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Fri, 23 Oct 2020 18:22:40 +0530Fri, 23 Oct 2020 18:22:40 +0530Jekyll v3.8.7Discussion Meeting on Representation Theory during December 10 - 12, 2020.<p><a href="https://sites.google.com/view/dmrt2020/home">Visit this page <br />
https://sites.google.com/view/dmrt2020/home</a></p>
Thu, 10 Dec 2020 00:00:00 +0530
http://math.iisc.ac.in/2020/12/10/discussion-meeting-on-representation-theory.html
http://math.iisc.ac.in/2020/12/10/discussion-meeting-on-representation-theory.htmlPh.D Research Program 2020.<p><a href="http://math.iisc.ac.in/phd2020result.html">CLICK HERE for list of candidates recommended for the PhD programme 2020.</a></p>
Mon, 27 Jul 2020 00:00:00 +0530
http://math.iisc.ac.in/2020/07/27/phdresult.html
http://math.iisc.ac.in/2020/07/27/phdresult.htmlIntegrated Ph.D Program 2020.<p><a href="http://math.iisc.ac.in/intphd2020result.html">CLICK HERE for list of candidates recommended for the Integrated PhD programme 2020.</a></p>
Mon, 27 Jul 2020 00:00:00 +0530
http://math.iisc.ac.in/2020/07/27/intphdresult.html
http://math.iisc.ac.in/2020/07/27/intphdresult.htmlWorkshop on Finite Elements for Nonlinear and Multiscale Problems during Feb 28 – Mar 03, 2020.<p><a href="http://math.iisc.ac.in/~gudi/FEM-Workshop.pdf">Visit this page <br />
http://math.iisc.ac.in/~gudi/FEM-Workshop.pdf</a></p>
Fri, 28 Feb 2020 00:00:00 +0530
http://math.iisc.ac.in/2020/02/28/Finite-Elements-for-Nonlinear-and-Multiscale-Problems.html
http://math.iisc.ac.in/2020/02/28/Finite-Elements-for-Nonlinear-and-Multiscale-Problems.htmlAlgebra Symposium<p>We cordially invite you to an <strong>Algebra Symposium</strong> at IISc. The organizers are R. Venkatesh and Apoorva Khare.</p>
<p><strong>Date:</strong> 12<sup>th</sup> February, 2020 (Wednesday)</p>
<p><strong>Venue:</strong> Lecture Hall-1, Department of Mathematics, IISc</p>
<table>
<thead>
<tr>
<th>Time</th>
<th> Speaker</th>
<th> Title</th>
</tr>
</thead>
<tbody>
<tr>
<td>9:00 am</td>
<td> Amalendu Krishna</td>
<td> <em>An application of $K$-theory in class field theory</em></td>
</tr>
<tr>
<td>10:00 am</td>
<td> Tea</td>
<td> </td>
</tr>
<tr>
<td>10:15 am</td>
<td> Radhika Ganapathy</td>
<td> <em>Congruences of parahoric group schemes</em></td>
</tr>
<tr>
<td>11:15 am</td>
<td> Tea</td>
<td> </td>
</tr>
<tr>
<td>11:30 am</td>
<td> Shaunak Deo</td>
<td> <em>Deformations of Galois representations</em></td>
</tr>
<tr>
<td>12:30 pm</td>
<td> Lunch</td>
<td> </td>
</tr>
<tr>
<td>2:30 pm</td>
<td> Mahesh Kakde</td>
<td> <em>On Hilbert’s 12th problem and Brumer-Stark conjecture</em></td>
</tr>
<tr>
<td>3:30 pm</td>
<td> Tea</td>
<td> </td>
</tr>
<tr>
<td>4:00 pm</td>
<td> Uri Onn</td>
<td> <em>Representation growth of arithmetic lattices</em></td>
</tr>
<tr>
<td>5:00 pm</td>
<td> High Tea</td>
<td> </td>
</tr>
</tbody>
</table>
<hr />
<h3 id="abstracts">Abstracts</h3>
<h4 id="lecture-1-">Lecture 1 </h4>
<p><strong>Speaker:</strong> <em>Amalendu Krishna</em> (TIFR, Mumbai)</p>
<p><strong>Title:</strong> An application of $K$-theory in class field theory</p>
<p><strong>Abstract:</strong> I will show how we can use algebraic $K$-theory to solve a higher dimensional class field theory problem. Time permitting, I will give an application to the solution of a conjecture of Deligne on $\ell$-adic local systems.</p>
<hr />
<h4 id="lecture-2">Lecture 2</h4>
<p><strong>Speaker:</strong> <em>Radhika Ganapathy</em> (IISc Mathematics)</p>
<p><strong>Title:</strong> Congruences of parahoric group schemes</p>
