166 citations · 562 across the 54 of their papers we have counts for
10 papers · 1 filter
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…
COPT: Coordinated Optimal Transport for Graph Sketching
Yihe Dong, Will Sawin
We introduce COPT, a novel distance metric between graphs defined via an optimization routine, computing a coordinated pair of optimal transport maps simultaneously. This gives an…
Freeness alone is insufficient for Manin-Peyre
Will Sawin
Manin's conjecture predicts the number of rational points of bounded height on a Fano variety. To make this prediction precise, it is necessary to remove a thin subset of rational…