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

September 5th Yunhua Zhou, Chongqing University

Quasi-Shadowing property for partially hyperbolic diffeomorphisms

Abstract: It is well known that an Anosov diffeomorphism has the shadowing property. However, we can not expect that in general the shadowing

property holds for a partially hyperbolic diffeomorphism because of the existence of the center direction. In this talk, I will introduce the

quasi-shadowing property for partially hyperbolic diffeomorphisms.In fact, it is showed that for any pseudo orbit {x

of points {y

this quasi-shadowing property.

September 12th Nikolai Vasilevski, Cinvestav, Mexico City

Two-dimensional singular integral operators via poly-Bergman spaces, and Toeplitz operators with peudodifferenti

certain two-dimensional singular integral operators.

We study then the C*-algebra generated by Toeplitz operators acting on the Bergman space over the unit disk, whose

pseudodifferent

integral operators (considered in the unit disk setting). As it turns out this Toeplitz algebra coincides with the algebra generated by

Toeplitz operators with just functional symbols. At the same time, the generating Toeplitz operators for above two algebras possess quite

different properties.

September 20th Klaus Schmidt, University of Vienna and Erwin Schrödinger Institute

(Thursday, Colloquium) Sandpiles and the Harmonic Model

Abstract: The critical sandpile model was introduced by Bak, Tang and Wiesenfeld in 1987–88 and attracted a lot of attention after the

discovery of a somewhat elusive abelian group structure of this lattice model by Deepak Dhar. In this lecture I will discuss some connections

between sandpiles, the classical spanning tree and dimer models, and the harmonic model (a Z

group). One of these connections is that all these models have identical entropies.

I will show that the sandpile model is an equal entropy symbolic cover of the harmonic model, which explains some of the algebraic

features of the sandpile model.

This is joint work with Evgeny Verbitskiy.

September 25th Piotr Hajac, Institute of Mathematics of the Polish Academy of Sciences and Warsaw University

(Tuesday) The K-theory of Heegaard quantum lens spaces

Abstract: Representing Z/NZ as roots of unity, we restrict a natural U(1)-action on the Heegaard quantum sphere to Z/NZ, and call the

quotient spaces Heegaard quantum lens spaces. Then we use this representation of Z/NZ to construct an associated complex line bundle. The

main result is the stable non-triviality of these line bundles over any of the quantum lens spaces we consider. We use the pullback structure

of the C*-algebra of the lens space to compute its K-theory via the Mayer-Vietoris sequence, and an explicit form of the odd-to-even

connecting homomorphism to prove the stable non-triviality of the bundles.

October 3rd Jingbo Xia, SUNY at Buffalo

Localization and Berezin Transform on the Fock space

Abstract: We introduce the class of sufficiently localized operators on the Fock space. This class contains many familiar operators,

including all the Toeplitz operators with bounded symbols. We show that if A is in the C*-algebra generated by the class of sufficiently

localized operators and if the Berezin transform of A vanishes at infinity, then A is compact. The main point of this work is that this

compactness is a consequence of a very simple inequality derived from a classic idea that dates back to the 1970s. This is joint work with

Dechao Zheng.

October 10th Xin Li, University of Münster

Semigroup C*-algebras and their K-theory

Abstract: We compute K-theory for semigroup C*-algebras. In a more general context, we obtain a K-theoretic formula for crossed products

attached to certain dynamical systems on totally disconnected spaces. This is joint work with J. Cuntz and S. Echterhoff.

October 17th Sheng-Chi Liu, Texas A&M University

Subconvexity and equidistribution of Heegner points in the level aspect

Abstract: We will discuss the equidistribution property of Heegner points of level q and discriminant D, as q and D go to infinity. We will

establish a hybrid subconvexity bound for certain Rankin-Selberg L-functions which are related to the equdistribution of Heegner points. This

joint work with Riad Masri and Matt Young.

October 31st Steve Lester, University of Rochester

The distribution of values of the Riemann zeta-function.

Abstract: In his 1859 paper "On the Number of Primes Less Than a Given Magnitude," Riemann provided an argument that showed why the

distribution of the prime numbers should be related to the zeros of a function of a complex variable. Riemann denoted this function by ζ(s)

and made five conjectures about its properties. All but one of these conjectures has been proved. The conjecture that has not been proved (or

disproved) is known as the Riemann Hypothesis and states that all the non-real zeros of ζ(s) lie on the line Re(s) = 1/2.

In this talk we will look at the problem of understanding the distribution of the points s at which ζ(s) = a, where a is a non-zero complex

number. These points are known as a-points and have long been an object of study. We will discuss many of the known properties of a-points

and how these properties compare to those of zeros of ζ(s). Additionally, we will describe recent joint work of ours with Steve Gonek

and Micah Milinovich on simple a-points and also discuss the problem of determining how many a-points lie on the line Re(s) = 1/2.

November 14th Huichi Huang, SUNY at Buffalo

Invariant subsets under compact quantum group actions

Abstract: We study invariant subsets and invariant states of compact quantum group actions on unital C*-algebras. Concerning compact quantum

group actions on commutative C*-algebras, we formulate the concept of compact quantum group orbits and prove some basic properties.Moreover,

through analyzing invariant subsets and invariant states, we derive some interesting results about ergodic actions. Especially, we show that

the unique invariant measure of a compact quantum homogeneous space with infinitely many points is non-atomic. As a result, countable compact

metrizable spaces with infinitely many points are not quantum homogeneous spaces.

November 28th Peter Cho, Fields Institute

Logarithmic derivatives of Artin L-functions at s=1

Abstract: Let K be a number field of degree n, and d

hypothesis, we show that the upper and lower bound of the logarithmic derivative of Artin L-functions attached to K at s=1 are log log

`|d`_{K}|

and -(n-1)log log

`|d`_{K}|

, resp. Unconditionally we
show that there are infinitely many number fields with the extreme
logarithmic derivatives. They are families of number fields whose Galois closures have the Galois group as C

Past Analysis Seminars