Workshop on Recent Developments in Hodge Theory and O-minimality

Abstract: We study a non-commutative counterpart $C_n(X)$ of the symmetric product $Sym^n X$ of a space $X$, defined as the space of nxn-matrix valued points on $X$. Our main result will be a precise formula for the cohomology of this space in great generality, but we see this as the first step in a wider non-commutative world. In particular, there is an appealing analogy with Weil restriction that we hope is illuminating and a taste of possible future directions. 

This is joint work with Yifeng Huang, Ruofan Jiang and Yifan Wei (who is on the job market and drove much of this current research!).