Status Confirmed Seminar Series MATH-IHES 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 rank-k 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 Benoist-Quint. A key step/result in this study is the classification of stationary measures on $X_{d,d}$. Later, Sargent-Shapira 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$which is Zariski-dense in a copy of SL(2,R) in G, we give a classification of$\mu$-stationary measures on$X_{k,d}$and prove corresponding equidistribution results. In contrast to the results of Benoist-Quint, the type of stationary measures that$\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

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