Analysis   Seminar    

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

September 16th                
Jack Buttcane,    SUNY at Buffalo            
                               Harmonic analysis and the Kuznetsov formula on GL(3,R), and subconvexity of GL(3) L-functions

Using harmonic analysis on symmetric spaces for GL(3,R), we determine the weight functions occurring in the GL(3) Kuznetsov formula explicitly,
                               and apply  this to subconvexity of GL(3) L-functions.

September 23rd                 Qingyun Wang,   University of Toronto
                               Classification of inductive limit actions of compact groups on AF algebras

                               Abstract: We shall study actions of compact groups on AF algebras of a special form, namely there is a sequence of finite dimensional subalgebras which are
                               invariant under the action and whose union is dense. If the restrictions on each finite dimensional C*-algebra are inner, then the actions are classified by
                               equivariant K-theory, by the result of David Handelman and Wulf Rossmann. We shall show that equivariant K-theory is not enough to classify if the
                               restrictions on finite dimensional C*-algebras are not inner, and discuss how we can classify such actions.

October 1st                    Lewis Bowen,  University of Texas at Austin
(Colloquium, Thursday)       
Entropy for sofic group actions

Abstract: In 1958, Kolmogorov defined the entropy of a probability measure preserving transformation. Entropy has since been central to the classification
                               theory of measurable dynamics. In the 70s and 80s researchers extended entropy theory to measure preserving actions of amenable groups (Kieffer, Ornstein-
                               Weiss). Recent work generalizes the entropy concept to actions of sofic groups; a class of groups that contains for example, all subgroups of GL(n,C).
                               Applications include the classification of Bernoulli shifts over a free group. This answers a question of Ornstein and Weiss. I'll give a broad overview
                               intended for a general audience.

October 7th                   
Eren Mehmet Kiral,  Texas A&M University
                               The Voronoi formula and double Dirichlet series

                               Abstract: A
Voronoi formula is an identity where on one side, there is a weighted sum of Fourier coefficients of an automorphic form twisted by additive
                               characters, and on the other side one has a dual sum where the twist is perhaps by more complicated exponential sums. It is a very versatile tool in
                               analytic studies of L-functions. In joint work with Fan Zhou we
come up with a proof of the identity for L-functions of degree N. The proof involves an
                               identity of a double Dirichlet series which in turn
yields the desired equality for a single Dirichlet coefficient. The proof is robust and applies to
                               L-functions which are not yet proven to
come from automorphic forms, such as Rankin-Selberg L-functions.

October 14th                   Jingbo Xia,  SUNY at Buffalo                    
                               Essential normality of submodules of the Drury-Arveson module


October 21st                   Yongle Jiang,  SUNY at Buffalo

                               Lower degree cohomology groups of algebraic group actions

                               Abstract: We study the 1st and 2nd cohomology groups of an algebraic action of a group G. Under natural assumptions, we could show that these cohomology   
                               groups "remember" the "algebraic data" of this action. Applying this result to principal algebraic actions, we show that the second cohomology group
                               H^2(G, ZG) is torsion free as an abelian group when G has property (T) as a direct corollary of Sorin Popa's celebrated cocycle superrigidity theorem; we
                               also use it  to answer, negatively, a question of Sorin Popa on the 2nd cohomology group of Bernoulli shift actions of property (T) groups.

October 28th                   Xiankun Ren,  Peking University & SUNY at Buffalo
                               Periodic measures are dense in invariant measures for residually finite amenable group actions with specification

                               Abstract: We prove that for actions of a discrete countable residually finite amenable group on a compact metric space with specification property, 
                               periodic measures are dense in the set of invariant measures. We also prove that certain expansiveactions of a countable discrete group by automorphisms of
                               compact abelian groups have specification property.

November 11th                  Bingbing Liang,   SUNY at Buffalo
                               Sofic mean length

                               Abstract: Given a unital ring R and a length function on R-modules we define a mean length function on RG-modules of a sofic group G and establish an
                               addition formula for it. We then use the mean length and the addition formula to prove an equality between the sofic mean topological dimension and the von
                               Neumann-L├╝ck rank. This is a joint work with Hanfeng Li.

Past Analysis Seminar