Mehtaab Sawhney

activity

20152026

most citedThe number of independent sets in an irregular graph

14 citations · 74 across the 75 of their papers we have counts for

collaborators

90 papers

math.CO2026

The proportion of permutations fixing a $k$ -set

Ben Green, Mehtaab Sawhney

Denote by $p (k)$ the limit, as $n \to \infty$ , of the probability that a random permutation on a set of size $n$ has an invariant set of size $k$ . We give an asymptotic for…

math.PR2026

On the maxima of Littlewood polynomials on $[- 1, 1]$

Brayden Letwin, Mehtaab Sawhney

A Littlewood polynomial is a polynomial of the form \[ f_n(x)=\sum_{k=0}^n \varepsilon_k x^k \] with $ε_{k} \in {- 1, 1}$ . Let $(ε_{k})_{k \geq 0}$ be i.i.d. Rademach…

math.CO2026

Short proofs in combinatorics, probability and number theory II

Boris Alexeev, Moe Putterman, Mehtaab Sawhney +2

We give a quintet of proofs resulting from questions posed by Erdős. These questions concern ordinary lines in planar point sets, sequences with uniformly small exponential sums, $…

math.CO2026

Short proofs in combinatorics and number theory

Boris Alexeev, Moe Putterman, Mehtaab Sawhney +2

We give a triplet of short proofs, each of which answers a question raised by Erdős. The first concerns the small prime factors of $(k n)$ , the second concerns whether an ad…

math.CO2026

On infinite sets with no $3$ on a line

Moe Putterman, Mehtaab Sawhney, Gregory Valiant

We give a construction of an infinite set of points $A$ in $R^{2}$ such that any subset $P \subseteq A$ has a constant density subset $P^{'}$ with no three points collinear and…

cs.CL2025★ 3 cited

Early science acceleration experiments with GPT-5

Sébastien Bubeck, Christian Coester, Ronen Eldan +11

AI models like GPT-5 are an increasingly valuable tool for scientists, but many remain unaware of the capabilities of frontier AI. We present a collection of short case studies in…

math.NT2025

Bounds for monochromatic solutions to ${x + y, x y}$

Ben Green, Mehtaab Sawhney

Let $r$ be a sufficiently large positive integer, and let $N \geq exp exp (r^{50})$ . Then any $r$ -colouring of $[N]$ contains a monochromatic copy of ${x + y, x y}$ with $x > y > 2$ .

math.PR2025

On random matrices with large corank

Zach Hunter, Matthew Kwan, Lisa Sauermann +1

Let $1 \leq k \leq n$ and $M$ be a random $n \times n$ matrix with independent uniformly random ${\pm 1}$ -entries. We show that there exists an absolute constant $c > 0$ such that \[\…

math.PR2025

Parities in random Latin squares

Matthew Kwan, Kalina Petrova, Mehtaab Sawhney

In a Latin square, every row can be interpreted as a permutation, and therefore has a parity (even or odd). We prove that in a uniformly random $n \times n$ Latin square, the $n$ ro…

math.PR2025

Convergent points for random power series on the unit circle

Marcus Michelen, Mehtaab Sawhney

Consider a random power series of the form $P (z) = \sum_{n \geq 1} ε_{n} a_{n} z^{n}$ where $a_{n} \in C$ are deterministic and $ε_{n}$ are chosen independently…

math.NT2025

On polynomial progressions via transference

Daniel Altman, Mehtaab Sawhney

We prove new cases of reasonable bounds for the polynomial Szemerédi theorem both over $Z / N Z$ with $N$ prime and over the integers. In particular, we prove reason…

math.CO2025

Quasipolynomial bounds for the corners theorem

Michael Jaber, Yang P. Liu, Shachar Lovett +2

Let $G$ be a finite abelian group and $A$ be a subset of $G \times G$ which is corner--free, meaning that there are no $x, y \in G$ and $d \in G ∖ {0}$ such that $(x, y)$ …

math.CO2025

The random graph process is globally synchronizing

Vishesh Jain, Clayton Mizgerd, Mehtaab Sawhney

The homogeneous Kuramoto model on a graph $G = (V, E)$ is a network of $∣ V ∣$ identical oscillators, one at each vertex, where every oscillator is coupled bidirectionally (with unit…

math.PR2024

Local limit theorem for joint subgraph counts

Ashwin Sah, Mehtaab Sawhney, Daniel G. Zhu

Extending a previous result of the first two authors, we prove a local limit theorem for the joint distribution of subgraph counts in the Erdős-Rényi random graph $G (n, p)$ . This li…

math.NT2024

New bounds for the Furstenberg-Sárközy theorem

Ben Green, Mehtaab Sawhney

Suppose that $A \subset {1, \dots, N}$ has no two elements differing by a square. Then $∣ A ∣ ≪ N e^{- c l o g N}$ .

