Analysis Seminar
Unless specified, all seminars are
Wednesday 4-5pm at 250 Math
Building.
January 13th
Organizational
Meeting
January 27th
Hanfeng Li, SUNY at
Buffalo
Entropy
and
Fuglede-Kadison
determinant,
Part
I
Abstract: For any discrete
group G and any element f in the integral group ring ZG of G, one may
consider the algebraic action of G associated to f, i.e., the shift
action of
G
on
the
Pontryagin
dual
of
ZG/ZGf.
When
G
is
amenable,
the
entropy
is
defined
for
actions
of
G.
I
will
discuss
the
relation
between
the
entropy of the above algebraic
action and the Fugelde-Kadison
determinant of f in the group von Neumann algebra of G.
February 3rd
Hanfeng Li,
SUNY
at
Buffalo
Entropy and Fuglede-Kadison determinant, Part II
February
11th
David Kerr,
Texas
A&M
University
(Thursday, Colloquium)
Topological
entropy
for
actions
of
sofic
groups
Abstract: Recently
Lewis Bowen introduced a notion of entropy for measure-preserving
actions of sofic groups which he used to solve the Bernoulli shift
isomorphism
problem for a large class of
nonamenable groups. I will show that by taking an
operator-algebraic viewpoint one can define a topological version of
Bowen's measure
entropy
and
then discuss
how the two are related via a variational principle.
February
24th
Joshua Isralowitz,
SUNY
at
Buffalo
Heat
flow,
BMO,
and
the
compactness
of
Toeplitz
operators
Abstract: Given a
BMO1 function f on Cn, we can take
the Berezin transform (better known as the ``heat transform") f~(t0)
of f with respect to the
weighted
Segal-Bargmann
space
H2 (Cn,
dμt0).
In
this talk, we discuss the question of whether
f~(t0) vanishing at infinity for
some t0 > 0
implies
that f~(t) vanishes at
infinity
for
all
t >
0. Moreover, we
discuss the same question in the context of the weighted Bergman space
of the unit ball, discuss what implications these results have for
the
compactness
of
Toeplitz
operators
in
both
the
weighted
Bergman
and
Segal-Bargmann space situation, and finally discuss some new
compactness and Schatten class
membership
results
for
Toeplitz
operators
on
H2 (Cn,
dμt).
This
is joint work with W. Bauer and L. Coburn.
March
17th
Jonathan Dimock,
SUNY
at
Buffalo
Renormalization
Group
Methods
March
31st
Nikolai Vasilevski,
CINVESTAV del I.P.N., Mexico
On
compactness
of
commutators
and
semi-commutators
of
Toeplitz
operators on the Bergman space
April
7th
David Blecher,
University
of
Houston
One-sided ideals and structure of operator algebras
Abstract: We begin by
describing a new noncommutative topology for
(possibly nonselfadjoint) operator algebras, related to the concept
of `open projections' for
C*-algebras.
We
connect
some
of
this to some ideas in Banach algebra
theory, and use it to study the structure of a new class of
nonselfadjoint algebras.
April
15th
Dechao Zheng,
Vanderbilt University
(Thursday, Colloquium)
The
spectrum
and
essential
spectrum of Toeplitz operators with
harmonic symbols
Abstract: On the Hardy space, by means of an elegant and
ingenious argument, Widom showed that the spectrum of a bounded
Toeplitz operator is always connected
and
Douglas
showed
that
the essential spectrum
of a bounded Toeplitz operator is also connected. On the Bergman space,
McDonald and Sundberg showed that the
essential
spectrum
of
Tφ
is connected for φ a harmonic function on D if φ is
either real-valued or piecewise continuous on the boundary of the unit
disk. They asked
the
problem
whether the essential spectrum of a Toeplitz operator on
the Bergman space with bounded harmonic symbol is connected. In
my
talk, I will present my joint
work
with
Sundberg to show
examples
that the spectrum and the essential spectrum of a Toeplitz
operator
with bounded harmonic symbol is disconnected.
Past Analysis Seminars