Past Events

Given a finite degree $d$ cover of curves $f: X \to \mathbb P^1$, we study $f_* \mathscr O_X$, which is a rank $d$ vector bundle on $\mathbb P^1$, hence can be written as a direct sum of line bundles $f_* \mathscr O_X \simeq \oplus_{i=1}^d \mathscr O(a_i)$. Naively, one might…

In the last few years there has been an explosion of new results about surfaces in 4-space. In this talk, we will start by discussing various kinds of surfaces and some basic questions about them, like what it means for two of them to be the equivalent. We will then discuss two ways to describe…

In 1976, Ken Ribet used modular techniques to prove an important relationship between class groups of cyclotomic fields and special values of the zeta function. Ribet’s method was generalized to prove the Iwasawa Main Conjecture for odd primes p by Mazur-Wiles over Q and by Wiles over arbitrary…

Nonlinear dynamics play a prominent role in many domains and are notoriously difficult to solve. Whereas previous quantum algorithms for general nonlinear equations have been severely limited due to the linearity of quantum mechanics, we gave the first efficient quantum algorithm for nonlinear…

Abstract: We describe a localized gluing result for the constraint equations in which a small mass rescaling of an asymptotically flat data set is glued into the neighborhood of a point inside of another data set. As the smallness parameter tends to zero,…

Using Bar-Natan's and Lee's deformations of Khovanov homology of links, we define minus, plus, and infinity versions of Khovanov homology. Given an unorientable cobordism in [0,1]\times S^3 from a link L_0 to a link L_1, we define a mixed invariant as a map from the minus version of…