<p><strong>Abstract:</strong> Let $F$ be a non-archimedean local field and let $T$ be a torus over $F$. With $\mathcal{T}^{N R}$ denoting the Neron-Raynaud model of $T$, a result of Chai and Yu asserts that the model $\mathcal{T}^{N R} \times_{\mathfrak{O}_F} \mathfrak{O}_F / \mathfrak{p}_F^m$ is canonically determined by $({\rm Tr}_l(F), \Lambda)$ for $l \gg m$, where $({\rm Tr}_l(F) = (\mathfrak{O}_F / \mathfrak{p}_F^l, \mathfrak{p}_F / \mathfrak{p}_F^{l+1}, \epsilon)$ with $\epsilon$ denoting the natural projection of $\mathfrak{p}_F / \mathfrak{p}_F^{l+1}$ on $\mathfrak{p}_F / \mathfrak{p}_F^l$, and $\Lambda := X_*(T)$. In this talk we will discuss the analogous question for parahoric group schemes attached to facets in the Bruhat-Tits building of a connected reductive group over $F$, and some applications of this result towards studying the representation theory of $p$-adic groups over close local fields.</p>
<hr />
<h4 id="lecture-3">Lecture 3</h4>
<p><strong>Speaker:</strong> <em>Shaunak Deo</em> (TIFR, Mumbai)</p>
<p><strong>Title:</strong> Deformations of Galois representations</p>
<p><strong>Abstract:</strong> One of the main themes of deformation theory of Galois representations is to study families of Galois representations obtained by interpolating various Galois representations having certain prescribed properties. In this talk, I will first review some basic facts and results of deformation theory of Galois representations. Then I will describe the basic anatomy of theorems comparing various universal deformation rings with appropriate Hecke algebras (which are popularly known as ‘R=T’ theorems in the literature and are important from Number theoretic point of view). In the second half of the talk, I will describe some of my own results in which establishing an R=T theorem has played a crucial role.</p>
<hr />
<h4 id="lecture-4">Lecture 4</h4>
<p><strong>Speaker:</strong> <em>Mahesh Kakde</em> (IISc Mathematics)</p>
<p><strong>Title:</strong> On Hilbert’s 12th problem and Brumer-Stark conjecture</p>
<p><strong>Abstract:</strong> In this talk I will state Hilbert’s 12th problem (explicit class field theory) and give a $p$-adic solution for totally real fields. This involves proving the Brumer-Stark conjecture and an integral refinement of the Gross-Stark conjecture. This is a joint work with Samit Dasgupta.</p>
<hr />
<h4 id="lecture-5">Lecture 5</h4>
<p><strong>Speaker:</strong> <em>Uri Onn</em> (Australian National University, Canberra, Australia)</p>
<p><strong>Title:</strong> Representation growth of arithmetic lattices</p>
<p><strong>Abstract:</strong> Let $G$ be a group and let $r(n,G)$ denote the number of equivalence classes of $n$-dimensional complex irreducible representations of $G$. Representation growth is a branch of asymptotic group theory that studies the asymptotic and arithmetic properties of the sequences $(r(n,G))$. In 2008 Larsen and Lubotzky conjectured that all irreducible lattices in a high rank semisimple Lie group have the same degree of polynomial representation growth. In this talk I will explain the conjecture and describe the ideas around the proof of a variant of the conjecture: if the lattices have polynomial representation growth (which is known to be true in most cases) then they have the same degree of polynomial growth. This is a joint work with Nir Avni, Benjamin Klopsch and Christopher Voll.</p>
Wed, 12 Feb 2020 00:00:00 +0530
http://math.iisc.ac.in/2020/02/12/algebra-symposium.html
http://math.iisc.ac.in/2020/02/12/algebra-symposium.htmlDiscussion Meeting on Representation Theory during December 14 - 16, 2019.<p><a href="http://math.iisc.ac.in/~rvenkat/dmrt19/">Visit this page <br />
math.iisc.ac.in/~rvenkat/dmrt19/</a></p>
Sat, 14 Dec 2019 00:00:00 +0530
http://math.iisc.ac.in/2019/12/14/discussion-meeting-on-representation-theory.html
http://math.iisc.ac.in/2019/12/14/discussion-meeting-on-representation-theory.html1st Math Symposium of Infosys Young Investigators<p>We cordially invite you to the <strong>1st Math Symposium of Infosys
Young Investigators</strong>: an in-House faculty symposium of the
Department of Mathematics, IISc, on Wednesday, 6th November, 2019.
