The Midwest Topology Seminar in Fall 2021 will be held in an online format. Two 1-hour talks will be separated by a networking event to support job applicants and employers.
Schedule
Thursday November 18 (all times eastern)
1:00-2:00pm, Michael Mandell (Indiana University)
2:15-2:45pm, Networking Event Session 1: Robert Burklund, Zachary Himes, Robert Housden, Ang Li, Stephen McKean, David Mehrle, Sarah Petersen, Emma Phillips, Elizabeth Tatum
2:45-3:15pm, Networking Event Session 2: Katharine Adamyk, Guy Boyde, Matt Feller, Andrei Konovalov, J.D. Quigley, Kelly Pohland, Joseph Rennie, Carissa Slone
3:20-4:20pm: Jenny Wilson (University of Michigan)
Networking Event
As a service to those who are seeking employment and to those who are offering employment, we are planning an online networking event. People with interests in algebraic topology and related fields are welcome to present.
Here’s how the event will work. Presenters will submit 5-10 minute videos that describe their research. These are like video versions of research statements. The videos will be posted on the Junior Mathematician Research Archive (JMRA). Prior to the event, potential employers (and other interested participants) will have the opportunity to view these videos.
During the event, each presenter will have an individual breakout room. Participants will be able to move themselves between breakout rooms and will be able to see who is in other rooms. The breakout rooms will provide an opportunity for small group conversation and one-on-one interaction. (Note: Breakout room functionality works imperfectly with a smartphone or tablet. It’s best to use a computer for this.)
Applications for presenters are due on Friday October 8. Organizers will notify applicants about the status of their applications by Friday October 15. Video research summaries must be submitted to JMRA by Monday October 25, and they will be posted by Monday November 1.
Registration
Registration is required only for job applicants who wish to present in the networking event.
Abstracts
Speaker: Michael Mandell, Indiana University
Title: Toward HHR norms and equivariant factorization homology for compact Lie groups
Abstract: The Hill-Hopkins-Ravenel norm for finite groups is a powerful technical tool and is now an intrinsic part of the foundations of equivariant stable homotopy theory. Beyond finite groups, we currently only know a construction of the norm for 1-dimensional compact Lie groups, and the relationship to THH hints that the norm for higher
dimensional compact Lie groups could open up exciting new directions in the subject. The norm is also the starting point for a genuine theory of equivariant factorization homology, and vice versa. This talk will be mostly background and discuss a preliminary project (joint with Andrew Blumberg) to adapt the proofs of foundational
theorems in factorization homology to better accommodate equivariant generalizations for positive dimensional compact Lie groups.
Speaker: Jenny Wilson, University of Michigan
Title: The high-degree rational cohomology of the special linear group
Abstract: In this talk I will describe some current efforts to understand the high-degree rational cohomology of SL_n(Z), or more generally the cohomology of SL_n(R) when R is a number ring. Although the groups SL_n(R) do not satisfy Poincare duality, they do satisfy a twisted form of duality, called Bieri-Eckmann duality. Consequently, their high-degree rational cohomology groups are governed by an SL_n(R)-representation called the Steinberg module. The key to understanding these representations is through studying the topology of certain associated simplicial complexes. I will survey some results, conjectures, and ongoing work on the Steinberg modules, and the implications for the cohomology of the special linear groups. This talk includes work joint with Brück, Kupers, Miller, Patzt, Sroka, and Yasaki. The talk is geared for topologists and will not assume prior expertise on the cohomology of arithmetic groups!
Organizers
Mark Behrens, Robert Bruner, Paul Goerss, Christy Hazel, Dan Isaksen, and Vesna Stojanoska
Acknowledgement
Special thanks to the Junior Mathematician Research Archive (JMRA) for hosting the video research summaries for this event.
Previous seminars
Winter/Spring 2021 Midwest Topology Seminar