Analysis   Seminar    


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_k}, there is a sequence
                         of points {y_k} tracing it in which y_k+1 is obtained from f(y_k) by a motion along center direction. I will also discuss some applications of
                         this quasi-shadowing property.         
                        

September 12th           Nikolai Vasilevski,   Cinvestav, Mexico City
                         Two-dimensional singular integral operators via poly-Bergman spaces, and Toeplitz operators with peudodifferential symbols

                      Abstract: We describe a direct and transparent connection between the poly-Bergman type spaces on the upper half-plane and the action of the
                         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
                         pseudodifferential defining symbols belong to the algebra generated by the multiplication operators and the above two-dimensional singular
                         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^{^2}-action by automorphisms of a compact abelian
                         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 infinity, 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_K be its discriminant. Then under the Artin conjecture, GRH and certain zero density
                         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 |dK|
                         and -(n-1)log log |dK|, 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_n, n=2,3,4,6, D_n, n=3,4,5, S₄ and A₅.

                                                                      
Past Analysis Seminars