Upcoming Events
Recently Emerton and Zhu formulated a categorical global arithmetic Langlands conjecture relating geometric cohomology of an open Shimura variety to coherent cohomology of a moduli stack of p-adic representations of a Galois group. In this talk, I will focus on these cohomologies' p-ordinary…
I will discuss large deviations for the largest eigenvalue of random matrices, and specifically the spherical integral approach.
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The ECH capacities are a collection of invariants of symplectic 4-manifolds, defined using Hutchings' theory of embedded contact homology. While these capacities have many applications to symplectic embeddings of convex domains, they remain poorly understood for more complicated symplectic…
How many distinct symbols should a password use if information about which symbols are used is leaked? For a password of fixed length n, the classical answer is roughly 0.72n. I will discuss some variants and their connections with condensation phenomena and equivalence of…
Heegaard Floer (HF) homology, developed by Ozsváth-Szabó in the early 2000s, was designed to be a combinatorially computable version of Monopole Floer homology (HM) for 3-manifolds. Miyazawa's detection of exotic RP^2 in S^4 used a "real" version of HM, denoted HMR, namely an invariant for 3-…
We prove that every complete finite index CMC hypersurface is either minimal or compact, provided that the six-dimensional ambient manifold is a Riemannian product of a closed manifold with non-negative sectional curvature and a Euclidean factor. This is related to a question posed by M. do…
Moduli spaces of 1-dimensional sheaves play an important role in the enumerative geometry of Calabi-Yau threefolds. In particular, the perverse filtration on their cohomology, induced by a natural support map, encodes the so-called BPS invariants which are expected to be “χ-independent”, where χ…