Analysis   Seminar    

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

February 14                   Jintao Deng,   SUNY at Buffalo                                                 
The maximal rational Novikov conjecture and the coarse embeddability

Let C be the smallest collection of countable, discrete groups that contains all coarsely embeddable groups and is closed under inductive
                                      limits and extensions. This collection contains many groups, including the non-coarsely embeddable groups constructed by Arzhantseva-Tessera and
                                      the Gromov's monster group. In this talk, I will talk about the result that the maximal rational Novikov conjecture holds for each group in C. I will also
                                      talk about the applications of the maximal rational Novikov conjecture in geometry. This is based on a recent result with G. Tian, Z. Xie and G. Yu.


February 21                   Jingbo Xia,   SUNY at Buffalo                                                 
Fock space: a bridge between Fredholm index and the quantum Hall effect

                                     Abstract: We identify the quantized Hall conductance of Landau levels with a Fredholm index, by using the theories of Helton-Howe-Carey-Pincus,
                                      and Toeplitz operators on the classic Fock space and higher Fock spaces.  The index computations reduce to the single elementary one for the lowest
                                      Landau level. This brings new insights to the extraordinarily accurate quantization of the Hall conductance as measured in quantum Hall experiments.

February 28                   Mohan Ramachandran,   SUNY at Buffalo                                                 
Maximal Spectrum, Stone Cech, and Stone Weierstrass theorems

                                     Abstract: In this talk I will use the maximal spectrum with Zariski Topology to give simple proofs of the theorems in the title. We use ideas from a paper
                                      of M H Stone from 1937 to give these simple proofs.

March 6                        
Jintao Deng,   SUNY at Buffalo                                                 
The maximal rational Novikov conjecture and the coarse embeddability, Part II

April 3                            Liang Guo,    East China Normal University
                                       Hilbert-Hadamard spaces and the equivariant coarse Novikov conjecture

                                       Abstract: The equivariant coarse Novikov conjecture synthesizes all the Novikov-type conjectures, including the strong Novikov conjecture for
                                       groups and the coarse Novikov conjecture for metric spaces. It has fruitful applications in topology and geometry. In a recent work of Sherry Gong,
                                       Jianchao Wu, and Guoliang Yu, a notion of Hilbert-Hadamard space is introduced to study the Novikov conjecture for specific groups, which can be
                                       seen as an infinite-dimensional Hadamard manifold. To generalize their idea to the equivariant coarse Novikov conjecture, in this talk, we study a
                                       dynamic system that admits an equivarinat coarse embedding into an admissible Hilbert-Hadamard space. I will start with several applications of
                                       the equivariant Novikov conjecture and show that the equivariant coarse Novikov conjecture holds for such a dynamic system. This is based on a
                                       joint work with Qin Wang, Jianchao Wu, and Guoliang Yu. 

April 10                          Wencai Liu,   Texas A&M University
                                       Algebraic geometry, complex analysis and combinatorics in spectral theory of periodic graph operators

                                       Abstract: In this talk, we will discuss the significant role that the algebraic and analytic properties of complex Bloch and Fermi varieties play in the
                                       study of periodic operators. I will begin by highlighting recent discoveries about these properties, especially their irreducibility. Then, I will show how
                                       we can use these findings, together with techniques from complex analysis and combinatorics, to study spectral and inverse spectral problems
                                       arising from periodic operators.

April 17                          Andy Zucker,   University of Waterloo
                                       Ultracoproducts and weak containment for flows of topological groups

                                       Abstract: We develop the theory of ultracoproducts and weak containment for flows of arbitrary topological groups. This provides a nice
                                       complement to corresponding theories for p.m.p. actions and unitary representations of locally compact groups.  We isolate a new class of
                                       topological groups, which we call Fubini groups, for which iterated ultracopowers of certain G-flows behave nicely.  Among the Fubini groups are
                                       the class of locally Roelcke precompact groups, for which the theory is especially rich. For these groups, we can define for certain families of G-flows
                                       a suitable compact space of weak type. When G is locally compact, all G-flows belong to one such family, yielding a single compact space describing
                                       all weak types of G-flows.

May 1                             Xin Ma,   Fields Institute
                                       Soficity, Amenability, and LEF-ness for topological full groups

                                       Abstract: Topological full groups, as an algebraic invariant, were introduced to study continuous orbit equivalence relations by Giordano, Putnam,
                                       and Skau. Then, there groups have been found applications to geometric group theory by providing interesting examples with certain properties
                                       such as simplicity, soficity, amenability, and LEF-ness. In this talk, I will show methods of establishing the soficity and LEF-ness for topological full
                                       groups. Moreover, I will explain how one can obtain amenability from the sofic approximations when the acting group is amenable and the action is

Past Analysis Seminar