I have moved. Redirecting to jainvishesh.github.io.
Simons Institute for the Theory of Computing
Email: visheshj at stanford dot edu
CV (Last updated: October 2020)
I am a Simons-Berkeley Research Fellow for the Fall 2020 program on Probability, Geometry, and Computation in High Dimensions.
Starting Winter 2021, I will be a Stein Fellow at the Department of Statistics at Stanford University. Starting Fall 2022, I will be an Assistant Professor
in Mathematical Computer Science at the University of Illinois at Chicago.
In May, 2020, I received a Ph.D. in mathematics from MIT, where I was fortunate to be advised by Elchanan Mossel.
In June, 2015, I received a B.S. in mathematics from Stanford University. I spent the 2013-14 academic year at Math in Moscow.
I am broadly interested in probability, combinatorics, and theoretical computer science.
Publications and Preprints
Invertibility of random matrices
- On the smallest singular value of symmetric random matrices, joint with Ashwin Sah and Mehtaab Sawhney. Submitted. [arXiv:2011.02344]
- Singularity of discrete random matrices II, joint with Ashwin Sah and Mehtaab Sawhney. Submitted. [arXiv:2010.06554]
- Singularity of discrete random matrices I, joint with Ashwin Sah and Mehtaab Sawhney. Submitted. [arXiv:2010.06553]
- The smallest singular value of dense random regular digraphs, joint with Ashwin Sah and Mehtaab Sawhney. Submitted. [arXiv:2008.04755]
- Quantitative invertibility of random matrices: a combinatorial perspective. Submitted. [arXiv:1908.11255]
- Approximate Spielman-Teng theorems for the least singular value of random combinatorial matrices. To appear in Israel Journal of Mathematics. [arXiv:1904.10592]
- On the counting problem in inverse Littlewood-Offord theory, joint with Asaf Ferber, Kyle Luh, and Wojciech Samotij. To appear in Journal of London Mathematical Society. [arXiv:1904.10425]
- Singularity of random symmetric matrices -- a combinatorial approach to improved bounds, joint with Asaf Ferber. Forum of Mathematics, Sigma, vol. 7, e22, 29 pages (2019). [Journal][arXiv:1809.04718]
Counting and sampling
- Towards the sampling Lovász Local Lemma, joint with Huy Tuan Pham and Thuy Duong Vuong. [arXiv:2011.12196]
- Perfectly sampling \(k \geq (8/3 + o(1))\Delta\)-colorings in graphs, joint with Ashwin Sah and Mehtaab Sawhney. Submitted. [arXiv:2007.06360]
- Optimal and algorithmic norm regularization of random matrices, joint with Ashwin Sah and Mehtaab Sawhney. Submitted. [arXiv:2012.00175]
- On the smoothed analysis of the smallest singular value with discrete noise, joint with Ashwin Sah and Mehtaab Sawhney. Submitted. [arXiv:2009.01699]
- On the real Davies' conjecture, joint with Ashwin Sah and Mehtaab Sawhney. Submitted. [arXiv:2005.08908]
Universality of ESDs
- Circular law for random block band matrices with genuinely sublinear bandwidth, joint with Indrajit Jana, Kyle Luh, and Sean O'Rourke. Submitted. [arXiv:2008.03850]
- Universality and least singular values of random product matrices: a simplified approach, joint with Rohit Chaudhuri and Natesh Pillai. Submitted. [arXiv:2007.03595]
- A note on the universality of ESDs of inhomogeneous random matrices, joint with Sandeep Silwal. Submitted. [arXiv:2006.05418]
- The strong circular law: a combinatorial view. To appear in Random Matrices: Theory and Applications. [arXiv:1904.11108]
- Mean-field approximation, convex hierarchies, and the optimality of correlation rounding: a unified perspective, joint with Frederic Koehler and Andrej Risteski. 51st ACM Symposium on the Theory of Computing (STOC 2019). [Conference][arXiv:1808.07226]
