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FALL 2009 Seminars Schedule
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Mondays
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Analysis Seminar
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Time: 4:00-5:00pm *
Location: Cupples I, Room 199
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Host: Prof. Richard Rochberg
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Tuesdays
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Combinatorics Seminar
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Time: 2:00-3:00pm *
Location: Cupples I, Room 199
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Host: Russ Woodroofe
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Wednesdays
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Algebraic Geometry Seminar
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Time: 4:00-5:30pm *
Location: Cupples I, Room 215
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Host: Prof. Mohan Kumar
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Thursdays
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Geometry and Topology Seminar
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Time: 3:00-4:00pm *
Location: Cupples I, Room 111
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Host: Prof. Xiang Tang
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Fridays
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Wavelet Seminar
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Time: 3:30-4:30pm *
Location: Cupples I, Room 199
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Host: Prof. Guido Weiss
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* Times may vary, please consult the schedule below for details:
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SEPTEMBER 2009
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Friday, September 4
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Wavelet Seminar
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Time: 3:30-4:30pm
Location: Cupples I, Room 199
Host: Prof. Guido Weiss
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Speaker: Professor Joe Lakey
Department of Mathematics, Washington University in St. Louis
Title: Gabor window functions and their Zak transforms
Abstract: The talk will be expository. It will point out the role that
the Zak transform can play in determining represenation and convergence
properties of Gabor expansions.
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Tuesday, September 8
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Combinatorics Seminar
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Time: 2:00-3:00pm
Location: Cupples I, Room 199
Host: Russ Woodroofe
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Speaker: Professor John Shareshian
Department of Mathematics, Washington University in St. Louis
Title: The q=-1 phenomenon via homology concentration (joint work with Patricia Hersh and Dennis Stanton)
Abstract: The q=-1 phenomenon occurs when a set X admits an involution w,
and there is a polynomial f(q) with nonnegative integer coefficients that
is the generating function for some interesting statistic on X, such that
f(1)=|X| and f(-1) is the number of elements of X fixed by w. There are
many known examples of this phenomenon. Note that f(-1) expresses a
nonegative number as an alternating sum of positive numbers. Since
something is being counted, it is natural to hope that it can be expressed
as a sum of positive numbers. We show how to find such an expression in
certain cases using homology of chain complexes.
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Wednesday, September 9
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Algebraic Geometry Seminar
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Time: 2:30-4:00pm
Location: Eads, Room 211
Host: Prof. Mohan Kumar
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Speaker: Professor Mohan Kumar
Department of Mathematics, Washington University in St. Louis
Title: On unimodular rows
Abstract: TBA
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Friday, September 11
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Minor Oral
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Time: 1:00-3:00pm
Location: Cupples I, Room 199
Hosts: Profs. Roya Beheshti, Mohan Kumar
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Speaker: Wei Deng
Department of Mathematics, Washington University in St. Louis
Title: Geometry of Smooth Cubic Hypersurfaces in P4.
Abstract: In analyzing the geometry of smooth cubic hypersurfaces in
P4, we first consider the degenerate case, i.e., smoothness is
replaced by the existence of one and only one singular point --- an
ordinary double point. We will analyze their intermediate Jacobians,
and in fact their geometries are characterized in their intermediate
Jacobians. As a corollary, we shall see that smooth cubic
hypersurfaces in P4 are not rational. The talk is based on the paper
"The intermediate Jacobian of the cubic threefold" by Clemens and
Griffiths.
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Friday, September 11
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Wavelet Seminar
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Time: 3:30-4:30pm
Location: Cupples I, Room 199
Hosts: Prof. Guido Weiss
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Speaker: Ben Manning
Department of Mathematics, Washington University in St. Louis
Title: MRA constructions via low pass filters
(matricial) in higher dimensions and in the composite case
Abstract: Ben Manning has a rather natural way of studying the MRA constructions via low pass
filters (matricial) in higher dimensions and in the composite case. He will
explain this and indicate how the Wutam connectivity can be transferred to
this case.
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Monday, September 14
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Analysis Seminar
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Time: 4:00-5:00pm
Location: Cupples I, Room 199
Host: Prof. Richard Rochberg
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Speaker: Professor Richard Rochberg
Department of Mathematics, Washington University in St. Louis
Title: Organization of the Seminar
Abstract:This will be a brief meeting to organize the seminar for the semester
and do preliminary scheduling.
