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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Ergodic Theory and Semisimple Groups
遍历理论 半简单群 马古利斯超刚性定理
2023/4/13
We go through Zimmer's book Chapter 2-3, making some preparations for Margulis super-rigidity theorem.
Diophantine approximation with restricted numerators and denominators on semisimple groups
Diophantine approximation restricted numerators and denominators semisimple groups Dynamical Systems
2012/5/25
We consider the problem of Diophantine approximation on semisimple algebraic groups by rational points with restricted numera- tors and denominators and establish a quantitative approximation result f...
Special representations of nilpotent Lie groups and the associated Poisson representations of current groups
Current group canonical representation special representation
2012/4/18
In this paper we describe the new model of the representations of the current groups with a semisimple Lie group of the rank one. In the earlier papers of 70-80-th (Araki, Gelfand-Graev-Vershik) had p...
More Universal Minimal Flows of Groups of Automorphisms of Uncountable Structures
Dynamical Systems
2012/4/17
In this paper, we compute universal minimal flows of groups of automorphisms of uncountable $\omega$-homogeneous graphs, $K_n$-free graphs, hypergraphs, partially ordered sets, and their extensions wi...
Generic representations of abelian groups and extreme amenability
Unitary representations measure-preserving actions Urysohn space extremely amenable group Polish group Baire category
2011/8/31
Abstract: If $G$ is a Polish group and $\Gamma$ is a countable group, denote by $\Hom(\Gamma, G)$ the space of all homomorphisms $\Gamma \to G$. We study properties of the group $\cl{\pi(\Gamma)}$ for...
Stable orbit equivalence of Bernoulli actions of free groups and isomorphism of some of their factor actions
Stable orbit equivalence Bernoulli actions isomorphism Dynamical Systems Group Theory
2011/8/26
Abstract: We give an elementary proof for Lewis Bowen's theorem saying that two Bernoulli actions of two free groups, each having arbitrary base probability spaces, are stably orbit equivalent. Our me...
Minimal hyperspace actions of homeomorphism groups of h-homogeneous spaces
Minimal hyperspace actions universal minimal space h-homogeneous homogeneous Boolean algebra maximal chains generalized Cantor sets
2011/8/29
Abstract: Let X be a h-homogeneous zero-dimensional compact Hausdorff space, i.e. X is a Stone dual of a homogeneous Boolean algebra. Using the dual Ramsey theorem and a detailed combinatorial analysi...
Non abelian tensor square of non abelian prime power groups
Tensor square non abelian p-groups
2011/2/22
For every p-group of order pn with the derived subgroup of order pm, Rocco in [7] has shown that the order of tensor square of G is at most pn(n−m). In the present paper not only we improve his ...
Nielsen equivalence of generating sets for closed surface groups
Nielsen equivalence of generating sets closed surface groups
2010/11/29
Generating sets for closed surfaces are either reducible or Nielsen equivalent to a standard generating set.