many aspects of the representation theory of $\mathfrak{gl}(m|n)$ are more akin to the study of Lie algebras and their representations in prime characteristic or to the BGG category $\mathcal{O}$. I will give a survey talk about this problem and explain why some approaches don’t work and what can be done about it. This will give me the chance to speak about a) the character formula for an irreducible representation $L(\lambda)$, b) Deligne’s interpolating category $Rep(GL_t)$ for $t \in \mathbb{C}$ and c) the process of semisimplification of a tensor category.

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Title: Stopping cocyles of the CCR flow

Speaker: Alexander Belton (Lancaster University, Lancaster, UK)

Date: Thu, 20 Dec 2018

Time: 3 pm

Venue: LH-1, Mathematics Department

The non-commutative generalisation of the notion of stopping time was introduced by Hudson. Such quantum stopping times may be used to stop the CCR flow and its isometric cocycles, i.e., left operator Markovian cocycles on Boson Fock space. This stopping of the CCR flow yields a homomorphism from the semigroup of stopping times into the semigroup of unital endomorphisms of the algebra of bounded operators on the ambient Fock space, and this homomorphism is a generalised version of the shift semigroup. Moreover, stopped cocycles satisfy a non-deterministic version of the cocycle relation, which is a significant generalisation of a result of Applebaum. (Joint work with K. B. Sinha)

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Title: The projective spectrum: 1. Applications to group theory

Speaker: Rongwei Yang (State University of New York, Albany, USA)

Date: Wed, 19 Dec 2018

Time: 4 pm

Venue: LH-1, Mathematics Department

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Title: The gamma function - an eclectic tour

Speaker: Gopal Srinivasan (IIT, Bombay)

Date: Thu, 13 Dec 2018

Time: 11 am

Venue: LH-1, Mathematics Department

In this talk we shall take an eclectic tour through three centuries since the inception of this function by Euler in 1729. The function has been the object of intense study by every great mathematician of the 19th century and continues to tantalize the modern mathematicians.

We shall dwell upon some of the more important identities, their modern ramifications and some new proofs of old results. We shall also discuss some recent developments that have occured in the last decade.

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Title: Algebra & Combinatorics Seminar: Combinatorial positive valuations

Speaker: Katharina Jochemko (KTH, Stockholm, Sweden)

Date: Wed, 12 Dec 2018

Time: 3 pm

Venue: LH-1, Mathematics Department

Valuations are a classical topic in convex geometry. The volume plays an important role in many structural results, such as Hadwiger’s famous characterization of continuous, rigid-motion invariant valuations on convex bodies. Valuations whose domain is restricted to lattice polytopes are less well-studied. The Betke-Kneser Theorem establishes a fascinating discrete analog of Hadwiger’s Theorem for lattice-invariant valuations on lattice polytopes in which the number of lattice points — the discrete volume — plays a fundamental role. In this talk, we explore striking parallels, analogies and also differences between the world of valuations on convex bodies and those on lattice polytopes with a focus on positivity questions and links to Ehrhart theory.

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Title: Wandering subspace problem for m-isometries

Speaker: Sameer Chavan (IIT, Kanpur)

Date: Tue, 11 Dec 2018

Time: 3 pm

Venue: LH-1, Mathematics Department

The wandering subspace problem for an analytic (norm-increasing) m-isometry T on a Hilbert space H asks whether every T-invariant subspace of H can be generated by a wandering subspace. An affirmative solution to this problem for m = 1 is ascribed to Beurling-Lax-Halmos, while that for m = 2 is due to Richter. In this talk, we discuss present status of this problem including some partial solutions in case m > 2.

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Title: Geometric Quantization in Complex and Harmonic Analysis

Speaker: Harald Upmeier, Marburg University

Date: Fri, 07 Dec 2018

Time: 3:00 pm

Venue: LH-1, Department of Mathematics

Professor H. Upmeier of the Marburg University would be visiting the Department of Mathematics, IISc as the InfoSys Visiting Professor during the period Dec 4 - Feb 28. He will give a series of lectures on the broad theme of “Geometric Quantization in Complex and Harmonic Analysis”. The first set of lectures will take place according to the following schedule

Lecture 1: Friday, Dec 7
Lecture 2: Monday, Dec 10
Lecture 3: Wednesday, Dec 12
Lecture 4: Friday, Dec 14
Lecture 5: Monday, Dec 17
Lecture 6: Wednesday, Dec 19

All lectures will take place in LH-1, Department of Mathematics.The first lecture will be at 3:00 pm. All subsequent lectures will be at 4:00 pm.

In this series, the speaker will discuss some basic material (connexions, curvature etc) and then cover, with full proofs, the Borel-Weil-Bott theorem and the Kodaira embedding theorem.

A second set of lectures will be announced subsequently.

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Title: On the structure and distances of repeated-root constacyclic codes

Speaker: Anuradha Sharma (IIIT, Delhi)

Date: Mon, 03 Dec 2018

Time: 3 pm

Venue: LH-1, Mathematics Department

The main aim of coding theory is to construct codes that are easier to encode and decode, can correct or at least detect many errors, and contain a sufficiently large number of codewords. To study error-detecting and error-correcting properties of a code with respect to various communication channels, several metrics (e.g. Hamming metric, Lee metric, Rosenbloom-Tsfasman (RT) metric, symbol-pair metric, etc.) have been introduced and studied in coding theory.

In this talk, we will establish algebraic structures of all repeated-root constacyclic codes of prime power lengths over finite commutative chain rings. Using their algebraic structures, we will determine Hamming distances, b-symbol distances, RT distances, and RT weight distributions of these codes. As an application of these results, we will identify MDS (maximum-distance separable) Hamming, MDS b-symbol and MDS RT codes within this particular class of constacyclic codes. We will also present an algorithm to decode these codes with respect to the Hamming, symbol-pair and RT metrics.

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Title: Polynomially convex embeddings of compact real manifolds

Speaker: Purvi Gupta (Rutgers University, USA)

Date: Mon, 19 Nov 2018

Time: 4 pm

Venue: LH-1, Mathematics Department

A compact subset of $\mathbb{C}^n$ is polynomially convex if it is defined by a (possibly infinite) family of polynomial inequalities. In this talk, we will discuss some questions and recent results regarding the minimum embedding (complex) dimension of abstract compact (real) manifolds subject to such convexity constraints. These embeddings arise naturally in connection with higher-dimensional analogues of the fact that the algebra of continuous functions on a circle can be generated by two smooth functions. We will expand on this connection, discuss the local and global challenges in constructing such embeddings, and discuss two distinct cases in which new bounds have been obtained.This is joint work with R. Shafikov.

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Title: Algebra & Combinatorics Seminar: Rings with several objects

Speaker: Abhishek Banerjee (IISc Mathematics)

Date: Fri, 16 Nov 2018

Time: 3 pm

Venue: LH-1, Mathematics Department

An ordinary ring may be seen as a preadditive category with just one object. This leads to the powerful analogy, first formulated explicitly by Mitchell in 1975, that a small preadditive category should be seen as a “ring with several objects”. We will trace the history and development of the category of modules over a preadditive category.

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Title: A $z^k$-invariant subspace without the wandering property

Speaker: Daniel Seco (ICMAT, Madrid, Spain)

Date: Wed, 14 Nov 2018

Time: 4 pm

Venue: LH-1, Mathematics Department

We study operators of multiplication by $z^k$ in Dirichlet-type spaces $D_\alpha$. We establish the existence of $k$ and $\alpha$ for which some $z^k$-invariant subspaces of $D_\alpha$ do not satisfy the wandering property. As a consequence of the proof, any Dirichlet-type space accepts an equivalent norm under which the wandering property fails for some space for the operator of multiplication by $z^k$ for any $k \geq 6$.

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Title: Eigenfunctions Seminar: A refinement of the Littlewood-Richardson rule

Speaker: K.N. Raghavan (IMSc, Chennai)

Date: Fri, 09 Nov 2018

Time: 3 – 5 pm (with a 15 minute break at 3:45)

Venue: LH-1, Mathematics Department

Symmetric polynomials are interesting not just in their own right. They appear naturally in various contexts, e.g., as characters in representation theory and as cohomology classes of Grassmannians and other homogeneous spaces in geometry. There are many different bases for the space of symmetric polynomials, perhaps the most interesting of which is the one formed by Schur polynomials. The Littlewood-Richardson (LR) rule expresses the product of two given Schur polynomials as a linear combination of Schur polynomials. The first half of the talk will be a tour of these topics that should be accessible even to undergraduate students.

The second half will be an exposition (which hopefully will continue to be widely accessible!) of recent joint research work with Mrigendra Singh Kushwaha and Sankaran Viswanath, both of IMSc. The LR rule above has a natural interpretation as giving the decomposition as a direct sum of irreducibles of the tensor product of two irreducible representations of the unitary (or general linear) group. A generalised version of it (due to Littelmann, still called the LR rule) gives the analogous decomposition for any reductive group. On the tensor product of two irreducible representations, there is the natural “Kostant-Kumar” filtration indexed by the Weyl group. This consists of the cyclic submodules generated by the highest weight vector tensor an extremal weight vector. We obtain a refined LR rule that gives the decomposition as a direct sum of irreducibles of the Kostant-Kumar submodules (of the tensor product). As an application, we obtain alternative proofs of refinements of “PRV type” results proved by Kumar and others. (PRV = Parthasarathy, Ranga Rao, Varadarajan)

This is joint work with Roger Behrend.

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Title: On the formality of some contact manifolds

In this talk I will briefly describe the idea of a proof of the Mordell-Weil Theorem and introduce the n-Selmer group and Tate-Shafarevitch group associated to Elliptic Curves. I will define the L-function and some other arithmetic invariants attached to the Elliptic Curves and state the celebrated Birch-Swinnerton-Dyer Conjecture.

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Title: Introduction to Elliptic Curves

Speaker: Shubham Sinha (Graduate Student at UC San Diego, USA)

Date: Fri, 27 Jul 2018

Time: 2 pm

Venue: LH-2, Mathematics Department

Elliptic curves are important objects of study in various areas of research in modern mathematics. In this talk I will develop some algebraic and geometric tools to understand the group structures on elliptic curves and their Isogenies (certain kind of homomorphisms). I will specialise the general study of Elliptic Curves over finite fields, define zeta functions of associated Elliptic Curve and state the Weil Conjectures.

