Manjunath Krishnapur: Home

Manjunath Krishnapur

Department of Mathematics

Contact
- Office N25, Dept. of Mathematics.
- Phone +91-80-2293 3207.
- E-mail manju-att- iisc-dot-ac-dot- 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 2009-2013 Indian Institute of Science, Bangalore.
- Postdoc 2006-2008, 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, non-crossing 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), 423--434 [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) 291--324 [Preprint, arXiv:1909.01333]
- A relative anti-concentration 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 183--194 (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), 1205--1234 [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), 597--631, [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), 145--199, [arXiv:1306.4832]
- The Ginibre ensemble and Gaussian analytic functions. (with Bálint Virág)
  Int. Math. Res. Not. IMRN 2014, no. 6, (2014), 1441--1464 [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), 5623--5644 [arXiv:1110.6333]
- Nodal length fluctuations for arithmetic random waves. (with Pär Kurlberg and Igor Wigman)
  Ann. Math. vol. 177, no. 2, (2013), 699--737 [arXiv:1111.2800]
- The single ring theorem. (with Alice Guionnet and Ofer Zeitouni)
  Ann. Math. vol. 174 (2011), 1189--1217 [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), 2023--2065. [arXiv.math.PR/0807.4898]
- From random matrices to random analytic functions.
  Ann. Probab. vol. 37 (2009), no. 1, 314--346 [arXiv.math.PR/0711.1378]
- Overcrowding estimates for zeroes of Planar and Hyperbolic Gaussian analytic functions.
  J. Stat. Phys. vol. 124 (2006), no. 6, 1399--1423. [arXiv.math.PR/0510588]
- Determinantal Processes and Independence. (with J.Ben Hough, Yuval Peres and Bálint Virág)
  Probab. Surv. vol. 3, 206--229, 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, 72--81, 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 LPS-VI, Kolkata (Dec 2011).
- Measure theory: Measure theory (a full semester course), Measure theory (as required for probability) A shorter version (from an IST mini-course), 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, Anti-concentration (IITB, Jan 2016), SLE seminar notes - Part 1 (complex analysis, mainly)
- Analysis: Topics in analysis, Fourier analysis and applications
Recorded lectures
- Measure theory (22 lecture course given in 2021)
- Gaussian processes (33 lecture course given in 2020. Thanks to Ritvik Radhakrishnan for creating this!)
- SLE short course (4 lectures) and SLE seminar (long) (Thanks to Ritvik Radhakrishnan again)
- Fourier analysis and applications
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)
- 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 (anti-concentration (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
- Random sets and potential theory [Spring 2022].
- SLE seminar [Fall 2021, Summer and Fall 2010].
- RMT seminar [Fall 2020].
Resources for students
- Suggested reading for students in probability Written with myself as a B.Stat/M.Stat student in mind, need not be useful to anyone today.
- ISI Bangalore course notes
- Some people: Borcherds. Aldous. Peres. Tsirelson
- TIFR lectures on mathematics
- OEIS
- WolframAlpha
- Probabilists in Bangalore There are probability faculty, students and postdocs at ICTS, ISI, TIFR-CAM, IIM and IISc

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