
Date Time 
Location  Speaker 
Title – click for abstract 

01/24 2:00pm 
BLOC 628 
Nigel Higson Pennsylvania State University 
[Colloquium] Asymptotic geometry and continuous spectrum
Early in his career, Hermann Weyl examined and solved the problem of decomposing a function on a halfline as a continuous combination of the eigenfunctions of a SturmLiouville operator with asymptotically constant coefficients. Weyl's theorem served as inspiration for HarishChandra in his pursuit of the Plancherel formula for semisimple groups, and for this and other reasons it continues to be of interest. I'll try to explain the (noncommutative) geometry behind Weyl's theorem and behind the extensions studied by HarishChandra. This is joint work with Tyrone Crisp and Qijun Tan. 

01/24 3:00pm 
BLOC 628 
Quanlei Fang City University of New York 
Multipliers of DruryArveson space
The DruryArveson Space, as a Hilbert function space, plays an important role in multivariable operator theory. In this talk we will discuss various properties of multipliers of the DruryArveson space.


02/14 2:00pm 
BLOC 628 
Zhizhang Xie Texas A&M University 
Khomology and sheaves
For smooth manifolds, typical examples of Khomology classes are given by elliptic differential operators. By definition, they are local or infinitesimal in the sense that their propagations are arbitrarily small. The concept of sheaves (again by definition) shares this fundamental property of being local. One naturally expects some close connections between these two important notions. In particular, making some of these connections precise allows us to prove interesting theorems in geometry and topology, such as GronthendieckRiemannRoch theorem for singular varieties. In this talk, I will try to explain some of these connections by discussing some interesting examples. The talk is based on ongoing joint work with N. Higson. 

02/23 09:00am 


Workshop on computability Of Ktheory for C*algebra


02/24 09:00am 


Workshop on computability Of Ktheory for C*algebra


02/25 09:00am 


Workshop on computability Of Ktheory for C*algebra


03/07 2:00pm 
BLOC 628 
Zhizhang Xie Texas A&M University 
Higher eta invariants, Rationality and Ktheory of C*algebras
In this talk, I will discuss Lott's higher eta invariants from a more Ktheoretic viewpoint. We not only obtain simpler and conceptual proofs of some of the results in literature, but also give new results regarding rationality of these invariants. The talk is based on joint work with G. Yu. 

03/21 2:00pm 
BLOC 628 
Hongzhi Liu Texas A&M University and Shanghai Center of Mathematical Sci 
Some notes on higher rho invariant
In this talk I would like to introduce the higher rho invariant as an obstruction class. I will then focus on its applications in topology and show how to define additive higher rho map from the structure group of a topological manifold to the K theory of a certain obstruction C*algebra. At last I hope to talk about the product formula for higher rho invariants.


03/28 2:00pm 
BLOC 628 
Yi Wang Texas A&M University 
Poincare type inequality and the ArvesonDouglas Conjecture
The Poincare inequality says that the Lp norm of a function is controlled by its gradient. Boas and Straube improved that inequality by adding a weight function on the gradient. By applying this inequality on the Hardy and Bergman spaces on bounded strongly pseudoconvex domains with smooth boundary, we show that the Hardy norm of a function is equivalent to a weighted Bergman norm of its gradient. This allows us to apply existing techniques for submodules of the Bergman module, and obtain essential normality for principal submodules of the Hardy module. 

04/04 2:00pm 
BLOC 628 
Dima Zanin UNSW 
Connes Character Formula for locally compact spectral triples
In this talk, I provide a natural condition on (locally compact) spectral triple which implies a number of interesting corollaries:
1) Asymptotic for heat semigroup. Surprisingly, it was not established before even for compact spectral triples.
2) Existence of the heat semigroup asymptotic easily provides analytic continuation of \zetafunction to a bigger halfplane.
3) Finally, the Connes Character formula in terms of singular traces on the ideal $\mathcal{L}_{1,\infty}.$ This is derived from the analytic continuation of \zetafunction to a neighborhood of the pole.
For compact spectral triples this condition simply defines the class of all smooth pdimensional spectral triples. This conditions holds in every situation of practical importance: Riemannian manifolds (without assumption of bounded geometry), noncommutative Euclidean spaces etc. 

04/11 2:00pm 
BLOC 628 
Jinsong Wu Havard University 
Noncommutative BrascampLieb inequalities
In this talk, I will introduce the BrascampLieb inequalities for subfactor planar algebras.


04/25 2:00pm 
BLOC 628 
Yanli Song Washington University at St. Louis 
Orbital integral and Ktheory
In this talk, I will discuss the Ktheory of group C*algebra and ConnesKasparov isomorphism for reductive Lie group. The main method we used is the orbital integral introduced by HarishChandra. I will try to explain some connections between the representation theory of Lie group and index of Dirac operators. This is a joint work with Higson and Tang.


05/02 2:00pm 
BLOC 628 
Peter Kuchment Texas A&M University 
On LiouvilleRiemannRoch theorems on cocompact abelian coverings
A generalization by Gromov and Shubin [23] of the classical RiemannRoch theorem describes the index of an elliptic operator on a compact manifold with a divisor of prescribed zeros and allowed singularities. On the other hand, Liouville type theorems count the number of solutions of a given polynomial growth of the LaplaceBeltrami (or more general elliptic) equation on a noncompact manifold. The solution of a 1975 Yau's conjecture [6] by Colding and Minicozzi [1] implies in particular, that such dimensions are finite for LaplaceBeltrami equation on a nilpotent cocompact covering. In the case of an abelian covering, much more complete Liouville theorems (including exact formulas for dimensions) have been obtained by Kuchment and Pinchover [45]. One wonders whether such results have a combined generalization that would allow for a divisor that "includes the infinity." Surprisingly, combining the two types of results turns out being rather nontrivial. The talk will present such a result obtained recently in a joint work with Minh Kha (former A&M PhD student, currently postdoc at U. Arizona).
[1] Colding, T. H., Minicozzi, W. P.: Harmonic functions on manifolds, Ann. of Math. 146 (1997), 725–747.
[2] M. Gromov and M. A. Shubin, The RiemannRoch theorem for elliptic operators, I. M. Gel'fand Seminar, 1993, pp. 211241.
[3] "  , The RiemannRoch theorem for elliptic operators and solvability of elliptic equations with additional conditions on compact subsets, Invent. Math. 117 (1994), no. 1, 165180.
[4] P. Kuchment and Y. Pinchover, Integral representations and Liouville theorems for solutions of periodic elliptic equations, J. Funct. Anal. 181 (2001), no. 2, 402446.
[5] " , Liouville theorems and spectral edge behavior on abelian coverings of compact manifolds, Trans. Amer. Math. Soc. 359 (2007), no. 12, 57775815.
[6] Yau, S. T.: Harmonic functions on complete Riemannian manifolds, Commun. Pure Appl. Math. 28 (1975), 201–228. 

05/21 09:00am 


Noncommutative geometry and index theory for group actions and singular spaces


05/22 09:00am 


Noncommutative geometry and index theory for group actions and singular spaces


05/23 09:00am 


Noncommutative geometry and index theory for group actions and singular spaces


05/24 09:00am 


Noncommutative geometry and index theory for group actions and singular spaces
