Spring 2023

** Organizers: Anna Marie
Bohmann, Rares Rasdeaconu, Ioana Suvaina**

__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)

__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)