Unless specified, all seminars are Wednesday 4-5pm at 250 Math Building.

February 7th

A double commutant relation in the Calkin algebra on the Bergman space

commutant relation. This is a surprising result, for it is the opposite of what happens on the Hardy space.

February 14th

Global Well-Posedness of the Non-Cutoff Boltzmann Equation with Polynomial Decay Perturbations

considered is near equilibrium where the deviation has a polynomial decay. The main step is to show a closed energy estimate for small data. This is achieved

by combining methods of moment propagation, spectral analysis of the linearized operator, and smoothness effect starting from data with weak regularity. This

is a joint work with Alonso, Morimoto, and Yang.

April 4th

The Second Moments of Hecke-Maass Forms for SL(3,Z)

April 11th

Idempotents, topologies and ideals

Banach space may be decomposed into a "returning" subspace and a "weakly mixing" subspace. Furthermore, following Dye, Bergelson and Rosenblatt

characterized the weakly mixing vectors as those for which the closure of the weak orbit of the vector contains zero. I wish to exhibit a generalization

of these results, inspired, in part, by some work of Ruppert on abelian groups. I will exhibit a bijective correspondence between

-- central idempotents in the weakly almost periodic compactification of G,

-- certain topologies on G, and

-- certain ideals in the algebra of weakly almost periodic functions.

Given time, I will indicate some applications to Fourier-Stieltjes algebras.

April 18th

Garden of Eden and specification

or Moore-Myhill property, for a dynamical system refers to the equivalence between surjectivity and certain weak form of injectivity for every

equivariant continuous map from the underlying space to itself. I will exhibit a general GOE theorem for algebraic actions of amenable groups.

May 9th

Group of intermediate growth, aperiodic order, and Schroedinger operators

the theory of (random) Schroedinger operator can meet together. The main result, to be discussed, is based on a joint work with D.Lenz and T.Nagnibeda. It

shows that a random Markov operator on a family of Schreier graphs of G associated with the action on a boundary of a binary rooted tree has a Cantor

spectrum of the Lebesgue measure zero. This will be used to gain some information about the spectrum of the Cayley graph. The main tool of investigation

is given by a substitution, that, on the one hand, gives a presentation of G in terms of generators and relations, and, on the other hand, defines a minimal

substitutional dynamical system which leads to the use of the theory of random Shroedinger operator.

No special knowledge is assumed, and the talk is supposed to be easily accessible for the audience.

Past Analysis Seminar