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Spring 2009 Seminars Schedule *
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Mondays
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Graduate-Organized Talks Seminar
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Time: 2:00-3:00pm *
Location: Cupples I, Room 199
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Host: Larry Lin
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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: Professor John McCarthy
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Tuesdays
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Algebraic Geometry Seminar
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Time: 3:00-4:30pm *
Location: Eads, Room 215
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Host: Professor Mohan Kumar
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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: Assistant Professor Nan Lin
Statistics Seminar Schedule
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Wednesdays
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Geometry and Topology Seminar
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Time: 3:00-4:00pm *
Location: Cupples I, Room 199
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Hosts: Professor Rachel Roberts and Assistant Professor Xiang Tang
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Graduate Student Seminar
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Time: 4:00-5:00pm *
Location: Cupples I, Room 199
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Host: Professor Steven Krantz
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Thursdays
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Combinatorics and Group Theory Seminar
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Time: 12:00-1:00pm *
Location: Cupples I, Room 199
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Host: Jonathan Browder
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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: Professor Guido Weiss
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* Times may vary, please consult the schedule below for details:
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APRIL 2009
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Wednesday, April 1
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Geometry and Topology Seminar
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Time: 3:00-4:00pm
Location: Cupples I, Room 199
Host: Profs. Rachel Roberts and Xiang Tang
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Speaker: Brad Henry
Department of Mathematics, Washington University in St. louis
Title: Khovanov Homology: Encoding the Jones polynomial as the Euler
characteristic of a knot homology invariant
Abstract: Around 1990, Mikhail Khovanov created a homology theory for knots in
R^3 whose graded Euler characteristic is the Jones polynomial of the
knot. What he ends up with is a new knot invariant which is at least
as strong as the Jones polynomial invariant. We will see how Khovanov
homology follows naturally from the Kauffman bracket defined during
the seminar on 3/18. The development will be primarily topological and
algebraic in nature and will follow the work of Dror Bar-Natan in
"Khovanov's Homology for Tangles and Cobordisms". Once we understand
the construction, we will consider the invariance proof. Finally, I
will indicate how the theory has evolved since the early 90's.
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Wednesday, April 1
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Graduate Student Seminar
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Time: 4:00-5:00pm
Location: Cupples I, Room 199
Host: Prof. Steven Krantz
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Speaker: Professor Xiang Tang
Department of Mathematics, Washington University in St. Louis
Title: Irrational Rotation and Quantum Tori
Abstract: In this talk, we are interested in the orbit space of rotating a
unit cirle by an irrational number. Such a space is a typical example of non
Hausdorff manifolds. We will explain how to study differential geometry of
such a space.
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Thursday, April 2
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Colloquium
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Time: 11:00am-12:00pm
Location: Cupples I, Room 199
Host: Prof. Ronald Freiwald
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Speaker: Professor Ravi Vakil
Department of Mathematics, Stanford University
Title: Generalizing the cross ratio: The moduli space of n points on the
projective line up to projective equivalence
Abstract: Four ordered points on the projective line, up to projective
equivalence, are classified by the cross ratio, a notion introduced by
Cayley. This theory can be extended to more points, leading to one of
the first important examples of an invariant theory problem, studied
by Kempe, Hilbert, and others. Instead of the cross ratio (a point on
the projective line), we get a point in a larger projective space, and
the equations necessarily satisfied by such points exhibit classical
combinatorial and geometric structure. For example, the case of six
points is intimately connected to the outer automorphism of S_6. We
extend this picture to an arbitrary number of points, completely
describing the equations of the moduli space. This is joint work with
Ben Howard, John Millson, and Andrew Snowden. This talk is intended
for a general mathematical audience, and much of the talk will be
spent discussing the problem, and an elementary graphical means of
understanding it.
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Thursday, April 2
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Loeb Undergraduate Mathematics Lecture
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Tea: 3:45pm, Cupples I, Room 200
Talk: 4:30-5:30pm, January Hall, Room 110
Host: Prof. Ronald Freiwald
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Speaker: Professor Ravi Vakil
Department of Mathematics, Stanford University
Title: The Mathematics of Doodling
Abstract: Doodling has many mathematical aspects including patterns,
shapes, numbers, and more. Not surprisingly, there is often
some sophisticated and fun mathematics buried inside common doodles.
I'll begin by doodling, and see where it takes us.
