Past Events
This talk centers around non-smooth metric measure spaces with low regularity. We will exhibit a series of regularity results and structure theorems for such metric spaces whose Ricci curvature has a uniform lower bound in the synthetic sense. These…
Pretraining a large language model means solving a single optimization problem — minimize next-token prediction loss — at a scale where each design choice costs millions of dollars in compute and months of GPU time. The resulting loss curves exhibit remarkably clean power-law structure, yet…
Zaremba's famous conjecture (1972) arose from the theory of numerical integration and relates to the field of continued fractions. It predicts that for any given prime p there is a positive integer a < p such that when expanded as a continued fraction a/p = 1/c_1+1/c_2 +... + 1/c_s all…
A widely accepted conjecture in the physical literature states that classical wave-fields propagating in random media over large distances eventually follow a complex circular Gaussian distribution. In this limit, the wave intensity becomes exponentially distributed, which corroborates the…
It is expected that taut foliations on 3-manifolds typically admit (almost) transverse pseudo-Anosov flows. This motivates a natural question: given a pseudo-Anosov flow $\phi$ on a 3-manifold $M$ and a suitable link $L \subset M$ of closed orbits of $\phi$, for which Dehn surgery multislopes…
In this talk, I will discuss forthcoming joint work with Alex Zupan introducing the notion of a derivative link in contact topology. Given an algebraically slice knot, a derivative link is a basis for a metabolizing subspace of the Seifert form. We provide several…
A mathematically precise definition of quantum field theories is a major and mostly unsolved goal of mathematical physics. One possible route to reaching this goal is through the program of constructive field theory, which is probabilistic at its core. This is one reason why there has been a…
The endoscopic classification of representations of quasi-split symplectic and orthogonal groups is a celebrated result of Arthur (extended to quasi-split unitary groups by Mok) which has had wide applications to representation theory and number theory. It is a collection of many interrelated…
I will introduce the Mean Curvature Flow in R^n and discuss its basic properties.