Topology Seminar
Upcoming Talks
The seminar will meet at 4:00pm on Tuesdays in Eckhart room 203 unless otherwise noted. There will also be a pretalk at 2:30pm in the same room.
To receive emails about the seminar, please subscribe to our mailing list by sending an email.

Jun Hou Fung (Harvard)
Strict units of commutative ring spectra
Just as an ordinary commutative ring has a multiplicative group of units, a E_\inftyring spectrum R also has a spectrum of units gl_1 R, which plays an important role for example in orientation theory and twisted cohomology theories. However, these spectra are typically very large, and to understand twists by EilenbergMac Lane spaces or to isolate those units that come from geometry, it sometimes suffices to study the space of \emph{strict units} of R. Previously, Hopkins and Lurie have computed the strict units of Morava Etheories, but much remains unknown about them in general. In this talk, I will introduce these strict units and illustrate various methods for computing them, and sketch how these calculations relate to other interesting questions in homotopy theory.

Yu Zhang (Ohio State)
TBA
TBA

Tim Campion (Notre Dame)
Duality in homotopy theory
We explore some implications of a fact hiding in plain sight: Namely, the nsphere has the remarkable property that the “swap” map σ: Sn ∧ Sn → Sn ∧ Sn can be “untwisted”: it is homotopic to (1)n ∧ 1. This simple fact remains true in equivariant and motivic contexts. One consequence is a structural fact about symmetric monoidal ∞categories with finite colimits and duals for objects: it turns out that any such category splits as the product of three canonical subcategories (for instance, one of these subcategories is characterized by being stable). As another consequence, we show that for any finite abelian group G, the symmetric monoidal ∞category of genuine finite Gspectra is obtained from finite Gspaces by stabilizing and freely adjoining duals for objects. This universal property vindicates one motivation sometimes given for studying genuine Gspectra: namely that genuine Gspectra (unlike naive Gspectra or Borel Gspectra) have a good theory of SpanierWhitehead duality. We take steps toward a similar universal property for nonabelian groups and also in motivic homotopy theory.

Christy Hazel (University of Oregon)
TBA
TBA

Candace Bethea (University of South Carolina)
TBA
TBA
If you have any questions, please contact Hana Jia Kong or XiaoLin Danny Shi.