In it, the most recent cohort of Infosys Young Investigators
in IISc Mathematics will present snapshots of their research
funded by the Infosys Foundation.</p>
<p><strong>Date:</strong> 6<sup>th</sup> November, 2019 (Wednesday)</p>
<p><strong>Venue:</strong> Lecture Hall-1, Department of Mathematics</p>
<table>
<thead>
<tr>
<th>Time</th>
<th> Speaker</th>
<th> Title</th>
</tr>
</thead>
<tbody>
<tr>
<td>2:00 pm – 2:30 pm</td>
<td> Subhojoy Gupta</td>
<td> <em>Meromorphic geometric structures on surfaces</em></td>
</tr>
<tr>
<td>2:35 pm – 3:05 pm</td>
<td> Vamsi Pritham Pingali</td>
<td> <em>Interpolation or the lack of thereof from affine hypersurfaces;</em></td>
</tr>
<tr>
<td> </td>
<td> </td>
<td> <em>a vector bundle version of the Monge-Ampere equation</em></td>
</tr>
<tr>
<td>3:05 pm – 3:25 pm</td>
<td> </td>
<td> Tea</td>
</tr>
<tr>
<td>3:25 pm – 3:55 pm</td>
<td> Apoorva Khare</td>
<td> <em>Polymath-14 - Groups with norms; Distance matrices and Zariski density</em></td>
</tr>
<tr>
<td>5:00 pm</td>
<td> </td>
<td> High Tea</td>
</tr>
</tbody>
</table>
<hr />
<p>Each lecture will be of 30 minutes, with a 5 minute break for Q&A and change of speaker.</p>
<h3 id="abstracts">Abstracts</h3>
<h4 id="lecture-1-">Lecture 1 </h4>
<p><strong>Speaker:</strong> Subhojoy Gupta</p>
<p><strong>Title:</strong> Meromorphic geometric structures on surfaces</p>
<p><strong>Abstract:</strong> I shall present results from two projects of mine that were supported by the Infosys Foundation. Both concern geometric structures on a punctured Riemann surface X, that are associated with holomorphic quadratic differentials on X via certain differential equations.</p>
<p>The first concerns projective structures, which are determined by quadratic differentials via the Schwarzian differential equation. If we fix the orders of the poles at the punctures, the space of such meromorphic projective structures admits a monodromy map to the space of surface-group representations to PSL(2,C).</p>
<p>I shall discuss a recent result characterizing the image of the monodromy map in the case the poles have order at most two. This is an analogue of a theorem of Gallo-Kapovich-Marden for closed surfaces, and clarifies a remark of Poincaré.</p>
<p>The second concerns solutions of the non-linear PDE satisfied by harmonic maps from X to a hyperbolic surface of the same topological type. In this case, a holomorphic quadratic differential is obtained as the Hopf differential of the harmonic map. In the case that X is a closed surface, this defines a homeomorphism between the Teichmüller space of X and the space of holomorphic quadratic differentials on X. This was work of M. Wolf, and independently N. Hitchin, in the mid-1980s. I shall discuss the analogue of this theorem in the case X has punctures, with the assumption that the orders of the poles are all greater than two.</p>
<hr />
<h4 id="lecture-2">Lecture 2</h4>
<p><strong>Speaker:</strong> Vamsi Pritham Pingali</p>
<p><strong>Title:</strong> Interpolation or the lack of thereof from affine hypersurfaces; a vector bundle version of the Monge-Ampere equation</p>
<p><strong>Abstract:</strong> There are two themes of my research funded by the Infosys Foundation. I shall present a typical representative of each theme.</p>
<p>1) PDE arising from Differential Geometry and Physics : The Monge–Ampere equation is a well-studied PDE in complex geometry and its solvability has ramifications in various sub-areas. Inspired by its success, in <a href="https://arxiv.org/abs/1804.03934">a preprint</a>, I introduced a vector bundle version of it, and proved a Kobayashi–Hitchin correspondence (essentially, the PDE has a solution if and only if some condition from algebraic geometry is met) in a special case, namely, for some equivariant rank-2 vortex bundles.</p>
