Large language models (LLMs) have demonstrated tremendous capabilities in solving
complex tasks, from quantitative reasoning to understanding natural language. However …

A randomness extractor is an algorithm which extracts randomness from a low-quality
random source, using some additional truly random bits. We construct new extractors which …

We present novel techniques for analyzing the problem of low-rank matrix recovery. The
methods are both considerably simpler and more general than previous approaches. It is …

We prove the l2 Decoupling Conjecture for compact hypersurfaces with positive definite
second fundamental form and also for the cone. This has a wide range of important …

During the past two decades there has been active interplay between geometric measure
theory and Fourier analysis. This book describes part of that development, concentrating on …

We show that for some constant β\gt0, any subset A of integers {1,...,N\} of size at least 2^-
O\left((\logN)^β\right)⋅N contains a non-trivial three-term arithmetic progression. Previously …

The classical random matrix theory is mostly focused on asymptotic spectral properties of
random matrices as their dimensions grow to infinity. At the same time many recent …

Given an n× n complex matrix A, let A (x, y):= 1 n|{1 ≤ i ≤ n, Re i ≤ x, Im i ≤ y\}| be the
empirical spectral distribution (ESD) of its eigenvalues λ i∈ ℂ, i= 1,…, n. We consider the …

Using the dichotomy of structure and pseudorandomness as a central theme, this accessible
text provides a modern introduction to extremal graph theory and additive combinatorics …

We study the dimension of self-similar sets and measures on the line. We show that if the
dimension is less than the generic bound of min {1, s}, where s is the similarity dimension …