Matrix Points on Varieties

Time：Thursday, 14:00-15:00 Oct. 30, 2025

Venue：C548, Shuangqing Complex Building

Organizer：Zhiwei Zheng

Speaker：Yifan Wei

Organizer：

Zhiwei Zheng 郑志伟

Speaker：

Yifan Wei

University of Wisconsin – Madison

Time：

Thursday, 14:00-15:00

Oct. 30, 2025

Venue：

C548, Shuangqing Complex Building

Title:

Matrix Points on Varieties

Abstract:

We study the cohomology of the moduli space Cn(X) of matrix points on a variety X, which we think of as non-commutative Weil restriction from the algebra of n-by-n matrices to the ground field. To achieve this, we constructed a more combinatorial space Sn(X), which is birationally isomorphic to Cn(X). Via a crucial application of base change for good moduli morphisms, we show that these two spaces have the same cohomology, and derive a nice combinatorial formula for the cohomology of Cn(X), validating the Weil restriction heuristic.

DATEOctober 29, 2025

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