If you are interested in participating in the seminar and can't make
this meeting please let me know.
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Tuesday, September 15
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Combinatorics Seminar
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Time: 2:00-3:00pm
Location: Cupples I, Room 199
Host: Russ Woodroofe
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Speaker: Professor John Shareshian
Department of Mathematics, Washington University in St. Louis
Title: The q=-1 phenomenon via homology concentration (joint work with Patricia Hersh and Dennis Stanton)
Abstract: The q=-1 phenomenon occurs when a set X admits an involution w,
and there is a polynomial f(q) with nonnegative integer coefficients that
is the generating function for some interesting statistic on X, such that
f(1)=|X| and f(-1) is the number of elements of X fixed by w. There are
many known examples of this phenomenon. Note that f(-1) expresses a
nonegative number as an alternating sum of positive numbers. Since
something is being counted, it is natural to hope that it can be expressed
as a sum of positive numbers. We show how to find such an expression in
certain cases using homology of chain complexes.
This is a continuation of last week's combinatorics seminar. Having talked about the classical viewpoint, John Shareshian will present the homological wiewpoint.
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Wednesday, September 16
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Algebraic Geometry Seminar
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Time: 4:00-5:30pm
Location: Cupples I, Room 215
Host: Prof. Mohan Kumar
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Speaker: Wei Deng
Department of Mathematics, Washington University in St. Louis
Title: Geometry of Smooth Cubic Hypersurfaces in P4
Abstract: In analyzing the geometry of smooth cubic hypersurfaces in P4, we
first consider the degenerate case, i.e., smoothness is replaced by the
existence of one and only one singular point --- an ordinary double point.
We will analyze their intermediate Jacobians, and in fact their geometries
are characterized in their intermediate Jacobians. As a corollary, we shall
see that smooth cubic hypersurfaces in P4 are not rational. The talk is
based on the paper "The intermediate Jacobian of the cubic threefold" by
Clemens and Griffiths.
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Thursday, September 17
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Geometry and Topology Seminar
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Time: 3:00-4:00pm
Location: Cupples I, Room 111
Host: Prof. Xiang Tang
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Speaker: Professor Xiang Tang
Department of Mathematics, Washington University in St. Louis
Title: Organization of the Seminar
Abstract: We will discuss the plan of the semester. Everybody interested in
geometry and topology is welcome to join us.
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Thursday, September 17
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Colloquium
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Time: Tea: 4:00-4:30pm
Talk: 4:30-5:30pm
Location: Cupples I, Room 199
Host: Prof. Richard Rochberg
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Speaker: Professor Guoliang Yu
Department of Mathematics, Vanderbilt University
Title: Higher index theory and its applications
Abstract: I will give an introduction to higher index theory of elliptic
differential operators and discuss its applications to geometry and
topology. I will make an effort for this talk to be accessible to a general
audience including graduate students.
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Friday, September 18
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Wavelet Seminar
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Time: 3:00-4:30pm
Location: Cupples I, Room 199
Host: Prof. Guido Weiss
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Speaker: Kabe Moen
Department of Mathematics, Washington University in St. Louis
Title: Rectangular weights on the torus, with applications to
Schauder bases for weighted Lebesgue spaces, principle shift
invariant spaces, and Gabor systems
Abstract: In this talk we will go over some basic results about
bases in vector spaces. We then give a connection between
rectangular A_p weights on the torus and Schauder bases for
corresponding L^p spaces. When p=2 we present applications
to principal shift invariant spaces and Gabor systems.
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Monday, September 21
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Analysis Seminar
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Time: 4:00-5:00pm
Location: Cupples I, Room 199
Host: Prof. Richard Rochberg
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Speaker: Nic Sedlock
Department of Mathematics, Washington University in St. Louis
Title: Multiplication of truncated Toeplitz operators
Abstract: In the Hardy space of the unit disc, there is a simple
necessary and sufficient condition for the product of two Toeplitz
operators to itself be a Toeplitz operators. In the setting of
backward shift-invariant subspaces of the Hardy space (so-called
model spaces), the equivalent question is more delicate. We will
present a necessary and sufficient condition for the product of two
truncated Toeplitz operators to itself be a truncated Toeplitz
operator, and discuss some consequences of the condition.
