Noncommutative Geometry Seminar
Organizers:
Zhizhang Xie,
Guoliang Yu,
Jianchao Wu,
Hao Guo
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 

08/19 1:00pm 
Zoom 942810031 
Yi Wang Vanderbilt University 
HeltonHowe trace formula on submodules
HeltonHowe trace formula gives an explicit description of the traces of antisymmetric sums of Toeplitz operators on the Bergman space. On a submodule of the Bergman module with relatively nice zero locus, previous results show that the cross commutators between the generalized Toeplitz operators with coordinate symbols belong to some Schatten class. A natural question is whether the same HeltonHowe trace formula remain true for such submodules. We answer this question in affirmative, using finite rank approximation and dilation techniques. Abstract 

08/26 1:00pm 
Zoom 942810031 
Giovanni Landi Trieste University 
Solutions to the quantum YB equation and related deformations
We present natural families of coordinate algebras of noncommutative Euclidean spaces and noncommutative products of Euclidean spaces. These coordinate algebras are quadratic ones associated with an Rmatrix which is involutive and satisfies the quantum Yang–Baxter equation. As a consequence they enjoy a list of nice properties, being regular of finite global dimension. Notably, we have spherical manifolds, and noncommutative quaternionic planes as well as noncommutative quaternionic tori. On these there is an action of the classical quaternionic torus SU(2)×SU(2) in parallel with the action of the torus U(1)×U(1) on a complex noncommutative torus. Abstract 

09/02 1:00pm 
Zoom 942810031 
Bruno de Mendonca Braga University of Virginia 
Coarse equivalences of metric spaces and outer automorphisms of Roe algebras
Given a metric space $X$, the Roe algebra of $X$, denoted by $\mathrm{C}^*(X)$, is a $ \mathrm{C} ^*$algebra which encodes many of $X$'s large scale geometric properties. In this talk, I will discuss some uniform approximability results for maps between Roe algebras (we call those "coarselike properties"). I will then talk about applications of these uniform approximability results to isomorphisms between Roe algebras. In particular, given a uniformly locally finite metric space $X$, we obtain that the canonical map from the group of coarse equivalences of $X$ modulo the relation of closeness to the group of outer automorphisms of $ \mathrm{C} ^*(X)$ is surjective if $X$ has property A. This is a joint work with Alessandro Vignati. Abstract 

09/09 1:00pm 
Zoom 942810031 
Anna Duwenig University of Wollongong 
Noncommutative Poincaré Duality of the Irrational Rotation Algebra
The irrational rotation algebra is known to be selfdual in a KKtheoretic sense. The required Khomology fundamental class was constructed by Connes out of the Dolbeault operator on the 2torus, but there has not been an explicit description of the dual element. In this talk, I will geometrically construct that Ktheory class by using a pair of transverse Kronecker flows on the 2torus.This is based on joint work with Heath Emerson (University of Victoria). Abstract 

09/16 1:00pm 
Zoom 942810031 
Kristin Courtney University of Münster (WWU) 
C*structure on images of completely positive order zero maps
A completely positive (cp) map is called order zero when it preserves orthogonality. Such maps enjoy a rich structure, which has made them a key component of completely positive approximations of nuclear C*algebras. Motivated by generalized inductive limits arising from such cp approximations, we consider the structure of the image of a cp order zero map. It turns out that this is captured by a few key properties that one can ask of a selfadjoint subspace of a C*algebra. We will discuss these properties and the implications for generalized inductive sequences. This is joint work with Wilhelm Winter. Abstract 

09/23 1:00pm 
Zoom 942810031 
Rudolf Zeidler University of Göttingen 
Scalar curvature comparison via the Dirac operator
In recent years, Gromov proposed studying the geometry of positive scalar curvature (abbreviated by "psc") via various metric inequalities. In particular, he proposed the following conjecture: Let $M$ be a closed manifold which does not admit a metric of psc. Then for any Riemannian metric on $V = M \times [1,1]$ of scalar curvature $\geq n(n1)$ the estimate $d(\partial_ V, \partial_+ V) \leq 2\pi/n$ holds, where $\partial_\pm V = M \times \{\pm 1\}$ and $n = \dim V$.
Previously, Rosenberg and Stolz conjectured similarly that if $M$ does not admit psc, then $M \times \mathbb{R}$ does not admit a complete metric of psc and $M \times \mathbb{R}^2$ does not admit a complete metric of uniformly psc.
In this talk, we will discuss a new geometric phenomenon consisting of a precise quantitative interplay between distance estimates and scalar curvature bounds which underlies these three conjectures. We will explain that this phenomenon arises if $M$ admits an obstruction to psc using the index theory of Dirac operators. Abstract 