|Date: Thursday, June 09, 2022
Location: Zoom: https://umich.zoom.us/j/96958211771?pwd=bmczN0JZa3RmREJNUndENlMvc3E2QT09 Passcode: 220609 Virtual (1:00 PM to 3:00 PM)
Title: Tensors, Cap Set and Invariant Theory
Abstract: G-stable rank is a new notion of tensor rank introduced by Harm Derksen. This thesis considers the applications of G-stable rank to the Cap Set Problem and invariant theory. We improve Ellenberg and Gijswijt’s best known upper bound for the Cap Set Problem and obtain more explicit bounds. We also define the symmetric G-stable rank for symmetric tensors, and show an analog of Comon's conjecture. As a consequence, we study the stability of symmetric tensors in invariant theory. Finally, we show that the log-canonical threshold of a singularity is bounded by the G-stable rank of the defining ideal.
Zhi's advisors are Harm Derksen and Karen Smith.
Speaker: Zhi Jiang