SFU Number Theory and Algebraic Geometry Seminar: Nathan Ilten

Introduced by Tate in 1957, a Koszul-Tate resolution allows one to replace any algebra with a free differential graded algebra. This can be used to compute important invariants of the original algebra such as BRST cohomology or cotangent cohomology. I will report on a re-interpretation of recent work by Hancharuk, Laurent-Gengoux, and Strobl that constructs explicit Koszul-Tate resolutions. Using this, I will then discuss some work in progress on higher cotangent cohomology for quotients of polynomial rings by monomial ideals. This is joint with Francesco Meazzini and Andrea Petracci. No prior knowledge of Koszul-Tate resolutions or cotangent cohomology is assumed.