Analysis Seminar
Unless specified, all seminars are
Wednesday 4-5pm via Zoom, or both Room 250 and Zoom. For
Zoom information please send email to hfli@math.buffalo.edu
August 31
Yi Wang,
Chongqing University
8PM, Zoom
Helton-Howe trace,
Connes-Chern character and quantization
Abstract: We study the Helton-Howe trace and
the Connes-Chern character for Toeplitz operators on
weighted Bergman spaces via the idea of
quantization. We prove a local formula for the large
t-limit of the Connes-Chern character as the weight
goes to infinity. And we show that the
Helton-Howe trace of Toeplitz operators is
independent of the weight and obtain a local formula
for the Helton-Howe trace for all weighted Bergman
spaces. The proofs are
based on an integration by parts formula and some
harmonic analysis. This talk is based on joint work
with Xiang Tang and
Dechao Zheng.
September
7
Mariusz
Tobolski, University of
Wroclaw
Zoom
The
Stone-von Neumann theorem for
locally compact quantum groups
Abstract: The Stone-von
Neumann theorem is a mathematical
result that rigorously proves the
equivalence between the two
fundamental approaches
to quantum mechanics, i.e. the
matrix mechanics of Heisenberg and
the wave mechanics of Schrödinger.
It
was then formulated by Mackey as a
theorem about certain unitary
representations of locally compact
abelian groups. In my talk, based on
yet another formulation due to
Rieffel, I will
present a Stone-von Neumann-type
theorem in the setting of locally
compact quantum groups introduced by
Kustermans and Vaes and
independently by Woronowicz.
September
14
Hanfeng
Li,
SUNY at
Buffalo
250
and Zoom
Entropy
and asymptotic
paris
Abstract:
Positive
entropy and
the existence
of nontrivial
asymptotic
pairs are both
kind of
chaotic
properties in
topological
dynamics. I
will discuss
the relation
between these
two properties
for algebraic
actions of
amemable
groups, and
how this is
related to the
strong Atiyah
conjecture in
L2-invariants
theory. This
is joint work
with Sebastian
Barbieri and
Felipe
Garcia-Ramos.
October 12
Yuqing
(Frank) Lin,
Texas
A&M
University
250
and Zoom
Entropy for actions of free groups under
bounded orbit
equivalence
Abstract:
Joint work with Lewis Bowen. The
f-invariant is
a notion of
entropy for
probability
measure
preserving
(pmp) actions
of free
groups.
It is
invariant
under measure
conjugacy and
is
an extension
of
Kolmogorov-Sinal
entropy for
actions of the
integers.
Two pmp
actions are
orbit
equivalent if
their orbits
can be matched
almost
everywhere in
a measurable
fashion.
Although
entropy is not
invariant
under orbit
equivalence in
general, work
of Austin and
Kerr-Li has
shown in
various
settings that
entropy is
invariant
under certain
stronger
notions of
quantitative
orbit
equivalence.
We add to
these results
by showing
that the
f-invariant is
invariant
under the
assumption of
bounded orbit
equivalence.
November
9
Hongming
Nie,
SUNY at
Stony Brook
250
and Zoom
A metric on
hyperbolic
components
Abstract:
In this talk,
under a mild
condition, I
will introduce
a metric on
hyperbolic
components of
rational maps.
This metric is
constructed by
considering
the
measure-theoretic
entropy with
respect to
some
equillibrium
state.
Moreover, this
metric is
conformal
equivalent to
the pressure
metric from
the
thermodynamics.
It is a joint
work with Y.M.
He.
November 16
Sagun
Chanillo,
Rutgers
University
Zoom
Local Version of Courant's Nodal Domain
Theorem
Abstract:
Let
$(M^n ,g)$ denote a smooth, compact Riemannian manifold with no
boundary. A fundamental object on this manifold is the
Laplace-Beltrami operator which has a discrete spectrum. If we
arrange the eigenvalues of the Laplacian in increasing order (for
the negative of the
Laplacian) with multiplicity, Courant's theorem states, that the
number of nodal components for the k-th eigenfunction is at most k.
A nodal
component of an eigenfunction u is the connected component of the
set where u does not vanish. In this talk we study a local version
of this
global result of Courant. The local question was raised by Donnelley
and C. Fefferman in the late 1980s. Our theorems are joint work with
A. Logunov, E. Mallinikova and D. Mangoubi.
November 30
Joseph
Hundley,
SUNY at
Buffalo
Zoom
Functorial
Descent in the
Exceptional
Groups
Abstract:
In this tallk,
I will discuss
the method of
functorial
descent. This
method, which
was discovered
by Ginzburg,
Rallis and
Soudry, uses
Fourier
coefficients
of residues of
Eisenstein
series to
attack the
problem of
characterizing
the image of
Langlands
functorial
liftings.
We'll discuss
the
general
structure, the
results of
Ginzburg,
Rallis and
Soudry in the
classical
groups, some
recent
attempts to
extend the
same ideas to
the
exceptional
groups, and
challenges and
new phenomena
which emerge
in these
attempts. The
new work
discussed will
mainly be
joint with
Baiying
Liu. Time
permitting I
may also
comment on
unpublished
work of
Ginzburg and
joint work
with Ginzburg.
Past
Analysis Seminar