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2-Segal spaces in homotopy theory, algebra, and algebraic K-theory - Julie Bergner (University of Virginia)
2024-06-11 10:15 - 11:15 UTC | External
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.
