166 citations · 562 across the 54 of their papers we have counts for
61 papers
Counting matrices with given characteristic polynomial
Tim Browning, Fabian Gundlach, Will Sawin
Let be a monic polynomial of degree with integer coefficients. We use Fourier analysis to prove a new upper bound on the number of matrices with characteristic…
Muon: Muon with Fractional Spectral Powers
Yihe Dong, Will Sawin
Muon is an increasingly widely used optimizer that replaces a gradient with its polar factor , thereby flattening the singular spectrum. However, full flatten…
Bilinear forms with trace functions
Étienne Fouvry, Emmanuel Kowalski, Philippe Michel +1
We obtain non-trivial bounds for bilinear sums of trace functions below the Pólya-Vinogradov range assuming only that the geometric monodromy group of the underlying ell-adic sheaf…
Conjectures for distributions of class groups of extensions of number fields containing roots of unity
Will Sawin, Melanie Matchett Wood
Cohen, Lenstra, and Martinet have given conjectures for the distribution of class groups of extensions of number fields, but Achter and Malle have given theoretical and numerical e…
The purity locus of matrix Kloosterman sums
Márton Erdélyi, Will Sawin, Árpád Tóth
We establish the exact structure of the cohomology associated to a certain matrix exponential sum investigated in prior work (arXiv:2109.00762) of the first and last author.
An improved lower bound for the union-closed set conjecture
Will Sawin
Gilmer has recently shown that in any nonempty union-closed family of subsets of a finite set, there exists an element contained in at least a proportion of the…
The moment problem for random objects in a category
Will Sawin, Melanie Matchett Wood
The moment problem in probability theory asks for criteria for when there exists a unique measure with a given tuple of moments. We study a variant of this problem for random objec…
General multiple Dirichlet series from perverse sheaves
Will Sawin
We give an axiomatic characterization of multiple Dirichlet series over the function field , generalizing a set of axioms given by Diaconu and Pasol. The key axiom,…
The size of wild Kloosterman sums in number fields and function fields
Will Sawin
We study p-adic hyper-Kloosterman sums, a generalization of the Kloosterman sum with a parameter k that recovers the classical Kloosterman sum when k=2, over general p-adic rings a…
Hecke's Theorem on the Different for -Manifolds
Will Sawin, Mark Shusterman
Hecke has shown that the different of an extension of number fields is a square in the class group. We prove an analog for branched covers of closed -manifolds saying that the b…
Representation of Squares by Nonsingular Cubic Forms
Lasse Grimmelt, Will Sawin
We prove an asymptotic formula for the number of representations of squares by nonsingular cubic forms in six or more variables. The main ingredients of the proof are Heath-Brown's…
Finite quotients of 3-manifold groups
Will Sawin, Melanie Matchett Wood
For and finite groups, does there exist a -manifold group with as a quotient but no as a quotient? We answer all such questions in terms of the gr…
Local parameters of supercuspidal representations
Wee Teck Gan, Michael Harris, Will Sawin +1
For a connected reductive group over a non-archime\-dean local field of positive characteristic, Genestier and Lafforgue have attached a semisimple parameter $\CL^{ss}(π)$…
An improved lower bound for multicolor Ramsey numbers and the half-multiplicity Ramsey number problem
Will Sawin
The multicolor Ramsey number problem asks, for each pair of natural numbers and , for the largest -coloring of a complete graph with no monochromatic clique of size…
Square-root cancellation for sums of factorization functions over squarefree progressions in
Will Sawin
We prove estimates for the level of distribution of the Möbius function, von Mangoldt function, and divisor functions in squarefree progressions in the ring of polynomials over a f…
Quantitative sheaf theory
W. Sawin, A. Forey, J. Fresán +1
We introduce a notion of complexity of a complex of ell-adic sheaves on a quasi-projective variety and prove that the six operations are "continuous", in the sense that the complex…
Möbius cancellation on polynomial sequences and the quadratic Bateman-Horn conjecture over function fields
Will Sawin, Mark Shusterman
We establish cancellation in short sums of certain special trace functions over below the Pólya-Vinogradov range, with savings approaching square-root cancellatio…
Cohen-Lenstra heuristics and bilinear pairings in the presence of roots of unity
Michael Lipnowski, Will Sawin, Jacob Tsimerman
Let be a quadratic extension of global fields. We study Cohen-Lenstra heuristics for the -part of the relative class group when contai…
HNHN: Hypergraph Networks with Hyperedge Neurons
Yihe Dong, Will Sawin, Yoshua Bengio
Hypergraphs provide a natural representation for many real world datasets. We propose a novel framework, HNHN, for hypergraph representation learning. HNHN is a hypergraph convolut…
The Hasse principle for random Fano hypersurfaces
Tim Browning, Pierre Le Boudec, Will Sawin
It is known that the Brauer--Manin obstruction to the Hasse principle is vacuous for smooth Fano hypersurfaces of dimension at least over any number field. Moreover, for such v…
Identifying measures on non-abelian groups and modules by their moments via reduction to a local problem
Will Sawin
Work on generalizations of the Cohen-Lenstra and Cohen-Martinet heuristics has drawn attention to probability measures on the space of isomorphism classes of profinite groups. As i…
Singularities and vanishing cycles in number theory over function fields
Will Sawin
This article is an overview of the vanishing cycles method in number theory over function fields. We first explain how this works in detail in a toy example, and then give three ex…
The Shafarevich conjecture for hypersurfaces in abelian varieties
Brian Lawrence, Will Sawin
Faltings proved that there are finitely many abelian varieties of genus over a number field , with good reduction outside a finite set of primes . Fixing one of these abe…
Topological reconstruction theorems for varieties
János Kollár, Max Lieblich, Martin Olsson +1
We study Torelli-type theorems in the Zariski topology for varieties of dimension at least 2, over arbitrary fields. In place of the Hodge structure, we use the linear equivalence…