Equations of tensor train varieties

Date

Apr 9, 2026

Time

3:00 PM - 4:00 PM

Speaker

Serkan Hoşten

Affiliation

San Francisco State University

Language

en

Main Topic

Biologie

Host

Local Organisers: Nikola Sadovek, Maximilian Wiesmann, Giulio Zucal

Description

Tensor train varieties are parametrized projective varieties used to approximate the solutions to the electronic Schroedinger equation in second quantization. In particular, Rayleigh-Ritz optimization on these varieties plays a prominent role. In the talk, I will use Rayleigh-Ritz optimization as a motivation to study tensor trains based on work with Borovik, Friedman, and Pfeffer. Then I will focus on the equations of the defining ideal of any tensor train variety. They consist of minors of particular flattenings of the underlying tensors and these equations were conjectured by Sturmfels in an unpublished note. The proof uses the description of the ideal of the general Markov model on trees by Draisma and Kuttler. Time permitting I will touch on Groebner bases, at least for the case of tensor trains in the space of tensors of order 3. The ongoing work on equations is with Skurt.

Last modified: Apr 9, 2026, 7:36:04 AM