Seminars: K. Kh. Rakhimov, Flat structure of meromorphic connections on Riemann surfaces

SEMINARS


Seminar on Modern Problems of Complex Analysis (Sadullaev Seminar) March 7, 2019 12:00, Tashkent, National University of Uzbekistan, Room A304 (Department of Mathematics)

Flat structure of meromorphic connections on Riemann surfaces K. Kh. Rakhimov University of Pisa
Abstract: One of the main open problems in local dynamics of several complex variables is the understanding of the dynamics, in a full neighborhood of the origin, of holomorphic germs tangent to the identity. In dimension one, the Leau-Fatou flower theorem provides exactly such an understanding. A few generalizations to several variables of the Leau-Fatou flower theorem have been proved, but none of them was strong enough to be able to describe the dynamics in a full neighborhood of the origin. Abate and Tovena, in 2011, has been able to show a strong relation between dynamics of time-1 maps of homogeneous vector fields in $\mathbb{C}^n$ and dynamics of geodesics of meromorphic connections of Riemann surfaces. In this talk, we will talk about our resent results on dynamics of geodesics of meromorphic connections on Riemann surfaces. Language: English