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

February 14

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

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

of M H Stone from 1937 to give these simple proofs.

March 6

April 3

Hilbert-Hadamard spaces and the equivariant coarse Novikov conjecture

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

Algebraic geometry, complex analysis and combinatorics in spectral theory of periodic graph operators

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

Ultracoproducts and weak containment for flows of topological groups

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

Soficity, Amenability, and LEF-ness for topological full groups

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

distal.

Past Analysis Seminar