Back to Commutative Algebra Seminar: Spring 2019
Commutative Algebra Seminar
Date: Tuesday, Mar 19, 2019
Time: 3:30PM - 4:30PM
Location: LCB 222
Jonathan Campbell
Vanderbilt University
Title |
Bicategorical duality theory with applications to topology and algebra |
Abstract |
In this talk I’ll describe how a bicategorical gadget, called the shadow, allows one to extract many interesting algebraic and topological invariants. For example, in algebraic bicategories, one easily recovers group characters, and in certain topological categories, one recovers the Lefschetz number. I’ll describe joint work with Kate Ponto generalizing work of Ben-Zvi–Nadler which allows us to simultaneously recover the Lefschetz theorem for DG-algebras due to Lunts and the theory of 2-characters due to Ganter Kapranov, along with many other results. Prerequisites: An appetite for category theory (but I will not assume knowledge of bicategories!). There will be some motivation from stable homotopy theory, but one need only believe in the stable homotopy category, not have knowledge of it. |
Commutative Algebra