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Thursday, April 2
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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. Jimin Ding
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Speaker: Professor Shuangge Ma
Department of Biological and Biomedical Sciences, Epidemiology and Public Health, Yale University
Title: Interval Censored Data with a Cured Subgroup
Abstract: Mixed case interval censored data arise when the event time of interest is
only known to lie in an interval obtained from a sequence of k random
examinations, where k is a random integer. We consider mixed case interval
censored data with a cured subgroup, where subjects in this subgroup are not
susceptible to the event of interest. Such data may be encountered in
medical and demographical studies with longitudinal follow up, where the
population of interest is composed of heterogeneous subjects. We propose
using a semiparametric two-part model, where the first part is a generalized
linear model and describes the probability of cure, and the second part is a
Cox model and describes the event time for susceptible subjects. We study
maximum likelihood estimate of this two-part model. Finite sample
properties, an effective computational algorithm, and inference with the
weighted bootstrap are investigated. Asymptotic properties, including
identifiability, consistency, and weak convergence, are established. We
conduct simulations and analyze the HDSD study using the proposed approach.
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Friday, April 3
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Major Oral
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Time: 1:00-2:00pm
Location: Eads, Room 208
Host: Profs. Mohan Kuman and Roya Beheshti-Zavareh
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Speaker: Sara Gharahbeigi
Department of Mathematics, Washington University in St. Louis
Title: Deformation of ropes on curves and their smoothing
Abstract: Let Y be a smooth irreducible projective curve. a rope Z on Y of
multiplicity m is a curve whose reduced structure is Y, and the
conormal bundle of Y in Z is a rank m-1 vector bundle.
By a rope being smoothable we mean that it is the flat limit of a
family of smooth irreducible curves. we present a few theorems to
find out when a rope can be smoothed.
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Friday, April 3
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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: Benjamin Manning
Department of Mathematics, Washington University in St. Louis
Title: On the Connectivity of Framelets
Abstract: An exposition on Marcin Bownik's work.
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Monday, April 6
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Graduate-Organized Talks Seminar
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Time: 2:00-3:00pm
Location: Cupples I, Room 199
Host: Larry Lin
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Speaker: Joshua Brady
Department of Mathematics, Washington University in St. Louis
Title: An introduction to the Navier-Stokes equations
Abstract: In this talk we will give a brief introduction and
derivation of the Navier-Stokes equations. Then, we will discuss how
one can potentially earn one million dollars by proving certain
properties of the Navier-Stokes equations!
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Monday, April 6
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Major Oral
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Time: 3:00-4:00pm
Location: Cupples I, Room 199
Host: Prof. David Wright
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Speaker: Andrew Lewis
Department of Mathematics, Washington University in St. Louis
Title: Pseudopolynomial Algebras
Abstract: An R-algebra A is called a pseudopolynomial R-algebra if it
becomes a polynomial ring after tensoring with the residue field of each
prime ideal of R. A priori, it is not clear if any non trivial examples
exist; in other words, one may ask if all pseudopolynomial algebras are
polynomial rings. In the case of one variable, or two variables and R
contains Q, then the answer is "yes". We will discuss this result, and also
give nontrivial examples of pseudopolynomial algebras in two variables.
These results are due to T. Asanuma.
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Tuesday, April 7
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Algebraic Geometry Seminar
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Time: 3:00-4:30pm
Location: Eads, Room 215
Hosts: Prof. Mohan Kumar
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Speaker: Professor Adrian Clingher
Department of Mathematics, Stanford University
Title: Special Involutions on Kummer
Surfaces
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Tuesday, April 7
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Major Oral
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Time: 4:30-5:30pm
Location: Cupples I, Room 199
Hosts: Prof. Nan Lin
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Speaker: Qing Li
Department of Mathematics, Washington University in St. Louis
Title: Bayesian Elastic Net
Abstract: Elastic net is a flexible regularization and
variable selection method which can handle the data with more
predictors than the sampler size. This paper proposes a Bayesian
elastic net method to solve the elastic net model using the Gibbs
sampler. While it yields theoretically equivalent estimators, the
Bayesian elastic net method has two major advantages over the
frequentist elastic net method. Firstly, as a Bayesian method, the
distributional results on the estimates are straightforward,
making the statistical inference available. Secondly, it chooses
the two penalty parameter simultaneously, avoiding the "double
shrinkage problem" in the elastic net method. Real data examples
and simulation studies shows that two methods behave comparably
but the Bayesian elastic net makes much less false exclusion of
the predictors.
