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
Abstract: 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.
Past
Analysis Seminar