Upcoming Talks

In Spring 2025, the UChicago Algebraic Topology Seminar will meet on Tuesdays at 4:00-5:00PM in TBA and will be preceded by a pretalk 3:30-4PM (unless otherwise noted).

To receive emails about the seminar, please email Nikolai Konovalov requesting to be subscribed to our mailing list.

• • Mar 252025

  Leor Neuhauser (Hebrew University of Jerusalem)

  Rigid algebras in $(\infty,2)$-categories

  Rigid monoidal categories have found recent use in a wide variety of applications, from geometric Langlands to continuous K-theory and condensed mathematics. Generalizing to an arbitrary symmetric monoidal $(\infty, 2)$-category, this talk concerns rigid algebras, which can be viewed as categorified Frobenius algebras. By bootstrapping this definition we will study the full $(\infty, 2)$-subcategory of rigid algebras, and see that it is in fact an $(\infty, 1)$-category. On the other hand, given an $(\infty, 1)$-category $C$ with finite colimits one can define a symmetric monoidal $(\infty, 2)$-category of cospans in $C$. We will see that under some restrictions those two constructions are adjoint.

  The pretalk will concern Frobenius algebras and rigid monoidal categories. In the main talk we will review $(\infty, 2)$-categories, define and study rigid algebras, and present the connection with cospans.

If you have any questions, please contact Toni Annala, Nikolai Konovalov, Akhil Mathew, Tomer Schlank, or Peter May.