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Wednesday, April 8
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Geometry and Topology Seminar
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Time: 3:00-4:00pm
Location: Cupples I, Room 199
Hosts: Profs. Rachel Roberts and Xiang Tang
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Speaker: Professor Xiang Tang
Department of Mathematics, Washington University in St. Louis
Title: Introduction to Jones' polynomial (Part II)
Abstract: This is a continuation of my talk 3 weeks' ago. This talk will
focus on the category of tangles.
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Thursday, April 9
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Hirschman Lecture
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Time: Tea: 4:00-4:30pm
Talk: 4:30-5:30pm
Location: Cupples I, Room 199
Hosts: Prof. Guido Weiss, Prof. Edward Wilson
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Speaker: Professor Steve Wainger
Department of Mathematics, University of Wisconsin
Title: The circle method of Hardy,
Littlewood and Ramanujan
Abstract: Click here to view the abstract.
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Friday, April 10
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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 Guido Weiss
Department of Mathematics, Washington University in St. Louis
Title: Cyclic
Subspaces for Unitary Representations of LCA groups
Abstract: Principal
Shift Invariant Subspaces and Gabor systems.
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Monday, April 13
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Graduate-Organized Talks Seminar
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CANCELLED
Time:2:00-3:00pm
Location: Cupples I, Room 199
Host: Larry Lin
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CANCELLED. Rescheduled for April 20th, 2009
Speaker: Andrew Lewis
Department of Mathematics,
Washington University in St. Louis
Title: Locally Nilpotent Derivations and Polynomial Automorphisms
Abstract: What is a locally nilpotent derivation (LND)? What do LNDs have
to do with polynomial automorphisms? Why are LNDs so useful? We'll attempt
to answer all of these questions while assuming minimal background.
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Monday, April 13
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Analysis Seminar
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Time:4:00-5:00pm
Location: Cupples I, Room 199
Host: Profs. Albert Baernstein and Guido Weiss
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Speaker: Professor Enrico Laeng
Department of Mathematics,
Milan Polytechnic Institute
Title: Evaluating best constants for linear and sub-linear operators. Recent
results and insights into some old open problems
Abstract: We will describe a novel approach, based on rearrangements, that
allows us to evaluate the norms of the non-centered Hardy-Littlewood Maximal
operator on some families of Lorentz and Marcinkiewicz spaces (L^p and
weak-L^p spaces are included). We will also discuss the case of the Hilbert
transform and some operators related to it, e.g., the truncated Hilbert
transform and the discrete Hilbert transform. A rearrangement approach is
perhaps possible also in these cases, but much more challenging. We will
show a new "factorization trick".
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Tuesday, April 14
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Thesis Defense
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Time:1:00-2:30pm
Location: Cupples I, Room 207
Host: Prof. Renato Feres
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Speaker: Emily Ronshausen
Department of Mathematics,
Washington University in St. Louis
Title: The Liouville Property in the Discrete Group-Action Setting
Abstract: Liouville's Theorem, drawn from classical potential theory, states
that every bounded harmonic function on R^n is constant. Since that
time, harmonic functions have been considered in many other settings,
and the Liouville property has become a term used to denote the
constantness of the harmonic functions in those settings. Here we
consider harmonic functions defined on a topological space with
respect to a group action on the space and a probability measure on
the group. In this incarnation, the Liouville property is said to
hold if all bounded harmonic functions on the space-group-measuring
pairing are constant along group orbits. We will show that the
Liouville property holds for all symmetric measures and countable
groups on the closed interval and the circle, and then exhibit groups
and measures on the higher dimensional spheres such that Liouville's
property does not hold. Additionally, concepts such as subgroup
recurrence, random walks and group harmonic functions will be
discussed.
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Tuesday, April 14
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Analysis Seminar
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Time:4:00-5:00pm
Location: Cupples I, Room 215
Host: Prof. John McCarthy
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Speaker: Professor Marco Peloso
Department of Mathematics,
Universitá degli Studi di Milano
Title: Analysis of the sublaplacian on complex spheres
Abstract: We consider a distinguished differential operator
defined on the sphere in multidimensional complex spaces, namely
the sublaplacian L. Such operator arises very naturally in a variety
of settings. I will present the basic properties of L, in particular the
connections with complex and harmonic analysis, and
the eigenspace decomposition of L^2. Finally I will discuss
the L^p convergence of Riesz means of these eigenfunction
expansions.
