Speaker: Dmitry Talalaev (MSU, YarSU, ITEP)

Date and time:  7.06.2023, 17:00 (GMT +03:00)

Title: Polynomial graph invariants, Sturm criterion, hyperbolic stability and total positivity

Abstract: I will talk about various manifestations of the phenomenon of total positivity in such seemingly remote areas as polynomial invariants of graphs, problems of localization of the roots of a polynomial, the geometry of flag varieties. Nevertheless, in all these problems, the condition we are interested in is expressed in terms of total positivity, or n-positivity, of some auxiliary matrix: Toeplitz matrix, Hankel matrix, or Sturm matrix, depending on the problem.

In particular, I will talk on logarithmic concavity of the conditional flow and chromatic polynomial and the criterion of hyperbolic stability of a polynomial.

The report is based on several joint works with B. Bychkov, D. Golitsyn, A. Kazakov, A. Kutuzova, E. Lerner and S. Mukhamedzhanova.

To access the online seminar please contact  Anna Tolbey bekvaanna@gmail.com