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SPRING 2010 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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Statistics Seminar
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Time: 4:30-5:30pm *
Location: Cupples I, Room 199
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Host: Prof. Nan Lin
Statistics Seminar Schedule
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Wednesdays
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Graduate Student Seminar
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Time: 1:00-2:00pm *
Location: Cupples I, Room 199
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Host: Prof. Guido Weiss
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Graduate Organized Talks Seminar
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Time: 4:00-5:00pm *
Location: Cupples I, Room 199
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Host: Raphiel Murden
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Math Club
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Time: 5:30-7:00pm *
Location: Cupples I, Room 199
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Host: Rajan Mehta
See Math Club page.
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Thursdays
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Combinatorics Seminar
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Time: 12:00-1:00pm *
Location: Cupples I, Room 199
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Host: Russ Woodroofe
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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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Geometry and Topology Seminar
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Time: 4:00-5:00pm *
Location: Cupples I, Room 207
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Host: Prof. Xiang Tang
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* Times may vary, please consult the schedule below for details:
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MARCH 2010
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Tuesday, March 2
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Algebraic Geometry Seminar
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Time: 4:00-5:30pm
Location: Cupples I, Room 216
Host: Prof. Mohan Kumar
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Speaker: Wei Deng
Department of Mathematics, Washington University in St. Louis
Title: Fourier-Mukai Transform and Generic Vanishing
Abstract: TBA
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Wednesday, March 3
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Minor Oral
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Time: 1:00-2:00pm
Location: Cupples I, Room 199
Host: Prof. Renato Feres
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Speaker: Timothy Chumley
Department of Mathematics, Washington University in St. Louis
Title: Martin Boundaries and Random Walks
Abstract: An introduction to discrete potential theory. We analogize
the Poisson integral representation of positive harmonic functions on
the disk to the realm of random walks on a discrete state space. We
will use such a representation to study the asymptotic behavior of a
transient random walk.
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Wednesday, March 3
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Graduate Organized Talks Seminar
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Time: 5:00-6:00pm
Location: Cupples I, Room 207
Host: Raphiel Murden
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Speaker: Safdar Quddus
Department of Mathematics, Washington University in St. Louis
Title: Classification of Non-commutative torus upto morita equivalence
Abstract: We shall see the definition of non-commutative torus, some
projections on it shall be constructed. Isomorphism of two of these torus
shall be defined and we shall when two are isomorphic. Later on we shall see
an equivalence relation on these torus and see when is that attained. I hope
this talk be accessible to everyone with basic functional analysis.
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Thursday, March 4
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Minor Oral
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Time: 11:00-12:30pm
Location: Cupples I, Room 199
Host: Prof. Xiang Tang
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Speaker: Safdar Quddus
Department of Mathematics, Washington University in St. Louis
Title: Non-commutative torus, K-Theory and morita equivalence
Abstract: For every irrational number we can define a non-commutative
torus associated to it. We shall define it then shall see how it is
different from torus, shall try to compute its K theory(K_0 and K_1).
And shall classify it upto isomorphism and morita equivalence.
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Thursday, March 4
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Combinatorics Seminar
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Time: 12:00-1:00pm
Location: Cupples I, Room 199
Host: Russ Woodroofe
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Speaker: Cindy Traub
Department of Mathematics, Southern Illinois University
Title: The computational complexity of optimal redistricting
Abstract: Measurements in population shifts from the US census dictate whether
existing boundaries of political districts will change or remain the
same. The drawing of these boundaries are governed by a complex mix
of rules describing "fairness", and the actual drawing is often left
to the party with majority representation. We will examine a result
of Puppe and Tasnadi that proves optimal partisan redistricting with
geographical constraints to be NP-Complete.
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Tuesday, March 16
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Algebraic Geometry Seminar
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Time: 4:00-5:30pm
Location: Cupples I, Room 216
Host: Prof. Mohan Kumar
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Speaker: Prof. Roya Beheshti-Zavareh
Department of Mathematics, Washington University in St. Louis
Title: A Characterization of
Rationally Connected Varieties
Abstract: TBA
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Wednesday, March 17
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Graduate Organized Talks Seminar
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Time: 4:00-5:00pm
Location: Cupples I, Room 199
Host: Raphiel Murden
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Speaker: Michael Deutsch
Department of Mathematics, Washington University in St. Louis
Title: Minimal curves and the spinor representation
Abstract: Suppose we have a curve. We want to compute its curvature at a
point. We can construct the Frenet frame, right? Not if its minimal!