<p>2) Analytic studies in Algebraic Geometry : A natural question arising from applied mathematics is, “When can one extend finite-energy analytic functions from subsets of <code class="language-plaintext highlighter-rouge">$\mathbb{C}^n$</code> to all of space whilst preserving the finite-energy condition ?” In a <a href="https://arxiv.org/abs/1810.00895">joint work with D. Varolin</a>, we discuss examples and counterexamples of such subsets arising as zeroes of polynomials.</p>
<hr />
<h4 id="lecture-3">Lecture 3</h4>
<p><strong>Speaker:</strong> Apoorva Khare</p>
<p><strong>Title:</strong> Polymath-14 - Groups with norms; Distance matrices and Zariski density</p>
<p><strong>Abstract:</strong> I shall present details of two disparate projects that received
funding from the Infosys Foundation. We first discuss the
<a href="http://michaelnielsen.org/polymath1/index.php?title=Linear_norm">Polymath-14 project</a>,
which arose out of a discussion literally made possible by Infosys funding!
In this project, we show that a group is abelian and torsion-free if and
only if it admits a “norm”, or equivalently a homogeneous length function.
This question was motivated by probability, connects algebra, geometry,
and analysis, was solved in five days on a blog, and used a computer.
(<a href="http://dx.doi.org/10.2140/ant.2018.12.1773">Joint work as D.H.J. Polymath</a>,
with Tobias Fritz, Siddhartha Gadgil, Pace Nielsen, Lior Silberman, and Terence Tao.)</p>
<p>Next, I discuss recent
<a href="http://arxiv.org/abs/1903.11566">joint work with Projesh Nath Choudhury</a>,
in which we study distance matrices of trees. We propose a model that subsumes
all previous variants to date (starting with Graham, Pollak, and Lovasz). In
this model, we compute the determinant, cofactor-sum, and inverse of the
distance matrix (and its minors), subsuming prior results, and answering an
open question of Bapat et al. The proofs use Zariski density, as our results
hold over all unital commutative rings.</p>
Wed, 06 Nov 2019 00:00:00 +0530
http://math.iisc.ac.in/2019/11/06/1st-infosys-symposium.html
http://math.iisc.ac.in/2019/11/06/1st-infosys-symposium.htmlDiscussion meeting at ICTS on “Mathematical Analysis and Theory of Homogenization (MATH-2019) during August 26 - september 06.<p><a href="https://www.icts.res.in/discussion-meeting/math2019">Visit this page <br />
https://www.icts.res.in/discussion-meeting/math2019</a></p>
Mon, 26 Aug 2019 00:00:00 +0530
http://math.iisc.ac.in/2019/08/26/mathematical-analysis-and-homogenization.html
http://math.iisc.ac.in/2019/08/26/mathematical-analysis-and-homogenization.htmlAdvanced Instructional School (AIS) on Riemannian geometry for the period July 8 to July 20, 2019.<p><a href="https://www.atmschools.org/school/2019/AIS/rg/speakers-and-syllabus">Visit this page <br />
https://www.atmschools.org/school/2019/AIS/rg/speakers-and-syllabus</a></p>
Sun, 28 Jul 2019 00:00:00 +0530
http://math.iisc.ac.in/2019/07/28/ais-riemannian-geometry.html
http://math.iisc.ac.in/2019/07/28/ais-riemannian-geometry.htmlRamanujan Medal Award Lecture<p>The Ramanujan Medal Award Lecture of the Indian National Science Academy
will be delivered by Kalyan B. Sinha, Jawaharlal Nehru Centre for
Advanced Scientific Research.</p>
<p>The lecture is at 4pm, on Thursday June 27, 2019, in
Lecture Hall LH-1 in the Department of Mathematics, IISc.</p>
<embed src="/images/2019-06-27-Ramanujan-Medal-Award-KBS.pdf" width="1000px" height="1500px" />
Thu, 27 Jun 2019 00:00:00 +0530
http://math.iisc.ac.in/2019/06/27/award-lecture.html
http://math.iisc.ac.in/2019/06/27/award-lecture.html