Geometry Seminar

                                                                                                                      Vanderbilt University
                                                                                                                                Spring 2023

Thursdays, 10:00-10:50am in SC 1312 or virtually on Zoom. The Zoom link for the seminar is here, Passcode: 174362   

    Organizers: Anna Marie Bohmann, Rares Rasdeaconu, Ioana Suvaina

              Thursday, March 2nd (SC1404)

Speaker:  Jack Calcut (Oberlin College)

Title: Mazur and Jester 4-manifolds

Abstract:   Mazur and Poenaru constructed the first compact, contractible manifolds distinct from disks. More recently,
Sparks modified Mazur's construction and defined Jester manifolds. Sparks used Jester manifolds to produce compact,
contractible 4-manifolds distinct from the 4-disk that split as the union of two 4-disks meeting in a 4-disk. We present
several very different proofs that all Mazur and Jester manifolds are not 4-disks. We discuss the problem of
distinguishing these 4-manifolds from one another. And, we present pertinent questions on knots in S^1xS^2 and hyperbolic
triangle groups. This is joint work with Alexandra Du.
(Contact person: Ioana Suvaina)

                Thursday, April 6th

Speaker:  Christy Hazel (UCLA)

Title: The cohomology of equivariant configuration spaces

Abstract:  Given a space X we can consider the configuration space of n distinct points from X. When X is a Euclidean space,
the singular (co)homology of these configuration spaces has rich structure. If we instead consider configurations of points in
G-representations where G is a finite group, then the configuration space inherits an action of the group G. We can thus investigate
the structure of the equivariant (co)homology of these configuration spaces. In this talk we'll review some of the classical
computations by Arnold and Cohen to compute the singular cohomology, and then discuss new techniques used to compute the
Bredon G-equivariant cohomology computations. This is joint work with Dan Dugger. (Contact Person: Anna Marie Bohmann)

                Thursday, April 20th

Speaker:  Justin Barhite (University of Kentucky)

Title:  Traces and Cotraces in Bicategories

Abstract:  Traces arise in many different places in math: traces of matrices, characters of group representations, and even the Euler
characteristic of a CW complex! There are very general notions of trace, expressed in the language of category theory, that capture these
examples of traces and whose properties imply familiar results like the Lefschetz fixed point theorem and the induction formula for
characters. The formalism of traces doesn't tell the whole story though; there are some constructions that feel trace-like in certain ways
but also have a distinct flavor, and what's really needed to explain them from this category-theoretic perspective is a dual notion of "cotrace."
I will talk about some of these things that I have been working to understand by developing a theory of bicategorical cotraces.
(Contact Person: Anna Marie Bohmann)



 Old Seminar Web-Pages