# Seminar at SMU Delhi

July 29, 2020 (Wednesday) , 3:30 PM at Webinar
Speaker: Hemant Kumar Mishra, ISI Delhi
Title: Fenchel subdifferentials and first-order directional derivatives of symplectic eigenvalues.
Abstract of Talk
For every $2n \times 2n$ positive definite matrix $A$ there exist $n$ positive numbers $d_1(A) \leq d_2(A) \leq \cdots \leq d_n(A)$ called the symplectic eigenvalues of $A$. It is known that the symplectic eigenvalue maps $d_1, d_2,...,d_n$ are continuous but not differentiable in general. We will show that the Fenchel subdifferential of the sum of the symplectic eigenvalue maps $d_1+d_2+...+d_m$ exists for all $m \leq n$, and find their expressions. We also prove the existence of the first-order directional derivatives of the symplectic eigenvalue maps and derive their expressions.