14h-14h45 : Aiden Suter 

Title: 3d Higgs branch conjecture and associated variety for psl(n|n) VOA

Abstract: 3d mirror symmetry is a duality between topological twists of 3-dimensional supersymmetric quantum field theories. One manifestation of this duality is an isomorphism between branches of the moduli space of vacua of mirror theories. These branches, called the Higgs branch and Coulomb branch, are hyperkahler manifolds and the duality between them was studied independently by mathematicians under the guise of ``symplectic duality”. In this talk, I will discuss work towards proving these isomorphisms using boundary vertex operator algebras (VOAs). These VOAs are defined on 2-dimensional boundary conditions of the twisted theories and it is conjectured that they contain the data of both the Higgs and Coulomb branches. This conjecture implies a number of duality properties for VOAs appearing in this manner. In particular, I will discuss joint work with Andrea Ferrari in which we prove the Higgs branch conjecture for 3D supers quantum electrodynamics.

15h15-16h: Yicheng Zhou

Title: On the profiniteness of mod p etale cohomology of partially proper rigid-analytic curves over Q_p

Abstract: The mod p etale cohomology groups of rigid spaces over p-adic fields is in general large and complicated, despite their finiteness for proper spaces proved by Scholze via the Primitive Comparison Theorem. Following an idea of Colmez–Niziol–Dospinescu, I will explain a profiniteness result for **partially proper** rigid curves over Q_p. The key result is the statement that the restriction map of F_p-coefficient étale cohomology groups along a **strict inclusion** of affinoid curves over Q_p has finite image. If time permits, I will sketch a proof of it and explain the difficulties to generalize it to higher dimensional spaces.