Sino-Russian Mathematics Center-JLU Colloquium (2024-035)—Noncommutative Poisson structure and invariants of matrices

Title: Noncommutative Poisson Structure and Invariants of Matrices
Speaker: Farkhod Eshmatov
Institution: New Uzbekistan University
Date & Time: December 5, 2024, 16:20–18:20
Location: Seminar Room 5, Mathematics Building, Jilin University

We introduce a novel approach utilizing techniques from noncommutative Poisson geometry to study the algebra of invariants of two $n\times n$ matrices. We completely resolve the open problem of computing the algebra of invariants for two $4\times 4$ matrices. As an application, we derive a complete description of the invariant commuting variety of $4\times 4$ matrices and the fourth Calogero-Moser space. This is joint work with X. García-Martínez and R. Turdibaev.

Professor Farkhod Eshmatov is the Director of the Department of Mathematics at New Uzbekistan University. His research focuses on noncommutative algebraic geometry and mathematical physics.