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Title: A Study of Conformal Metrics and Invariants on Planar Domains

Speaker: Amar Deep Sarkar (IISc Mathematics)

Date: Fri, 27 Jul 2018

Time: 3 pm

Venue: LH-3, Mathematics Department

The main aim of this thesis is to explain the behaviour of some conformal metrics and invariants near a smooth boundary point of a domain in the complex plane. We will be interested in the invariants associated to the Carathéodory metric such as its higher order curvatures that were introduced by Burbea and the Aumann-Carathéodory rigidity constant, the Sugawa metric and the Hurwitz metric. The basic technical step in all these is the method of scaling the domain near a smooth boundary point.

To estimate the higher order curvatures using scaling, we generalize an old theorem of Suita on the real analyticity of the Caratheodory metric on planar domains and in the process, we show convergence of the Szego and Garabedian kernels as well. By using similar ideas we also show that the Aumann-Caratheodory rigidity constant converges to 1 near smooth boundary points.

We also study the Hurwitz metric that was introduced by D. Minda. It’s construction is similar to the Kobayashi metric but the essential difference lies in the class of holomorphic maps that are considered in its definition. We show that this metric is continuous and also strengthen Minda’s theorem about its comparability with the quasi-hyperbolic metric by estimating the constants in a more natural manner.

Finally, we get some weak estimates on the generalized upper and lower curvatures of the Sugawa and Hurwitz metrics.

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Title: On bases for local Weyl modules

Speaker: B. Ravinder (Chennai Mathematical Institute, Chennai)

Date: Thu, 26 Jul 2018

Time: 11 am

Venue: LH-3, Mathematics Department

Let G be a finite-dimensional complex simple Lie algebra and G[t] be its current algebra. The degree grading on the polynomial ring gives a natural grading on G[t] and makes it a graded Lie algebra. Local Weyl modules introduced by Chari and Pressley are interesting finite-dimensional graded G[t]-modules. Corresponding to a dominant integral weight x of G there is a local Weyl module denoted by W(x). The zeroth graded piece of W(x) is the irreducible G-module V(x). In this talk, we discuss how to obtain a basis for W(x) from the basis of V(x) given by Gelfand-Tsetlin patterns, when G is of type A and C.

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Title: Four Flavours of Combinatorics (Enumerative, Probabilistic, Extremal, and Geometric)

Speaker: Kunal Dutta (INRIA Sophia-Antipolis, France)

Date: Tue, 24 Jul 2018

Time: 4 pm

Venue: LH-3, Mathematics Department

In this talk we shall see three very different areas of applications of combinatorics in mathematics and computer science, illustrating four different flavours of combinatorial reasoning.

The first problem is on the decomposition, into irreducible representations, of the Weil representation of the full symplectic group associated to a finite module of odd order over a Dedekind domain. We shall discuss how a poset structure defined on the orbits of finite abelian p-groups under automorphisms can be used to show the decomposition of the Weil representation is multiplicity-free, as well as parametrize the irreducible subrepresentations, compute their dimensions in terms of p, etc. Joint works with Amritanshu Prasad (IMSc, Chennai).

Time: 11 am

Venue: LH-1, Mathematics Department

Let $K$ be a bounded domain and $K:\Omega \times \Omega \to \mathbb{C}$ be a sesqui-analytic function. We show that if $\alpha,\beta>0$ be such that the functions $K^{\alpha}$ and $K^{\beta}$, defined on $\Omega\times\Omega$, are non-negative definite kernels, then the $M_m(\mathbb{C})$ valued function

Venue: LH-3, Mathematics Department

We consider a finite version of the one-dimensional Toom model with closed boundaries. Each site is occupied either by a particle of type 0 or of type 1, where the total number of particles of type 0 and type 1 are fixed to be n_0 and n_1 respectively. We call this an (n_0,n_1)-system. The dynamics are as follows: the leftmost particle in a block can exchange its position with the leftmost particle of the block to its right.

In this thesis, we have shown the following. Firstly, we have proven a conjecture about the density of 1’s in a system with arbitrary number of 0’s and 1’s. Secondly, we have made progress on a conjecture for the nonequilibrium partition function. In particular, we have given an alternate proof of the conjecture for the (1, n_1)-system and (n_0, 1)-system, using an enriched two-dimensional model.

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Title: An introduction to toric geometry

Speaker: Yifei Chen (Chinese Academy of Sciences, Beijing, China)

Date: Tue, 12 Jun 2018

Time: 3 - 5 pm

Venue: LH-3, Mathematics Department

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Title: Duality for spaces of holomorphic functions into a locally convex topological vector space

Speaker: Kriti Sehgal (IISc Mathematics)

Date: Thu, 07 Jun 2018

Time: 2:30 pm

Venue: LH-1, Mathematics Department

In this talk, we present a portion of the paper “Sur certains espaces de fonctions holomorphes.I.” by Alexandre Grothendieck. For a function f: O → E, where O is an open subset of the complex plane and E a locally convex topological vector space, we define two notions: holomorphicity and weak derivability. We discuss some properties of the holomorphic functions and see the condition under which these two notions coincide.

For Ω_1 a subset of the Riemann sphere, we consider the space of locally holomorphic maps of Ω_1 into E vanishing at infinity if infinity belongs to Ω_1, denoted by P(Ω_1,E). For two complementary subsets Ω_1 and Ω_2 of the Riemann sphere we prove that given two locally convex topological vector spaces E and F in separating duality, under some general conditions, we can define a separating duality between P(Ω _1,E) and P(Ω_2,F).

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Title: An introduction to birational geometry in positive characteristic fields

Speaker: Yifei Chen (Chinese Academy of Sciences, Beijing, China)

Date: Tue, 05 Jun 2018

Time: 3 pm

Venue: LH-1, Mathematics Department

We will survey recent progress of birational geometry in positive characteristic fields. As well, we will introduce subadditiviy of Kodaira dimension and canonical bundle formula in positive characteristics. These are joint work with Caucher Birkar, Lei Zhang and Yi Gu.

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Title: Number of Solutions of Polynomial equations over Finite Fields

Speaker: Sudhir Ghorpade (IIT, Bombay)

Date: Mon, 04 Jun 2018

Time: 3 pm

Venue: LH-1, Mathematics Department

We will consider the following question:

Given a system of a fixed number of linearly independent homogeneous polynomial equations of a fixed degree with coefficients in a finite field F, what is the maximum number of common solutions they can have in the corresponding protective space over F?

Venue: LH-1, Mathematics Department

An embedding of a metric graph $(G, d)$ on a closed hyperbolic surface is called \emph{essential}, if each complementary region has a negative Euler characteristic. We show, by construction, given any metric graph, its metric can be rescaled so that it can be essentially and isometrically embedded on a closed hyperbolic surface. The essential genus $g_e(G)$ of a metric graph $(G, d)$ is the lowest genus of a surface on which such an embedding of the graph is possible. In the next result, we establish a formula to compute $g_e(G)$. Furthermore, we show that for every integer $g\geq g_e(G)$, $(G, d)$ can be essentially and isometrically embedded (possibly after a rescaling the metric $d$) on a surface of genus $g$.

Next, we study minimal embeddings, where each complementary region has Euler characteristic $-1$. The maximum essential genus $g_e^{\max}(G)$ a graph $(G, d)$ is the largest genus of a surface on which the graph is minimally embedded. Finally, we describe a method explicitly for an essential embedding of $(G, d)$, where $g_e(G)$ and $g_e^{\max}(G)$ are realized.

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Title: Computation of sparse representation of high dimensional time series date and experimental applications

Speaker: Sandeep K. Modi (IISc Mathematics)

Date: Thu, 26 Apr 2018

Time: 2:30 pm

Venue: LH-2, Mathematics Department

Obtaining a sparse representation of high dimensional data is often the first step towards its further analysis. Conventional Vector Autoregressive (VAR) modelling methods applied to such data results in noisy, non-sparse solutions with a too many spurious coefficients. Computing auxiliary quantities such as the Power Spectrum, Coherence and Granger Causality (GC) from such non-sparse models is slow and gives wrong results. Thresholding the distorted values of these quantities as per some criterion, statistical or otherwise, does not alleviate the problem.

We propose two sparse Vector Autoregressive (VAR) modelling methods that work well for high dimensional time series data, even when the number of time points is relatively low, by incorporating only statistically significant coefficients. In numerical experiments using simulated data, our methods show consistently higher accuracy compared to other contemporary methods in recovering the true sparse model. The relative absence of spurious coefficients in our models permits more accurate, stable and efficient evaluation of auxiliary quantities. Our VAR modelling methods are capable of computing Conditional Granger Causality (CGC) in datasets consisting of tens of thousands of variables with a speed and accuracy that far exceeds the capabilities of existing methods.

Using the Conditional Granger Causality computed from our models as a proxy for the weight of the edges in a network, we use community detection algorithms to simultaneously obtain both local and global functional connectivity patterns and community structures in large networks.

We also use our VAR modelling methods to predict time delays in many-variable systems. Using simulated data from non-linear delay differential equations, we compare our methods with commonly used delay prediction techniques and show that our methods yield more accurate results.

We apply the above methods to the following real experimental data:

Analysis of data from the Human Connectome Project (HCP): fMRI data from the HCP database is used to compute sparse brain functional connectivity networks. The network and community structures obtained are consistent over independent recording sessions and show good spatial correspondence with known functional and anatomical regions of the brain.
Analysis of ADHD-200 data: fMRI data from children with ADHD (Attention Deficit Hyperactive Disorder) is used to compute sparse brain functional connectivity networks. Analysis of the network measures obtained provide new ways of differentiating between ADHD and typically developing children using global and node-level network measures. They also enable refinement of published results relating to the rFIC-ACC interaction in fMRI resting state data.
Time-delay prediction from LFP recordings:When applied to Local Field Potential (LFP) recordings from the rat and monkey, our methods predict consistent delays across a range of sampling frequencies.
Application to the Hela gene interaction dataset: The network obtained by applying our methods to this dataset yields results that are at least as good as those from a specialized method for analysing gene interaction. This demonstrates that our methods can be applied to any time series data for which VAR modelling is valid.

In addition to the above methods, we apply non-parametric Granger Causality analysis (originally developed by A. Nedungadi, G. Rangarajan et al) to mixed point-process and real time-series data. Extending the computations to Conditional GC and by increasing the efficiency of the original computer code, we can compute the Conditional GC spectrum in systems consisting of hundreds of variables in a relatively short period. Further, combining this with VAR modelling provides an alternate faster route to compute the significance level of each element of the GC and CGC matrices. We use these techniques to analyse mixed Spike Train and LFP data from monkey electrocorticography (ECoG) recordings during a behavioural task. Interpretation of the results of the analysis is an ongoing collaboration.

