Analysis   Seminar    


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

February 1st                                Hanfeng Li,     SUNY at Buffalo
                                                   Entropy and L²-torsion, Part I

                                                    Abstract: Given any countable discrete group G and any countable left module M of the integral grout ring of G, one may consider the natural action of G on the Pontryagin dual of M. 
                                                    Under suitable conditions, the entropy of this action and the L²-torsion of M are defined. I will discuss the relation between the entropy and the L²-torsion, and indicate how this
                                                     confirms the conjecture of Wolfang Luck that the universal covering space of any aspherical connected finite CW-complex with nontrivial amenable fundamental group has trivial
                                                     L²-torsion. This is joint work with Andreas Thom.

February 8th                                Hanfeng Li,     SUNY at Buffalo
                                                   Entropy and L²-torsion, Part II 

February 22nd                             Jingbo Xia,    SUNY at Buffalo
                                                    Invariant subspaces for certain finite-rank perturbations of diagonal operators

                                                    Abstract: Suppose that {e_k} is an orthonormal basis for a separable, infinite-dimensional Hilbert space H. Let D=∑_k=1^∞λ_ke_k⊗e_k be a bounded operator that is diagonal with respect to  
                                                    the orthonormal basis {e_k}. Consider the operator
                                                                                                  T=D+u₁⊗v₁+…+u_n⊗v_n.
                                                    Improving a result of Foias, Jung, Ko, and Pearcy of 2007, we show that if the vectors u₁, …, u_n and v₁, …, v_n satisfy an l¹-condition with respect to the orthonormal basis {e_k}, and if T
                                                    is not a scalar multiple of the identity operator, then T has a non-trivial hyperinvariant subspace. This is joint work with Quanlei Fang.

February 29th                              Huichi Huang,   SUNY at Buffalo

March 7th                                   Anthony Weston,    Canisius College

March 29th                                 Vitaly Bergelson,    Ohio State University
(Thursday, Colloquium)

April 11th

April 25th



                                                                      
Past Analysis Seminars