**I have moved. Redirecting to jainvishesh.github.io.**

Simons Institute for the Theory of Computing Office: 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.

*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]

*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]

*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]

*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.

- 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).
- Recitation 1 problems. Partial solutions.
- Recitation 2 problems. Partial solutions .
- Recitation 3 problems. Partial solutions .
- Recitation 4 problems. Partial solutions .
- Recitation 5 problems. Partial solutions .
- Recitation 6 problems. Partial solutions .
- Recitation 7 problems. Partial solutions .
- Recitation 8 problems. Partial solutions .
- Recitation 9 problems. Partial solutions .
- Recitation 10 problems. Partial solutions .
- Recitation 11 problems. Partial solutions .
- Recitation 12 problems. Partial solutions .
- 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) .