Title: A Generalization of the Geroch Conjecture with Arbitrary EndsThe Geroch conjecture (proven by Schoen-Yau and Gromov-Lawson) says that the torus T^n does not admit a metric of positive scalar curvature. In this talk, I will explain how to generalize it to some non-compact settings using μ-bubbles. In particular, I will talk about why the […]
Title: Tannaka duality for algebraic 2-groupsAbstract: The Tannakian formalism is a web of statements which, in its most basic form, attempts to recover a group G from its symmetric monoidal category of representations. The goal of this talk is to explain a Tannaka duality result that applies to groups in Artin stacks. In this case, […]
Title: Pyknotic/condensed sets II Abstract: We will continue the discussion of pyknotic sets, and introduce the notion of condensed sets.
Title: Symmetries of Fano varieties.Abstract: A landmark result of Birkar, Prokhorov, and Shramov shows that automorphism groups of Fano (or more generally rationally connected) varieties over C of a fixed dimension are uniformly Jordan. This means in particular that there is some upper bound on the size of symmetric groups acting faithfully on rationally connected varieties of […]
Title: An introduction to Hopf Rings.Abstract: An old guy’s perspective on what homotopy theory used to be about and why complex cobordism has become central to the study.And, I’ll show one approach to getting more (and different) information about complex cobordism.If time permits (it won’t), I’ll show some of how chromatic homotopy theory comes out […]