Speaker: Subhajit Goswami (IHES, France)

Date: Mon, 19 Mar 2018

Time: 2 pm

Venue: LH-1, Mathematics Department

In this talk I will give a brief introduction to Liouville first-passage percolation (LFPP) which is a model for random metric on a finite planar grid graph. It was studied primarily as a way to understand the random metric associated with Liouville quantum gravity (LQG), one of the major open problems in contemporary probability theory. In short the Liouville quantum gravity is a (conjectured) one parameter family of ``canonical’’ random metrics on a Riemann surface. I will discuss some recent results on this metric and the main focus will be on estimates of the typical distance between two points. I will highlight the apparent disagreement of these estimates with a prediction made in the physics literature about the LQG metric. I will also mention some (of many) future problems in this program. Based on a joint work with Jian Ding.

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Title: Holomorphic functions into a locally convex topological vector space

Speaker: Kriti Sehgal (IISc Mathematics)

Date: Mon, 19 Mar 2018

Time: 11:15 am

Venue: LH-1, Mathematics Department

In the second half of this talk, a law of large numbers is proven for spaces with infinite “volume” (measure) as opposed to the above version for probability measures (“volume” =1).

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Title: Self-intersections and Poisson line processes on hyperbolic surfaces

Speaker: Jayadev Athreya (University of Washington, Seattle, USA)

Date: Wed, 17 Jan 2018

Time: 4 pm

Venue: LH-1, Mathematics Department

In joint work with Steve Lalley and Jenya Sapir, we study the tessellation of a compact, hyperbolic surface induced by a typical long geodesic segment. We show, that when properly scaled, the local behavior of a typical geodesic is that of a Poisson line process. This implies that the global statistics of the tessellation – for instance, the fraction of triangles – approach those of the limiting Poisson line process.

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Title: Dynamics Of Determinantal Point Processes

Speaker: Alexander Bufetov (CNRS, Marseilles, France; and Steklov Mathematical Institute, IITP RAS, NRU Higher School of Economics, Russia)

Date: Wed, 17 Jan 2018

Time: 2:30 pm

Venue: LH-1, Mathematics Department

Determinantal point processes, which first appeared in Dyson’s work on random matrices, arise in diverse problems of asymptotic combinatorics, ergodic theory, representation theory. They have strong chaotic properties: for example, the sine-process has the Kolmogorov property and satisfies the Central Limit Theorem. A Functional Limit Theorem for the sine-process has been established in joint work with A. Dymov.

A delicate aspect of the behaviour of a determinantal point process is that particles interact at infinite radius. For instance, Ghosh and Peres showed that, under the sine-process, the number of particles in a bounded interval is determined by the configuration in the outside of the interval. For determinantal point processes with so-called integrable kernels, an explicit description is given of conditional measures of the process in a bounded interval with respect to the fixed exterior. These conditional measures are given by orthogonal polynomial ensembles with explicitly found weights. A key step in the argument is that projections inducing our processes satisfy a weaker analogue of the division axiom of de Branges: in fact, this weak division property, as shown in joint work with Roman Romanov, characterizes integrable kernels. Similar results for determinantal point processes governed by orthogonal projections onto Hilbert spaces of holomorphic functions are obtained in joint work with Y. Qiu. The talk is based on the preprints

https://arxiv.org/abs/1707.03463, (joint with R. Romanov), https://arxiv.org/abs/1701.00111 (joint with A. Dymov), and the paper

Alexander I. Bufetov, Yanqi Qiu, “Conditional measures of generalized Ginibre point processes”, J. Funct. Anal., 272:11 (2017), 4671–4708.

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Title: Eigenfunctions Seminar: Homogeneous length functions on Groups: A polymath adventure

Speaker: Siddhartha Gadgil and Apoorva Khare (IISc Mathematics)

Date: Mon, 15 Jan 2018

Time: 4 – 5 pm

Venue: LH-1, Mathematics Department

Terence Tao posted on his blog a question of Apoorva Khare, asking whether the free group on two generators has a length function $l: F_2 \to\mathbb{R}$ (i.e., satisfying the triangle inequality) which is homogeneous, i.e., such that $l(g^n) = nl(g)$. A week later, the problem was solved by an active collaboration of several mathematicians (with a little help from a computer) through Tao’s blog. In fact a more general result was obtained, namely that any homogeneous length function on a group $G$ factors through its abelianization $G/[G, G]$.

Venue: LH-5, Mathematics Department

Gorenstein rings are very common and significant in many areas of mathematics. The following are two important and widely open problems in commutative algebra and algebraic geometry:

characterization of possible Hilbert functions of Gorenstein K-algebras; and
classification of Gorenstein K-algebras with given Hilbert functions.

Recently, in a joint work with M.E. Rossi, we obtained partial results to these problems in some cases (K-algebras of socle degree 4). In this talk, we will discuss these new developments.

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Title: Compactness and Structural Stability of Nonlinear Flows

Speaker: Augusto Visintin (Universita' degli Studi di Trento, Italy)

Date: Thu, 11 Jan 2018

Time: 2:30 - 3:30 and 4 - 5 pm

Venue: LH-3, Mathematics Department

Venue: LH-1, Mathematics Department

I will describe our work that establishes (akin to) von Neumann’s conjecture on condition number, the ratio of the largest and the smallest singular values, for sparse random matrices. Non-asymptotic bounds on the extreme singular values of large matrices have numerous uses in the geometric functional analysis, compressed sensing, and numerical linear algebra. The condition number often serves as a measure of stability for matrix algorithms. Based on simulations von Neumann and his collaborators conjectured that the condition number of a random square matrix of dimension $n$ is $O(n)$. During the last decade, this conjecture was proved for dense random matrices.

Sparse matrices are abundant in statistics, neural networks, financial modeling, electrical engineering, and wireless communications. Results for sparse random matrices have been unknown and requires completely new ideas due to the presence of a large number of zeros. We consider a sparse random matrix with entries of the form $\xi_{i,j} \delta_{i,j}, \, i,j=1,\ldots,n$, such that $\xi_{i,j}$ are i.i.d. with zero mean and unit variance and $\delta_{i,j}$ are i.i.d. Ber$(p_n)$, where $p_n \downarrow 0$ as $n \to \infty$. For $p_n < \frac{\log n}{n}$, this matrix becomes non-invertible, and hence its condition number equals infinity, with probability tending to one. In this talk, I will describe our work showing that the condition number of such sparse matrices (under certain assumptions on the moments of $\{\xi_{i,j}\}$) is $O(n^{1+o(1)})$ for all $p_n > \frac{\log n}{n}$, with probability tending to one, thereby establishing the optimal analogous version of the von Neumann’s conjecture on condition number for sparse random matrices.

Venue: LH-1, Mathematics Department

In this talk we discuss a formulation of Quantum Theory of Dark matter and discuss some operators on Hilbert spaces of singular measures.

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Title: For good measure ... and bad

Speaker: Malabika Pramanik (UBC, Canada)

Date: Wed, 02 Aug 2017

Time: 3:30 pm

Venue: LH-1, Mathematics Department

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Title: The Pick--Nevanlinna interpolation problem: complex-analytic methods in special domains

Speaker: Vikramjit Singh Chandel (IISc Mathematics)

Date: Mon, 17 Jul 2017

Time: 3 pm

Venue: LH-1, Mathematics Department

The Pick–Nevanlinna interpolation problem in its fullest generality is as follows:

Given domains $D_1$, $D_2$ in complex Euclidean spaces, and a set ${(z_i,w_i): 1\leq i\leq N}\subset D_1\times D_2$, where $z_i$ are distinct and $N$ is a positive integer $\geq 2$, find necessary and sufficient conditions for the existence of a holomorphic map $F$ from $D_1$ into $D_2$ such that $F(z_i) = w_i$, $1\leq N$.

When such a map $F$ exists, we say that $F$ is an interpolant of the data. Of course, this problem is intractable at the above level of generality. However, two special cases of the problem – which we shall study in this thesis – have been of lasting interest:

INTERPOLATION FROM THE POLYDISC TO THE UNIT DISC: This is the case $D_1 = D^n$ and $D_2 = D$, where $D$ denotes the open unit disc in the complex plane and $n$ is a positive integer. The problem itself originates with Georg Pick’s well-known theorem (independently discovered by Nevanlinna) for the case $n=1$. Much later, Sarason gave another proof of Pick’s result using an operator-theoretic approach, which is very influential. Using this approach for $n\geq 2$, Agler–McCarthy provided a solution to the problem with the restriction that the interpolant is in the Schur–Agler class. This is notable because when $n = 2$ the latter result completely solves the problem for the case $D_1 = D^2$, $D_2 = D$. However, Pick’s approach can also be effective for $n\geq 2$. In this thesis, we give an alternative characterization for the existence of a $3$-point interpolant based on Pick’s approach and involving the study of rational inner functions.

Cole, Lewis and Wermer lifted Sarason’s approach to uniform algebras – leading to a characterization for the existence of an interpolant in terms of the positivity of a large, rather abstractly-defined family of $(N\times N)$ matrices. McCullough later refined their result by identifying a smaller family of matrices. The second result of this thesis is in the same vein, namely: it provides a characterization of those data that admit a $D^n$-to-$D$ interpolant in terms of the positivity of a family of matrices parametrized by a class of polynomials.

INTERPOLATION FORM THE UNIT DISC TO THE SPECTRAL UNIT BALL: This is the case $D_1 = D$ and $D_2$ is the set of all $(n\times n)$ matrices with spectral radius less than $1$. The interest in this arises from problems in Control Theory. Bercovici, Fois and Tannenbaum adapted Sarason’s methods to give a (somewhat hard-to-check) characterization for the existence of an interpolant under a very mild restriction. Later, Agler–Young established a relation between the interpolation problem in the spectral unit ball and that in the symmetrized polydisc – leading to a necessary condition for the existence of an interpolant. Bharali later provided a new inequivalent necessary condition for the existence of an interpolant for any $n$ and $N=2$. We shall present a necessary condition for the existence of a $3$-point interpolant. This we shall achieve by modifying Pick’s approach and applying the aforementioned result due to Bharali.

