Monday, February 5, 2024
Time  Items 

All day 

4:00pm 
02/05/2024  4:00pm In the theory of Kleinian groups, Sullivan’s classical theorem establishes the correspondence between PattersonSullivan measures and Hausdorff measures on the limit sets for convex cocompact Kleinian groups. This connection provides a geometric understanding of PattersonSullivan measures, emphasizing their association with the internal metric on limit sets. Recent advancements in the theory of infinite covolume discrete subgroups of higherrank Lie groups have brought Anosov subgroups into focus as a natural higherrank extension of convex cocompact Kleinian groups. This raises an intriguing question: under what conditions do PattersonSullivan measures for Anosov subgroups emerge as Hausdorff measures on limit sets with appropriate metrics? In this talk, we disuss joint work with Dongryul Kim and Hee Oh, which provides a definitive answer to this question. We will also discuss several applications, including the analyticity of (p,q)Hausdorff dimensions as functions on the Teichmuller spaces and spectral properties of the associated locally symmetric manifolds.
Location:
KT205
02/05/2024  4:30pm I'll describe a perturbative classical field theory defined on 11manifolds with a rank 6 transversely holomorphic foliation and a transverse Calabi–Yau structure. The theory has an infinitedimensional algebra of gauge symmetries preserving the trivial background, which is $L_\infty$ equivalent to a Lie 2extension of the infinitedimensional exceptional simple super Lie algebra $E(510)$. Conjecturally, this theory describes the minimal twist of elevendimensional supergravity. After describing this conjecture, and evidence for it, I'll describe twisted avatars of the $AdS_7\times S^4$ and $AdS_4\times S^7$ backgrounds, and how two other infinitedimensional exceptional simple super Lie algebras $E(36)$ and $E(16)$ appear as asymptotic symmetries. Enumerating gravitons on such backgrounds naturally leads to refinements of generating functions of representationtheoretic significance, such as the MacMahon function. Time permitting, I'll explain how our results combined with holographic techniques can be used to produce enhancements of familiar vertex algebras such as the Heisenberg and Virasoro algebras, to holomorphic factorization algebras in three complex dimensions, and furnish geometric constructions of representations thereof. This talk is based on joint work with Ingmar Saberi and Brian Williams. Location:
KT217