Cartan considered (and solved) the problem of determining curvature of
parameterized complex curves in C^3 whose tangent vector has "zero
length." We will present a slick spin-geometric approach to Cartan's
problem which we think makes the notion of curvature in this context
actually understandable.
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Friday, March 19
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Colloquium
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Time: Tea: 3:30-4:00pm
Talk: 4:00-5:00pm
Location: Cupples I, Room 199
Host: Prof. Nan Lin
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Speaker: Professor Yazhen Wang
Department of Mathematics, University of Wisconsin at Madison
Title: Modeling and Analyzing High-Frequency Financial Data
Abstract: Volatilities of asset returns are central to the theory and practice
of asset pricing, portfolio allocation, and risk management. In
financial economics,
there is extensive research on modeling and forecasting volatility up
to the daily level based on Black-Scholes, diffusion, GARCH,
stochastic
volatility models and implied volatilities from option prices.
Nowadays, thanks to technological innovations, high-frequency
financial data are
available for a host of different financial instruments on markets of
all locations and at scales like individual bids to buy and sell, and
the full
distribution of such bids. The availability of high-frequency data
stimulates an upsurge interest in statistical research on better
estimation of volatility.
This talk will start with a review on low-frequency financial time
series and high-frequency financial data. Then I will introduce
popular realized
volatility computed from high-frequency financial data and present my
work on analyzing jump and volatility variations and estimating
volatility matrices of large size.
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Friday, March 19
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Geometry and Topology Seminar
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Time: 4:00-5:00pm
Location: Cupples I, Room 207
Host: Prof. Xiang Tang
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Speaker: Rajan Mehta
Department of Mathematics, Washington University in St. Louis
Title: Adjoint superrepresentations of a Lie groupoid
Abstract: Lie groupoids are a generalization of Lie groups that incorporate both
"internal" and "external" symmetries. Representation theory is a valuable
tool for studying Lie groups, so it would be nice to similarly utilize
representation theory in the study of Lie groupoids. There is a reasonably
natural definition of Lie groupoid representation, but it unfortunately
fails to include an adjoint representation. However, it turns out that this
problem can be averted if we allow for the more general notion of
"superrepresentation". Although the adjoint superrepresentations are not
canonical, they all arise as manifestations of something that is canonical.
I will describe this canonical object and sketch how superrepresentations
can be produced from it.
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Tuesday, March 23
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Algebraic Geometry Seminar
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Time: 4:00-5:30pm
Location: Cupples I, Room 216
Hosts: Prof. Mohan Kumar
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Speaker: Professor Adrian Clingher
Department of Mathematics, University of Missouri, St. Louis
Title: Special Two-Isogenies on K3 Surfaces
Abstract: Let Z be the minimal resolution of a double cover of the
projective
plane branched over six distinct lines. The surface Z is a K3 surface with
Picard rank 16 or higher. I will describe a special involution of Z that
determines a two-isogeny of K3 surfaces.
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Wednesday, March 24
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Colloquium
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Time: Tea: 3:00-3:30pm
Talk: 3:30-4:30pm
Location: Cupples I, Room 199
Host: Prof. Quo-Shin Chi
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Speaker: Professor Reiko Miyaoka
Department of Mathematics, Tohoku University
Title: Isoparametric hypersurface theory and its applications
Abstract: Starting with an introduction, I will
mention the latest results on the classification problem
of the isoparametric hypersurfaces.
Also, I'd like to talk about the relations with special manifolds,
calibrated submanifolds, and a few other topics.
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Thursday, March 25
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Senior Honor Thesis Presentation
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Time: 10:00-11:00am
Location: Cupples I, Room 199
Hosts: Prof. Ronald Freiwald
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Speaker: Andrew Wilson
Department of Mathematics, Washington University in St. Louis
Title: Explorations of a Generalization of
the Descent Statistic
Abstract: In his recent PhD thesis, Denis Chebikin defined a number
of variations on the standard notions of descents and inversions from
the theory of permutations. One of these variations is a
generalization of the descent statistic. Traditionally, a permutation
is said to have a descent at position i if its value at position i is
greater than its value at position i+1. In the generalized form
proposed by Chebikin, a permutation is said to have a k-descent at
position i if the subsequence of length k beginning at position i has
an odd relative ordering. In this paper, we explore two properties of
this generalization that have not yet been addressed by Chebikin.