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Title: The representation homology of spaces

Speaker: Ajay Ramadoss (Indiana University, USA)

Date: Wed, 12 Jul 2017

Time: 4 pm

Venue: LH-1, Mathematics Department

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Title: Analytic models, dilations, wandering subspaces, and inner functions

Speaker: Monojit Bhattacharjee (IISc Mathematics)

Date: Mon, 03 Jul 2017

Time: 3 pm

Venue: LH-1, Mathematics Department

In this talk we will discuss an analytic model theory for pure hyper- contractions (introduced by J. Agler) which is analogous to Sz.Nagy-Foias model theory for contractions. We then proceed to study analytic model theory for doubly commuting $n$-tuples of operators and analyze the structure of joint shift co-invariant subspaces of reproducing kernel Hilbert spaces over polydisc. In particular, we completely characterize the doubly commuting quotient modules of a large class of reproducing kernel Hilbert Modules, in the sense of Arazy and Englis, over the unit polydisc.

Inspired by Halmos, in the second half of the talk, we will focus on the wandering subspace property of commuting tuples of bounded operators on Hilbert spaces. We prove that for a large class of analytic functional Hilbert spaces $H_k$ on the unit ball in $\mathbb{C}^n$, wandering subspaces for restrictions of the multiplication tuple $M_z = (M_{z_1},…,M_{z_n})$ can be described in terms of suitable $H_k$-inner functions. We also prove that $H_k$-inner functions are contractive multipliers and deduce a result on the multiplier norm of quasi-homogeneous polynomials as an application. Along the way we also prove a refinement of a result of Arveson on the uniqueness of the minimal dilations of pure row contractions.

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Title: Homogeneous Operators

Speaker: Somnath Hazra (IISc Mathematics)

Date: Mon, 19 Jun 2017

Time: 11 am

Venue: LH-1, Mathematics Department

It is known that the characteristic function $\theta_T$ of a homogeneous contraction $T$ with an associated representation $\pi$ is of the form $\theta_T(a) = \sigma_{L}(\phi_a)^{*} \theta(0) \sigma_{R}(\phi_a),$ where, $\sigma_{L}$ and $\sigma_{R}$ are projective representation of the M"{o}bius group M"{o}b with a common multiplier. We give another proof of the “product formula’’.

Also, we prove that the projective representations $\sigma_L$ and $\sigma_R$ for a class of multiplication operators, the two representations $\sigma_{R}$ and $\sigma_{L}$ are unitarily equivalent to certain known pair of representations $\sigma_{\lambda + 1}$ and $\sigma_{\lambda - 1},$ respectively. These are described explicitly.

Let $G$ be either (i) the direct product of $n$-copies of the bi-holomorphic automorphism group of the disc or (ii) the bi-holomorphic automorphism group of the polydisc $\mathbb D^n.$

A commuting tuple of bounded operators $\mathsf{T} = (T_1, T_2,\ldots ,T_n)$ is said to be $G$-homogeneous if the joint spectrum of $\mathsf{T}$ lies in $\overline{\mathbb{D}}^n$ and $\varphi(\mathsf{T}),$ defined using the usual functional calculus, is unitarily equivalent with $\mathsf{T}$ for all $\varphi \in G.$

We show that a commuting tuple $\mathsf{T}$ in the Cowen-Douglas class of rank $1$ is $G$-homogeneous if and only if it is unitarily equivalent to the tuple of the multiplication operators on either the reproducing kernel Hilbert space with reproducing kernel $\prod_{i = 1}^{n} \frac{1}{(1 - z_{i}\overline{w}_{i})^{\lambda_i}}$ or $\prod_{i = 1}^{n} \frac{1}{(1 - z_{i}\overline{w}_{i})^{\lambda}},$ where $\lambda,$ $\lambda_i$, $1 \leq i \leq n,$ are positive real numbers, according as $G$ is as in (i) or (ii).

Let $\mathsf T:=(T_1, \ldots ,T_{n-1})$ be a $G$-homogeneous $(n-1)$-tuple of rank $1$ Cowen-Douglas class, where $G$ is the the direct product of $n-1$-copies of the bi-holomorphic automorphism group of the disc. Let $\hat{T}$ be an irreducible homogeneous (with respect to the bi-holomorphic group of automorphisms of the disc) operator in the Cowen-Douglas class on the disc of rank $2$. We show that every irreducible $G$-homogeneous operator, $G$ as in (i), of rank $2$ must be of the form $(T_1\otimes I_{\widehat{H}},\ldots , T_{n-1}\otimes I_{\widehat{H}}, I_H \otimes \hat{T}).$

We also show that if $G$ is chosen to be the group as in (ii), then there are no irreducible $G$-homogeneous operators of rank $2$.

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Title: Homological Invariants and Combinatorics of Finite Simple Graphs

Speaker: Arindam Banerjee (Purdue University, USA)

Date: Thu, 15 Jun 2017

In this talk the interplay between the combinatorial structures of finite simple graphs and various homological invariants like regularity, depth etc. of related algebraic objects shall be discussed. Some open problems, recent developments and ongoing projects shall be discussed. In particular some new techniques developed in my thesis to study Castelnuovo-Mumford regularity of algebraic objects related to graphs shall be discussed in some details.

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Title: Boundary values, resonances and scattering poles on symmetric spaces of rank one

Speaker: Aprameyan Parthasarathy (University of Paderborn, Germany)

Date: Wed, 14 Jun 2017

Time: 4 pm

Venue: LH-1, Mathematics Department

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Title: Random structures: Phase transitions, scaling limits, and universality

Speaker: Sanchayan Sen (McGill University, Canada)

Date: Thu, 08 Jun 2017

Time: 3 pm

Venue: LH-1, Mathematics Department

The aim of this talk is to give an overview of some recent results in two interconnected areas:

a) Random discrete structures: One major conjecture in probabilistic combinatorics, formulated by statistical physicists using non-rigorous arguments and enormous simulations in the early 2000s, is as follows: for a wide array of random graph models on $n$ vertices and degree exponent $\tau>3$, typical distance both within maximal components in the critical regime as well as on the minimal spanning tree on the giant component in the supercritical regime scale like $n^{\frac{\tau\wedge 4 -3}{\tau\wedge 4 -1}}$. In other words, the degree exponent determines the universality class the random graph belongs to. The mathematical machinery available at the time was insufficient for providing a rigorous justification of this conjecture.

More generally, recent research has provided strong evidence to believe that several objects, including (i) components under critical percolation, (ii) the vacant set left by a random walk, and (iii) the minimal spanning tree, constructed on a wide class of random discrete structures converge, when viewed as metric measure spaces, to some random fractals in the Gromov-Hausdorff sense, and these limiting objects are universal under some general assumptions. We will discuss recent developments in a larger program aimed at a complete resolution of these conjectures.

Venue: LH-1, Mathematics Department

The study of weighted inequalities in Classical Harmonic Analysis started in 70’s, when B. Muckenhoupt characterised in 1972 the weights $w$ for which the Hardy–Littlewood maximal function is bounded in $L^p(w)$. At that time the question about how the operator depended on the constant associated with $w$, which we denote by $[w]_{A_p}$, was not considered (i.e., quantitative estimates) were not investigated.

From the beginning of 2000’s, a great activity has been carried out in order to obtain the sharp dependence for singular integral operators, reaching the solution of the so-called $A_2$ conjecture by T. P. H\“ytonen.

In this talk we consider operators with homogeneous singular kernels, on which we assume smoothness conditions that are weaker than the standard ones (this is why they are called rough). The first qualitative weighted estimates are due to J. Duoandikoetxea and J. L. Rubio de Francia. For the norm of these operators in the space $L^2(w)$ we obtain a quantitative estimate which is quadratic in the constant $[w]_{A_2}$.

Venue: LH-1, Mathematics Department

The Hadamard product of two matrices is formed by multiplying corresponding entries, and the Schur product theorem states that this operation preserves positive semidefiniteness.

Speaker: Kartick Adhikari (IISc Mathematics)

Date: Tue, 31 Jan 2017

Time: 11 am

Venue: LH-1, Mathematics Department

Consider the infinite Ginibre ensemble (the distributional limit of the eigenvalues of nxn random matrices with i.i.d. standard complex Gaussian entries) in the complex plane. For a bounded set $U$, let $H_r(U)$ denote the probability (hole probability) that no points of infinite Ginibre ensemble fall in the region $rU$. We study the asymptotic behavior of $H_r(U)$ as $r \to \infty$. Under certain conditions on $U$ we show that $\log H_r(U)=C_U \cdot r^4 (1+o(1))$ as $r \to \infty$. Using potential theory, we give an explicit formula for $C_U$ in terms of the minimum logarithmic energy of the set with a quadratic external field. We calculate $C_U$ explicitly for some special sets such as the annulus, cardioid, ellipse, equilateral triangle and half disk.

Moreover, we generalize the above hole probability results for a class of determinantal point processes in the complex plane.

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Title: The Space of Metric Measure Spaces

Speaker: Sayantan Maitra (IISc Mathematics)

Date: Fri, 20 Jan 2017

Time: 11 am

Venue: LH-1, Mathematics Department

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Title: Linking numbers for algebraic cycles

Speaker: Souvik Goswami (ICMAT, Madrid, Spain)

Date: Wed, 18 Jan 2017

Time: 4 pm

Venue: LH-1, Mathematics Department

In algebraic geometry the concept of height pairing (a particular example of linking numbers) of algebraic cycles lies at the confluence of arithmetic, Hodge theory and topology. In a series of two talks, I will explain the notion of Beilinson’s height pairing for cycles homologous to zero. This will bring into picture the notion of Arakelov/arithmetic intersection theory. I will give sufficient background of this theory and provide examples. Finally, I will talk about my recent work with Dr. Jose Ignacio Burgos, about a generalization of Beilinson’s height pairing for higher algebraic cycles.

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Title: Approximate controllability of an impulsive sub-diffusion equation

Speaker: Lakshman Mahato (IIIT Dharwad)

Date: Fri, 13 Jan 2017

In this talk, I shall consider an abstract Cauchy problem for a class of impulsive sub-diffusion equation. Existence and regularity of solution of the problem shall be established via eigenfunction expansion. Further, I shall establish the approximate controllability of the problem by applying unique continuation property via internal control acts on a sub-domain.

