Speaker: Hamoon Mousavi (UC Berkeley)
Title: Two Open Problems in Noncommutative Polynomial Optimization
Abstract:
In recent years, the theory of noncommutative polynomial optimization has seen rapid progress, driven in part by questions arising from quantum information. This emerging theory often mirrors the well-established theory of commutative polynomial optimization, itself a landmark achievement in theoretical computer science. My talk at IQUIST on Tuesday will explore these tight analogies.
Despite these advances, several key gaps remain in the noncommutative theory. In this talk, I will propose two open problems that I consider critical missing pieces:
1. the noncommutative Grothendieck inequality in the unbounded-dimensional setting, and
2. the "noncommutative plurality is the stablest" conjecture.
I will motivate these problems from a purely mathematical perspective, and I will present them as standalone problems without delving into their broader connections to quantum information topics such as nonlocal games, MIP*, quantum constraint satisfaction problems, Bell inequalities, quantum correlations, or the Tsirelson problem. Some versions of these problems appear in my joint works with Eric Culf and Taro Spirig: arxiv:2312.16765 and arxiv:2409.20028.
About the seminar: Weekly seminar hosted by the Quantum Working Group. Topics include quantum information theory and related topics in operator algebra. Contact: Felix Leditzky (leditzky@illinois.edu)