2-Segal spaces in homotopy theory, algebra, and algebraic K-theory

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• Julie Bergner (University of Virginia)
• Tuesday 11 June 2024, 11:15-12:15
• External.

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TRHW01 - Workshop on topology, representation theory and higher structures

The notion of Segal space has been useful for modeling up-to-homotopy topological categories, and can be described via the so-called Segal maps.  Two different approaches have led to the same generalization, known as 2-Segal spaces: while Dyckerhoff and Kapranov sought to generalize the Segal maps from a geometric point of view, Galvez-Carrillo, Kock and Tonks were motivated by making homotopy-theoretic versions of constructions in combinatorics.   A key example of a 2-Segal space is the output of Waldhausen’s S-construction when applied to an exact category, and 2-Segal spaces satisfying certain finiteness assumptions provide a unifying treatment to Hall algebra constructions.  In this minicourse, we will give definitions and basic examples, then introduce these connections with algebraic K-theory and algebra.

This talk is part of the Isaac Newton Institute Seminar Series series.

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