The **Winter Midwest Topology Seminar** will take place at **UIUC**, in **Urbana-Champaign, IL**, on **Saturday, February 23, 2019**.

**Registration:** You can register here. If you are requesting funding, please indicate as much on the registration form. Also, please register, regardless if you are requesting funding, to help us get enough refreshments for the conference.

**Funding:** A small amount of funding is available for graduate students, postdocs, and those without other sources of support. To be fully considered for funding, please register by **January 20th**. If you have other sources of funding, we encourage you to use it, so that our limited funding can be used to support others.

**Location:** The main conference talks will take place in 314 Altgeld Hall, 1409 W. Green Street, Urbana, IL. Refreshments will be available in 239 Altgeld Hall. Here is a **campus map** and here is a google map with potential **points of interest**.
The Illinois campus and surrounding Urbana-Champaign area is pretty walkable, but is also serviced by public transportation. A bus ride costs $1, and maps and schedules can be found here.

**Local information:** We have reserved a block of rooms at a discounted rate at the Hampton Inn. These can be accessed via the following link. Additionally, you could also book a room at the Illini Union or at TownePlace Suites.

**Schedule:** Talks will occur between the times 10a-5p, with coffee and lunch breaks. Details forthcoming.

**9:00-10:00**Registration, coffee, and Breakfast**10:00-11:00**Anna Marie Bohmann,*A multiplicative comparison of Segal and Waldhausen K-theory***11:30-12:30**Jim Davis,*Assembly Maps***12:30-2:30**Lunch**2:00 - 2:30**Coffee**2:30-3:30**Evangelia Gazaki,*On the product of homotopy invariant sheaves and an application to zero-cycles on products of elliptic curves***4:00-5:00**Jay Shah,*The genuine stabilization of a G-topos*

**Speakers:**

Jim Davis

Evangelia Gazaki

Jay Shah

**Titles and Abstracts:**

Jim Davis (website) Assembly Maps

There will be four parts to this talk. (1) I will explain the Davis-Lück approach to assembly maps via groupoids and the orbit category. (2) I will explain the notion of an isomorphism conjecture, the prototypical one being the Farrell-Jones Conjecture. (3) I will talk some recent computations (joint with Wolfgang Lück) of the structure group of BG and connections with equivariant topological K-theory. (4) I will discuss work in progress with Carmen Rovi about a local-to-global bordism approach to the assembly map in L-theory and applications to the Farrell-Jones Conjecture.

Evangelia Gazaki (website) On the product of homotopy invariant sheaves and an application to zero-cycles on products of elliptic curves

B. Kahn and T. Yamazaki recently defined a new abelian category with objects homotopy invariant sheaves with transfers. Distinguished objects in this category arise from abelian varieties, torii and groups of zero-cycles on smooth projective varieties. This category has a product, which has significant applications to algebraic geometry, namely to the theory of zero-cycles. The purpose of my talk will be to present such a geometric application. In a recent joint work with Isabel Leal, we obtain some finiteness results about the Chow group of zero-cycles, CH_0(E_1\times E_2), on a product of elliptic curves, verifying in this case a very open conjecture of Colliot-Thelene.

Anna Marie Bohmann (website) A multiplicative comparison of Segal and Waldhausen K-theory

In influential work of the 70s and 80s, Segal and Waldhausen each construct a version of K-theory that produces spectra from certain types of categories. These constructions agree, in the sense that appropriately equivalent categories yield weakly equivalent spectra. In the 2000s, work of Elmendorf--Mandell and Blumberg--Mandell produced more structured versions of Segal and Waldhausen K-theory, respectively. These versions are "multiplicative," in the sense that appropriate notions of pairings of categories yield multiplication-type structure on their resulting spectra. In this talk, I will discuss joint work with Osorno in which we show that these constructions agree as multiplicative versions of K-theory. Consequently, we get comparisons of rings spectra built from these two constructions. Furthermore, the same result also allows for comparisons of related constructions of spectrally-enriched categories.

Jay Shah (website) The genuine stabilization of a G-topos

Let G be a finite group and X a topos with homotopy coherent G-action. From this, we construct a stable homotopy theory Sp^G(X) which recovers and extends the theory of genuine G-spectra. We explain what our construction yields when: (i) X is the topos of sheaves on a topological space with G-action (ii) X is the etale C_2-topos of a scheme S adjoined a square root of -1. We conclude with an application to realization functors out of the stable motivic homotopy category of a scheme. This is joint work with Elden Elmanto.

**Travel Information**
The closest airport is CMI, University of Illinois Willard Airport. From there one would have to take a taxi to campus. More often than not, flying to Chicago's O'Hare airport is the most convenient option, and there is a direct bus service to Champaign-Urbana, run by Peoria Charter, with a stop directly in front of the math building (Altgeld Hall) where the conference will be held.

**Parking Information**
One can find parking information provided by the University of Illinois **here**. Additionally one can park in garage C7 (on John and 5th). This is the closest parking garage to Altgeld Hall and no permit is required to park there from 5p Friday to 6a Monday.

**Contact us:** Dominic Culver, Jeremiah Heller, Charles Rezk, Vesna Stojanoska.