Analysis   Seminar    

Unless specified, all seminars are Wednesday 4-5pm at Room 250. 

September 6                 Jintao Deng,   SUNY at Buffalo                                                 
The equivariant coarse Baum-Connes conjecture Part I

                                      Abstract: The equivariant coarse Baum-Connes conjecture claims that a certain assembly map from the equivariant K-homology of a metric space with
                                      a group action to the K-theory of the Roe algebras is an isomorphism. It has important applications in the study of the existence of Riemannian metric
                                      with positive scalar curvature. In this talk, I will talk about the concept of Roe algebras which encode the large-scale geometry of a metric space and
                                      group actions. The higher index of an elliptic operator is an element of the K-theory of this algebra. The equivariant coarse Baum-Connes conjecture
                                      provides an algorithm to compute its K-theory. I will talk about our recent result that the equivariant coarse Baum-Connes conjecture holds for a
                                      metric space with a group action under the conditions that the group is amenable and the associated quotient space is coarsely embeddable into
                                      Hilbert space. This is a joint work with Qin Wang and Benyin Fu.


September 13               Jintao Deng,   SUNY at Buffalo                                                 
The equivariant coarse Baum-Connes conjecture Part II

September 20               Min Woong Ahn,   SUNY at Buffalo                                                 
Hausdorff dimensions in Pierce expansions

The Pierce expansion is one of many real number representation systems. Shallit (1986) established the law of large numbers, the central
                                     limit theorem, and the law of the iterated logarithm of the digits of the Pierce expansions. Additionally, it was shown that the series of iterates under
                                     a mapping that yields the Pierce expansion converges Lebesgue-almost everywhere. In this talk, I will discuss the Hausdorff dimensions of such sets
                                     with Lebesgue measure zero.  

October 18                   Francesc Perera,   Universitat Autonoma de Barcelona                                              
Traces on ultrapowers of C*-algebras

Every sequence of traces on a C*-algebra A induces a limit trace on a free ultrapower of A. Using Cuntz semigroup techniques, we
                                     characterize when these limit traces are dense. Quite unexpectedly, we obtain as an application that every simple C*-algebra that is (m,n)-pure in the
                                     sense of Winter is already pure. This is joint work with Ramon Antoine, Leonel Robert, and Hannes Thiel.

October 26                   Lei Yang,   Institute for Advanced Study                                               
(Colloquium, Thu)       E
ffective versions of Ratner's equidistribution theorem

I will talk about recent progress in the study of quantitative equidistribution of unipotent orbits in homogeneous spaces, namely, effective
                                     versions of Ratner's equidistribution theorem. In particular, I will explain the proof for unipotent orbits in SL(3,R)/SL(3,Z). The proof combines new
                                     ideas from harmonic analysis and incidence geometry. In particular, the quantitative behavior of unipotent orbits is closely related to a Kakeya model.

November 1                 Jinmin Wang,   Texas A&M University                                         
Stoker's problem and index theory on manifolds with polytope singularities

The Stoker problem states that the dihedral angles of a convex Euclidean polyhedron determine the angles of each face. In this talk, I will
                                     present joint works with Zhizhang Xie and Guoliang Yu that answer positively to Stoker's problem, and prove a more general dihedral rigidity for
                                     manifolds with polytope singularities. I will briefly introduce our approach, the index theory of Dirac-type operators on manifolds with polytope
                                     singularities under certain boundary conditions. One of the key observations is the essential self-adjointness of the Dirac-type operators near conical


Past Analysis Seminar