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Tuesday, September 22
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Combinatorics Seminar
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Time: 2:00-3:00pm
Location: Cupples I, Room 199
Host: Russ Woodroofe
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Speaker: Russ Woodroofe
Department of Mathematics, Washington University in St. Louis
Title: Spectral sequences in combinatorics
Abstract: An important invariant of many combinatorial objects is given by
the homology of associated simplicial complexes. I'll introduce the tool
of spectral sequences for computing homology. I'll start with some
general background on and examples of spectral sequences. I'll then
specialize to a situation considered by Kozlov for computing homology of
posets.
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Wednesday, September 23
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Geometry and Topology Seminar
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Time: 3:00-4:00pm
Location: Cupples I, Room 111
Host: Prof. Xiang Tang
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Speaker: Professor Jerome Kaminker
Department of Mathematics, UC Davis & IUPUI
Title: Homotopy invariance of characteristic numbers
Abstract: First we will discuss characteristic numbers of manifolds and
the origin of questions regarding whether they are homotopy invariant or
not. One of the approaches to studying this involves index theory of
elliptic operators, so we will survey this next. Finally, some joint work
with Xiang Tang applying these ideas to a certain class of characteristic
numbers will be discussed.
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Wednesday, September 23
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Algebraic Geometry Seminar
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Time: 4:00-5:30pm
Location: Cupples I, Room 215
Host: Prof. Mohan Kumar
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Speaker: Sara Gharahbeigi
Department of Mathematics, Washington University in St. Louis
Title: Smoothness of Hilbert scheme of ropes
Abstract: A curve C is a d-Rope on a reduced curve Y if it defines a
multiplicity d
structure on Y.
consider the Hilbert scheme of 2-ropes with a fixed genus, we will
investigate the smoothness of this Hilbert scheme at a point corresponding
to a 2-rope.
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Thursday, September 24
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Colloquium
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Time: Tea: 4:00-4:30pm
Talk: 4:30-5:30pm
Location: Cupples I, Room 199
Host: Prof. Xiang Tang
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Speaker: Professor Nigel Higson
Department of Mathematics, Penn State
Title: C*-algebras and the parametrization of irreducible group representations
Abstract: C*-algebras were invented, in part, as a tool to address the unitary
representation theory of Lie groups. However close associations
between C*-algebra theory and representation theory more or less ended
in the 1950's, in the infancy of both fields. A reconciliation of
sorts began in the 1980's with the development of new C*-algebra
methods inspired by the Atiyah-Singer index theorem. I shall try to
present one aspect of this: an approach to parametrizing the tempered
irreducible representations of a semisimple group using its so-called
Cartan motion group.
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Friday, September 25
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Wavelet Seminar
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Time: 3:30-4:30pm
Location: Cupples I, Room 199
Host: Prof. Guido Weiss
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Speaker: Professor Ilya Krishtal
Department of Mathematics, Northern Illinois University
Title: Wiener's Lemma and Frame memory localization
Abstract: Noncommutative Wiener's lemma extensions are usually
presented as statements about inverse closedness of certain Banach
algebras of infinite matrices. In this talk I will argue that Wiener's
lemma is really a statement about the preservation of memory
localization by inverse operators, and the way the memory is defined
is irrelevant to a large extent. In particular, I will present
versions of Wiener's lemma in cases when the memory of an operator is
defined with respect to frames, fusion frames, fuzzy fusion frames,
and even g-frames.
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Tuesday, September 29
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Combinatorics Seminar
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Time: 2:00-3:00pm
Location: Cupples I, Room 199
Host: Russ Woodroofe
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Speaker: Russ Woodroofe
Department of Mathematics, Washington University in St. Louis
Title: Spectral sequences in combinatorics, Part II
Abstract: Last week I discussed
the general set-up of a spectral sequence; this week I will briefly review
this general set-up, then specialize to the approach of Kozlov for using
spectral sequences to compute homology of posets.
