The **Winter Midwest Topology Seminar** will take place at **Northwestern University**, in **Evanston, IL**, on **Saturday, March 3, 2018**.

**Registration:** You can register here.

**Funding:** A small amount of funding is available for graduate students, postdocs, and those without other sources of support. The deadline for applying for funding is Friday, February 2.

**Local information:** Talks will take place at **Swift Hall, room 107**. Here's a map of the area.

We have a special rate at The Homestead hotel. Just mention that you'll be participating in the Midwest Topology Seminar at Northwestern when you book your rooms. The rooms are not being held, so reserve them as soon as you can!

**Schedule:**

**9:30-10:00**Registration and coffee**10:00-11:00**Akhil Mathew,*Rigidity in algebraic*K*-theory and topological cyclic homology***11:30-12:30**Bhargav Bhatt,*Topological Hochschild homology and*p*-adic cohomology***12:30-3:00**Lunch**3:00-4:00**Mona Merling,*Towards the equivariant stable parametrized*h*-cobordism theorem***4:30-5:30**Nat Stapleton,*The character of the total power operation***6:30**Reception

**Speakers and abstracts:**

Akhil Mathew
(website)
Rigidity in algebraic *K*-theory and topological cyclic homology

We show that for a henselian pair *(R, I)*, the relative *K*-theory and relative topological cyclic homology with mod *p* coefficients agree. This yields a generalization of the Gabber-Gillet-Suslin-Thomason rigidity theorem (when *p* is invertible on the ring) and the Dundas-McCarthy theorem (when *I* is nilpotent). This recovers several computations in *p*-adic algebraic *K*-theory and leads to some new structural results. Our methods are based on the new description of the homotopy theory of cyclotomic spectra given by Nikolaus and Scholze. This is joint work with Dustin Clausen and Matthew Morrow.

Bhargav Bhatt
(website)
Topological Hochschild homology and *p*-adic cohomology

I will give an overview of my joint work with Matthew Morrow and Peter Scholze giving precise relations between topological Hochschild homology and integral *p*-adic cohomology theories arising in arithmetic geometry (such as crystalline cohomology or the recently constructed *A*_{inf}-cohomology). Instead of giving the most general possible results, I will try to emphasize certain features of *p*-adic cohomology theories that are most easily seen through the topological perspective

Mona Merling (website)
Toward the equivariant stable parametrized *h*-cobordism theorem

Waldhausen's introduction of *A*-theory of spaces revolutionized the early study of pseudo-isotopy theory. Waldhausen proved that the *A*-theory of a manifold splits as its suspension spectrum and a factor *Wh(M)* whose first delooping is the space of stable *h*-cobordisms, and its second delooping is the space of stable pseudo-isotopies. I will describe a joint project with C. Malkiewich aimed at telling the equivariant story if one starts with a manifold *M* with group action by a finite group *G*.

Nat Stapleton (website) The character of the total power operation

In the 90's Goerss, Hopkins, and Miller proved that the Morava *E*-theories are *E*_{∞}-ring spectra in a unique way. Since then several people including Ando, Hopkins, Strickland, and Rezk have worked on explaining the effect of this structure on the homotopy groups of the spectrum. In this talk, I will present joint work with Barthel that shows how a form of character theory due to Hopkins, Kuhn, and Ravenel can be used to reduce this problem to a combination of combinatorics and the *GL _{n}(*

**Q**

*-action on the Drinfeld ring of full level structures which shows up in the local Langlands correspondence.*

_{p})**Contact us:** Lauren Bandklayder, Sam Nariman, Paul VanKoughnett.