Events for 01/20/2023 from all calendars

Student/Postdoc Working Geometry Seminar

Time: 1:00PM - 2:30PM

Location: BLOC 628

Speaker: Tim Seynnaeve

Title: Signature tensors and their representation theory

Abstract: In stochastic analysis, the k-th signature of a path is a k-way tensor which encodes information about the path in a compact form. When the path varies, the signatures parametrize a subvariety of tensor space, giving a connection to algebraic geometry. In this talk I will present some recent results on varieties on signature tensors, and report on some work in progress (joint with Carlos Amendola, Francesco Galuppi, Angel Rios, and Pierpaola Santarsiero), where we look at these varieties through the lens of representation theory.

Geometry Seminar

Time: 4:00PM - 5:00PM

Location: BLOC 302

Speaker: Tim Seynnaeve

Title: Matrix product states, geometry, and invariant theory

Abstract: Matrix product states play an important role in quantum information theory to represent states of many-body systems. They can be seen as low-dimensional subvarieties of a high-dimensional tensor space. In this talk, I will introduce two variants: homogeneous matrix product states and uniform matrix product states. Studying the linear spans of these varieties leads to a natural connection with invariant theory of matrices. For homogeneous matrix product states, a classical result on polynomial identities of matrices leads to a formula for the dimension of the linear span, in the case of 2x2 matrices. I will explain this connection, and the difficulties that arise when generalizing it to the case of uniform matrix product states. This talk is partially based on joint work with Claudia De Lazzari and Harshit Motwani.