Primes of the form \(p^2 + nq^2\)
Ben Green and Mehtaab Sawhney. Acta Mathematica, to appear arXiv:2410.04189
The Exact Rank of Sparse Random Graphs
Margalit Glasgow, Matthew Kwan, Ashwin Sah and Mehtaab Sawhney. Journal of the European Mathematical Society, to appear arXiv:2303.05435
The limiting spectral law for sparse iid matrices
Ashwin Sah, Julian Sahasrabudhe and Mehtaab Sawhney. Forum of Mathematics, Pi, to appear arXiv:2310.17635
The existence of subspace designs
Peter Keevash, Ashwin Sah and Mehtaab Sawhney. Proceedings of the London Mathematical Society, to appear arXiv:2212.00870
An explicit economical additive basis
Vishesh Jain, Huy Tuan Pham, Mehtaab Sawhney and Dmitrii Zakharov. Combinatorics, Probability and Computing, to appear arXiv:2405.08650
Effective bounds for Roth's theorem with shifted square common difference
Sarah Peluse, Ashwin Sah and Mehtaab Sawhney. American Journal of Mathematics, to appear arXiv:2309.08359
A central limit theorem for the matching number of a sparse random graph
Margalit Glasgow, Matthew Kwan, Ashwin Sah and Mehtaab Sawhney. Journal of the London Mathematical Society, 2025, 111(4), e70101. arXiv:2402.05851
On the Spielman-Teng Conjecture
Ashwin Sah, Julian Sahasrabudhe and Mehtaab Sawhney. Geometric and Functional Analysis, 2025, 35, 633–671. arXiv:2405.20308
Vinogradov's theorem for primes with restricted digits
James Leng and Mehtaab Sawhney. International Mathematics Research Notices, 2025, Issue 3, rnae294. arXiv:2409.06894
The sparse circular law, revisited
Ashwin Sah, Julian Sahasrabudhe and Mehtaab Sawhney. Bulletin of the London Mathematical Society, to appear arXiv:2310.17600
Improved bounds for five-term arithmetic progressions
James Leng, Ashwin Sah and Mehtaab Sawhney. Mathematical Proceedings of the Cambridge Philosophical Society, 2024, 177(3), 371–413. arXiv:2312.10776
High-Girth Steiner Triple Systems
Matthew Kwan, Ashwin Sah, Mehtaab Sawhney and Michael Simkin. Annals of Mathematics, (2) 200(3): 1059-1156 (November 2024). arXiv:2201.04554
On Perfectly Friendly Bisections of Random Graphs
Dor Minzer, Ashwin Sah and Mehtaab Sawhney. Annals of Probability, 2024, Vol. 52, No. 6, 2281-2341. arXiv:2305.03543
The intransitive dice kernel: \(\frac{\mathbf{1}_{x\ge y}-\mathbf{1}_{x\le y}}{4} - \frac{3(x-y)(1+xy)}{8}\)
Ashwin Sah and Mehtaab Sawhney. Probability Theory and Related Fields, 2024, Volume 189, pages 1073–1128. arXiv:2302.11293
Distribution of the threshold for the symmetric perceptron
Ashwin Sah and Mehtaab Sawhney. FOCS 2023 arXiv:2301.10701
Anticoncentration in Ramsey graphs and a proof of the Erdős-McKay conjecture
Matthew Kwan, Ashwin Sah, Lisa Sauermann and Mehtaab Sawhney. Forum of Mathematics, Pi, (2023) Vol. 11:e21 1–74 arXiv:2208.02874
Subgraph distributions in dense random regular graphs
Ashwin Sah and Mehtaab Sawhney. Compositio Mathematica, 159 (2023) 2125--2148 arXiv:2209.00734
Paths of given length in tournaments
Ashwin Sah, Mehtaab Sawhney and Yufei Zhao. Combinatorial Theory, 3 (2)(2023), #5. arXiv:2012.00262
Cayley graphs that have a quantum ergodic eigenbasis
Assaf Naor, Ashwin Sah, Mehtaab Sawhney and Yufei Zhao. Israel Journal of Mathematics, 256 (2023), 599--617 arXiv:2207.05527
Threshold for Steiner triple systems
Ashwin Sah, Mehtaab Sawhney and Michael Simkin. Geometric and Functional Analysis, 33(4) (2023), 1141--1172 arXiv:2204.03964
Optimal minimization of the covariance loss
Vishesh Jain, Ashwin Sah and Mehtaab Sawhney. IEEE Transactions in Information Theory, 69(2) (2023), 813--818 arXiv:2205.01773
