## Algebra

•  Noncommutative resolutions and intersection cohomology for quotient singularities
•  02/10/2021
•  4:00 PM - 5:00 PM
•  Online (virtual meeting) (Virtual Meeting Link)
•  Laure Flapan (flapanla@msu.edu)

It is an important problem to define a K-theoretic version of intersection cohomology, with expected applications in representation theory. One step further is to look for a categorification of intersection cohomology. For good moduli spaces $X$ of Artin stack $Y$ (as defined by Alper), we construct some noncommutative resolutions $D(X)$ inside the category $D^b(Y)$. Further, we construct subcategories $I(X)$ of $D(X)$ whose periodic cyclic homology is given by the intersection cohomology of $X$. In particular, the K-theory of $I(X)$ is a natural definition of intersection K-theory for the variety $X$. Passcode: MSUALG

## Contact

Department of Mathematics
Michigan State University