Unless specified, all seminars are Wednesday 4-5pm via Zoom, or both Room 250 and Zoom. For Zoom information please send email to hfli@math.buffalo.edu

August 31

8PM, Zoom

quantization. We prove a local formula for the large t-limit of the Connes-Chern character as the weight goes to infinity. And we show that the

Helton-Howe trace of Toeplitz operators is independent of the weight and obtain a local formula for the Helton-Howe trace for all weighted Bergman

spaces. The proofs are based on an integration by parts formula and some harmonic analysis. This talk is based on joint work with Xiang Tang and

Dechao Zheng.

September 7

Zoom

to quantum mechanics, i.e. the matrix mechanics of Heisenberg and the wave mechanics of Schrödinger. It was then formulated by Mackey as a

theorem about certain unitary representations of locally compact abelian groups. In my talk, based on yet another formulation due to Rieffel, I will

present a Stone-von Neumann-type theorem in the setting of locally compact quantum groups introduced by Kustermans and Vaes and

independently by Woronowicz.

September 14

250 and Zoom

the relation between these two properties for algebraic actions of amemable groups, and how this is related to the strong Atiyah conjecture in

L2-invariants theory. This is joint work with Sebastian Barbieri and Felipe Garcia-Ramos.

October 12

250 and Zoom

invariant under measure conjugacy and is an extension of Kolmogorov-Sinal entropy for actions of the integers. Two pmp actions are orbit

equivalent if their orbits can be matched almost everywhere in a measurable fashion. Although entropy is not invariant under orbit equivalence in

general, work of Austin and Kerr-Li has shown in various settings that entropy is invariant under certain stronger notions of quantitative orbit

equivalence. We add to these results by showing that the f-invariant is invariant under the assumption of bounded orbit equivalence.

November 9

250 and Zoom

considering the measure-theoretic entropy with respect to some equillibrium state. Moreover, this metric is conformal equivalent to the pressure

metric from the thermodynamics. It is a joint work with Y.M. He.

November 16

Zoom

Laplace-Beltrami operator which has a discrete spectrum. If we arrange the eigenvalues of the Laplacian in increasing order (for the negative of the

Laplacian) with multiplicity, Courant's theorem states, that the number of nodal components for the k-th eigenfunction is at most k. A nodal

component of an eigenfunction u is the connected component of the set where u does not vanish. In this talk we study a local version of this

global result of Courant. The local question was raised by Donnelley and C. Fefferman in the late 1980s. Our theorems are joint work with

A. Logunov, E. Mallinikova and D. Mangoubi.

November 30

Zoom

coefficients of residues of Eisenstein series to attack the problem of characterizing the image of Langlands functorial liftings. We'll discuss the

general structure, the results of Ginzburg, Rallis and Soudry in the classical groups, some recent attempts to extend the same ideas to the

exceptional groups, and challenges and new phenomena which emerge in these attempts. The new work discussed will mainly be joint with Baiying

Liu. Time permitting I may also comment on unpublished work of Ginzburg and joint work with Ginzburg.

Past Analysis Seminar