I am the organizer of functional analysis seminar in the Department of Mathematics at University of Georgia.

**Analysis Seminar-2021 **Fall:

For more details such as schedule and speakers, please go to Department of Mathematics.

**Analysis Seminar-2021 Spring**:

**Feb 24, 2021-Speaker: Jintao Deng(University of Waterloo) **

Title: The coarse Baum-Connes conjecture for certain relative expanders.

Abstract: In 2000, G. Yu verified the coarse Baum–Connes conjecture for any metric spaces which admit a coarse embedding Hilbert spaces. However, there are counterexamples which are not coarsely embeddable into Hilbert spaces. Those counterexamples are so-called relative expanders. In a joint work with Qin Wang and Guoliang Yu, we proved the coarse Baum-Connes for a large class of relative expanders. In this talk, I will talk about the construction of relative expanders by G. Arzhantseva and R. Tessera and the strategy to prove the coarse Baum-Connes conjecture for certain relative expanders.

**March 17, 2021-Speaker: Xin Ma(SUNNY at Buffalo) **

Title: Dynamical comparison and its interaction with structure theory of C*-algebras

Abstract: In the first part of the talk, I will discuss the concept called dynamical comparison, which was first introduced by Winter and then refined by Kerr as a dynamical analogue of strict comparison in the structure theory of C*-algebras. I will survey some results on how dynamical comparison, as a good intermediate property, helps in establishing desired C*-algebraic properties of crossed products such as Z-stability and purely infiniteness. On the other hand, motivated by Rordam’s classical result on equivalence of strict comparison and almost unperforation of the Cuntz semigroup, it is conjectured that dynamical comparison may have a similar characterization. In the second part of the talk, I will discuss how such algebraic characterization of dynamical comparison can be established through a new dynamical semigroup called generalized type semigroup.

**March 24, 2021-Speaker: David P. Blecher (University of Houston) **

Title: Noncommutative integration and noncommutative function algebras

Abstract: We first give a brief survey of noncommutative measure and integration theory, and of some aspects of the classical theory of function algebras involving classical measure and integration. Then we propose a new merger of the two fields.

Finally we consider and solve the problem of the `existence of representing measures’ in this noncommutative situation.

**April 12, 2021-Speaker: Ismail Nikoufar (Payame Noor University)**

Title: Noncommutative operator perspective and applications

Abstract: We first give a brief survey of the classical notion of the perspective, and some aspects and applications of the commutative operator perspective introduced by Edward G. Effros. Then we introduce the notion of the noncommutative operator perspective and its properties and applications. Finally, we consider the characterization of the noncommutative operator perspective in some sense and find some equivalence relations.