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Tuesday, April 14
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Statistics Seminar
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Time:4:30-5:30pm
Location: Cupples I, Room 199
Host: Prof. Nan Lin
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Speaker: Andrew Womack
Department of Mathematics,
Washington University in St. Louis
Title: Adaptive Monte Carlo Methods
Abstract: We will discuss some old and some more modern results in Adaptive Monte Carlo Integration. In particular, we will look at some of the general theorems that guarantee the convergence and proper stationarity of the chain. Limitations of the necessary assumptions for such chains to converge will be discussed. We will also take a look at a particular type of global adaptation on which I am working with Prof. Jeff Gill.
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Wednesday, April 15
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Geometry and Topology Seminar: Minor Oral
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Time:3:00-4:00pm
Location: Cupples I, Room 199
Host: Profs. Gary Jensen, Rachel Roberts, and Xiang Tang
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Speaker: Michael Deutsch
Department of Mathematics, Washington University in St. Louis
Title: Monopoles, Instanons, and Yang-Mills fields
Abstract: Yang-Mills theory is a gem of 20th century physics, not only
because of its success in applications and its role in the standard model,
but also because it beautifully emerges from very natural mathematical
ideas. Although we will not explain the theory in any generality, nor any
notions of quantization, we will indicate it's origins and discuss a few
classical examples that suggest a general theme of mathematical physics,
that many physical phenomena can be interpreted as manifestations of the
topology/geometry of the spaces on which they are modeled.
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Wednesday, April 15
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Graduate Student Seminar
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Time:4:00-5:00pm
Location: Cupples I, Room 199
Host: Prof. Steven Krantz
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Speaker: Professor Stanley Sawyer
Department of Mathematics, Washington University in St. Louis
Title: Sex for pathogenic bacteria meets queueing theory
Abstract: Gene conversion means the copying of a segment of DNA from one creature
or chromosome to another. Gene conversion is homologous if it occurs at
the same place in two different creatures or chromosomes: That is, if DNA
from several organisms are aligned horizontally, then two rows in the
alignment become identical in a particular range of columns.
Sex in biology means a genetic exchange of information, so that offspring
can inherit advantageous traits from two different parents. The offspring
may then be able to outcompete both parental types. This gives sexual
organisms a strong evolutionary advantage over nonsexual organisms.
Bacteria and viruses use gene conversion as one form of sex. In
particular, genes causing pathogenic behavior (that is, causing bacteria
or viruses to be nasty to humans) are often spread by gene conversion.
Gene conversion can also directly cause positive and negative effects in
humans, but that is another story.
Bacteria and viruses that show evidence of gene conversion are more
dangerous than bacteria and viruses that do not, since pathogenic genes
can spread rapidly. Thus it is of interest to be able to detect gene
conversion from aligned DNA sequences. One approach is to look for
evidence of gene conversion in runs of DNA positions in which two
chromosomes are identical between two chromosomes that are otherwise
diverse. One should also allow for old gene conversion events overlaid by
later point mutations, as well as the possibility that a run of a given
length might have happened by chance in a long alignment. Both questions
can be addressed by results that came originally from queueing theory.
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Thursday, April 16
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Thesis Defense
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Time: 10:00-11:00am
Location: Cupples I, Room 199
Host: Prof. Rachel Roberts
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Speaker: Tim Lott
Department of Mathematics, Washington University in St. Louis
Title: Cosmetic surgery: not just for Hollywood anymore
Abstract: In this talk, we will explore the notion of cosmetic surgery. This
phenomenon occurs when Dehn filling can be performed (on a manifold
with torus boundary) along two distinct slopes to produce homeomorphic
manifolds. In our examination, we turn to the well-studied family of
(hyperbolic) punctured-torus bundles. After discussing their
construction and a choice of framing, we look at the exceptional
fillings, i.e., those producing non-hyperbolic manifolds. We list all
exceptional cosmetic fillings, and give a complete classification
(with the exception of two pairs)---namely, we list all of the
manifolds produced by the fillings, and also show that all of the
cosmetic fillings are trivial in an appropriate sense.
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Thursday, April 16
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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. Jimin Ding, Prof. Nan Lin
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Speaker: Professor Ji Zhu
Department of Mathematics, University of Michigan
Title: Partial Correlation Estimation by Joint Sparse Regression Models
Abstract: In this talk, we propose a computationally efficient
approach for selecting non-zero partial correlations under the
high-dimension-low-sample-size setting. This method assumes the
overall sparsity of the partial correlation matrix and employs sparse
regression techniques for model fitting. We illustrate the performance
of our method by extensive simulation studies. It is shown that our
method performs well in both non-zero partial correlation selection
and the identification of hub variables, and also outperforms two
existing methods. We then apply our method to a microarray breast
cancer data set and identify a set of "hub genes" which may provide
important insights on genetic regulatory networks. Finally, we prove
that, under a set of suitable assumptions, the proposed procedure is
asymptotically consistent in terms of model selection and parameter
estimation.
