Analysis Seminar
Unless specified, all seminars are
Wednesday 4-5pm at Room 250.
September
6
Jintao Deng, SUNY at
Buffalo
The equivariant coarse
Baum-Connes conjecture Part I
Abstract: The equivariant coarse
Baum-Connes conjecture claims that a certain
assembly map from the equivariant K-homology of a
metric space with
a group action to the K-theory of the Roe algebras
is an isomorphism. It has important applications
in the study of the existence of Riemannian metric
with positive scalar curvature. In this talk, I
will talk about the concept of Roe algebras which
encode the large-scale geometry of a metric space
and
group actions. The higher index of an elliptic
operator is an element of the K-theory of this
algebra. The equivariant coarse Baum-Connes
conjecture
provides an algorithm to compute its K-theory. I
will talk about our recent result that the
equivariant coarse Baum-Connes conjecture holds
for a
metric space with a group action under the
conditions that the group is amenable and the
associated quotient space is coarsely embeddable
into
Hilbert space. This is a joint work with Qin Wang
and Benyin Fu.
September
13
Jintao Deng,
SUNY at Buffalo
The
equivariant coarse Baum-Connes
conjecture Part II
September
20
Min Woong Ahn,
SUNY at
Buffalo
Hausdorff
dimensions in Pierce
expansions
Abstract: The
Pierce expansion is
one of many real
number
representation
systems. Shallit
(1986) established
the law of large
numbers, the central
limit theorem, and
the law of the
iterated logarithm
of the digits of the
Pierce expansions.
Additionally, it was
shown that the
series of iterates
under
a mapping that
yields the Pierce
expansion converges
Lebesgue-almost
everywhere. In this
talk, I will discuss
the Hausdorff
dimensions of such
sets
with Lebesgue
measure zero.
October 18
Francesc
Perera,
Universitat
Autonoma de
Barcelona
Traces on ultrapowers of C*-algebras
Abstract:
Every sequence of traces on a C*-algebra A
induces a
limit trace on
a free
ultrapower of
A. Using Cuntz
semigroup
techniques, we
characterize
when these
limit traces
are dense.
Quite
unexpectedly,
we obtain as
an application
that every
simple
C*-algebra
that is
(m,n)-pure in
the
sense of
Winter is
already pure.
This is joint
work with
Ramon Antoine,
Leonel Robert,
and Hannes
Thiel.
October 26
Lei Yang,
Institute for Advanced Study
(Colloquium,
Thu) Effective versions of
Ratner's equidistribution theorem
Abstract: I will talk about recent
progress in the study of quantitative
equidistribution of unipotent orbits in homogeneous
spaces, namely, effective
versions of Ratner's equidistribution theorem. In
particular, I will explain the proof for unipotent
orbits in SL(3,R)/SL(3,Z). The proof combines new
ideas from harmonic analysis and incidence geometry.
In particular, the quantitative behavior of
unipotent orbits is closely related to a Kakeya
model.
November
1
Jinmin Wang,
Texas
A&M
University
Stoker's problem and index theory on
manifolds with
polytope
singularities
Abstract:
The Stoker problem states that the dihedral
angles of a
convex
Euclidean
polyhedron
determine the
angles of each
face. In this
talk, I will
present joint
works with
Zhizhang Xie
and Guoliang
Yu that answer
positively to
Stoker's
problem, and
prove a more
general
dihedral
rigidity for
manifolds with
polytope
singularities.
I will briefly
introduce our
approach, the
index theory
of Dirac-type
operators on
manifolds with
polytope
singularities
under certain
boundary
conditions.
One of the key
observations
is the
essential
self-adjointness
of the
Dirac-type
operators near
conical
singularities.
Past
Analysis Seminar