Manjunath Krishnapur

• 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

  • On the area of polynomial lemniscates (with Erik Lundberg and Koushik Ramachandran) [Preprint, arXiv:2503.18270 ]
    
  • Log-concavity in one-dimensional Coulomb gases and related ensembles (with Jnaneshwar Baslingker and Mokshay Madiman ) [Preprint, arXiv:2412.15116]
    
  • Stationary random measures : Covariance asymptotics, variance bounds and central limit theorems (with D. Yogeshwaran) [Preprint, arXiv:2411.08848]
    
  • The Paquette-Zeitouni laws of fractional logarithm for the GUE minor process and the Plancherel growth process (with Jnaneshwar Baslingker, and Riddhipratim Basu and Sudeshna Bhattacharjee) [Preprint, arXiv:2410.11836]
    
  • Optimal tail estimates in β-ensembles and applications to last passage percolation (with Jnaneshwar Baslingker, and Riddhipratim Basu and Sudeshna Bhattacharjee)
    To appear in Probability and Mathematical Physics [Preprint, arXiv:2405.12215]
    
  • Inradius of random lemniscates (with Erik Lundberg and Koushik Ramachandran)
    Journal of Approximation Theory 299 (2024) Paper no. 106018 [Preprint, arXiv:2301.13424]
    
  • The number of limit cycles bifurcating from a randomly perturbed center (with Erik Lundberg and Oanh Nguyen)
    To appear in Ann. Probab. [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. 54 (2023), no. 1, 146–158. [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 β-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]
    
  • Continuum Percolation for Gaussian zeroes and Ginibre eigenvalues. (with Subhroshekhar Ghosh and Yuval Peres)
    Ann. Probab. Volume 44, Issue 1, (2016), 3357-3384, [arXiv:1211.2514 ]
    
  • 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.

• Lecture notes, Book, Thesis

  • 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 (jointly with Sanchayan Sen) Some results on beta ensembles and on scaling limits of random graphs (2025)
    • 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 (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)), Shashank S I (probabilistic method (2024)), Aishee Bhattacharya (random graphs (2024)), Swastika Dey (mixing times (2024)), Srivatsa B (high dimensional probability (2024)), S. S. Meyvizhi (Markov chains (2024)), Siddhesh Patil (discrete probability (2024)), Anvita Bhat (random matrices (2025)), Anurag Ramachandran (random graphs (2025)), Srijan Saha (Gaussian processes (2025)), Sauparna Kar (Percolation, Gaussian processes (2025)), Srijan Bhowmik (random matrices (2025)), Swastika Dey (Mixing of Markov chains (2025)), Archisman Bhattachrya (random walks, electrical networks (2025)), Agastya Agrawal (data science (2025)), Samadrita Bhattacharya (random walks (2025)), Srujan Patil (random walks and electrical networks (2025))

• 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 ( [Spring 2025], [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

  • Bangalore probability seminar calendar and you tube channel
  • One world probability seminar
  • Lectures on Probability and Stochastic Processes

  • 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
  • TIFR lectures on mathematics
  • OEIS
  • WolframAlpha
  • Probabilists in Bangalore There are probability faculty, students and postdocs at ICTS, ISI, TIFR-CAM, IIM and IISc




Comments on the UGC draft Learning outcome based curriculum-2025 in mathematics for undergraduate program B.A./B.Sc.

A petition signed by nearly 950 mathematicians and educators asking the UGC to form a new committee of experts to redraft the curriculum.

Statement issued by the Mathematics Teachers' Association (India).

Some media coverage of the petition: Hindustan times. The Indian Express. India Today. The Hindu. The Economic Times. Aaj Tak. Shiksha. Discourse on development. Deccan Herald. Telegraph India. Times of India. India Today. India Today (different from previous). Edex Live. Vartha Bharathi.

In The Indian Express, R Ramanujam of APU, one of the best in India in the intersection of mathematics and its pedagogy, explains how this curriculum will make students less capable. An ex-chair of UGC asserts that everything about the curriculum is good, no reason to worry, none at all...

In a rebuttal of the above article, distinguished mathematician Mahan Mj of TIFR explains why it fails to address any of the questions raised.

Another excellent article by Ziya Uddin, Luckshay Batra, Satpal Singh, Aradhana Narang, Palak Goel and Himanshu Upreti that addresses the problems with the curriculum and also refutes some of the assertions in the above article by the ex-chair of UGC. The same or similar article has also appeared in Deccan Herald, Northeast News, The Diplomat.

In an interview with The Education Times, the ex-chair of UGC repeats some of the claims from his article and adds more. Here is my response (not exhaustive).

Myth over math by Tata Sivaiah has the subtitle UGC’s Blueprint for Academic Suicide

An article in The Print says that "The Centre has constituted a committee of experts to review the draft curriculum released by the University Grants Commission (UGC) for various subjects, following allegations of factual inaccuracies and inclusion of outdated topics". We await details.

Apparently a letter signed by ~40 fellows of the Indian Academy of Sciences expressing concern about the curriculum was forwarded by the President of the academy to the UGC chair.

UGC draft Maths LOCF risks diluting academic rigour: An article in Education Times that has quotes of wisdom and experience from Nadita Narain and Amber Habib, among others. They particularly explain how the core content is compromised by spurious courses of no value.

A meeting of subject experts, ex-vice chancellors of universities, etc., was organized in Bangalore on 16th October by AlSEC. From mathematics, there were Professors Dani and Ramanujam and I participated. Some media coverage of the event is here (the articles are not very accurate with quotation marks but almost everything that is mentioned was said by somebody). The Hindu, The New Indian Express, ETV Bharat, Bangalore Mirror, News Trail. Unlike other things linked here, this was not restricted to mathematics, and there were comments on the proposed curricula in political science, commerce (Prof. Sayantani Banerjee, St Josephs university), anthropology (Prof. Vasavi, formerly of NIAS) in greater detail than can appear in a media article (hopefully some of them will post them in full somewhere). Some participants had larger questions on centralization and autonomy, and the NEP itself.



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