- The Vertex Sample Complexity of Free Energy is Polynomial, joint with Frederic Koehler and Elchanan Mossel. 31st Annual Conference on Learning Theory (COLT 2018). [Conference][arXiv:1802.06129]
- The Mean-Field Approximation: Information Inequalities, Algorithms, and Complexity, joint with Frederic Koehler and Elchanan Mossel. 31st Annual Conference on Learning Theory (COLT 2018). [Conference][arXiv:1802.06126]
- Towards the linear arboricity conjecture, joint with Asaf Ferber and Jacob Fox. Journal of Combinatorial Theory, Series B, Volume 142, May 2020, Pages 56--79. [Journal][arXiv:1809.04716]
- Number of 1-factorizations of regular high-degree graphs, joint with Asaf Ferber and Benny Sudakov. Combinatorica, 2020. [Journal][arXiv:1803.10360]
- On the k-planar local crossing number, joint with John Asplund, Thao Do, and Arran Hamm. Discrete Mathematics, vol. 342, issue 4, pp. 927--933 (2019). [Journal][arXiv:1804.02117]
- 1-factorizations of pseudorandom graphs, joint with Asaf Ferber. 59th Annual IEEE Symposium on Foundations of Computer Science (FOCS 2018). Random Structures and Algorithms. [Conference][Journal][arXiv:1803.10361]
- Fast and memory-optimal dimension reduction using Kac's walk, joint with Natesh Pillai, Ashwin Sah, Mehtaab Sawhney, and Aaron Smith. Submitted. [arXiv:2003.10069]
- Accuracy-Memory Tradeoffs and Phase Transitions in Belief Propagation, joint with Frederic Koehler, Jingbo Liu, and Elchanan Mossel. 32nd Annual Conference on Learning Theory (COLT 2019). [Conference][arXiv:1905.10031]
- On the number of Hadamard matrices via anti-concentration, joint with Asaf Ferber and Yufei Zhao. Submitted. [arXiv:1808.07222]
- On discontinuity of planar optimal transport maps, joint with Otis Chodosh, Michael Lindsey, Lyuboslav Panchev, and Yanir Rubinstein. Journal of Topology and Analysis, vol. 7, no. 2, pp. 239--260 (2015). [Journal][arXiv:1312.2929]
Preprints not intended for publication
- The probability of selecting k edge-disjoint Hamilton cycles in the complete graph, joint with Asaf Ferber and Kaarel Haenni. [arXiv:2001.01149]
- Uniformity-independent minimum degree conditions for perfect matchings in hypergraphs, joint with Asaf Ferber. [arXiv:1903.12207]
- A Counterexample to the "Majority is Least Stable" Conjecture. [arXiv:1703.07657]
- An expanded version of a MathOverflow comment by Nazarov, giving a simple proof of an inequality due to Feige.
- Unedited and informal notes from a three-hour reading group talk on the Balogh-Morris-Samotij proof of the hypergraph containers theorem .
- Unedited and informal notes from a two-hour reading group talk on Peter Keevash's Counting Designs.
Teaching, Mentoring, and TAing
- In Spring 2020, I was a grader for 18.676 (Stochastic Calculus) and 18.455 (Advanced Combinatorial Optimization).
- In Summer 2019, I was a mentor for UROP+.
- In Spring 2019, I was a grader for 18.218 (Probabilistic Method in Combinatorics).
- In Fall 2018, I was a recitation instructor for 18.600 (Probability & Random Variables).
- In Spring 2018, I was a recitation instructor for 18.04 (Complex Analysis with Applications).
- In Fall 2017, I graded for 18.155 (Differential Analysis I).
- In Spring 2017, I graded for 18.117 (Hodge Theory).
- In IAP 2017, I was a mentor for the MIT math department's Directed Reading Program.
- In Fall 2016, I graded for 18.965 (Geometry of Manifolds I).
- In Summer 2016, I was a mentor for the Research Science Institute (RSI) .