Past Events
The monopole Floer homology of an oriented closed 3-manifold was defined by Kronheimer-Mrowka around 2007 and has greatly influenced the study of 3-manifold topology since its inception.
In this talk, we will generalize their construction and define the monopole Floer homology for any…
We introduce the $N\times N$ random matrices $X_{j,k}=\exp(2\pi i \sum_{q=1}^d \omega_{j,q} k^q)$ with i.i.d. random variables $\omega_{j,q}$ for $1\leq j\leq N$ and $1\leq q\leq d}$, where $d$ is a fixed integer. We prove that the distribution of their singular values converges to the…
You have a matrix A and a vector b. How hard could it be to find x that solves Ax=b? Just do Gaussian elimination, right? Sometimes this is the best choice, but there are also many other algorithms to choose from. In this talk I'll go over some of the complications…
Abstract: In this talk we will discuss two central problems in algebraic number theory and their interconnections: explicit class field theory (also known as Hilbert's 12th Problem), and the special values of L-functions. The goal of explicit class field theory is to describe the abelian…
Abstract: I will discuss recent work calculating the top weight cohomology of the moduli space $A_g$ of principally polarized abelian varieties of dimension $g$ for small values of $g$. The key idea is that this piece of cohomology is encoded combinatorially via the…
Abstract: The Teukolsky equation is one of the fundamental equations governing linear gravitational perturbations of the Kerr black hole family. We study fixed frequency solutions and obtain estimates which are uniform in the frequency parameters. Due to the separability of the Teukolsky…
It has been a classical question which manifolds admit Riemannian metrics with positive scalar curvature. I will present some recent progress on this question, ruling out positive scalar curvature on closed aspherical manifolds of dimensions 4 and 5 (as conjectured by Schoen-Yau and by Gromov),…
I will discuss some simplified models for the shape of liquid droplets on rough solid surfaces. These are elliptic free boundary problems with oscillatory coefficients. I will talk about the large scale effects of small scale surface roughness, e.g. contact line pinning…