First, we aim to calculate exactly how many permutations have a
certain descent set. We are able to calculate these values for k =
n-1 and k = n-2, and we state some ideas about the general case.
Second, we attempt to understand how the Solomon descent algebra
functions in relation to the new concept of descents. Specifically,
when k = n-1, we see that, if we assume the descent algebra exists,
it has an interesting structure, but when k = n-2, we find that the
traditional descent algebra does not exist.
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Thursday, March 25
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Combinatorics Seminar
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Time: 12:00-1:00pm
Location: Cupples I, Room 199
Hosts: Russ Woodroofe
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Speaker: Rajan Mehta
Department of Mathematics, Washington University in St. Louis
Title: Simplicial sets, groups, and the resulting insanity
Abstract: I will review the "nerve" construction, which provides a way to
construct the classifying space of a group as a simplicial set.
One of the interesting features of this construction is that it
is in some sense reversible--any simplicial set satisfying
certain properties is the classifying space of a group. If you
look at this statement the right way, you may even be led to
the scandalous conclusion that "simplicial set satisfying
certain properties" is the right way to *define* a group. And
if you're feeling brazen, you might think to tweak those
properties and see what happens. Go ahead and do it, I dare
you.
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Thursday, March 25
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Taibleson Lecture
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Time: Tea: 4:00-4:30pm
Talk: 4:30-5:30pm
Location: Cupples I, Room 199
Hosts: Profs. Al Baernstein, Guido Weiss
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Speaker: Professor Rodrigo Bañuelos
Department of Mathematics, Purdue University
Title: Lévy processes and Fourier multipliers
Abstract: Martingales arising from Brownian motion can be used to study properties of several classical Fourier multipliers, including the Hilbert transform, the Riesz transforms (and their Gaussian versions) and the Beurlin-Ahlfors operator. In this lecture we will explore similar techniques where stochastic integrals with respect to Brownian motion are replaced by similar quantitites arising from Lévy processes. This approach leads to a class of Fourier (Lévy) multipliers for which one gets $L^p$ estimates that are similar to those obtained for the above mentioned singular integrals.
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Friday, March 26
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Geometry and Topology Seminar
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Time: 4:00-5:00pm
Location: Cupples I, Room 207
Hosts: Prof. Xiang Tang
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Speaker: Professor Hongkun Zhang
Department of Mathematics and Statistics, University of Massachusetts Amherst
Title: Spectral gaps of transfer operators for billiards
Abstract: In this talk I will first introduce classical billiards, which originated
from the Boltzman-Sinai's Ergodic Hypotheses.
For chaotic billiards, the system-generated stochastic processes has
exponential decay of correlations if the transfer operator has a spectral
gap (at 1). It was shown that there are many types of classical billiards
including the Bunimovich Stadium and billiards with cusps that only have
slow decay of correlations. As a result, there are no spectral gaps for
these systems. On the other hand, for a class of random
billiards that is the subject of this talk, we are able to show that their
transfer
operators, or Markov operators have a positive
spectral gap even if the boundary of the billiard cell contains arcs and
cusps. Furthermore we are able to relate the gap and the curvatures of the
boundary. This talk is based on a joint work with Renato Feres.
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APRIL 2010
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Thursday, April 1
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Combinatorics Seminar
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Time: 12:00-1:00pm
Location: Cupples I, Room 199
Host: Russ Woodroofe
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Speaker: Rajan Mehta
Department of Mathematics, Washington University in St. Louis
Title: Simplicial sets, groups, and the resulting insanity, Part II
Abstract: I will review the "nerve" construction, which provides a way to
construct the classifying space of a group as a simplicial set.
One of the interesting features of this construction is that it
is in some sense reversible--any simplicial set satisfying
certain properties is the classifying space of a group. If you
look at this statement the right way, you may even be led to
the scandalous conclusion that "simplicial set satisfying
certain properties" is the right way to *define* a group. And
if you're feeling brazen, you might think to tweak those
properties and see what happens. Go ahead and do it, I dare
you.
