Past Events
Abstract: Khovanov homology is a combinatorially-defined invariant which has proved to contain a wealth of geometric information. In 2006 Seidel and Smith introduced a candidate analog of the theory in Lagrangian Floer analog cohomology, which has been shown by Abouzaid and Smith to be…
Given a Gaussian energy function H(x) and another random process O(x) (an observable) both defined on the same configuration space, what is the law of O(y) for y sampled from the Gibbs measure associated to H(x)? We will see the answer to this question in the high-temperature phase in a general…
I will talk about a series of joint papers with Alexander Ritter, where we examine a large class of non-compact symplectic manifolds, including semiprojective toric varieties, conical symplectic resolutions, Higgs moduli spaces, etc.These manifolds admit a Hamiltonian circle action which is…
In this talk, I will survey several notions of dimension for (pre-)triangulated categories naturally arising from topology and symplectic geometry. I will discuss joint work with Andrew Hanlon and Jeff Hicks in which we prove new bounds on these dimensions and raise several questions for…
Igusa stacks are p-adic geometric objects that roughly parametrize abelian varieties up to isogeny. In a joint work with Daniels, van Hoften, and Zhang, we constructed Igusa stacks for Hodge type Shimura data, and discussed how its cohomology relates to the cohomology of Shimura varieties.…
Counting special lattices inside the "moduli space" of all lattices with extra symmetry leads to interesting invariants e.g. L-functions and orbital integrals, and interesting questions e.g. the fundamental lemma. I will explain my related research on a generalization of this toy model to "…
The theme for Student Analysis in the second half of fall quarter is geometric wave equations and wave maps. This will be the second talk on this theme.
There is a remarkable but hidden continuity in the development of classical mechanics from Archimedes to Poincaré. Textbooks on the subject often give unmotivated definitions and rely on calculation where a picture would better explain what’s really going on. Einstein, for instance, wrote:…
Given two vertex-ordered graphs G and H, the ordered Ramsey number R_<(G,H) is the smallest N such that whenever the edges of a vertex-ordered complete graph K_N are red/blue-colored, then there is a red (ordered) copy of G or a blue (ordered) copy of H. Let P_n^t denote the t-th power of a…