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Title: Limiting measure for TASEP with a slow bond

Speaker: Sourav Sarkar (UC Berkeley, USA)

Date: Wed, 11 Jan 2017

Time: 3 pm

Venue: LH-1, Mathematics Department

It was shown by Basu, Sidoravicius and Sly that a TASEP starting with the step initial condition, i.e., with one particle each at every nonpositive site of $\mathbb{Z}$ and no particle at positive sites, with a slow bond at the origin where a particle jumping from the origin jumps at a smaller rate $r < 1$, has an asympototic current which is strictly less than 1/4. Here we study the limiting measure of the TASEP with a slow bond. The distribution of regular TASEP started with the step initial condition converges to the invariant product Bernoulli measure with density 1/2. The slowdown due to the slow bond implies that there is a long range effect near the origin where the region to the right of origin is sparser and there is a traffic jam to the left of the slow bond with particle density higher than a half. However, the distribution becomes close to a product Bernoulli measure as one moves far away from the origin, albeit with a different density ? < 1/2 to the right of the origin and ?’ > 1/2 to the left of the origin. This answers a question due to Liggett. The proof uses the correspondence between TASEP and directed last passage percolation on $\mathbb{Z}^2$ with exponential passage times, and the geometric properties of the maximal paths there.

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Title: Upscaling of a System of Semilinear Diffusion Reaction Equations in a Heterogeneous Medium: MultiScale Modeling and Periodic Homogenization

Speaker: Hari Shankar Mahato (University of Georgia, USA)

Date: Tue, 10 Jan 2017

Time: 11 am

Venue: LH-1, Mathematics Department

A porous medium (concrete, soil, rocks, water reservoir, e.g.) is a multiscale medium where the heterogeneities present in the medium are characterized by the micro scale and the global behaviors of the medium are observed at the macro scale. The upscaling from the micro scale to the macro scale can be done via averaging methods.

In this talk, diffusion and reaction of several mobile chemical species are considered in the pore space of a heterogeneous porous medium. The reactions amongst the species are modelled via mass action kinetics and the modelling leads to a system of multispecies diffusion; reaction equations (coupled semi-linear partial differential equations) at the micro scale where the highly nonlinear reaction rate terms are present at the right hand sides of the system of PDEs, cf. [2]. The existence of a unique positive global weak solution is shown with the help of a Lyapunov functional, Schaefer’s fixed point theorem and maximal Lp-regularity, cf. [2, 3]. Finally, with the help of periodic homogenization and two-scale convergence we upscale the model from the micro scale to the macro scale, e.g. [1, 3]. Some numerical simulations will also be shown in this talk, however for the purpose of illustration, we restrict ourselves to some relatively simple 2- dimensional situations.

As an extension to the previous model, we consider the mixture of two fluids. For such models, a system of Stokes-Cahn-Hilliard equations will be considered at the micro scale in a perforated porous medium. We first explain the periodic setting of the model and the existence results. At the end homogenization of the model will be shown using some extension theorems on Sobolev spaces, two-scale convergence and periodic unfolding.

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Title: The Perron-Frobenius theorem and its application to a class of dynamical systems

Speaker: Sandeep Krishna, NCBS.

Date: Fri, 28 Oct 2016

Venue: Simons Centre, Ground Floor.

The Perron-Frobenius theorem is a powerful and useful result about the eigenvalues and eigenvectors of a non-negative matrix. I will not be proving the theorem but will instead focus on its applications. In particular, I will discuss how it can be used to understand the behaviour of a certain class of dynamical systems, namely certain systems of first-order ordinary differential equations where the couplings between variables are specified by a graph. Some familiarity with graph theory will be useful, but I will try to recapitulate all the basic concepts needed for this talk.

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Title: Eigenfunctions Seminar: Algorithmic Applications of An Approximate Version of Caratheodory's Theorem

Title: Epimorphically Preserved Semigroup Identities

Speaker: Wajih Ashraf

Date: Fri, 23 Sep 2016

Time: 4 pm

Venue: LH-1

Title: Rank-level duality of Conformal Blocks

Speaker: Swarnava Mukhopadhyay University of Maryland

Date: Mon, 25 Jul 2016

Time: 3:30 - 4:30 p.m.

Venue: Lecture Hall I, Department of Mathematics

Classical invariants for representations of one Lie group can often be related to invariants of some other Lie group. Physics suggests that the right objects to consider for these questions are certain refinements of classical invariants known as conformal blocks. Conformal blocks appear in algebraic geometry as spaces of global sections of line bundles on the moduli stack of parabolic bundles on a smooth curve. Rank-level duality connects a conformal block associated to one Lie algebra to a conformal block for a different Lie algebra.

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Title: Rank-level duality of Conformal Blocks

Speaker: Swarnava Mukhopadhyay (Univ of Maryland, College Park)

Date: Mon, 25 Jul 2016

Time: 3:30 pm

Venue: LH-1

Venue: Lecture Hall I, Department of Mathematics, IISc.

In the 1980s, Goldman introduced a Lie algebra structure on the free vector space generated by the free homotopy classes of oriented closed curves in any orientable surface F. This Lie bracket is known as the Goldman bracket and the Lie algebra is known as the Goldman Lie algebra.

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Title: Funk and Hilbert geometry: Euclidean, non-Euclidean and timelike

Speaker: Athanase Papadopolous Universite de Strasbourg

Date: Thu, 04 Feb 2016

Venue: LH3 Math Dept IISc

I will present the Funk and Hilbert metrics on convex sets in the setting of Euclidean, non-Euclidean and timelike geometries. I will explain the motivation for studying these metrics and highlight some of their main properties, concerning geodesics, infinitesima structures and isometries.

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Title: Eigenfunctions Seminar: Electoral methods and the probability of the Alabama paradox

Speaker: Svante Linusson (KTH, Stockholm, Sweden)

Date: Fri, 29 Jan 2016

Time: 3:30 – 4:30 pm

Venue: LH-1, Mathematics Department

There exists various possible methods to distribute seats proportionally between states (or parties) in a parliament. In the first half of the talk I will describe some often used methods and discuss their pros and cons (it’s all in the rounding).

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Title: Iwasawa theory and the Birch and Swinnerton-Dyer conjecture:

Speaker: Sujatha Ramdorai (University of British Columbia, Vancouver, Canada)

Date: Mon, 31 Aug 2015

Time: 2 pm

Venue: LH 2

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Title: Contact Structures and Contact Invariants in Heegaard Floer Homology.

Speaker: Dheeraj Kulkarni, RKMVU, Kolkata

Date: Mon, 31 Aug 2015

Time: 3:30 p.m

Venue: L-1, Department of Mathematics, IISc

There is a dichotomy of contact structures– tight vs overtwisted. Classification of overtwisted contact structures up to isotopy, due to Eliashberg, is well understood. However, there have been few results towards classification of tight contact structures. In general, given a contact structure it is difficult to know whether it is tight or not.

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Title: Iwasawa theory and the Birch and Swinnerton-Dyer conjecture:

Speaker: Sujatha Ramdorai (University of British Columbia, Vancouver, Canada)

Date: Tue, 25 Aug 2015

Time: 2 pm

Venue: LH 2

Speaker: Prof K. R. Parthasarthy ISI Delhi

Date: Fri, 13 Feb 2015

Time: 4:00 - 5:00 p.m.

Venue: Lecture Hall I, Department of Mathematics

TBA

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Title: Indeterminate moment problems and growth of associated entire functions

Speaker: Prof Christian Berg University of Copenhagen

Date: Fri, 06 Feb 2015

Time: 2:00 - 3:00 p.m.

Venue: Lecture Hall I, Department of Mathematics

Speaker: Professor A. Raghuram Indian Institute of Science Education and Research (IISER) Pune, Maharashtra, India

Date: Thu, 16 Oct 2014

Time: 4:00 pm to 5:00 pm

Venue: Lecture Hall III, Ground Floor, Department of Mathematics, IISc, Bangalore

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Title: The BNS invariant and its application to twisted conjugacy

Speaker: Prof. Parameswaran Sankaran IMSc

Date: Tue, 14 Oct 2014

Time: 3:30 - 4:30 p.m.

Venue: Lecture Hall I, Department of Mathematics

Results of this character are motivated by a remarkable theorem of H. Alexander about proper holomorphic self-maps of the Euclidean ball. The first part of the talk will focus on the meanings of the terms in the above theorem. We will give an elementary proof that the automorphism group of a bounded symmetric domain acts transitively on it. But the existence of an involutive symmetry at each point is restrictive in many other ways. For instance, it yields a complete classification of the bounded symmetric domains. This follows from the work of Elie Cartan.

Venue: LH-1, Mathematics Department

Given n non-zero real numbers v_1,…,v_n, what is the maximum possible number of subsets {i_1,…,i_k} that can have the same subset sum v_{i_1}+…+v_{i_n}? Littlewood and Offord raised the question, showed that the answer is at most 2^nlog(n)/\sqrt{n} and conjectured that the log(n) can be removed. Erdos proved the conjecture and raised more questions that have continued to attract attention, primarily relating the arithmetic structure of v_1,…,v_n and the maximum number of subsets with a given subset-sum.

In the first lecture, we shall review and prove several of these results (due to Littlewood–Offord, Erdos, Moser, Stanley, Halasz, Tao–Vu, Rudelson–Vershynin…) and show an application to random matrices.

In the second part, we start with a question in random polynomials and see how it leads to a variant of the Littlewood–Offord problem that has not been considered before.

In this talk we consider a linear parabolic problem with time dependent coefficients oscillating rapidly in the space variable. The existence and uniqueness results are proved by using Rothe’’s method combined with the technique of two-scale convergence. Moreover, we derive a concrete homogenization algorithm for giving a unique and computable approximation of the solution.

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Title: HOMOTOPY AND HOMOLOGY OF NONCOMMUTATIVE SPACES

Speaker: Snigdhayan Mahanta University of Muenster

Date: Mon, 28 Jul 2014

Time: 3:30 - 4:30pm

Venue: Lecture Hall V, Department of Mathematics

In noncommutative geometry (NCG) one typically treats unital C-algebras as noncommutative compact spaces via Gelfand-Naimark duality. In various applications of NCG to problems in geometry or topology it is customary to first reformulate these problems in terms of certain (co)homology theories for noncommutative spaces. The celebrated Baum-Connes conjecture, that reduces the Novikov conjecture to an assertion in bivariant K-theory, is a prime example of this principle. However, the category of C-algebras is well-known to be de ficient from the viewpoint of homotopy theory or index theory. In this talk I am going to first survey certain (co)homology theories for noncommutative spaces, then present my proposed solution to the aforementioned problem, and finally (time permitting) discuss some applications. I will try to keep it non-technical and accessible to a wide range of audience.