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Thursday, April 1
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Colloquium
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Time: Tea: 3:30-4:00pm
Talk: 4:00-5:00pm
Location: Cupples I, Room 199
Host: Prof. Nan Lin
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Speaker: Professor Sid Chib
Onlin Business School, Washington University in St. Louis
Title: Dealing with the Compliance Problem in Randomized Trials
Abstract: In randomized trials with human subjects, compliance with the
assigned treatment is often less than perfect and, because of
the concern that the lack of compliance is due to observed
and unobserved confounders, the trial takes on the features of an
observational study. One goal of the analysis now is to find the
causal effect of
the intake, instead of the causal effect
of the assignment. We present some Bayesian ways of
finding this causal effect and illustrate the ideas in a toy example
and a more substantial real data example.
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Friday, April 2
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Geometry and Topology Seminar
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Time: 4:00-5:00pm
Location: Cupples I, Room 207
Host: Prof. Xiang Tang
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Speaker: Professor Xiang Tang
Department of Mathematics, Washington University in St. Louis
Title: Let $G$ be a finite group and $Y$ a $G$-gerbe over an orbifold
$B$. We will explain a construction of a new orbifold $\widehat{Y}$ and
a flat $U(1)$-gerbe $c$ on $\widehat{Y}$. Motivated by a proposal in
physics, we study a mathematical duality of $G$-gerbes, which asserts that
the geometry of $Y$ is
equivalent to the geometry
of $\widehat{Y}$ twisted by $c$. The Mackey machine provides us the right
tool to study such a problem. We will discuss some results in symplectic
topology with the
help of noncommutative geometry. This is a joint work with Hsian-hua Tseng.
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Thursday, April 8
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Combinatorics Seminar
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Time: 12:00-1:00pm
Location: Cupples I, Room 199
Hosts: Prof. Russ Woodroofe
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Speaker: Professor Erin Chambers
Department of Mathematics, St. Louis University
Title: TBA
Abstract: TBA
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Thursday, April 8
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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
Hosts: Prof. Quo-Shin Chi
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Speaker: Professor Yng-Ing Lee
Department of Mathematics, National Taiwan University
Title: Soliton Solutions for Lagrangian Mean Curvature Flow
Abstract: The mean curvature vector points in the direction in
which the volume decreases most rapidly and mean curvature
flow deforms the submanifold in the direction of the mean
curvature vector. However, finite-time singularities may
occur along the flow. In geometric flows such as Ricci flow
or mean curvature flow, singularities are often locally
modeled on soliton solutions. In the case of mean curvature
flows, two types of soliton solutions of particular interest
are those moved by scaling or translation in Euclidean space.
They play an important role in understanding singularities.
When the initial submanifold is Lagrangian in a Kahler-Einstein
manifold, the smooth solution of the mean curvature flow will
still be Lagrangian. In this talk, I will report some of my
work on Lagrangian soliton solutions with different properties
and particularly emphasize those examples related to Schoen-Wolfson
cones that appear to be an obstruction to the existence of special
Lagrangian surfaces. The results presented in this talk consist
of two papers with Mu-Tao Wang, and a paper with Dominic Joyce
and Mao-Pei Tsui.
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Friday, April 9
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Geometry and Topology Seminar
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Time: Talk: 4:00-5:00pm
Location: Cupples I, Room 207
Hosts: Prof. Quo-Shin Chi
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Speaker: Professor Yng-Ing Lee
Department of Mathematics, National Taiwan University
Title: The Existence of Hamiltonian Stationary Lagrangians
Abstract: Hamiltonian stationary Lagrangians are Lagrangian submanifolds that are
critical points of the area functional under Hamiltonian deformations.
They are generalizations of special Lagrangians. We show the existence of
many compact Hamiltonian stationary Lagrangians in every compact
symplectic manifold with a compatible metric. A local criterion in Kahler
manifolds where a family of Hamiltonian stationary Lagrangian tori can be
found is also derived. The first result is a joint work with Joyce and
Schoen.
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Wednesday, April 14
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Colloquium
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Time: Tea: 3:15pm in Cupples I, Room 199; Talk: 4:00-5:00pm
Location: Crow, Room 204
Hosts: Profs. David Wright, Ken Kelton, Ram Cowsik
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Speaker: Professor Srinivasa Varadhan, 2007 recipient of the Abel Prize
Courant Institute of Mathematical Sciences, New York University
Title: Large Deviations, theory and examples
Abstract: The theory of large deviations is ubiquitous and plays both a
direct and indirect role in many applications.
