seminars:anal

## The Analysis Seminar

The seminar meets Wednesdays in WH-100E at 3:30-4:30 p.m. There are refreshments and snacks in WH-102 at 3:15.

The seminar is partly funded as one of Dean's Speaker Series in Harpur College (College of Arts and Sciences) at Binghamton University.

Organizers: Paul Loya, Xiangjin Xu, Lu Zhang, and Gang Zhou

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### Fall 2017

* August 23th, Wednesday (3:30-4:30pm)

Speaker :
Topic: organizational meeting

* August 30th, Wednesday (3:30-5:00pm)

Speaker : Adam Weisblatt (Binghamton University)
Topic: The dirichlet problem on manifolds with corners.

Abstract: It is well known that the dirichlet problem in R^2 has a solution when the boundary of the region is smooth. We will use geometric techniques to construct an integral operator which gives the solution of the dirichlet problem when the boundary has corners.

* September 6th, Wednesday (3:30-4:30pm)

Speaker : Adam Weisblatt (Binghamton University)
Topic: The dirichlet problem on manifolds with corners.(continued)

Abstract: It is well known that the dirichlet problem in R^2 has a solution when the boundary of the region is smooth. We will use geometric techniques to construct an integral operator which gives the solution of the dirichlet problem when the boundary has corners.

* September 13th, Wednesday (3:30-4:30pm)

Speaker : Gang Zhou (Binghamton University)
Topic: Derivation of an effective evolution equation for a strongly coupled polaron

Abstract: Polaron theory is a model of an electron in a crystal lattice. It is in the framework of nonequilibrium statistic mechanics, which becomes important in recent year because people can conduct better experiments. There are two different mathematical models for polaron: H. Frohlich proposed a quantum model in 1937; L. Landau and S. I. Pekar proposed a system of nonlinear PDEs in 1948. In a joint work of Rupert Frank, we proved that these two models are equivalent to certain orders.

* September 20th, Wednesday (3:30-4:30pm) (Rosh Hashanah)

Speaker: Adam Weisblatt (Binghamton University)
Topic: The dirichlet problem on manifolds with corners.(continued)

Abstract: It is well known that the dirichlet problem in R^2 has a solution when the boundary of the region is smooth. We will use geometric techniques to construct an integral operator which gives the solution of the dirichlet problem when the boundary has corners.

* September 27th, Wednesday (3:30-4:30pm)

Speaker: Gang Zhou (Binghamton University)

Topic: On the evolution of surfaces under mean curvature flow

Abstract: In this talk I will present the progresses made in the past few years on the evolution of surfaces under mean curvature flow. Our contributions were to prove the uniqueness of limit cylinder at the time of blowup and to unify different approaches by different parties, and to address some open problems, especially in four dimensional manifolds. These were made possible by applying different techniques learned from theoretical physics and mathematical physics. Joint works of Dan Knopf and Michael Sigal.

* October 4th, Wednesday (3:30-4:30pm)

Speaker: Marius Beceanu (Albany University -SUNY)
Topic: Strichartz estimates for the wave and Klein–Gordon equations

Abstract: In this talk I shall present some new Strichartz-type estimates for wave and Klein–Gordon equations, with a few sample applications.

* October 11th, Wednesday (3:30-4:30pm)

Speaker: Lu Zhang (Binghamton University)
Topic: Multi-parameter singular Radon transforms

Abstract: I will give a brief introduction to a type of the multi-parameter singular Randon transforms. Such type of operators was originally studied by Christ, Nagel, Stein and Wainger. The theory was extended to the cases involving product kernels and general multi-parameter setting by B. Street and Stein.

* October 18th, Wednesday (3:30-4:30pm)

Speaker: Philippe Sosoe (Cornell University)
Topic: A sharp quasi-invariance result for the quartic NLS equation with Gaussian initial data

Abstract: I will discuss a recent result, with T. Oh and N. Tzvetkov, proving that the distribution of the solution of a dispersive equation on the circle with random initial data according to some Gaussian measure remains regular at positive times. This result is optimal in two senses which will be clarified in the talk.

* October 25th, Wednesday (3:30-4:30pm)

Speaker: Yakun Xi (University of Rochester)
Topic: Geodesic period integrals of eigenfunctions on Riemannian surfaces.

Abstract: We use the Gauss-Bonnet theorem and the triangle comparison theorems of Rauch and Toponogov to show that on compact Riemannian surfaces of negative curvature, period integrals of eigenfunctions over geodesics go to zero at the rate of $O((\log \lambda)^{(-1/2)})$ if $\lambda$ are their frequencies. No such result is possible in the constant curvature case if the curvature is $≥ 0$.

* November 1st, Wednesday (3:30-4:30pm)

Speaker:
Topic: the Analysis Caucus Meeting for next year's teaching

Abstract: To discuss and make recommendations on what analysis courses, numbered above Math 330 for both graduate and undergraduate, should be offered in 2018-19, and who should (or would like to) teach them.

* November 8th, Wednesday (3:30-4:30pm)

Speaker: Zhenfu Wang (University of Pennsylvania)
Topic: Quantitative estimates of propagation of chaos for stochastic particle systems

Abstract: We derive quantitative estimates proving the propagation of chaos for large stochastic systems of interacting particles. We obtain explicit bounds on the relative entropy between the joint law of the particles and the tensorized law at the limit. We have to develop for this new laws of large numbers at the exponential scale. But our result only requires very weak regularity on the interaction kernel in the negative Sobolev space $W^{-1, \infty}$ , thus including the Biot-Savart law and the point vortices dynamics for the 2d incompressible Navier-Stokes.

* November 15th, Wednesday (3:30-4:30pm)

Speaker:
Topic:

Abstract:

* November 22rd, Wednesday (Thanksgiving)

Speaker:
Topic:

Abstract:

* November 29th, Wednesday (3:30-4:30pm)

Speaker: Rongwei Yang (SUNY Albany)
Topic: Projective Spectrum and Finitely Generated Groups

Abstract: For a tuple $A= (A_1; A_2;\ldots.. A_n)$ of elements in a unital Banach algebra $B$, its projective spectrum $P(A)$ is the collection of $z\in \mathbb{C}^n$ such that the multiparameter pencil $A(z) =z_1 A_1+z_2 A_2+\ldots+z_n A_n$ is not invertible. If $(\rho;H)$ is a unitary representation of a finitely generated group $G=< g_1;g_2;;g_{nj}>$ and $Ai=(g_i);i= 1,2,\ldots,n;$ then $P(A)$ reflects the structure of $G$ as well as the property of $\rho$. In this talk we will see how projective spectrum characterizes amenability, Haagerup's property and Kazhdan's property (T) of the groups. Projective spectrum can be computed explicitly for some groups. We will have an in-depth look at the case of the in nite dihedral group $D1$, and will indicate a connection with group of intermediate growth.

A big part of this talk is joint work with R. Grigorchuk.

* December 6th, Wednesday (3:30-4:30pm)(Cancelled)

Speaker: Kunal Sharma (Binghamton University)
Topic: Some remarks on Calderon-Seeley projector

Abstract: We will show how Calderon-Seeley projector comes up in study of boundary values problems for elliptic operators on a compact manifold with boundary. Its properties and applications to address Fredholmness of the operator will be discussed.

seminars/anal.txt · Last modified: 2017/12/06 20:27 by xxu