Generic Border Subrank

by Chia-Yu Chang

Tuesday Mar 11, 2025, 11:00 AM → 12:00 PM Europe/Paris

Salle Picard (IMT)

The subrank and border subrank play central roles in several areas including algebraic complexity theory, quantum information theory, and combinatorics. In this talk, I will define subrank and border subrank of tensors, which are generalizations of matrix rank and first introduced by Strassen. The rank and border rank of a generic tensor are the same and equal to the maximal border rank. However, we know less about the behavior of the subrank and border subrank. I will state the main result that the growth rate of the generic subrank is the same as the growth rate of the generic border subrank. Then I will give an idea of proof of the main result. This is joint work with Benjamin Biaggi, Jan Draisma, and Filip Rupniewski.