University of Washington

Residue calculus is, of course, a very powerful way to evaluate many different kinds of integrals. For multivariate integrals, however, it may get really cumbersome, to the point that one sometimes gets stuck in purely combinatorial complexity. I...

A graph is Ramsey if its largest clique or independent set is of size logarithmic in the number of vertices. While almost all graphs are Ramsey, there is still no known explicit construction of Ramsey graphs. We discuss recent progress on finding...

A linear conic programming problem aims at minimizing a linear objective over the intersection of an affine set and a closed convex cone. The conic feasibility problems we study in this talk naturally arise from the optimality conditions of linear...

Otto calculus is a fundamental toolbox in mathematical optimal transport, imparting the Wasserstein space of probability measures with a Riemmanian structure. In particular, one can compute the Riemannian gradient of a functional over this space and...

Diophantine geometry is a modern-day incarnation of mathematicians' perennial interest in solving algebraic equations in integers. Its fundamental idea is to study the geometric objects defined by algebraic equations in order to understand their...

The space of homomorphisms from the fundamental group of a compact surface to a Lie group is a remarkably rich and versatile object, playing a key role in mathematical developments spanning disciplines of algebra, analysis, geometry, and mathematical...

There are several notions that are used to characterize algebraic varieties in terms of their similarity to a projective space. Two of these notions are rationality and unirationality. The problem of determining whether a variety is rational or...

A group is just a set together with a multiplication with certain properties, and these are ubiquitous in modern mathematics. In homotopy theory, we often see less-rigid objects, with many of the properties like associativity or commutativity only...

Remarkable recent successes of deep learning have heavily relied on very large neural networks. Time and time again, larger networks have shown better performance than smaller networks trained on comparably sized data sets. Since large networks...

Over the last two decades we have developed good understanding of how to quantify the impact of strategic user behavior on outcomes in many games (including traffic routing and online auctions) and showed that the resulting bounds extend to repeated...