math.PR2024

Hitting time mixing for the random transposition walk

Vishesh Jain, Mehtaab Sawhney

Consider shuffling a deck of $n$ cards, labeled $1$ through $n$ , as follows: at each time step, pick one card uniformly with your right hand and another card, independently and uni…

math.NT2024

Primes of the form $p^{2} + n q^{2}$

Ben Green, Mehtaab Sawhney

Suppose that $n$ is $0$ or $4$ modulo $6$ . We show that there are infinitely many primes of the form $p^{2} + n q^{2}$ with both $p$ and $q$ prime, and obtain an asymptotic for their nu…

math.NT2024★ 1 cited

Vinogradov's theorem for primes with restricted digits

James Leng, Mehtaab Sawhney

Let $g$ be sufficiently large, $b \in {0, \dots, g - 1}$ , and $S_{b}$ be the set of integers with no digit equal to $b$ in their base $g$ expansion. We prove that every suffic…

math.PR2024

Free Energy Universality of Spherical Spin Glasses

Mehtaab Sawhney, Mark Sellke

We prove the free energy and ground state energy of spherical spin glasses are universal under the minimal moment assumptions. Previously such universality was known only for Ising…

math.CO2024

An explicit economical additive basis

Vishesh Jain, Huy Tuan Pham, Mehtaab Sawhney +1

We present an explicit subset $A \subseteq N = {0, 1, \dots}$ such that $A + A = N$ and for all $ε > 0$ , \[\lim_{N\to \infty}\frac{\big|\big\{(n_1,n_2):…

math.PR2024

On the Spielman-Teng Conjecture

Ashwin Sah, Julian Sahasrabudhe, Mehtaab Sawhney

Let $M$ be an $n \times n$ matrix with iid subgaussian entries with mean $0$ and variance $1$ and let $σ_{n} (M)$ denote the least singular value of $M$ . We prove that \[\mathbb{P}\big…

math.NT2024

On further questions regarding unit fractions

Yang P. Liu, Mehtaab Sawhney

We prove that a subset $A \subseteq [1, N]$ with \[\sum_{n\in A}\frac{1}{n} \ge (\log N)^{4/5 + o(1)}\] contains a subset $B$ such that \[\sum_{n\in B} \frac{1}{n} = 1.\] Our techni…

math.CO2024

Improved Bounds for Szemerédi's Theorem

James Leng, Ashwin Sah, Mehtaab Sawhney

Let $r_{k} (N)$ denote the size of the largest subset of $[N] = {1, \dots, N}$ with no $k$ -term arithmetic progression. We show that for $k \geq 5$ , there exists $c_{k} > 0$ such that \[r_…

math.CO2024

Quasipolynomial bounds on the inverse theorem for the Gowers $U^{s + 1} [N]$ -norm

James Leng, Ashwin Sah, Mehtaab Sawhney

We prove quasipolynomial bounds on the inverse theorem for the Gowers $U^{s + 1} [N]$ -norm. The proof is modeled after work of Green, Tao, and Ziegler and uses as a crucial input rece…

The proportion of permutations fixing a k-set

On the maxima of Littlewood polynomials on [−1,1]

Short proofs in combinatorics, probability and number theory II

Short proofs in combinatorics and number theory

On infinite sets with no 3 on a line

Early science acceleration experiments with GPT-5

Bounds for monochromatic solutions to {x+y,xy}

On random matrices with large corank

Parities in random Latin squares

Convergent points for random power series on the unit circle

On polynomial progressions via transference

Quasipolynomial bounds for the corners theorem

The random graph process is globally synchronizing

Local limit theorem for joint subgraph counts

New bounds for the Furstenberg-Sárközy theorem

Hitting time mixing for the random transposition walk

Primes of the form p2+nq2

Vinogradov's theorem for primes with restricted digits

Free Energy Universality of Spherical Spin Glasses

An explicit economical additive basis

On the Spielman-Teng Conjecture

On further questions regarding unit fractions

Improved Bounds for Szemerédi's Theorem

Quasipolynomial bounds on the inverse theorem for the Gowers Us+1[N]-norm

The proportion of permutations fixing a $k$ -set

On the maxima of Littlewood polynomials on $[- 1, 1]$

On infinite sets with no $3$ on a line

Bounds for monochromatic solutions to ${x + y, x y}$

Primes of the form $p^{2} + n q^{2}$

Quasipolynomial bounds on the inverse theorem for the Gowers $U^{s + 1} [N]$ -norm