October 1, 2019
Julie Bergner to present math department's 15th Virginia L. Chatelain Memorial Lecture
Julie Bergner, University of Virginia, will present the math department's 15th Virginia L. Chatelain Memorial Lecture at 2:30 p.m. Tuesday, Oct. 8, in 102 Cardwell Hall.
Bergner will present "2-Segal Sets, Algebraic K-Theory, and Hall Algebras" as part of the Mathematics Department Colloquium Lecture series.
The abstract for the lecture is: The notion of 2-Segal space was defined by Dyckerhoff and Kapranov, and independently under the name of decomposition space by G'alvez-Carrillo, Kock, and Tonks. These structures encode algebraic objects for which composition need not always exist or be unique, yet still satisfy associativity. There are many examples of 2-Segal spaces, but two main applications stand out. First, 2-Segal spaces arise from the Waldhausen S-construction in algebraic K-theory. Second, they give rise to Hall algebra constructions, of interest in representation theory. In this talk, we'll look at a specific family of discrete 2-Segal spaces, or 2-Segal sets, associated to finite graphs, and how we can understand these two very general constructions in this setting. In particular, we'll show that many of the associated Hall algebras can be identified with cohomology algebras of familiar topological spaces.
The math department is a part of K-State’s College of Arts and Sciences. To learn more about opportunities in math at K-State, visit the math department website.