Spencer's theorem in nearly-input sparsity time
Vishesh Jain, Ashwin Sah and Mehtaab Sawhney. SODA 2023 arXiv:2206.04549
Friendly bisections of random graphs
Asaf Ferber, Matthew Kwan, Bharghav Narayanan, Ashwin Sah and Mehtaab Sawhney. Communications of the American Mathematical Society, 2 (2022), 380--416 arXiv:2105.13337
Enumerating Matroids and Linear Spaces
Matthew Kwan, Ashwin Sah and Mehtaab Sawhney. Comptes Rendus Mathématique, 361 (2023), 565--575 arXiv:2112.03788
Sparse recovery properties of discrete random matrices
Asaf Ferber, Ashwin Sah, Mehtaab Sawhney and Yizhe Zhu. Combinatorics, Probability and Computing, 32(2) (2023), 316--325 arXiv:2203.06115
Substructures in Latin squares
Matthew Kwan, Ashwin Sah, Mehtaab Sawhney and Michael Simkin. Israel Journal of Mathematics, 256 (2023), 363--416 arXiv:2202.05088
Enumerating coprime permutations
Ashwin Sah and Mehtaab Sawhney. Mathematika, 68(4) (2023), 1120-1134 arXiv:2203.06268
Singularity of the \(k\)-core of a random graph
Asaf Ferber, Matthew Kwan, Ashwin Sah and Mehtaab Sawhney. Duke Mathematical Journal, 172(7) (2023), 1293--1332 arXiv:2106.05719
Random symmetric matrices: rank distribution and irreducibility of the characteristic polynomial
Asaf Ferber, Vishesh Jain, Ashwin Sah and Mehtaab Sawhney. Mathematical Proceedings of the Cambridge Philosophical Society, 174(2) (2023), 233-246 arXiv:2106.04049
Majority Dynamics: The Power of One
Ashwin Sah and Mehtaab Sawhney. Israel Journal of Mathematics, 2025, 267, 85–133. arXiv:2105.13301
Rank deficiency of random matrices
Vishesh Jain, Ashwin Sah and Mehtaab Sawhney. Electronic Communications in Probability, 27 (2022), 1-9. arXiv:2103.02467
Fast and memory optimal dimension reduction using Kac's walk.
Vishesh Jain, Natesh Pillai, Ashwin Sah, Mehtaab Sawhney and Aaron Smith. Annals of Applied Probability, 32(5) (2022), 4038-4064. arXiv:2003.10069
Online Edge Coloring via Tree Recurrences and Correlation Decay
Janardhan Kulkarni, Yang Liu, Ashwin Sah, Mehtaab Sawhney and Jakub Tarnawski. STOC 2022 arXiv:2111.00721
Approximate counting and sampling via local central limit theorems
Vishesh Jain, Will Perkins, Ashwin Sah and Mehtaab Sawhney. STOC 2022 arXiv:2108.01161
Optimal and algorithmic norm regularization of random matrices
Vishesh Jain, Ashwin Sah and Mehtaab Sawhney. Proceedings of the American Mathematical Society, 150(10) (2022), 4503-4518. arXiv:2012.00175
Large deviations in random Latin squares
Matthew Kwan, Ashwin Sah and Mehtaab Sawhney. Bulletin of the London Mathematical Society, 54(4) (2022), 1420-1438. arXiv:2106.11932
A Gaussian fixed point random walk
Yang Liu, Ashwin Sah and Mehtaab Sawhney. ITCS 2022 arXiv:2104.07009
Non-classical polynomials and the inverse theorem
Aaron Berger, Ashwin Sah, Mehtaab Sawhney and Jonathan Tidor. Mathematical Proceedings of the Cambridge Philosophical Society, 173(3) (2022), 525-537. arXiv:2107.07495
Popular differences for matrix patterns
Aaron Berger, Ashwin Sah, Mehtaab Sawhney and Jonathan Tidor. Transactions of the American Mathematical Society, 375(4) (2022), 2677-2704. arXiv:2102.01684
On the smallest singular value of symmetric random matrices
Vishesh Jain, Ashwin Sah and Mehtaab Sawhney. Combinatorics, Probability and Computing, 31(4) (2022), 662-683. arXiv:2011.02344
Singularity of discrete random matrices
Vishesh Jain, Ashwin Sah and Mehtaab Sawhney. Geometric and Functional Analysis, 31(5) (2021), 1160-1218. arXiv:2010.06554
The smallest singular value of dense random regular digraphs.
