UC Berkeley

Commutative Algebra and Algebraic Geometry Seminar

April 19, 2011

939 Evans Hall

3:45PM: Equivariant Chow Groups

Charley Crissman

Given an algebraic group $G$ and an action of $G$ on an algebraic variety $X$, one can build ``equivariant Chow groups" from the invariant cycles on $X$, modulo $G$-invariant rational equivalence. Unfortunately, this construction lacks many desirable properties; for example, it may be impossible to define an intersection product even in the case that $X$ is smooth. Following Edidin and Graham, I will present a different construction of the equivariant Chow groups based on ideas from equivariant cohomology. These groups have the nice properties of the usual Chow groups, and have the additional advantage that they frequently agree with the Chow groups of the quotient X/G. My talk will consist mostly of definitions and examples. In particular, I will outline a computation of the Chow ring of the stack $M_{1,1}$.

5:00PM: Matrix factorizations in the non-affine case

Daniel Pomerleano

I will survey some recent developments in the theory of matrix factorization categories, describing some new points of view on these categories and how they facilitate the calculation of Hochschild invariants, the description of generating objects and understanding when these matrix factorization categories are Calabi Yau categories. The story will be told from the beginning, so listeners need not know much about matrix factorizations or much else. In particular, while our motivations for considering these categories come from 2d Topological Quantum Field Theory, I will try to give just a flavor of that. I will end by describing some questions we have been thinking about more recently that may be of interest and that we would love to know the answer to. This is joint work with Kevin Lin.

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