Status  Confirmed 
Seminar Series  MATHIHES 
Subjects  math 
Date  Monday 3 October 2022 
Time  16:00 
Institute  IHES 
Seminar Room  Amphithéâtre Léon Motchane 
Speaker's Last Name  Sert 
Speaker's First Name  Cagri 
Speaker's Email Address  
Speaker's Institution  Universität Zürich 
Title  Stationary Measures for SL(2,R)actions on Homogeneous Bundles over Flag Varieties 
Abstract  Let $X_{k,d}$ denote the space of rankk lattices in $R^d$. Topological and statistical properties of the dynamics of discrete subgroups of G=SL(d,R) on $X_{d,d}$ were described in the seminal works of BenoistQuint. A key step/result in this study is the classification of stationary measures on $X_{d,d}$. Later, SargentShapira initiated the study of dynamics on the spaces $X_{k,d}. When $k \ne d$, the space $X_{k,d}$ is of a different nature and a clear description of dynamics on these spaces is far from being established. Given a probability measure $\mu$ which is Zariskidense in a copy of SL(2,R) in G, we give a classification of $\mu$stationary measures on $X_{k,d}$ and prove corresponding equidistribution results. In contrast to the results of BenoistQuint, the type of stationary measures that $\mu$ admits depends strongly on the position of SL(2,R) relative to parabolic subgroups of G. I will start by reviewing preceding major works and ideas. The talk will be accessible to a broad audience. Joint work with Alexander Gorodnik and Jialun Li. 
arXiv Preprint Number  
Comments  Séminaire Géométrie et groupes discrets 
Attachments 
To Generate a poster for this seminar : [ Postscript  PDF ]

[ English version ] 