This is joint work with Jie Peng, Pei Wang and Nengfeng Zhou.
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Friday, April 17
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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 Guido Weiss
Department of Mathematics, Washington University in St. Louis
Title: Cyclic
Subspaces for Unitary Representations of LCA groups
Abstract: Principal
Shift Invariant Subspaces and Gabor systems.
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Monday, April 20
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Graduate-Organized Talks Seminar
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Time:2:00-3:00pm
Location: Cupples I, Room 199
Host: Larry Lin
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Speaker: Andrew Lewis
Department of Mathematics,
Washington University in St. Louis
Title: Locally Nilpotent Derivations and Polynomial Automorphisms
Abstract: What is a locally nilpotent derivation (LND)? What do LNDs have
to do with polynomial automorphisms? Why are LNDs so useful? We'll attempt
to answer all of these questions while assuming minimal background.
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Monday, April 20
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Analysis Seminar - Major Oral
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Time: 4:00-5:00pm
Location: Cupples I, Room 199
Host: Prof. John McCarthy
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Speaker: Nic Sedlock
Department of Mathematics,
Washington University in St. Louis
Title: Complex Symmetric Operators
Abstract: Complex symmetric operators are an interesting class of operators
which have a special, often hidden, symmetry. Many commonly seen operators
are actually CSOs. This talk will give examples of CSOs and talk about
properties they have.
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Monday, April 20
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Math Club
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Time: 5:30-6:15pm
Location: Cupples I, Room 199
Host: Prof. John McCarthy
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Speaker: Professor Richard Rochberg
Department of Mathematics,
Washington University in St. Louis
Title: Benford’s Law
Abstract: If you go through the first few pages of a newspaper and list all the numbers you find there, what percent of them do you suspect will start with the digit 1? What is the general pattern? What is the history of this observation? What is the theory behind it? Why is the Internal Revenue Service interested?
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Tuesday, April 21
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Thesis Defense
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Time: 12:30-2:30pm
Location: Lopata House, Room 16
Host: Prof. Richard Rochberg
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Speaker: Yonhow Lawrence Lin
Department of Mathematics,
Washington University in St. Louis
Title: The Interplay Between Harmonic Analysis, Function Theory and
Operators
Abstract: The connections between harmonic analysis and other fields of
mathematics has become more abundant in modern times. In this talk we
discuss two such relationships.
Hankel operators are an important class of operators that arise
naturally in various different ways. Multilinear singular Fourier
multipliers are an object of continuing interest in harmonic analysis.
The first relationship we will discuss is a connection between
multilinear singular Fourier multipliers and truncations of Hankel
operators.
In the classical case of the Hardy spaces, the John-Nirenberg theorem
characterizes the rate of growth of functions that give rise to
Carleson measures. In this talk, we will give a brief overview of the
classical case, then state an analogue of the John-Nirenberg theorem
for Dirichlet spaces.
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Tuesday, April 21
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Statistics Seminar - Thesis Defense
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Time:4:30-6:30pm
Location: Cupples I, Room 199
Host: Prof. Nan Lin
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Speaker: Haley Abel
Department of Mathematics,
Washington University in St. Louis
Title: The role of positive selection in molecular evolution:
alternative models for within-locus selective effects
Abstract: A key question in population genetics is the extent to which
positive selection drives molecular evolution. According to the
selectionist viewpoint, evolution at the molecular level occurs by natural
selection acting on DNA sequence mutations, with selectively favorable
mutations more likely to eventually reach fixation in a species. On the
other hand, the neutral theory of evolution postulates that random genetic
drift, not selection, is the major driving force behind evolution at the
molecular level.
Here, we address this question within a Poisson Random Field
framework, based on aligned DNA sequence data from two closely related
species. We investigate heavy-tailed distributions for within-locus
selection coefficients, specifically a double-exponential and a Student's t
distribution. Using Markov Chain Monte Carlo methods on a set of coding
sequences from 91 autosomal genes in Drosophila melanogaster and Drosophila
simulans, we estimate that while few (~10%) of new mutations are beneficial,
many (~40%) of observed polymorphisms and most (~95%) fixations are due to
positive selection. While these results are necessarily model-dependent,
they are in accord with previous estimates based on a normal random effects
model. As a second aim, we develop programs for forward simulation of
polymorphism and divergence data under varying levels of selection and
recombination and perform a series of simulation studies for validation of
the Poisson Random Field model.
