Matrix Points on Varieties

We study a non-commutative counterpart Cn(X) of the symmetric product SymnX 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!).