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Texas A&M University
Mathematics

Noncommutative Geometry Seminar

Spring 2019

 

Date:January 16, 2019
Time:2:00pm
Location:BLOC 628
Speaker:Jianchao Wu, Pennsylvania State University
Title:The Novikov conjecture, the group of volume preserving diffeomorphisms, and Hilbert-Hadamard spaces
Abstract:The Novikov conjecture is a central problem in manifold topology. Noncommutative geometry provides a potent approach to tackle this conjecture. Using C*-algebraic and K-theoretic tools, we prove that the Novikov conjecture holds for any discrete group admitting an isometric and metrically proper action on an admissible Hilbert-Hadamard space, which is an infinite-dimensional analogue of complete simply connected nonpositively curved Riemannian manifolds. In particular, these groups include geometrically discrete subgroups of the group of volume preserving diffeomorphisms of a compact smooth manifold with a fixed volume form. This is joint work with Sherry Gong and Guoliang Yu.

Date:February 13, 2019
Time:2:00pm
Location:BLOC 628
Speaker:Clément Dell'Aiera, University of Hawaii
Title:Decomposition complexity, a dynamical approach
Abstract:Finite Decomposition Complexity was introduced by E. Guentner, R. Tessera and G. Yu as a generalization of finite asymptotic dimension. We will investigate how it can be suitably defined for topological actions of discrete groups (more generally topological groupoids), and present some applications in Operator Algebras and K-theory, e.g. one can obtain the Künneth formula for the uniform Roe algebra of some groups which are not coarsely embeddable into Hilbert space. Other applications include the Baum-Connes conjecture.

Date:February 20, 2019
Time:2:00pm
Location:BLOC 628
Speaker:Qin Wang, East China Normal University
Title:The coarse Novikov conjecture and Banach spaces with property (H)
Abstract:The coarse Novikov conjecture is a geometric analogue of the strong Novikov conjecture, while property (H) is a geometric condition for Banach spaces introduced by G. Kasparov and G. Yu in studying the strong Novikov conjecture. In this talk, I will discuss applications of coarse embeddings or fibred coarse embeddings of metric spaces into Banach spaces with property (H) to the coarse Novikov conjecture.

Date:March 6, 2019
Time:2:00pm
Location:BLOC 628
Speaker:Hao Guo, Texas A&M University
Title:A Lichnerowicz vanishing theorem for the maximal roe algebra
Abstract:Let M be a complete spin Riemannian manifold. Then the Dirac operator on M has an index taking values in the K-theory of the maximal Roe algebra. One of the basic properties one would like to have for this index is that it vanishes when the M has uniformly positive scalar curvature. But as distinct from the setting of the reduced Roe algebra, one cannot directly apply a functional calculus argument on the maximal Roe algebra to show this vanishing. In this talk we outline the steps to a proof of this fact using a uniform version of the maximal Roe algebra. This is joint work with Zhizhang Xie and Guoliang Yu.

Date:March 20, 2019
Time:2:00pm
Location:BLOC 628
Speaker:Zhuang Niu, University of Wyoming
Title:[Colloquium] Comparison radius and mean dimension
Abstract:Comparison radius of a C*-algebra was introduced by Toms to measure the regularity of a C*-algebra, and it can be regarded as a C*-version of dimension growth. Mean topological dimension was introduced by Gromov and developed by Lindenstrauss and Weiss, and it is an invariant for topological dynamical systems which measures dimension growth along orbits. In the talk, I will discuss some estimations of the comparison radius of the crossed product C*-algebra in terms of the mean dimension of the dynamical system.

Date:March 27, 2019
Time:2:00pm
Location:BLOC 628
Speaker:Rudolf Zeidler, University of Münster
Title:Slant products on the analytic structure group via the stable Higson corona
Abstract:We show injectivitiy of certain exterior product maps on the K-theory of the Roe algebra and the analytic structure group by a partial pairing (or "slant product") with the K-theory of the stable Higson corona. We will explore applications in primary and secondary index theory, in particular to positive scalar curvature. This is ongoing joint work with Alexander Engel and Christopher Wulff.

Date:April 3, 2019
Time:2:00pm
Location:BLOC 628
Speaker:Stuart White, University of Glasgow
Title:Simple amenable C*-algebras
Abstract:I’ll discuss recent developments in the structure and classification of simple amenable C*-algebras: how do we recognise C*-algebras which should be classified, and once we’ve found them, how should they be classified? New results will be based on joint work with Castillejos, Evington, Tikuisis and Winter, and with Carrion, Gabe, Schafhauser and Tikuisis.