Vishesh Jain



Massachusetts Institute of Technology
Department of Mathematics
Office: 2-232A
Email:   visheshj at mit dot edu
CV

I am a fifth-year Ph.D. candidate in mathematics at MIT, broadly interested in probability, combinatorics, and theoretical computer science. I am fortunate to be advised by Elchanan Mossel. Previously, I received a B.S. in mathematics from Stanford University in June, 2015. I spent the 2013-14 academic year at Math in Moscow.

Publications and Preprints

Invertibility of random matrices

  1. Smoothed analysis of the condition number without inverse Littlewood-Offord theory. [arXiv:1908.11255]
  2. The strong circular law: a combinatorial view. Submitted. [arXiv:1904.11108]
  3. Approximate Spielman-Teng theorems for the least singular value of random combinatorial matrices. Submitted. [arXiv:1904.10592]
  4. On the counting problem in inverse Littlewood-Offord theory, joint with Asaf Ferber, Kyle Luh, and Wojciech Samotij. Submitted. [arXiv:1904.10425]
  5. 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]

Mean-field approximation

  1. 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]
  2. 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]
  3. 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]

Graph decompositions

  1. Towards the linear arboricity conjecture, joint with Asaf Ferber and Jacob Fox. To appear in Journal of Combinatorial Theory, Series B. [arXiv:1809.04716]
  2. Number of 1-factorizations of regular high-degree graphs, joint with Asaf Ferber and Benny Sudakov. To appear in Combinatorica. [arXiv:1803.10360]
  3. 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]
  4. 1-factorizations of pseudorandom graphs, joint with Asaf Ferber. 59th Annual IEEE Symposium on Foundations of Computer Science (FOCS 2018). To appear in Random Structures and Algorithms. [Conference][arXiv:1803.10361]

Miscellaneous

  1. 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]
  2. On the number of Hadamard matrices via anti-concentration, joint with Asaf Ferber and Yufei Zhao. Submitted. [arXiv:1808.07222]
  3. 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

  1. Uniformity-independent minimum degree conditions for perfect matchings in hypergraphs, joint with Asaf Ferber. [arXiv:1903.12207]
  2. A Counterexample to the "Majority is Least Stable" Conjecture. [arXiv:1703.07657]

Expository

  1. An expanded version of a MathOverflow comment by Nazarov, giving a simple proof of an inequality due to Feige.
  2. Unedited and informal notes from a three-hour reading group talk on the Balogh-Morris-Samotij proof of the hypergraph containers theorem .
  3. Unedited and informal notes from a two-hour reading group talk on Peter Keevash's Counting Designs.

Upcoming talks

Teaching, Mentoring, and TAing