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#### Hauptseminar Geometrie

„Parametrizing spaces of positive representations“
Dr. Eugen Rogozinnikov, Université Strasbourg, Frankreich

Hauptseminar Geometrie "Parametrizing spaces of positive representations" Dr. Eugen Rogozinnikov Université de Strasbourg, Frankreich Abstract: The theory of generalized Lusztig’s positivity (or $\Theta$-positivity) developed by O. Guichard and A. Wienhard generalizes the total positivity for split real Lie groups and the maximality for Hermitian Lie groups to a larger class of simple Lie groups (e.g. $\SO(p,q)$, $p \neq q$, some exceptional Lie groups). Lie groups $G$ with a positive structure are of particular interest in the higher Techmüller theory because the representation space $\Hom(\pi_1(S),G)/G$, where $S$ is an orientable surface of finite type, admits connected components that consist entirely of discrete and faithful representations (so-called higher rank Teichmüller spaces). In my talk, I explain how the spaces of positive framed representations of the fundamental group of a punctured surface into a Lie group with a positive structure can be parametrized, and how we can describe the topology of this spaces using this parametrization. This is a joint work with O. Guichard and A. Wienhard. Dienstag, den 26. Juli 2022 um 13.00 Uhr, SRB, EG, INF 205 Before the seminar, starting at 12:15, there will be sandwiches and drinks for everyone in the foyer at the basement.

Dienstag, den 26. Juli 2022 um 13:00 Uhr, in INF205, SRB Dienstag, den 26. Juli 2022 at 13:00, in INF205, SRB

Der Vortrag folgt der Einladung von The lecture takes place at invitation by Prof. A. Wienhard, Prof. P. Albers