Vishesh Jain, Ashwin Sah and Mehtaab Sawhney. International Mathematics Research Notices, 24 (2022), 19300--19334. arXiv:2008.04755
The cylindrical width of transitive sets
Ashwin Sah, Mehtaab Sawhney and Yufei Zhao. Israel Journal of Mathematics, 253 (2) (2023), 647--672. arXiv:2101.11207
Local limit theorems for subgraph counts.
Ashwin Sah and Mehtaab Sawhney. Journal of the London Mathematical Society, 105(2) (2022), 950-1011. arXiv:2006.11369
On the smoothed analysis of the smallest singular value with discrete
noise
Vishesh Jain, Ashwin Sah and Mehtaab Sawhney. Bulletin of the London Mathematical Society, 54(2) (2022), 369-388. arXiv:2009.01699
Patterns without a popular difference.
Ashwin Sah, Mehtaab Sawhney and Yufei Zhao. Discrete Analysis, 2021:8. arXiv:2004.07722
Anticoncentration versus the number of subset sums
Vishesh Jain, Ashwin Sah and Mehtaab Sawhney. Advances in Combinatorics, 2021:6. arXiv:2101.07726
On the real Davies' conjecture.
Vishesh Jain, Ashwin Sah and Mehtaab Sawhney. Annals of Probability, 49(6) (2021), 3011-3031. arXiv:2005.08908
Perfectly Sampling \(k\ge(8/3+o(1))\Delta\)-Colorings in Colors.
Vishesh Jain, Ashwin Sah and Mehtaab Sawhney. STOC 2021 arXiv:2007.06360
Discrepancy Minimization via a Self-Balancing Walk.
Ryan Alweiss, Yang Liu and Mehtaab Sawhney. STOC 2021 arXiv:2006.14009
A counterexample to the Bollobás-Riordan conjectures on sparse graph limits.
Jonathan Tidor, Ashwin Sah, Mehtaab Sawhney and Yufei Zhao. Combinatorics, Probability and Computing, 30(5) (2021), 796-799. arXiv:2003.05272
Cayley graphs without a bounded eigenbasis.
Ashwin Sah, Mehtaab Sawhney and Yufei Zhao. International Mathematics Research Notices, 2022(8), 6157-6185. arXiv:2005.04502
Number of arithmetic progressions in dense random subsets of \(\mathbb{Z}/n\mathbb{Z}\).
Ross Berkowitz, Ashwin Sah and Mehtaab Sawhney. Israel Journal of Mathematics, 244 (2021), 589-620. arXiv:1907.11807
Bounded Degree Spanners of the Hypercube.
Rajko Nenadov, Mehtaab Sawhney, Benny Sudakov and Adam Wagner. Electronic Journal of Combinatorics, 27 (2020), P3.3. arXiv:1910.09868
Exponential improvements for superball packing upper bounds.
Ashwin Sah, Mehtaab Sawhney, David Stoner and Yufei Zhao. Advances in Mathematics, 365 (2020), 107056. arXiv:1904.11462
Triforce and Corners.
Jacob Fox, Ashwin Sah, Mehtaab Sawhney, David Stoner and Yufei Zhao. Mathematical Proceedings of the Cambridge Philosophical Society, 169 (2020), 209–223. arXiv:1903.04863
A reverse Sidorenko inequality.
Ashwin Sah, Mehtaab Sawhney, David Stoner and Yufei Zhao. Inventiones Mathematicae, 221 (2020), 665–711. arXiv:1809.09462
The number of independent sets in an irregular graph.
