MenuNoncommutative Geometry Seminar
Spring 2018
| Date: | January 24, 2018 |
| Time: | 2:00pm |
| Location: | BLOC 628 |
| Speaker: | Nigel Higson, Pennsylvania State University |
| Title: | [Colloquium] Asymptotic geometry and continuous spectrum |
| Abstract: | Early in his career, Hermann Weyl examined and solved the problem of decomposing a function on a half-line as a continuous combination of the eigenfunctions of a Sturm-Liouville operator with asymptotically constant coefficients. Weyl's theorem served as inspiration for Harish-Chandra 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 Harish-Chandra. This is joint work with Tyrone Crisp and Qijun Tan. |
| Date: | January 24, 2018 |
| Time: | 3:00pm |
| Location: | BLOC 628 |
| Speaker: | Quanlei Fang, City University of New York |
| Title: | Multipliers of Drury-Arveson space |
| Abstract: | The Drury-Arveson 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 Drury-Arveson space. |
| Date: | February 14, 2018 |
| Time: | 2:00pm |
| Location: | BLOC 628 |
| Speaker: | Zhizhang Xie, Texas A&M University |
| Title: | K-homology and sheaves |
| Abstract: | For smooth manifolds, typical examples of K-homology 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 Gronthendieck-Riemann-Roch 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. |
| Date: | February 23, 2018 |
| Time: | 09:00am |
| Location: | |
| Title: | Workshop on computability Of K-theory for C*-algebra |
| Date: | February 24, 2018 |
| Time: | 09:00am |
| Location: | |
| Title: | Workshop on computability Of K-theory for C*-algebra |
| Date: | February 25, 2018 |
| Time: | 09:00am |
| Location: | |
| Title: | Workshop on computability Of K-theory for C*-algebra |
| Date: | March 7, 2018 |
| Time: | 2:00pm |
| Location: | BLOC 628 |
| Speaker: | Zhizhang Xie, Texas A&M University |
| Title: | Higher eta invariants, Rationality and K-theory of C*-algebras |
| Abstract: | In this talk, I will discuss Lott's higher eta invariants from a more K-theoretic 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. |
| Date: | March 21, 2018 |
| Time: | 2:00pm |
| Location: | BLOC 628 |
| Speaker: | Hongzhi Liu , Texas A&M University and Shanghai Center of Mathematical Sci |
| Title: | Some notes on higher rho invariant |
| Abstract: | 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. |
| Date: | March 28, 2018 |
| Time: | 2:00pm |
| Location: | BLOC 628 |
| Speaker: | Yi Wang, Texas A&M University |
| Title: | Poincare type inequality and the Arveson-Douglas Conjecture |
| Abstract: | 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. |
| Date: | April 4, 2018 |
| Time: | 2:00pm |
| Location: | BLOC 628 |
| Speaker: | Dima Zanin, UNSW |
| Title: | Connes Character Formula for locally compact spectral triples |
| Abstract: | 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 \zeta-function to a bigger half-plane. 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 \zeta-function to a neighborhood of the pole. For compact spectral triples this condition simply defines the class of all smooth p-dimensional spectral triples. This conditions holds in every situation of practical importance: Riemannian manifolds (without assumption of bounded geometry), noncommutative Euclidean spaces etc. |
| Date: | April 11, 2018 |
| Time: | 2:00pm |
| Location: | BLOC 628 |
| Speaker: | Jinsong Wu, Havard University |
| Title: | Noncommutative Brascamp-Lieb inequalities |
| Abstract: | In this talk, I will introduce the Brascamp-Lieb inequalities for subfactor planar algebras. |
| Date: | April 25, 2018 |
| Time: | 2:00pm |
| Location: | BLOC 628 |
| Speaker: | Yanli Song, Washington University at St. Louis |
| Title: | Orbital integral and K-theory |
| Abstract: | In this talk, I will discuss the K-theory of group C*-algebra and Connes-Kasparov isomorphism for reductive Lie group. The main method we used is the orbital integral introduced by Harish-Chandra. 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. |
| Date: | May 2, 2018 |
| Time: | 2:00pm |
| Location: | BLOC 628 |
| Speaker: | Peter Kuchment, Texas A&M University |
| Title: | On Liouville-Riemann-Roch theorems on co-compact abelian coverings |
| Abstract: | A generalization by Gromov and Shubin [2-3] of the classical Riemann-Roch 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 Laplace-Beltrami (or more general elliptic) equation on a non-compact manifold. The solution of a 1975 Yau's conjecture [6] by Colding and Minicozzi [1] implies in particular, that such dimensions are finite for Laplace-Beltrami equation on a nilpotent co-compact 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 [4-5]. 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 non-trivial. 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 Riemann-Roch theorem for elliptic operators, I. M. Gel'fand Seminar, 1993, pp. 211--241. [3] --" -- , The Riemann-Roch theorem for elliptic operators and solvability of elliptic equations with additional conditions on compact subsets, Invent. Math. 117 (1994), no. 1, 165--180. [4] P. Kuchment and Y. Pinchover, Integral representations and Liouville theorems for solutions of periodic elliptic equations, J. Funct. Anal. 181 (2001), no. 2, 402--446. [5] --"-- , Liouville theorems and spectral edge behavior on abelian coverings of compact manifolds, Trans. Amer. Math. Soc. 359 (2007), no. 12, 5777--5815. [6] Yau, S. T.: Harmonic functions on complete Riemannian manifolds, Commun. Pure Appl. Math. 28 (1975), 201–228. |
| Date: | May 21, 2018 |
| Time: | 09:00am |
| Location: | |
| Title: | Noncommutative geometry and index theory for group actions and singular spaces |
| Date: | May 22, 2018 |
| Time: | 09:00am |
| Location: | |
| Title: | Noncommutative geometry and index theory for group actions and singular spaces |
| Date: | May 23, 2018 |
| Time: | 09:00am |
| Location: | |
| Title: | Noncommutative geometry and index theory for group actions and singular spaces |
| Date: | May 24, 2018 |
| Time: | 09:00am |
| Location: | |
| Title: | Noncommutative geometry and index theory for group actions and singular spaces |
