Manjunath Krishnapur
Department of Mathematics

Contact
 Office N25, Dept. of Mathematics.
 Phone +91802293 3207.
 Email manjuatt iiscdotacdot in

Education
 Ph.D. 2006, University of California, Berkeley.
 M.Stat 2001, Indian Statistical Institute, Bangalore, Kolkata.
 B.Stat (Hons) 1999, Indian Statistical Institute, Kolkata.

Employment
 Associate professor 2013
 Assistant Professor 20092013 Indian Institute of Science, Bangalore.
 Postdoc 20062008, University of Toronto, Canada.
 Postdoc 2006, SAMSI and UNC, Chapel Hill.

Papers

Inradius of random lemniscates (with Erik Lundberg and Koushik Ramachandran)
Journal of Approximation Theory (2022)
[Preprint, arXiv:2301.13424]

The number of limit cycles bifurcating from a randomly perturbed center (with Erik Lundberg and Oanh Nguyen)
[Preprint, arXiv:2112.05672]

One idea and two proofs of the KMT theorems
[Preprint, arXiv:2008.03287]

Random words in free groups, noncrossing matchings and RNA secondary structures (with Siddhartha Gadgil)
Indian J. Pure Appl. Math. (2022)
[Preprint, arXiv:2007.12109]

How Many Modes Can a Mixture of Gaussians with Uniformly Bounded Means Have? (with Navin Kashyap)
Information and Inference: Volume 11, Issue 2, (2022), 423434
[Preprint, arXiv:2005.01580]

Lower Deviations in $\beta$ensembles and Law of Iterated Logarithm in Last Passage Percolation. (with Riddhipratim Basu,
Shirshendu Ganguly and
Milind Hegde)
Israel Journal of Mathematics 242, (2021) 291324 [Preprint, arXiv:1909.01333]

A relative anticoncentration inequality. (with Sourav Sarkar)
[Preprint, arXiv:1612.09045]

Persistence probabilities in centered, stationary, Gaussian processes in discrete time. (with Krishna M.)
Indian J. Pure Appl. Math. 47, pages 183194 (2016)
[Preprint, arXiv:1506.00753]

Rigidity hierarchy in random point fields: random polynomials and determinantal processes. (with Subhroshekhar Ghosh)
Communications in Mathematical Physics, 388, (2021), 12051234
[Preprint, arXiv:1510.08814]

Phase Transitions for the Uniform Distribution in the PML Problem and its Bethe Approximation. (with Chun Lam Chan, Winston Fernandes and Navin Kashyap)
SIAM J. Discrete Math. Volume 31, No. 1, (2017), 597631,
[Preprint, arXiv:1510.08814]

Universality of the Stochastic Airy Operator. (with Brian Rider and Bálint Virág)
Communications on Pure and Applied Mathematics Volume 69, Issue 1, (2016), 145199,
[arXiv:1306.4832]

The Ginibre ensemble and Gaussian analytic functions. (with Bálint Virág)
Int. Math. Res. Not. IMRN 2014, no. 6, (2014), 14411464
[arXiv:1112.2457]

Lipschitz correspondence between metric measure spaces and random distance matrices. (with Siddhartha Gadgil)
Int. Math. Res. Not. IMRN 2013, no. 24, (2013), 56235644
[arXiv:1110.6333]

Nodal length fluctuations for arithmetic random waves. (with Pär Kurlberg and Igor Wigman)
Ann. Math. vol. 177, no. 2, (2013), 699737
[arXiv:1111.2800]

The single ring theorem. (with Alice Guionnet and Ofer Zeitouni)
Ann. Math. vol. 174 (2011), 11891217
[arXiv:0909.2214]

Derivation of an eigenvalue probability density function relating to the Poincare disk. (with Peter Forrester)
J. Phys. A: Math. Theor. vol. 42 (2009), 385204
[arXiv:0906.5223]

Appendix to Random matrices: Universality of ESDs and the circular law.
(Main authors: Terence Tao and Van Vu)
Ann. Probab. 38 (2010), 20232065. [arXiv.math.PR/0807.4898]

From random matrices to random analytic functions.
Ann. Probab. vol. 37 (2009), no. 1, 314346
[arXiv.math.PR/0711.1378]

Overcrowding estimates for zeroes of Planar and Hyperbolic Gaussian analytic functions.
J. Stat. Phys. vol. 124 (2006), no. 6, 13991423.
[arXiv.math.PR/0510588]

Determinantal Processes and Independence. (with J.Ben Hough, Yuval Peres
and
Bálint Virág)
Probab. Surv. vol. 3, 206229, 2006.
[arXiv.math.PR/0503110]

Recurrent graphs where two independent random walks collide finitely often. (with Yuval Peres)
Electron. Comm. Probab. vol. 9, paper no. 8, 7281, 2004.
[arXiv.math.PR/0406487]

Zeros of Random Analytic Functions [arXiv.math.PR/0607504]
Ph.D. thesis University of California, Berkeley. Spring 2006.

Thesis, Book, Lecture notes

Ph.D. thesis Zeros of Random Analytic Functions [arXiv.math.PR/0607504]
University of California, Berkeley. Spring 2006.

