Massachusetts Institute of Technology
Department of Mathematics
Email: visheshj at mit dot edu
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
- Smoothed analysis of the condition number without inverse Littlewood-Offord theory. [arXiv:1908.11255]
- The strong circular law: a combinatorial view. Submitted. [arXiv:1904.11108]
- Approximate Spielman-Teng theorems for the least singular value of random combinatorial matrices. Submitted. [arXiv:1904.10592]
- On the counting problem in inverse Littlewood-Offord theory, joint with Asaf Ferber, Kyle Luh, and Wojciech Samotij. Submitted. [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]
- 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. To appear in Journal of Combinatorial Theory, Series B. [arXiv:1809.04716]
- Number of 1-factorizations of regular high-degree graphs, joint with Asaf Ferber and Benny Sudakov. To appear in Combinatorica. [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). To appear in Random Structures and Algorithms. [Conference][arXiv:1803.10361]
- 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
- 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.
- Joint Mathematical Meetings 2020, Special Session on Extremal and Probabilistic Combinatorics, January 16.
- Joint Mathematical Meetings 2020, Special Session on Random Matrices and Integrable Systems, January 18.
Teaching, Mentoring, and TAing
- 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) .