Why Condensed Mathematics is Better Than Topology

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• Jiacheng Tang, University of Manchester
• Friday 06 December 2024, 16:00-17:00
• MR13.

If you have a question about this talk, please contact Julian Wykowski.

The classic way to study algebra and topology together is through topological groups: groups with a compatible topology. However, topological abelian groups do not have nice categorical properties, nor is there a satisfactory theory of tensor products. Condensed mathematics was developed recently as an attempt to combine algebra and topology in a nicer way. I will explain the problems with classic topology and how condensed mathematics (partially) solves them. As an example, we will see that many condensed notions (Ext, tensor products, group rings…) generalise the corresponding notions for profinite modules, suggesting that the condensed world is a better place to study profinite modules than the topological world.

This talk is part of the Junior Geometry Seminar series.

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