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Title: A transference result between radial Fourier multipliers and zonal multipliers on the unit sphere.

Speaker: Sriram Alladi

Date: Thu, 24 Jul 2014

Time: 4:00 pm

Venue: LH-1

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Title: On open three-manifolds

Speaker: Gerard Besson Fourier Institut, Grenoble

Date: Fri, 07 Mar 2014

Time: 3:30 - 4:30 p.m.

Venue: Lecture Hall I, Department of Mathematics

We will describe quite carefully two classes of open three-manifolds. For one of them almost nothing is known about its Riemannian geometry and we will state open questions. For the second class a theorem is available as well as a complete classification.

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Title: On the Gromov hyperbolicity of convex domains

Speaker: Herve Gaussier Fourier Institut, Grenoble

Date: Wed, 05 Mar 2014

Time: 3:30 - 4:30 p.m.

Venue: Lecture Hall I, Department of Mathematics

Speaker: Prof Mahan Mj RKM Vivekananda University

Date: Tue, 10 Dec 2013

Time: 3:30 - 4:30 p.m.

Venue: Lecture Hall I, Department of Mathematics

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Title: Homotopy type and volume of locally symmetric spaces

Speaker: Prof C S Aravinda TIFR Bangalore

Date: Wed, 23 Oct 2013

Time: 3:30 - 4:30 p.m.

Venue: Lecture Hall I, Department of Mathematics

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Title: Ramanujan and hypergeometric series

Speaker: Dr.K. Srinivasa Rao, FNASc.,FTNASc., Senior Professor (Retd.), IMSc

Date: Thu, 12 Sep 2013

Time: 3:00 - 4:00 p.m.

Venue: Lecture Hall III, Department of Mathematics

Title: Generalized Radon transforms in image reconstruction problems

Speaker: Prof. Gaik Ambartsoumian University of Texas at Arlington

Date: Thu, 20 Jun 2013

Time: 4:00 - 5:00 p.m.

Venue: Lecture Hall I, Department of Mathematics

Title: A new class of high order finite volume schemes

Speaker: Prof. Philip Roe University of Michigan

Date: Mon, 13 May 2013

Time: 4:00 pm- 5:00pm

Venue: Department of Mathematics, LH-I

A robust, inexpensive, general-purpose CFD algorithm of better than second-order accuracy would have transformative impact on scientific computing. This talk will describes progress toward this objective.

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Title: Geometrical treatment of geometric shock waves

Speaker: Prof. Philip Roe University of Michigan

Date: Fri, 10 May 2013

Time: 4:00 pm- 5:00pm

Venue: Department of Mathematics, LH-I

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Title: Differential Modular forms on Shimura curves over totally real fields

Speaker: Prof. Debargha Benerjee Australian National University

Date: Thu, 02 May 2013

Time: 4:00 pm- 5:00pm

Venue: Department of Mathematics, LH-III

In this talk, we will introduce the theory of differential modular forms for compact Shimura curves over totally real fields. These are the modular forms obtained by applying the arithmetic jet space functor (adjoint to the Witt vector functor) to the ring of modular forms (global sections of certain line bundle). We will show that these differential modular forms help us to detect the ordinary quaternionic abelian schemes and schemes with Frobenius lifts (local analogue of CM abelian schemes). These are also useful to understand the categorical quotient of Shimura curves modulo Hecke correspondences/isogeny. We also construct the Serre-Tate expansions of such differential modular forms as a possible alternative to the Fourier expansion maps.

Title: Languages and Generalized Code Chains.

Speaker: Prof. R. D. Giri, Nagpur University.

Date: Wed, 20 Feb 2013

Time: 3:00 pm-4:00 pm

Venue: LH-III, Department of Mathematics

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Title: On condition numbers of a basis

Speaker: Professor B. V. Limaye (IIT Bombay)

Date: Tue, 19 Feb 2013

Time: 11:30 am-12:30 pm

Venue: LH-II, Department of Mathematics

Title: Switching in biological networks

Speaker: Prof. Badal Joshi University of Minnesota

Date: Mon, 11 Feb 2013

Time: 4:00 pm- 5:00pm

Venue: Department of Mathematics, LH-I

(Bio)chemical reaction networks are used in systems biology to model gene regulatory, protein, metabolic, and other cellular networks. Since existence of multiple steady states (MSS) provides the underpinnings for switching in chemical reaction networks, it is a fundamental problem to determine which network structures permit MSS. There exist several criteria which, when satisfied, establish that a network does not permit MSS regardless of the parameter values. On the other hand, results that establish that a network does permit MSS are rare. I will describe our recent work which provides a novel approach towards solving this problem. In the second part of the talk, I will describe stochastic switching which occurs in a network of neurons which is responsible for the distinct brain states of sleep and wake and for the transitions between the two states.

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Title: Derived Geometry and Topological String Theory

Speaker: Dr. Pranav Pandit, University of Vienna

Date: Thu, 07 Feb 2013

Time: 3:30 p.m.

Venue: LH-III, Department of Mathematics

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Title: Switching in biological networks

Speaker: Prof. Badal Joshi University of Minnesota

Date: Wed, 06 Feb 2013

Time: 4:00 pm- 5:00pm

Venue: Department of Mathematics, LH-I

Date: Mon, 29 Oct 2012

Time: 11:30 am- 12:30 pm

Venue: Department of Mathematics, Lecture Hall I

We characterize the higher order Riesz transforms on the Heisenberg group and also show that they satisfy dimension-free bounds under some assumptions on the multipliers. We also prove the boundedness of the higher order Riesz transforms associated to the Hermite operator. Using transference theorems, we deduce boundedness theorems for Riesz transforms on the reduced Heisenberg group and hence also for the Riesz transforms associated to special Hermite and Laguerre expansions.

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Title: Riesz transforms associated with Heisenberg groups and Grushin operator

Speaker: Mr. Sanjay P. K. IISc, Bangalore

Date: Mon, 29 Oct 2012

Time: 11:30 am- 12:30 pm

Venue: Department of Mathematics, Lecture Hall I

Title: Pricing Credit Derivatives in a Markov Modulated Market.

Title: Introduction to Harmonic analysis on NA groups

Speaker: Dr. Pratyoosh Kumar

Date: Wed, 08 Aug 2012

Time: 4:00 pm- 5:00 pm

Venue: Department of Mathematics, Lecture Hall 1

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Title: An introduction to GKM graphs

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Let D_1,…D_n be a system of commuting, formally self-adjoint, left invariant operators on a Lie group G. Under suitable hypotheses, we show that D_1,…D_n are essentially self-adjoint on L^2(G) and admit a joint spectral resolution, and we characterize their joint L^2 spectrum as the set of eigenvalues corresponding to a class of generalized joint eigenfunctions. Moreover, in the case G is a homogeneous group and D_1,…D_n are homogeneous, we obtain L^p-boundedness results for operators of the form m(D_1,…D_n), analogous to the Mihlin-Hormander and Marcinkiewicz multiplier theorems.

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Title: Joint spectral multipliers on nilpotent Lie groups

Speaker: Prof. Alessio Martini Universitaet zu Kiel

Date: Wed, 25 Jan 2012

Time: 4:00 p.m.

Venue: Department of Mathematics, Lecture Hall I

Title: Holomorphic Morse inequalities and the Green-Griffiths-Lang conjecture--Part I

Speaker: Prof. Jean-Pierre Demailly Institut Fourier, Universite de Grenoble France

Date: Wed, 23 Nov 2011

Time: 4:00-5:00 p.m.

Venue: Department of Mathematics, Lecture Hall I

Speaker: Prof. Sunil K. Chebolu Illinois State University, U.S.A.

Date: Fri, 20 May 2011

Time: 4:00-5:00 p.m.

Venue: Lecture Hall I, Department of Mathematics

Let G be the absolute Galois group of a field that contains a primitive p-th root of unity. This is a profinite group which is a central object of study in arithmetic algebraic geometry. In joint work with Ido Efrat and Jan Minac, we have shown that a remarkably small quotient of this big group determines the entire Galois cohomology of G. As application of this result, we give new examples of profinite groups that are not realisable as absolute Galois groups of fields. I will present an overview of this work. ALL ARE CORDIALLY INVITED

                           ALL ARE INVITED

Title: Forbidden configurations, extremal set systems, and Steiner designs

Speaker: Prof. Niranjan Balachandran Caltech U.S.A.

Date: Tue, 14 Dec 2010

Time: 4:00-5:00 p.m.

Venue: Lecture Hall I, Department of Mathematics

One of the fundamental problems in Extremal Combinatorics concerns maximal set systems with forbidden subconfigurations. One such open problem concerns the conjecture due to Anstee and Sali on the order of maximal configurations with certain forbidden subconfigurations. I shall talk about some well known results, talk about the Anstee-Sali conjecture, and finally talk about some of my recent work concerning Steiner designs occuring as maximal forbidden configurations for certain natural choices of subconfigrations. This generalizes a result of Anstee and Barekat.

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Title: Hilbert spaces based on complex Hermite polynomials, and related quantizations

Speaker: Prof. Jean-Pierre Gazeau Universit Paris-7 Denis Diderot France

Date: Mon, 13 Dec 2010

Time: 4:00-5:00 p.m.

Venue: Lecture Hall I, Department of Mathematics

I will report on the existence and properties of Hilbert spaces based on different families of complex, holomorphic or not, functions, like Hermite polynomials. The resulting coherent state quantizations of the complex plane will be presented. Some interesting issues will be examined, like the existence of the usual harmonic oscillator spectrum despite the absence of canonical commutation rules.

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Title: An iterated observer method for recovering the initial state for a class of PDE's

Speaker: Prof. Marius Tucsnak Institut Elie Cartan Universite Nancy-1 France

Date: Wed, 24 Nov 2010

Time: 4:00-5:00 p.m.

