# Schedule

**All talks will take place in Stevenson Center 1308.**

(This is on the ground level of the Mathematics Building which is called Stevenson Center 1)

Reception and coffee breaks will take place in Stevenson Center 1425

**Saturday, March 25:**

*9:00-9:30: Registration; coffee and bagels *

9:30-10:30: Mike Mandell

*10:30-11:00: Coffee*

11:00-12:00: Dan Ramras

*12:00-2:00: Lunch break*

2:00-3:00: Kate Ponto

*3:00-3:30: Coffee*

3:30-4:30: John Lind

*4:40-5:50: Informal reception
*

**Sunday, March 26:**

*9:00-9:30: Coffee*

9:30-10:30: Teena Gerhardt

*10:30-11:00: Coffee*

11:00-12:00: Paul Goerss

**Abstracts:**

**Mike Mandell** (Indiana University)

Title: The strong Kunneth theorem for periodic topological cyclic homology

Abstract: Hesselholt has recently been advertising “periodic topological cyclic homology” (TP) as potentially filling some of the same roles for finite primes as periodic cyclic homology plays rationally. It is constructed from topological Hochschild homology (THH) analogously to the way periodic cyclic homology is constructed from Hochschild homology. In joint work with Andrew Blumberg, we prove a strong Kunneth theorem for the periodic topological cyclic homology of smooth and proper dg categories over a finite field k.

**Dan Ramras** (IUPUI)

Title: Coassembly for representation spaces

Abstract: I’ll describe a homotopy-theoretical framework for studying the relationships between (families of) finite-dimensional unitary representations, vector bundles, and flat connections. Applications to surfaces, 3-manifolds, and groups with Kazhdan’s property (T) will be discussed.

**Kate Ponto** (University of Kentucky)

Title: Traces for periodic point invariants

Abstract: Up to homotopy, the Lefschetz number and its refinement to the Reidemeister trace capture the essential information about fixed points of an endomorphism. These invariants can be applied to iterates of an endomorphism to describe periodic points, but in this case they provide far less complete information.

I will describe an approach to refining these invariants through refinements of the associated symmetric monoidal and bicategorical traces. This gives richer invariants that also apply to endomorphisms of spaces with more structure (such as bundles).

**John Lind** (Reed College)

Title: The transfer map of free loop spaces

Abstract: Associated to a fibration E –> B with homotopy finite fiber is a stable wrong way map LB –> LE of free loop spaces coming from the transfer map in THH. This transfer is defined under the same hypotheses as the Becker-Gottlieb transfer, but on different objects. I will use duality in bicategories to explain why the THH transfer contains the Becker-Gottlieb transfer as a direct summand. The corresponding result for the A-theory transfer may then be deduced as a corollary. When the fibration is a smooth fiber bundle, the same methods give a three step description of the THH transfer in terms of explicit geometry over the free loop space. (Joint work with C. Malkiewich)

**Teena Gerhardt **(Michigan State University)

Title: Algebraic K-theory of Pointed Monoid Algebras

Abstract: Methods in equivariant stable homotopy theory make some algebraic K-theory computations more accessible. Using these methods to compute the algebraic K-theory of pointed monoid algebras is particularly interesting, as the full power of equivariant homotopy groups is used. I will present some successes of these methods and a new approach for tackling other questions in this area. As an example of this new approach I will present some of my recent joint work with Angeltveit on the algebraic K-theory of the group ring Z[C_2].

**Paul Goerss** (Northwestern University)

Title: Qualitative Transchromatic Phenomena

Abstract: Chromatic stable homotopy theory uses the algebraic geometry of formal groups or, more generally, p-divisible groups to organize the calculations and the search for large scale phenomena. In this process there are two steps: calculations at a height and then the assembly of information from various heights. We know surprisingly little about the latter and some of what we do know has been won by very hard calculation by Shimomura, Henn, Beaudry and others, all following ideas of Hopkins. These calculations have revealed some surprising patterns. In this talk I’ll try to tell you what these are, why they matter, and give a conceptual argument that will explain where they came from.

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