What does a large permutation conditioned to satisfy some given conditions look like? This talk will provide a few different approaches to answer this question. The…
Given a surface S in R^3 diffeomorphic to the sphere, a classical question is to prove the existence of disk-type surfaces with constant mean curvature whose boundary…
The emergence of complex spatial structures in physical systems often occurs after a simpler background state becomes unstable. Localized fluctuations then grow and…
Recently, Annala, Hoyois, and Iwasa have defined and studied the 𝐏¹-homotopy theory, a generalization of 𝐀¹-homotopy theory that does not require 𝐀¹ to be contractible,…
The six-vertex model, also known as the square-ice model, is one of the central and most studied systems of 2d statistical mechanics. It offers various combinatorial…
We present a new framework for designing worst-case to average-case reductions. For a large class of problems, it provides an explicit transformation of algorithms…
Non-linear Dirac operators arise in various problems in gauge theory, calibrated geometry, and holomorphic Floer theory. They are used to define generalized Seiberg-…
In recent years, experiments have shown that twisted bilayer graphene and other so-called ``moiré materials'' realize a variety of important strongly-correlated…
Department of Mathematics