Entropy in some form is a basic ingredient.
We will review the basic theory and illustrate some of the
applications.
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Thursday, April 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. Al Baernstein
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Speaker: Professor Terry Sheil-Small
Department of Mathematics, University of York, England
Title: An extremal problem for non-vanishing functions on Bergman space
Abstract: Click here.
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Tuesday, April 20
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Thesis Defense
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Time: 10:00am-12:00pm
Location: Cupples I, Room 199
Host: Prof. Richard Rochberg
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Speaker: Nicholas Sedlock
Department of Mathematics, Washington University in St. Louis
Title: Multiplication of Truncated Toeplitz Operators
Abstract: We discuss the multiplication of truncated Toeplitz
operators (or TTOs) on backward shift invariant subspaces of the
Hardy space of the unit disc. Specifically we discuss when the
product of two TTOs is itself a TTO, finding an equivalent to a
similar result of Brown and Halmos for ordinary Toeplitz operators.
This leads us to investigate the commutants of certain rank-one
perturbations of the compressed shift operator, deriving a symbol
calculus for TTOs, as well as several other results.
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Wednesday, April 21
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Department Awards Ceremony
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Time: Tea: 4:00-4:30pm
Talk: 4:30-5:30pm
Location: Room 199
Host: Prof. Ronald Freiwald
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Awards to mathematics faculty, graduate students, undergraduate students, ... , and more.
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Thursday, April 22
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Loeb Undergraduate Lecture in Mathematics
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Time: Tea: 3:45-4:30pm, Cupples I, Room 200
Talk: 4:30-5:30pm
Location: January Hall, Room 110
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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Thursday, April 29
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Roever Colloquium
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Time: Tea: 4:00-4:30pm
Talk: 4:30-5:30pm
Location: Cupples I, Room 199
Host: Prof. Quo-Shin Chi
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Speaker: Professor Simon Brendle
Department of Mathematics, Stanford University
Title: Curvature, sphere theorems, and the Ricci flow
Abstract: In 1926, Hopf proved that any compact, simply connected Riemannian
manifold with constant curvature 1 is isometric to the standard sphere.
Motivated by this result, Hopf posed the question of whether a compact,
simply connected manifold with suitably pinched curvature is topologically a
sphere. This question has been studied by many authors over the past six
decades, a milestone being the Topological Sphere Theorem proved by Berger
and Klingenberg in 1960.
In this lecture, I will discuss the history of this problem, and describe
the proof (joint with R. Schoen) of the Differentiable Sphere Theorem. This
theorem classifies all manifolds with 1/4-pinched curvature up to
diffeomorphism. The distinction between homeomorphism and diffeomorphism is
significant in light of the exotic spheres constructed by Milnor; the
proof uses the Ricci flow technique introduced by Hamilton.
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Friday, April 30
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Roever Seminar
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Time: 3:00-4:00pm
Location: Cupples I, Room 199
Host: Prof. Quo-Shin Chi
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Speaker: Professor Simon Brendle
Department of Mathematics, Stanford University
Title: Blow-up phenomena for the Yamabe equation
Abstract: The Yamabe problem asserts that any Riemannian metric on a compact
manifold can be conformally deformed to one of constant scalar curvature.
However, this metric is not, in general, unique, and there are examples of
manifolds that admit many metrics of constant scalar curvature in a given
conformal class.
It was conjectured by R. Schoen in the 1980s (and later by Aubin) that
the set of all metrics of constant scalar curvature 1 in a given conformal
class is compact, except if the underlying manifold is conformally
equivalent to the sphere $S^n$ equipped with its standard metric.
I will discuss counterexamples to this conjecture in dimension 52 and
higher. I will also describe joint work with F. Marques, which extends these
counterexamples to dimension 25 and higher. The condition $n \geq 25$ turns
out to be optimal.
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MAY 2010
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Thursday, May 06
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Colloquium
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Time: Tea: 4:00-4:30pm
Talk: 4:30-5:30pm
Location: Cupples I, Room 113
Host: Prof. Guido Weiss
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Speaker: Professor Maciej Paluszynski
Department of Mathematics, University of Wrocal
Title: TBA
Abstract: TBA
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