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# Events for September 13, 2017 from General and Seminar calendars

## Noncommutative Geometry Seminar

**Abstract:** In this talk, we will introduce the concept of Roe C*-algebra for a locally compact groupoid whose unit space is in general not compact, and that is equipped with an appropriate coarse structure and Haar system. Using Connes' tangent groupoid method, we will define an analytic index for an elliptic differential operator on a Lie groupoid equipped with additional metric structure, which takes values in the K-theory of the Roe C*-algebra. And we will discuss applications of our developments to longitudinal elliptic operators on an open foliated manifold. This is joint work with Rufus Willett and Yi-Jun Yao.

## Groups and Dynamics Seminar

**Abstract:** An action of a group G on a set X is said to be amenable if X admits a G-invariant mean (i.e., finitely additive probability measure). The group G is said to be amenable if the left translation action of G on itself is an amenable action. While these notions were introduced in 1929 by von Neumann, a systematic study of amenable actions of nonamenable groups was not initiated until roughly 1990. I will discuss this setting, and how the tension which arises between the nonamenability of the group and the amenability of the action results in surprising structural consequences for the acting group. This tension becomes particularly pronounced in the case of an atomless mean for the conjugation action, i.e., when the group is inner amenable. I will highlight some recent results and applications of inner amenability, particularly to orbit equivalence and measured group theory.

## Promotion Talk - Professor Zhizhang Xie

**Description:**

## First Year Graduate Student Seminar

**Time:** 2:00PM - 2:50PM

**Location:** BLOC 628

**Speaker:** Xiang Tang, Washington University at St. Louis

**Title:** *A longitudinal index theorem on an open foliation manifold*

**Time:** 3:00PM - 4:00PM

**Location:** BLOC 220

**Speaker:** Robin Tucker-Drob, Texas A&M

**Title:** *Invariant means and inner amenable groups*

**Time:** 4:00PM - 5:00PM

**Location:** BLOC 220

**Speaker:** Zhizhang Xie, Texas A&M University

Higher invariants of differential operators are fundamental in the studies of geometry and topology. They played fundamental roles in some of the major advances in geometry and topology, such as the Novikov conjecture, the Baum-Connes conjecture, and the Gromov-Lawson-Rosenberger conjecture. In recent years, there has been a great amount of progress in developing new higher invariants to obtain more refined geometric and topological applications. In this talk, I will survey two such significant applications: (1) positive scalar curvature problem in geometry; (2) manifold rigidity problem in topology.Title: Higher invariants in geometry and topology

Abstract:

**Time:** 5:30PM - 6:30PM

**Location:** BLOC 628

**Speaker:** Ola Sobieska-Snyder, Ayo Adeniran, and Peter Howard

**Title:** *Outreach opportunities, and other things students should start doing now to prepare for the job search*