Ashwin Sah, Mehtaab Sawhney, David Stoner and Yufei Zhao. Journal of Combinatorial Theory, Series B, 138 (2019), 172-195. arXiv:1805.04021
Hypercube Packings and Coverings with Higher Dimensional Rooks.
Mehtaab Sawhney and David Stoner. Australasian Journal of Combinatorics, 77 (2020), 9--34. arXiv:1801.10607
Properties of non-symmetric Macdonald polynomials at \(q = 1\) and \(q = 0\).
Per Alexandersson and Mehtaab Sawhney. Annals of Combinatorics, 23, No.2, 219--239 (2019). arXiv:1801.04550
On the Discrepancy Between Two Zagreb Indices.
Ashwin Sah and Mehtaab Sawhney. Discrete Mathematics, 341 (2018), 2575--2589. arXiv:1801.02532
Characters of Independent Stanley Sequences.
Richard Moy, Mehtaab Sawhney and David Stoner. European Journal of Combinatorics, 70 (2018), 354--363. arXiv:1708.01849
On a conjecture regarding permutations which destroy arithmetic progressions
Mehtaab Sawhney and David Stoner. Electronic Journal of Combinatorics, 25 (2018), P2.42. arXiv:1708.00144
On Symmetric But Not Cyclotomic Numerical Semigroups
Mehtaab Sawhney and David Stoner. SIAM Journal of Discrete Mathematics, 32 (2018), 1296--1304. arXiv:1707.00782
A major-index preserving map on fillings.
Per Alexandersson and Mehtaab Sawhney. Electronic Journal of Combinatorics, 24, No.4, 2017. arXiv:1703.03088
Further Results on Bar and Arc \(k-\)Visibility Graph.
Mehtaab Sawhney and Jonathan Weed. Minnesota Journal of Undergraduate Mathematics, Volume 3 (2018). arXiv:1601.01231
Two classes of modular \(p-\)Stanley sequences.
Mehtaab Sawhney and Jonathan Tidor. Journal of Combinatorics, 11 (2020), 127--140 arXiv:1506.07941
Parities in random Latin squares
Matthew Kwan, Kalina Petrova and Mehtaab Sawhney. Submitted arXiv:2509.13125
Convergent points for random power series on the unit circle
Marcus Michelen and Mehtaab Sawhney. Submitted arXiv:2509.02729
On polynomial progressions via transference
Daniel Altman and Mehtaab Sawhney. Submitted arXiv:2506.13010
Quasipolynomial bounds for the corners theorem
Michael Jaber, Yang P. Liu, Shachar Lovett, Anthony Ostuni and Mehtaab Sawhney. Submitted arXiv:2504.07006
The random graph process is globally synchronizing
Vishesh Jain, Clayton Mizgerd and Mehtaab Sawhney. Submitted arXiv:2501.12205
Local limit theorem for joint subgraph counts
Ashwin Sah, Mehtaab Sawhney and Daniel G. Zhu. Submitted arXiv:2412.09535
New bounds for the Furstenberg-Sárközy Theorem
Ben Green and Mehtaab Sawhney. Submitted arXiv:2411.17448
Hitting time mixing for the random transposition walk
Vishesh Jain and Mehtaab Sawhney. Submitted arXiv:2410.23944
Free Energy Universality of Spherical Spin Glasses
Mehtaab Sawhney and Mark Sellke. Submitted arXiv:2408.13701
On further questions regarding unit fractions
Yang P. Liu and Mehtaab Sawhney. Submitted arXiv:2404.07113
Improved Bounds for Szemerédi's Theorem
James Leng, Ashwin Sah and Mehtaab Sawhney. Submitted arXiv:2402.17995
Quasipolynomial bounds on the inverse theorem for the Gowers \(U^{s+1}[N]\)-norm
James Leng, Ashwin Sah and Mehtaab Sawhney. Submitted arXiv:2402.17994
A Toolkit for Robust Thresholds
Huy Tuan Pham, Ashwin Sah, Mehtaab Sawhney and Michael Simkin. Submitted arXiv:2210.03064