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Graduate Student Geometry-Topology Seminar

Monday, November 7, 2022 - 4:30pm

Ben Keigwin



University of Pennsylvania

DRL 4N49

Over the real numbers, the categories of topological vector spaces and Banach spaces are not very well-behaved. Both fail to be abelian categories, and in particular it can be a bit tricky to work in the derived category of either of them. An alternative to each of these categories is provided by condensed vector spaces and p-liquid vector spaces respectively. Both of these categories are abelian with wonderful categorical properties. Somewhat surprisingly, arriving at either of these categories comes from viewing the real numbers in an atypical way: as a quotient of a profinite set. We will explain why this perspective can be helpful sometimes and give some applications.