A useful article for getting the general background is "You could
have invented spectral sequences!" by Tim Chow, for anyone who missed last
week or just wants more.
http://www-math.mit.edu/~tchow/spectral.pdf
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Wednesday, September 30
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Colloquium
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CANCELLED
Time: Tea: 4:00-4:30pm
Talk: 4:30-5:30pm
Location: Cupples I, Room 199
Host: Prof. Roya Beheshti-Zavareh
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CANCELLED
Speaker: Professor Joseph Landsberg
Department of Mathematics, Texas A&M
Title: Some algebraic geometry useful for signal processing, statistics
and complexity theory
Abstract: In many areas of science one needs to measure properties of tensors. Two
important such properties are the rank and border rank. In this talk I
will explain some of the geometry of these properties. (Relevant
geometric objects are the secant varieties of Segre varieties).
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OCTOBER 2009
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Thursday, October 1
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Geometry and Topology Seminar
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Time: 3:00-4:00pm
Location: Cupples I, Room 111
Host: Prof. Xiang Tang
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Speaker: Liwei Chen
Department of Mathematics, Washington University in St. Louis
Title: An Introduction to Morse Homology
Abstract: In this talk, I give a definition of Morse homology by outlining the basic ideas and showing some examples.
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Thursday, October 8
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Geometry and Topology Seminar
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Time: 3:00-4:00pm
Location: Cupples I, Room 111
Host: Prof. Xiang Tang
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Speaker: Liwei Chen
Department of Mathematics, Washington University in St. Louis
Title: An Introduction to Morse Homology, Part II
Abstract: I will give a proof for the isomorphism between Morse homology
and Singular homology.
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Friday, October 9
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Wavelet Seminar
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Time: 3:30-4:30pm
Location: Cupples I, Room 199
Host: Prof. Guido Weiss
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Speaker: Joe Lakey
Department of Mathematics, Washington University in St. Louis
Title: Sampling in principle shift invariant spaces
Abstract: The Shannon sampling theorem says that elements of the
Paley-Wiener space of square-integrable functions bandlimited to a unit
interval can be expressed as sums of their integer samples interpolated by
shifted sinc functions.
This minor miracle relies on the fact that the sinc function has an
interpolation property: its value at the origin is one and its value at
all other integers is zero, and that the sinc function is orthogonal to
its integer shifts.
The miracle is tempered by the fact that the sinc function has lousy
decay, so a lot of samples are needed to approximate a bandlimited
function at any given point. Membership in the Paley-Wiener space is a
physical property, but so is membership in other shift invariant spaces.
Does such a space also admit a "sampling formula"?
This talk will discuss some work done in the past 10 years that has
sought, in part, to provide conditions under which the answer to this
question is "yes" but has also sought descriptions of when one sampling
formula is better than another. Some of this is joint work with Jeff
Hogan.
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Wednesday, October 14
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Lecture
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Time: 10:00-11:30am
Location: Eads, Room 003
Host: Prof. Steven Krantz
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Speaker: Lance Carnes
CEO of PC-TeX
Title: LaTeX in Short Order
Authors: Heike Hofmann, Di Cook, and the ISU Statistical Graphics group
Note:It is best (though not compulsory) for participants to
bring a notebook computer with some form of TeX installed.
We have a site license for PC-TeX, and Steven Xiao can
tell you how to install it.
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Wednesday, October 14
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Lecture
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Time: 2:30-4:00pm
Location: Eads, Room 013
Host: Prof. Steven Krantz
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Speaker: Lance Carnes
CEO of PC-TeX
Title: LaTeX in Short Order
Authors: Heike Hofmann, Di Cook, and the ISU Statistical Graphics group
Note:It is best (though not compulsory) for participants to
bring a notebook computer with some form of TeX installed.
We have a site license for PC-TeX, and Steven Xiao can
tell you how to install it.
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Thursday, October 15
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Colloquium
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Time: Tea: 4:00-4:30pm
Talk: 4:30-5:30pm
Location: Cupples I, Room 199
Host: Prof. Nan Lin
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Speaker: Professor Dianne Cook
Department of Statistics, Iowa State University
Title: Delayed, Cancelled, On Time, Boarding...Flying in the USA
Authors: Heike Hofmann, Di Cook, and the ISU Statistical Graphics group
Abstract:As part of the Joint Statistical meetings in 2009, the Statistical
Graphics and Computing sections of the American Statistical
Association hosted a data expo competition. The data provided by from
the Research and Innovative Technology Administration (RITA) and the
Bureau of Transportation Statistics contained details for all
commercial flights in the USA between October 1987 and December
2008. That's about 12Gb of data!
In this talk we will discuss our findings about air travel in the USA,
performance of the major carriers, problems with particular airports,
and the ways to analyze such a large amount of data. You might even
gain some tips to improve the quality of your next flight.