Venue: Lecture Hall I, Department of Mathematics

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Title: Distributed Processing and Temporal Codes in Neuronal Networks

Speaker: Prof. Wolf Singer Director, Max Planck Institute for Brain Research Frankfurt/Main Frankfurt Institute for Advanced Studies (FIAS)

Date: Thu, 18 Nov 2010

Time: lh 1, department of mathematics indian institute of science, bangalore

Venue: 11:00

Higher cognitive functions require the coordination of large assemblies of

spatially distributed neurons in ever changing constellations. It is

proposed that this coordination is achieved through temporal coordination

of oscillatory activity in specific frequency bands. Since there is no

supra-ordinate command centre in the brain, the respective patterns of

synchronous activity self-organize, which has important implications on

concepts of intentionality and top down causation. Evidence will be

provided that synchronisation supports response selection by attention,

feature binding, subsystem integration, short-term memory, flexible

routing of signals across cortical networks and access to the work-space

of consciousness. The precision of synchronisation is in the millisecond

range, suggesting the possibility that information is encoded not only in

the co-variation of discharge rates but also in the precise timing of

individual action potentials. This could account for the high speed with

which cortical circuits can encode and process information. Recent studies

in schizophrenic patients indicate that this disorder is associated with

abnormal synchronisation of oscillatory activity in the high frequency

range (beta and gamma). This suggests that some of the cognitive deficits

Venue: Lecture Hall III, Department of Mathematics

Speaker: K. R. Arun, Research student, Department of Mathematics, IISc

Date: Tue, 11 May 2010

We derive the conservation form of equations of evolution of a front propagating in three dimensions. We obtain a system of six conservation laws, known as 3-D kinematical conservation laws (KCL) in a ray coordinate system. The conservative variables of 3-D KCL are also constrained by a stationary vector constraint, known as geometric solenoidal constraint, which consists of three divergence-free type conditions. The 3-D KCL is an under-determined system, and therefore, additional closure relations are required to get a complete set of equations. We consider two closure relations for 3-D KCL: (1) energy transport equation of a weakly nonlinear ray theory (WNLRT) to study the propagation of a nonlinear wavefront, (2) transport equations of a shock ray theory (SRT) to study the propagation of a curved weak shock front. In both the cases we obtain a weakly hyperbolic system of balance laws. For the numerical simulation we use a high-resolution semi-discrete central scheme. The second order accuracy of the scheme is based on MUSCL type reconstructions and TVD Runge-Kutta time stepping procedures. A constrained transport technique is used to enforce the geometric solenoidal constraint and in all the test problems considered, the constraint is satisfied up to very high accuracy. We present the results of extensive numerical experiments, which confirm the efficiency and robustness of the method and also its ability to capture many physically realistic features of the fronts.

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Title: Some aspects of the Kobayashi and Caratheodary metrics on pseudoconvex domains.

Speaker: Dr. Harish Seshadri, IISc.

Date: Tue, 29 Dec 2009

Time: 10:00 a.m.

Venue: Lecture Hall - I, Dept. of Mathematics

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Title: String Topology

Speaker: Prof. Dennis Sullivan, Stony Brook.

Date: Mon, 21 Dec 2009

Time: 4:00 p.m.

Venue: Lecture Hall - I, Dept. of Mathematics

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Speaker: Dr. V. Sreekar

Date: Fri, 24 Jul 2009

Time: 4 - 5 pm.

Venue: LH-III, Department of Mathematics

Gaussian Minkowski functionals (GMFs) for reasonably smooth subsets of Euclidean spaces, are defined as coefficients appearing in the the Gaussian-tube-formula in finite dimensional Euclidean spaces. The fact that the measure in consideration here is Gaussian, itself makes the whole analysis an infinite dimensional one. Therefore, one might want to generalize the definition of Gaussian Minkowski functionals to the subsets of Wiener space which arise from reasonably smooth (in Malliavin sense) Wiener functionals. As in the finite dimensional case, we shall identify the GMFs in the infinite dimensional case, as the coefficients appearing in the tube formula in Wiener space. Finally, we shall try to apply this infinite dimensional generalization to get results about the geometry of excursion sets of a reasonably large class of random fields defined on a “smooth” manifold.

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Title: Wave Propagation on Networks

Speaker: Prof. E. Zuazua Scientific Director BCAM - Basque Center for Applied Mathematics, Spain

Date: Fri, 24 Jul 2009

Time: lh 1, department of mathematics indian institute of science, bangalore

Venue: 4:00

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Title: The ubiquity of the symplectic Hamiltonian equations in mechanics

Speaker: Prof. Manuel de Len Instituto de Ciencias Matemticas Consejo Superior de Investigaciones Cientificas

Date: Tue, 21 Jul 2009

Time: lh 1, department of mathematics indian institute of science, bangalore

Venue: 4:00

                           ALL ARE INVITED

                         Coffee/Tea: 3:45 pm

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Title: Horocycles on the modular surface and diophantine approximation

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Title: Operator Theory and Algebraic Topology

Speaker: R. G. Douglas Texas A&M University

Date: Fri, 05 Jun 2009

Time: l h 1, department of mathematics indian institute of science, bangalore

Venue: 4.00

About thirty-five years ago, several problems in operator theory concerning almost normal operators led L. G. Brown, P. A. fillmore and me to introduce methods and point of view from algebraic topology to solve them. By the time we were done concrete realization of K-homology was introduced as well as new insight obtained for the index theorem of Atiyah-Singer.

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Title: Systems Biology Approaches for the Environmental Biotechnology Applications

Speaker: Prof. Radhakrishnan Mahadevan Department of Chemical Engineering and Applied Chemistry University of Toronto

Date: Wed, 06 May 2009

Time: 2:00 pm

Venue: Lecture Hall I, Department of Mathematics

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Title: On spectrum and arithmetic

Speaker: Prof. C. S. Rajan, TIFR, Mumbai

Date: Mon, 20 Apr 2009

Time: 4:00 p.m.

Venue: Lecture Hall - I, Dept. of Mathematics

We will discuss the notion of spectrum and arithmetic of spaces, and expound on the expectation that they should mutually determine each other for the class of locally symmetric spaces associated to congruent arithmetic lattices.

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Title: The homogeneous shifts via inductive algebras

Speaker: Prof. M. K. Vemuri Chennai Mathematical Institute Chennai

Date: Mon, 20 Apr 2009

Time: lh -1, department of mathematics indian institute of science, bangalore

Venue: 11.30

Title: Size biasing with applications to Markov chains and branching processes.

Speaker: K. B. Athreya, Iowa State university

Date: Thu, 19 Mar 2009

Time: 4:00 p.m.

Venue: Lecture Hall - I, Dept. of Mathematics

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Title: Assessing copy number variation using genome-wide alignments

Speaker: Dr. Deepayan Sarkar, Fred Hutchinson Cancer Research Institute USA

Date: Mon, 02 Mar 2009

Time: 4:00 p.m.

Venue: Lecture Hall - I, Dept. of Mathematics

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Title: Polynomial and Rational Hulls

Speaker: Prof. Nikolay Shcherbina Department of Mathematics University of Wuppertal, Germany

Date: Fri, 20 Feb 2009

Time: department of mathematics indian institute of science, bangalore

Venue: 4PM

We will discuss the notions of polynomial and rational convexity. In particular, the question of existence of analytic structure on the additional part of the hull will be considered. Applications of polynomial and rational convexity to other problems of complex analysis will also be given.

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Title: An unusual problem in large deviations

Speaker: S.R.S. Varadhan, Courant Institute

Date: Thu, 12 Feb 2009

Time: 4:00 p.m.

Venue: Lecture Hall - I, Dept. of Mathematics

We will investigate the large deviation rates for sums of the form $\sum_i f(x_i) g(x_{2i})$ where $\{x_i\}$ is a nice Markov process. In other words calculate

$\lim_{n\to\infty}{1\over n}\log E[\exp \sum_{i=1}^n f(x_i) g(x_{2i})]$

where $\{x_i\}$ is Markov Chain with transition probability $\pi(x, y)$.

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Title: Recent Trends in Invariant Theory

Speaker: Prof. Roger Howe Mathematics Department, Yale University

Date: Tue, 10 Feb 2009

Time: l h 1, department of mathematics indian institute of science, bangalore

Venue: 04:00pm

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Title: Modulation Spaces and Banach Gelfand Triples

Speaker: Prof. Hans G. Feichtinger University of Vienna, Austria

Date: Mon, 19 Jan 2009

Time: l h i, department of mathematics indian institute of science, bangalore

Venue: 11:15

http://www.univie.ac.at/nuhag-php/scheduler/index.php

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Title: Analysis of the Wright{Fisher Equation

Speaker: Prof. D. W. Stroock M.I.T, USA

Date: Fri, 16 Jan 2009

Time: l h 1, department of mathematics indian institute of science, bangalore

Venue: 4:00

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Title: Homogeneous Vector bundles in Operator theory.

Speaker: Prof. A. Koranyi, Lehman College, CUNY

Date: Thu, 15 Jan 2009

Time: 4:00 p.m.

Venue: Lecture Hall - I, Dept. of Mathematics

Date: Fri, 12 Sep 2008

Time: 4.00 p.m.

Venue: Lecture Hall - I, Dept. of Mathematics

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Title: Conservation laws admitting delta shock wave type solutions

Speaker: Prof. Prof. G. D. Veerappa Gowda TIFR-CAM, Bangalore

Date: Fri, 29 Aug 2008

Time: 4.00 p.m.

Venue: Lecture Hall - I, Dept. of Mathematics

Title: 3-D Kinematical Conservation Laws: equations of evolution of a surface

Speaker: Prof. Phoolan Prasad

Date: Fri, 22 Feb 2008

Venue: Lecture Hall 3, Department of Mathematics

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Date: Tue, 22 Jan 2008

Time: 4:00 p. m.

Venue: Lecture Hall III, Dept. of Mathematics

Title: The Newton Polygon

Speaker: Prof. Sriram Abhyankar, Purdue Universtiy

Date: Fri, 14 Dec 2007

Time: 4.00 p.m.

Venue: Lecture Hall - I, Dept. of Mathematics

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Title: Ergodic theory, abelian groups, and point processes associated with stable random fields

Speaker: Dr. Parthanil Roy, ETH Zurich and Michigan State University

Date: Mon, 10 Dec 2007

Time: 10.00 a.m.

Venue: Lecture Hall - I, Dept. of Mathematics

We consider a point process sequence induced by a stationary symmetric -stable (0 < < 2) discrete parameter random eld. It is easy to prove, following the arguments in the one-dimensional case in Resnick and Samorodnitsky (2004), that if the random eld is generated by a dissipative group action then the point process sequence converges weakly to a cluster Poisson process. For the conservative case, no general result is known even in the one-dimensional case. We look at a specic class of stable random elds generated by conservative actions whose eective dimensions can be computed using the structure theorem of nitely generated abelian groups. The corresponding point processes sequence is not tight and hence needs to be properly normalized in order to ensure weak convergence. This weak limit is computed using extreme value theory and some counting techniques. (This talk is based on a joint work with Gennady Samorodnitsky) All interested are Welcome

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Title: Some queer diffusions

Speaker: Prof. Daniel Stroock, MIT

Date: Fri, 07 Dec 2007

Time: 4.00 p.m.

