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 

08/28 2:00pm 
BLOC 628 
Sherry Gong UCLA 
On the KronheimerMrowka concordance invariant
We will talk about Kronheimer and Mrowka’s knot concordance invariant, $s^\sharp$. We compute the invariant for various knots. Our computations reveal some unexpected phenomena, including that $s^\sharp$ differs from Rasmussen's invariant $s$, and that it is not additive under connected sums. We also generalize the definition of $s^\sharp$ to links by giving a new characterization of the invariant in terms of immersed cobordisms.


09/13 4:00pm 
BLOC 220 
Caterina Consani Johns Hopkins University 
[Colloquium] Under and above Spec(Z)
The talk will describe some recent geometric constructions related to the algebraic spectrum of the integers and the adele class space of the rationals which are part of a joint work with A. Connes. 

10/02 2:00pm 
BLOC 628 
Clément Dell'Aiera University of Hawai'i 
Exhaustivity of representations at infinity of Roe algebras
Exhaustive representations were introduced by Nistor and Prudhon, motivated by characterizations of Fredholm operators and spectral theory of Nbody Hamiltonians. Coarse geometry deals with the geometry at infinity of metric spaces with bounded geometry via the Roe algebra. In particular, Spakula and Willlett show how to construct a family of representations of the Roe algebra which can be thought of "the representations at infinity". We will be studying when this family is exhaustive. This is joint work with Yu Qiao. 

10/09 2:00pm 
BLOC 628 
Chunlan Jiang Hebei Normal University 
Similarity invariants of essentially normal CowenDouglas operators and Chern polynomials
In this talk, I will discuss our resent work on a class of essentially normal operators by using the geometry method from the CowenDouglas theory and a BrownDouglasFillmore theorem in the CowenDouglas theory. More precisely, the Chern polynomials and the second fundamental forms are
the similarity invariants (in the sense of Herrero) of this class of essentially normal operators. 

10/16 2:00pm 
BLOC 628 
Jianchao Wu Texas A&M University 
The Ktheory of C*algebras associated to certain infinite dimensional spaces
Noncommutative geometry provides a potent approach to the study of the algebraic geometry (e.g., Ktheory) of infinite dimensional manifolds. In this talk, I will outline the construction of C*algebras associated to HilbertHadamard spaces, understood as a kind of (typically infinite dimensional) nonpositively curved manifolds. Under mild assumptions, these C*algebras retain a remnant of Bott periodicity, which we exploit to prove the Novikov conjecture of geometrically discrete groups of diffeomorphisms. This is joint work with Sherry Gong and Guoliang Yu. 

10/23 2:00pm 
BLOC 628 
Rufus Willett University of Hawai'i 
Decompositions and Ktheory
We introduce a notion of 'local decomposability' for a C*algebra, inspired by the theory of nuclear dimension (due to Winter and Zacharias) and of dynamical complexity (due to Guentner, Yu and the speaker). We derive the existence of a sortof controlled MayerVietoris sequence in this setting, inspired by work of OyonoOyono and Yu in controlled Ktheory (although not using that language), and give applications to BaumConnes theory and to the Künneth formula.


10/30 2:00pm 
BLOC 628 
Quanlei Fang The City University of New York 
TBA
TBA 

11/20 2:00pm 
BLOC 628 
Peter Hochs University of Adelaide 
TBA
TBA 