Speaker: Prof. Jialun Li (École Polytechnique)

Time: 14:30-16:00  Nov. 14 (Tuesday), Nov. 16 (Thursday), Nov. 21 (Tuesday)

Place: MCM110 & Online (Zoom ID: 3329836068  Password: mcm1234)

Title: On the dimension of limit sets on the real projective plane via stationary measures

Abstract: I will present a dimension jump result of limit sets on RP^2 for representations of surface groups in SL(3,R). For Anosov representations, we prove the equality between the Hausdorff dimension and the affinity exponent. In particular, it exhibits a dimension jump under perturbation. The key tool is to study the stationary measures of finitely supported random walks on SL(3,R). We show the Hausdorff dimensions equal the Lyapunov dimensions under certain assumption. This is based on ongoing joint work with Wenyu Pan and Disheng Xu.

In the minicourse, I will also explain the two main ingredients of the proof: the entropy growth argument due to Hochman and the variational principle of the affinity exponent.

Speaker: Prof. Enlin Yang (Peking University)

Time: 10:30-11:30am, November 15, 2023 (Wednesday)

Place: MCM110

Title: Cohomological Milnor formula for constructible etale sheaves

Abstract: In this talk, we will sketch the construction of non-acyclicity classes for constructible etale sheaves on (not necessarily smooth) varieties, which is defined in a recent joint work with Yigeng Zhao. This cohomological class is supported on the non-locally acyclicity locus. As applications, we show that the Milnor formula and Bloch's conductor formula can be reformulated in terms of the functorial properties of non-acyclicity classes. Based on this formalism, we propose a Milnor type formula for non-isolated singularities.