University of Washington

I will survey the state of the art on the regularity theory for multiplicity 2 integral stationary currents. The talk will be based on joint work with C. De Lellis and J. Hirsch, and will touch upon recent work of Becker Kahn, Minter and...

Synchronization occurs in many natural and technological systems, from cardiac pacemaker cells to coupled lasers. In the synchronized state, the individual cells or lasers coordinate the timing of their oscillations, but they do not move through...

In mathematics, a proof not only demonstrates that a statement is true; it also allows others to confirm its correctness by verifying the argument. This talk highlights two places where the same “prove and verify” principle is applied to build...

I will discuss a microlocal analysis approach to spectral theory on asymptotically Minkowski spaces both for scalar wave operators and also for Dirac type operators. This in turn gives rise to complex powers of the operators, allowing for the...

We discuss a differential geometric construction of distinguished holomorphic 2-spheres inside a K3 surface. These 2-spheres degenerate to a line on an affine 3-manifold. The example illustrates a general principle in the SYZ program, where graphs on...

We will review different notions of anti-concentration, arising from geometry, analysis, and probability. One focus of the talk will be on understanding how these definitions relate to each other, sometimes leading to surprising and nontrivial...

Given a Jordan curve in the plane, we can associate a circle homeomorphism (conformal welding) via the conformal welding correspondence. These homeomorphisms arise naturally in Teichmuller theory, Mathematical physics and dynamics. In this talk, we...

Not all convex functions have finite minimizers; some can only be minimized by a sequence as it heads to infinity. In this work, we aim to develop a theory for understanding such minimizers at infinity. We study astral space, a compact extension of...

I will review the progress of large language models for mathematics over the last 3 years, from barely solving high school level mathematics to solving some minor open problems in convex optimization, combinatorics and probability theory. The...

A good way to understand the structure of a finite group is through its representations. The family of representations of a group on a fixed field has several properties: it is closed by finite direct sums, by tensor products, it contains the dual...