[Binghamton Geometry Topology Seminar] This week: Julie Bergner

[jwilliams at math.binghamton.edu]

Speaker: Julie Bergner (University of Virginia)

Title: An introduction to 2-Segal sets via combinatorial examples

Abstract: The notion of a 2-Segal object was recently defined by
Dyckerhoff and Kapranov, and independently by Gálvez-Carrillo, Kock, and
Tonks under the name of decomposition space. Whereas 1-Segal sets model
the structure of a category, in which composition is defined and is
associative, 2-Segal sets instead encode a more general structure in which
composition need not exist or be unique, but is still associative when it
is defined. The 2-Segal set associated to a graph gives a nice example
where maps can be composed in different ways. In particular, following a
definition of Dyckerhoff and Kapranov, this 2-Segal set has an associated
Hall algebra which is much smaller than most natural examples of such
algebras and has a curious description as a cohomology ring.

Thursday, Sept 13, 2:50pm in WH-100E