Venue: Lecture Hall - I, Dept. of Mathematics

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Title: Least area surfaces are incompressible

Speaker: Dr. Siddhartha Gadgil, IISc

Date: Thu, 06 Dec 2007

Time: 4:00 p.m.

Venue: Lecture Hall - I, Dept. of Mathematics

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Title: Least area surfaces are incompressible

Speaker: Dr. Siddhartha Gadgil, IISc

Date: Wed, 05 Dec 2007

Time: 4:00 p.m.

Venue: Lecture Hall - I, Dept. of Mathematics

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Title: Domains with non-compact automorphism group

Speaker: Dr. Kaushal Verma, IISc

Date: Fri, 30 Nov 2007

Time: 4.00 p.m.

Venue: Lecture Hall - I, Dept. of Mathematics

The purpose of the talk will be to discuss the problem about classifying domains in C^n that have a non-compact group of holomorphic automorphisms. Examples and a flavour of some of the techniques that have been successful so far will be provided.

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Title: Linear and integer programming: The state of the art

Title: Chern-Cheeger-Simons theory of secondary classes

Speaker: Dr. Jaya Iyer, IMSc.

Date: Tue, 13 Nov 2007

Time: 2.00 p.m.

Venue: Lecture Hall - III, Dept. of Mathematics

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Title: Cycles on complete intersections

Speaker: Dr. Jaya Iyer, IMSc.

Date: Mon, 12 Nov 2007

Time: 4.00 p.m.

Venue: Lecture Hall - I, Dept. of Mathematics

We discuss some questions on the triviality of rational Chow groups and give some examples in this direction.

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Title: Ergodic theory, abelian groups, and point processes associated with stable random fields

Speaker: Dr. Parthanil Roy, ETH Zurich and Michigan State University

Date: Sat, 10 Nov 2007

Time: 10.00 a.m.

Venue: Lecture Hall - I, Dept. of Mathematics

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Title: History of irrational and transcendental numbers

Speaker: Prof. Michel Waldschmidt, Institut de Mathmatiques de Jussieu, Paris

Date: Tue, 06 Nov 2007

Time: 2.00 p.m.

Venue: Lecture Hall - III, Dept. of Mathematics

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Title: Negatively curved Kahler manifolds

Speaker: Martin Deraux (Institut Fourier, Grenoble)

Date: Wed, 31 Oct 2007

Lecture Series on “ Negatively curved Kahler manifolds” (4 Lectures)

Speaker: Dr. Martin Deraux, Institut Fourier, Grenoble

Time and place: LH 2, IISc Math Dept

Wednesdays (31st Oct and 7th Nov) 11-12.30 PM
Thursdays (1st Nov and 8th Nov) 3-4.30 PM

Abstract:

Basics of Kahler geometry, uniformization.
Intro to complex hyperbolic geometry, review about symmetric spaces, constructions of discrete groups and lattices, Calabi conjecture and Yau uniformization.
Overview of Deligne-Mostow theory.
Branched covering constructions and non-locally symmetric examples.

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Title: Non-negative isotropic curvature

Speaker: Dr. Harish Seshadri, IISc

Date: Fri, 26 Oct 2007

Time: 4.00 p.m.

Venue: Lecture Hall - III, Dept. of Mathematics

Supp(A)=\\Sum_{i=1}^n i\\cdot l_i=n-l_1

Evaluation of the coefficient of the calss-sum C in the product of the class sums A and B is reduced to a combinatorial problem in S_k, where k=min{Supp(A),Supp(B),Supp(C)}

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Title: Multivariate Distributions, Quantiles and their Monotonicity Properties.

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Title: On the numerical approximation of nonconservative hyperbolic balance laws

Title: How interesting are orbifolds?

Speaker: Mainak Poddar ISI Kolkata

Date: Fri, 23 Mar 2007

Time: 4:00 p.m.

Venue: Lecture Hall - I, Department of Mathematics

Orbifolds are generally regarded as generalizations of manifolds. On the other hand, finite groups are also orbifolds. In this survey talk, I will focus on how orbifolds appear naturally in some important areas of Mathematics and Physics. I will also describe some features of the geometry of orbifolds.

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Title: Numerical Modeling of Hyperbolic Balance Laws using Bicharacteristics

Speaker: Prof. M. Lukacova, Hamburg University of Technology

Date: Wed, 14 Mar 2007

Time: 4.00 p.m.

Venue: Lecture Hall - I, Dept. of Mathematics

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Title: Numerical Modeling of Hyperbolic Balance Laws using Bicharacteristics

Speaker: Prof. M. Lukacova, Hamburg University of Technology

Date: Tue, 13 Mar 2007

Time: 4.00 p.m.

Venue: Lecture Hall - II, Dept. of Mathematics

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Title: Zariski-Lipman Conjecture

Speaker: Prof. Dilip Patil, IISc

Date: Thu, 08 Mar 2007

Time: 4.00 p.m.

Venue: Lecture Hall - I, Dept. of Mathematics

In this lecture I will give a brief survey on the well-known Zariski-Lipman Conjecture which is still open in general. However, there are some partial results have been proved. I will state these results by giving necessary definitions and concepts required.

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Title: Mathematical issues for some control problems in fluid mechanics

Speaker: Prof. Jean-Pierre Raymond Universit Paul Sabatier, Toulouse, France HRI, Allahabad

Date: Wed, 28 Feb 2007

Time: 4.00 p.m.

Venue: Lecture Hall - I, Dept. of Mathematics

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Title: Real vs. Strongly Real Elements in Algebraic Groups

Speaker: Dr. Anupam Kumar Singh, TIFR, Mumbai

Date: Tue, 27 Feb 2007

Time: 4.00 p.m.

Venue: Lecture Hall - II, Dept. of Mathematics

Let $k$ be a field of characteristic not 2 and $G$ be an algebraic group defined over $k$. An element $t$ in $G(k)$ is called real if there exists $g \in G(k)$ such that $gtg^{-1}=t^{-1}$. An element $t\in G(k)$ is called strongly real if $t=\tau_1\tau_2$ where $\tau_i\in G(k)$ and $\tau_i^2=1$. We discuss when a semisimple real element is strongly real in $G(k)$. We investigate this question for classical groups and the groups of type $G_2$ in detail.

Department of Mathematics

INDIAN INSTITUTE OF SCIENCE

Seminars

By Year

Title: APRG Seminar: Macdonald's conjecture on hypergeometric functions associated to Jack polynomials

Speaker: Siddhartha Sahi (Rutgers University, USA)

Date: Thu, 06 Jun 2019

Time: 3:30 pm

Venue: LH-1, Mathematics Department

Title: Algebra & Combinatorics Seminar: Metaplectic Representations of Hecke algebras

Speaker: Siddhartha Sahi (Rutgers University, USA)

Date: Tue, 04 Jun 2019

Time: 3:30 pm

Venue: LH-1, Mathematics Department

Title: Problem governed by the von Kármán equations Morley finite element for a distributed optimal control

Speaker: Sudipto Chowdhury (IIT, Bombay)

Date: Tue, 21 May 2019

Time: 11 am

Venue: LH-1, Mathematics Department

Title: Algebra & Combinatorics Seminar: Alternating Schur Algebras and Koszul Duality

Speaker: Amritanshu Prasad (IMSc, Chennai)

Date: Wed, 08 May 2019

Time: 3 pm

Venue: LH-5, Mathematics Department

Title: Algebra & Combinatorics Seminar: Path models for Kostant-Kumar submodules of a tensor product

Speaker: Sankaran Viswanath (IMSc, Chennai)

Date: Tue, 07 May 2019

Time: 11:30 am

Venue: LH-5, Mathematics Department

Title: Algebra & Combinatorics Seminar: The Brylinski filtration and W-algebras

Speaker: Sankaran Viswanath (IMSc, Chennai)

Date: Fri, 03 May 2019

Time: 3 pm

Venue: LH-1, Mathematics Department

Title: Algebra & Combinatorics Seminar: Suslin Matrices vs Clifford Algebras

Speaker: Vineeth Chintala (IIT, Bombay)

Date: Wed, 01 May 2019

Time: 3 pm

Venue: LH-1, Mathematics Department

Title: Determinantal processes and stochastic domination

Speaker: Raghavendra Tripathi (IISc Mathematics)

Date: Tue, 30 Apr 2019

Time: 11:30 am

Venue: LH-1, Mathematics Department

Title: Geometry & Topology Seminar: Coarse geometry, Baum-Connes conjecture, and metrics of positive scalar curvature on spin foliations

Speaker: Indrava Roy (IMSc, Chennai)

Date: Mon, 29 Apr 2019

Time: 4 pm

Venue: LH-1, Mathematics Department

Title: On derivatives of Modular forms

Speaker: Siegfried Bocherer (University of Mannheim, Germany)

Date: Mon, 22 Apr 2019

Time: 3 pm

Venue: LH-1, Mathematics Department

Title: Algebra & Combinatorics Seminar: Spinorial Representations of Symmetric Groups

Speaker: Jyotirmoy Ganguly (IISER Pune)

Date: Tue, 16 Apr 2019

Time: 2 pm

Venue: LH-1, Mathematics Department

Title: Eigenfunctions Seminar: The Pick-Nevanlinna problem: from metric geometry to matrix positivity

Speaker: Gautam Bharali (IISc Mathematics)

Date: Fri, 12 Apr 2019

Time: 4 pm

Venue: LH-1, Mathematics Department

Title: Eigenfunctions Seminar: Schoenberg: from metric geometry to matrix positivity

Speaker: Apoorva Khare (IISc Mathematics)

Date: Fri, 12 Apr 2019

Time: 3 pm

Venue: LH-1, Mathematics Department

Title: Algebra & Combinatorics Seminar: Crossed products of noncommutative tori by cyclic groups

Speaker: Sayan Chakraborty (ISI, Kolkata)

Date: Mon, 08 Apr 2019

Time: 2:30 pm

Venue: LH-1, Mathematics Department

Title: Geometry & Topology Seminar: A chain model for the Goresky-Hingston product

Speaker: Arun Maiti (IISc Mathematics)

Date: Mon, 08 Apr 2019

Time: 4 pm

Venue: LH-1, Mathematics Department

Title: Algebra & Combinatorics Seminar: Determinants, linear recurrences and some combinatorial identities