Analysis Seminar
Unless specified, all seminars are
Wednesday 4-5pm via Zoom. For Zoom information please send
email to hfli@math.buffalo.edu
September 29
Jingbo Xia, SUNY
at Buffalo
The Helton-Howe trace formula for submodules
Abstract
October 20
Xin Ma,
University of Memphis
4:30-5:30pm
Fiberwise
amenability and almost elementariness for
\'{e}tale groupoids
Abstract: In this talk, I will
discuss two new properties for locally compact
Hausdorff \'{e}tale groupoids. One is from a coarse
geometric view
called fiberwise amenability. Another one is called
almost elementariness, which is a new
finite-dimensional approximation property. I will
explain
how these notions relate to almost finiteness
defined by Matui and refined by Kerr and show our
almost elementariness implying tracial Z-stability
of reduced groupoid C*-algebras. As an application.
This implies that Matui's almost finiteness in the
groupoid setting also implies Z-stability when
the groupoid is minimal 2nd countable and
topological amenable. This was open in general
before. I will also present more applications if
time
permits. This is based on joint work with Jianchao
Wu.
November
3
Nathan
Wagner, Washington University in St.Louis
Weighted sstimates for the Bergman and Szego projections on strongly
pseudoconvex domains
Abstract: The Bergman and Szego projections are fundamental
operators in complex analysis in one and several complex variables.
Consequently,
the mapping properties of these operators on L^p and other function
spaces have been extensively studied. In this talk, we discuss some
recent
results for these operators on strongly pseudoconvex domains with
near minimal boundary smoothness. In particular, weighted L^p
estimates are
obtained, where the weight belongs to a suitable generalization of
the Bekolle-Bonami or Muckenhoupt class. For these domains with less
boundary regularity, we use an operator-theoretic technique that
goes back to Kerzman and Stein. We also obtain weighted estimates
for the
endpoint p=1, including weighted weak-type (1,1) estimates. Here we
use a modified version of singular-integral theory and a
generalization of the
Riesz-Kolmogorov characterization of precompact subsets of Lebesgue
spaces. This talk is based on joint work with Brett Wick and Cody
Stockdale.
November
10
Sherry Gong, Texas A&M University
Non-orientable link
cobordisms and torsion order in Floer homologies
Abstract: In a recent paper,
Juhasz, Miller and Zemke proved an inequality
involving the number of local maxima and the genus
appearing in an
oriented knot cobordism using a version of knot
Floer homology. In this talk I will be discussing
some similar inequalities for non-orientable knot
cobordisms using the torsion orders of unoriented
versions of knot Floer homology and instanton Floer
homology. This is a joint work with Marco
Marengon.
November
17
Byung-Jay Kahng, Canisius
College
Construction of a
C*-algebraic quantum groupoid from purely algebraic
data
Abstract: To properly develop a
theory of C*-algebraic quantum groupoids, some
rather technical notions such as relative tensor
product of Hilbert
spaces are needed, which can be daunting. Things can
become simpler if there exists a certain projection,
E, which can be considered as Delta(1). At
the purely algebraic level, there exists a natural
notion called Weak Multiplier Hopf algebras, which
include as special cases Hopf algebras, Multiplier
Hopf algebras,
and Weak Hopf algebras.
In this talk, we will start from only a purely
algebraic data of a WMHA, assuming the existence of
a left-invariant functional, and aim to construct a
C*-algebraic object, which should be a C*-algebraic
quantum groupoid. The construction data will
be all purely algebraic, and we will use tools from
the (vN and C*-)
weight theory.
December
1
Alexandru Chirvasitu, SUNY at Buffalo
Chain
groups and center reconstruction for
locally compact groups
Abstract: A result of Muger's
says that the center of a compact
group G can be recovered from the
category of G-representations as the
dual of the
chain group of that category: the
universal group by which the
category in question can be graded.
Trying to extend this to locally
compact groups raises a number of
interesting questions I will
mention, along with extensions of
Muger's theorem to
various classes of groups (e.g.
discrete groups with infinite
conjugacy classes, semisimple
connected Lie groups, and others).
December
8
Jiseong Kim, SUNY at Buffalo
Shifted sums of Hecke
eigenvalue squares
Abstract: The
additive divisor problem states some asymptotic
formulas for shifted convolution sums of two divisor
functions. This problem is still
open, but Matomaki, Radziwill and Tao showed that
the asymptotic formulas hold for almost all shifts.
In this talk, we will talk about an analogue of
the additive divisor problem for Hecke eigenvalue
squares.
Past
Analysis Seminar