Monday, March 4, 2024
Time | Items |
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All day |
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4:00pm |
03/04/2024 - 4:00pm In rank one, the Hopf-Tsuji-Sullivan dichotomy theorem states the dichotomy for the ergodicity of geodesic flow in terms of the divergence/convergence of the Poincaré series at the critical exponent. Burger-Landesberg-Lee-Oh initiated the study of higher rank version of the Hopf-Tsuji-Sullivan dichotomy for a one-dimensional diagonal flow and the associated Poincaré series. In this talk, we discuss the Hopf-Tsuji-Sullivan dichotomy for higher dimensional flows which we call subspace flows of Weyl chamber flows. Just like the dimension dichotomy for Brownian motions in $\mathbb{R}^n$, the codimension dichotomy of the flow occurs for Anosov homogeneous spaces. This is based on joint work with Hee Oh and Yahui (Amy) Wang. Location:
KT205
03/04/2024 - 4:30pm I will introduce the basics of toroidal algebras and certain extensions of them, together with their representations using vertex operator algebraic techniques. I will also introduce certain extensions of toroidal algebras including a generalization to lie super algebras. The purpose of this generalization will be related to the other main topic of the lecture, which will be the equivariant cohomology of moduli spaces of sheaves on elliptic surfaces which serve as weight spaces for representations of the algebras. The action of autoequivalences of the derived category of the elliptic surfaces will be identified with automorphisms of toroidal algebras. Time permitting, we will discuss other representations of toroidal lie algebras related to flags of sheaves and their relations with superconformal algebras. Location:
KT217
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