Lenny Taelman (University of Amsterdam)

Condensed mathematics: new foundations for topology (after Clausen & Scholze)

Thursday, 11 April 2024, 16:00-17:00 in HG00.616

Abstract

I will survey an exciting ongoing development at the interface between topology and algebra. In the past few years, Clausen and Scholze (and independently Barwick and Haine) have developed an alternative way to equip sets (or vector spaces, or ...) with the structure of a topology. Whereas classically the most fundamental topological space is arguably the unit interval, in the 'condensed' approach, the most fundamental space is the Cantor set. Despite the apparently pathological nature of this space, this has significant technical advantages, especially when mixing topology and analysis with algebra (as in functional analysis, for example).

This talk is expressly aimed at non-experts (including master students), and for most of this talk only some undergraduate topology will be needed.