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Thursday, October 22
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Colloquium
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Time: Tea: 4:00-4:30pm
Talk: 4:30-5:30pm
Location: Cupples I, Room 199
Host: Prof. Nan Lin
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Speaker: Professor Tiejun Tong
Department of Applied Mathematics, University of Colorado at Boulder
Title: Improved mean estimation for high-dimensional data and its application to diagonal discriminant analysis
Abstract: High-dimensional data such as microarrays have created new challenges to
traditional statistical methods. In particular, the standard estimates of the mean vector
are usually unreliable when the number of samples is small. To address this problem, we
propose a family of shrinkage estimators for the mean vector under the assumptions of
unequal and unknown variances. We show that the proposed estimators are minimax and
thus dominate the sample mean under the quadratic loss function. The proposed method
is general and widely applicable, whereas we illustrate its usefulness in the framework
of discriminant analysis. Speci¯cally, we propose a shrinkage-based diagonal discrimi-
nant rule and demonstrate its improvement over the original competitor through both
simulations and real data analysis.
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NOVEMBER 2009
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Wednesday, November 4
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Colloquium
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Time: Tea: 4:00-4:30pm
Talk: 4:30-5:30pm
Location: Cupples I, Room 199
Host: Prof. Roya Beheshti-Zavareh
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Speaker: Professor Dragos Oprea
Department of Mathematics, University of California, San Diego
Title: TBA
Abstract: TBA
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Monday, November 9
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Analysis Seminar
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Time: 4:00-5:00pm
Location: Cupples I, Room 199
Host: Prof. Richard Rochberg
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Speaker: Professor Jeremy Chapman
Department of Mathematics, University of Missouri, Columbia
Title: TBA
Abstract: TBA
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Thursday, November 19
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Colloquium
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Time: Tea: 4:00-4:30pm
Talk: 4:30-5:30pm
Location: Cupples I, Room 199
Host: Prof. Nan Lin
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Speaker: Professor Yuhong Yang
School of Statistics, University of Minnesota
Title: TBA
Abstract: TBA
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SPRING 2010 Seminars Schedule
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APRIL 2010
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Wednesday, April 14, 2010
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Colloquium
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Time: 4:00-5:00pm
Location: TBA
Hosts: Profs. David Wright, Ken Kelton, Ram Cowsik
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Speaker: Professor Srinivasa Varadhan
Courant Institute of Mathematical Sciences, New York University
Title: TBA
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Thursday, April 15, 2010
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Colloquium
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Time: Tea: 4:00-4:30pm
Talk: 4:30-5:30pm
Location: Cupples I, Room 199
Host: Prof. Al Baernstein
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Speaker: Professor Terry Sheil-Small
Department of Mathematics, University of York, England
Title: TBA
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Thursday, April 22, 2010
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Loeb Undergraduate Lecture in Mathematics
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Time: Tea: 4:00-4:30pm
Talk: 4:30-5:30pm
Location: TBA
Host: Prof. Ronald Freiwald
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Speaker: Professor Martin Golubitsky
Department of Mathematics and Director of the Mathematical
Biosciences Institute, Ohio State University
Title: Symmetries and Animal Gaits
Abstract: Many gaits of four-legged animals can be described by
spatio- temporal symmetries. For example, when a horse paces it moves
both left legs in unison and then both right legs and so on. The
motion is
described by two symmetries: Interchange front and back legs, and
swap left and right legs with a half-period phase shift.
Biologists postulate the existence of a central pattern generator
(CPG) in the
neuronal system that sends periodic signals to the legs. CPGs can
be thought of as electrical circuits that produce periodic signals
and can be modeled by coupled systems of differential equations
with
symmetries based on leg permutation. In this lecture we discuss
animal gaits; describe how periodic solutions with prescribed spatio-
temporal symmetry can be formed in symmetric systems; construct a
CPG
architecture that naturally produces quadrupedal gait rhythms; and
make several testable predictions about gaits.
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