Noncommutative Geometry Seminar
Organizers:
Simone Cecchini,
Jinmin Wang,
Zhizhang Xie,
Guoliang Yu,
Bo Zhu
Please feel free to contact any one of us, if you would like to give a talk at our seminar.

Date Time 
Location  Speaker 
Title – click for abstract 

08/15 09:00am 
BLOC 306 
YMNCGA 
Young Mathematicians in Noncommutative Geometry and Analysis workshop


08/16 09:00am 
BLOC 306 
YMNCGA 
Young Mathematicians in Noncommutative Geometry and Analysis workshop


08/17 09:00am 
BLOC 306 
YMNCGA 
Young Mathematicians in Noncommutative Geometry and Analysis workshop


08/18 09:00am 
BLOC 306 
YMNCGA 
Young Mathematicians in Noncommutative Geometry and Analysis workshop


09/16 1:00pm 
ZOOM 
Omar Mohsen ParisSaclay University 
Characterization of Maximally Hypoelliptic Differential Operators Using Symbols, and Index Theory
In this talk we will give an introduction to maximally hypoelliptic differential operators. This is a class of differential operators generalizing elliptic operators and includes operators like Hormander’s sum of squares. We will present our work where we define a principal symbol and show that maximally hypoellipticity is equivalent to invertibility of our principal symbol generalizing the classical regularity theorem for elliptic operators.
We will also give a topological index formula for maximally hypoelliptic differential operators using our symbol. Explicit examples of index computations will be included at the end.
This talk is based on joint work with Androulidakis and Yuncken. Abstract 

09/28 2:00pm 
BLOC 302 
Rudolf Zeidler University of Munster 
Nonnegative scalar curvature on manifolds with at least two ends
I will present an obstruction to positive scalar curvature (psc) on complete manifolds with at least two ends based on the existence of incompressible hypersurfaces that do not admit psc. This result mixes an analytic technique based on $\mu$bubbles, an augmentation of the classical minimal hypersurface obstructions to psc, with a topological argument based on positive scalar curvature surgery. Due to the latter a surprising (but necessary!) spin condition enters our result even though our methods are not based on the Dirac operator. Concretely, let $M$ be an orientable connected $n$dimensional manifold with $n\in\{6,7\}$ and $Y\subset M$ a twosided closed connected incompressible hypersurface that does not admit a metric of psc. Suppose that the universal covers of $M$ and $Y$ are either both spin or both nonspin. Then $M$ does not admit a complete metric of psc. As a consequence, our result answers questions of RosenbergStolz and Gromov up to dimension $7$. Joint work with Simone Cecchini and Daniel Räde. Abstract 

09/29 11:00am 
BLOC 302 
Christopher Wulff University of Goettingen 
Generalized asymptotic algebras and Etheory for nonseparable C*algebras
Many common ad hoc definitions of bivariant Ktheory for nonseparable C*algebras have some kind of drawback, usually that one cannot expect the long exact sequences to hold in full generality. I report on my current project to define Etheory for nonseparable C*algebras without such disadvantages via a generalized notion of asymptotic algebras. The intended model is appropriate to define cycles in situations where an approximation procedure is not done over a real parameter but over more complex directed sets. I will also pose the question whether the equivariance of bivariant Ktheory can be generalized in a potentially very useful way. Abstract 

10/05 2:00pm 
BLOC 302 
Ryo Toyota TAMU 
Controlled Ktheory and Khomology
I will introduce a new perspective of Khomology of spaces. This work is motivated by a paper of Guoliang Yu, where he showed that the Ktheory of the localization algebra is isomorphic to Khomology for finite simplicial complexes. The localization algebra consists of functions from [1,\infty) to Roe algebra whose propagations go to 0. "The reason" we get Khomology is that by focusing operators whose propagation is small, we can recover some local information on spaces we lost by taking Roe algebras. Here we discuss how we can recover Khomology by focusing on operators whose propagation is smaller than a certain threshold r instead of thinking of operator valued functions. I will report what we can prove and what should be true. 