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

September 6

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

September 20

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

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

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

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

singularities.

Past Analysis Seminar