## EVENT DETAILS AND ABSTRACT

**Topology Seminar**
**Title:** Algebraic and geometric cobordism

**Speaker:** Toni Annala

**Speaker Info:** IAS

**Brief Description:**

**Special Note**:

**Abstract:**

In my thesis, I constructed a cohomology theory of schemes called algebraic cobordism Ω^*, extending the similarly named theory of Levine--Morel from smooth varieties in characteristic 0 to all finite-Krull-dimensional Notherian schemes admitting an ample line bundle. This is a non-A^1-invariant cohomology theory that is closely related to the (higher) algebraic cobordism MGL that is constructed in recent work with Marc Hoyois and Ryomei Iwasa. In particular, we expect that Ω^n(X) = MGL^{2n,n}(X) whenever both sides are well defined. I will discuss results about Ω^* related to this comparison, and explain why obtaining the desired isomorphism, or an interesting weakening of it, seems hopeless unless someone has a smart idea, or alternatively someone proves resolution of singularities in positive characteristic.

**Date:** Monday, April 10, 2023

**Time:** 4:00pm

**Where:** Lunt 104

**Contact Person:** Benjamin Antieau

**Contact email:** antieau@northwestern.edu

**Contact Phone:** 847-491-5544

Copyright © 1997-2024
Department of Mathematics, Northwestern University.