Book Zeros of Gaussian analytic functions and Determinantal point processes (joint with J.Ben Hough, Yuval Peres and Bálint Virág )
Published by AMS (American Mathematical Society)
 Real and complex zeros of random polynomials and analytic functions  Lectures given at LPSVI, Kolkata (Dec 2011).
 Measure theory: Measure theory (a full semester course), Measure theory (as required for probability) A shorter version (from an IST minicourse), Also lecture videos
 Probability: First course in probability and statistics, Measure theory (condensed), Basics of probability theory, Martingales and Brownian motion.
 Problem sets: Problems in measure theory, Problems in probability theory, Problems on martingales, Problems on Brownian motion
 Special topics in Probability: Random matrix theory course notes (An older but quite different version), Gaussian processes course notes, Anticoncentration (IITB, Jan 2016), SLE seminar notes  Part 1 (complex analysis, mainly)
 Analysis: Topics in analysis, Fourier analysis and applications

Recorded lectures

Students
 PhD. students:
 Tulasi Ram Reddy On Critical Points of Random Polynomials and Spectrum of Certain Products of RandomMatrices (2016)
 Kartick Adhikari Hole probabilities for determinantal point processes in the complex plane (2017)
 Nanda Kishore Reddy Eigenvalues of products of random matrices (2017)
 Lakshmi Priya M.E. Nodal sets of random functions
(2021)
 Jnaneshwar Baslingker (in progress, jointly with Sanchayan Sen)
 Sudeshna Bhattacharjee (in progress, jointly with Riddhipratim Basu)
 M.S. thesis students:
 Raghavendra Tripathi (Determinantal processes and stochastic domination  2019)
 Indrajit Jana (Matchings between point processes  2012)
 Int. PhD. project students: Sourish Parag Maniyar (2022), Raghavendra Tripathi (2018), Prateek Kumar Vishwakarma (2017), Indrajit Jana (2011), Kartick Adhikari (2011)
 UG project students: Terrence George George (2015), Venkata Ramana (2015), Anamay Chaturvedi (2016), Pranav Nuti (2018), Dhanus Lal (2022)
 External students: Nishad Bapatdhar (IISER Pune masters thesis (2018)), Ananya Singhal (CBS semester long projects (2021) and (2022)), Elizabeth Sara Roy (KSoM masters project, 2023)
 Summer students: Arundhati Krishnan (basic probability (2009), real analysis (2010)), Sujayam Saha (random matrix theory (2010)), Subhabrata Sen and Pragya Sur (Random walks, mixing times (2011)), Suryateja Gavva (Analytic number theory (2011)), Hitesh Gakhar, Ashish Chandra and Sourav Sarkar (Random walks (2012)), Jigyasa Gaurav (Basic analytic number theory (2012)), Pratyay Datta, Rushil Nagda and Tanya Goyal (2013), Supriya N (Markov chains (2014)), Sourav Sarkar (anticoncentration (2014)), Debatosh Das and Arnab Datta (branching processes (2014)), Soumyo Biswas (continued fractions (2014)), Sanal Prasad (analytic number theory (2014)), Sridhar Venkatesh (analytic number theory (2015)) and Bhavya Teja (random walks (2015)), Sunidhi Taneja and Rameez Qureshi (discrete probability (2016)), Samyak (hyperbolic plane (2016)), Abhratanu Saha (Real analysis (2016)), Sayantan Khan (Fourier analysis (2016)), Prasenjit Dubey (Statistics (2016)), Gaurang Sriramanan (analytic number theory, Primes in P (2017)), Raunak Ray, Siddhaarth Sarkar, Aditya Raut (random walks, mixing times (2017)), Shubhamoy Nandan (weak convergence (2017)), Nishad Bapatdhar (Statistics in high dimensions (2017)), Anirban Basak, Saptarsi Ghosal, Somak Laha and Sayak Chatterjee (Markov chains (2019)), Deep Ghoshal and Arghya Chakraborty (percolation (2019)), Nafia Saleem (basic algebra (2019)), Swarup Pakiriswamy (analytic number theory (2019)), Chinmay S I (random walks (2020)), Aytijhya Saha (data science (2022)), Soham Mallick and Supratik Basu (random polynomials (2022)), Arunava Gantait and Samprit Chakraborty (discrete probability (2022)), Upendra Singh Parmar (Markov chains (2022)), Bijayan Ray (topics in analysis (2022)), Rathindra Karmakar (discrete probability (2023))

Teaching

Martingales and Brownian motion ( [Spring 2023], 2020 and 2015)

Probability Theory ( [Fall 2024], 2022, 2020, 2019 Fall 2015 and Spring 2015 and Spring 2010)
 Measure and integration ([Spring 2022], [Spring 2021], [Spring 2020], [Spring 2018])

Fourier analysis with applications ( [Fall 2021] )

Gaussian processes ( [2020], [Spring 2014])

Topics in analysis
( [Spring 2024], [Spring 2019], [Spring 2017] and [Fall 2014])

Introduction to probability and statistics ([Fall 2023], [Fall 2018], Fall 2016, Fall 2013 and Fall 2012)

Random matrix theory ([Fall 2017] and Spring 2011)

Probability models ([Fall 2017], Fall 2011)

Problems in Brownian motion ( [Spring 2012])

Functional Analysis ( [Fall 2010] )

Brownian motion (or is it this link?) ( [Fall 2009])

Seminars

Resources for students
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