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Wednesday, April 22
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Geometry and Topology Seminar
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Time:3:00-4:00pm
Location: Cupples I, Room 199
Host: Profs. Rachel Roberts and Xiang Tang
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Speaker: Professor Larry Conlon
Department of Mathematics,
Washington University in St. Louis
Title: Geodesic laminations of open surfaces and
foliations of finite depth
Abstract: In the talk I will sketch the unpublished work of Handel and
Miller on the classification, up to isotopy, of endperiodic maps of
surfaces and indicate how it can be used to classify taut, depth one
foliations of sutured 3-manifolds (work of John Cantwell and myself which
we are currently correcting, simplifying and generalizing). The
Handel-Miller theory somewhat resembles Thurston's classification of
homeomorphisms of compact surfaces via geodesic laminations. In some ways
it is easier but presents some challenging complications not found in the
compact case. The classification of foliations somewhat resembles
Thurston's classification of fibrations over the circle (the "fibered
faces" of the Thurston ball). If time permits, extensions of these ideas
to higher depth foliations will be indicated.
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Wednesday, April 22
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Graduate Student Seminar
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Time:4:00-5:00pm
Location: Cupples I, Room 199
Host: Prof. Steven Krantz
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Speaker: Professor Nan Lin
Department of Mathematics,
Washington University in St. Louis
Title: Clustering short time-course microarray data using order-restricted
inference
Abstract: Time-course microarray experiments produce vector gene
expression profiles across a series of time points. Clustering genes based
on these profiles is important in discovering functional related and
co-regulated genes. Many existing clustering algorithms do not take
advantage of the ordering in a time-course study, or require long time
series. I will discuss a clustering algorithm, ORICC, for short
time-course microarray data based on an information criterion for
order-restricted inference. Our method changes the clustering problem into
a model selection problem after specifying candidate cluster profiles as
inequality constraints. Genes are assigned to the profile which they best
match determined by the information criterion. In addition, we also
developed a procedure to assess ORICC's clustering reliability for every
gene. In a real data example, our algorithm identifies new and interesting
genes that previous analyses failed to reveal.
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Thursday, April 23
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Dissertation Defense
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Time: 10:00am-12:00pm
Location: Cupples I, Room 100
Host: Prof. John Shareshian
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Speaker: Robert Brieler
Department of Mathematics,
Washington University in St. Louis
Title: Symmetric and Alternating Groups as
Monodromy Groups of Compact Riemann Surfaces: The Case of Four Branch
Point
Abstract: I consider indecomposable degree d covers of compact Riemann surfaces with monodromy group a symmetric or alternating group of degree n. If the cover has four branch points, I show that the genus g grows rapidly with n unless either d = n or d = (n\atop 2). In those cases I show that the monodromy 4-tuple associated with the covering can be classified up to the cycle shape of its elements, verifying a conjecture of Guralnick and Shareshian.
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Thursday, April 23
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Thesis Defense
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Time: 1:00am-2:30am
Location: Psychology Building, Room 249
Host: Prof. Stanley Sawyer
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Speaker: Chunlin Fan
Department of Mathematics, Washington University in St. Louis
Title: Contributions to the Theory of Copula
Abstract: First, I will discuss the measure of concordance and give an explicit
closed-form formula to calculate the Spearman's rho value and I will
investigate the relationship between Kendall's tau and Spearman's rho and
I establish a necessary and sufficient conditions for the inequality
between 3tau and 2rho. After that, I construct a 3-dim copula with three
given copulas as its 2 dimensional margins and discuss the how to generate
other families of Archimedean copula. Finally, I will talk about the
Archimedean survival copula and I will develop the asymptotic test
procedure to justify the assumption that the copula of two random
variables is Archimedean.
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Thursday, April 23
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Annual Department Awards Ceremony
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Time: Tea: 4:00-4:30pm, Ceremony: 4:30-6:00pm
Location: Cupples I, Room 199
Host: Prof. Ronald Freiwald
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Awards to mathematics faculty, graduate students, undergraduate students, ... , and more.
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Friday, April 24
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Thesis Defense
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Time: 11:15am-1:00pm
Location: Cupples I, Room 199
Host: Prof. John Shareshian
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Speaker: Joe Bohanon
Department of Mathematics, Washington University in St. Louis
Title: Groups in which the Normalizer of Every Non-normal Subgroup is
Maximal
Abstract: We examine groups with the property that every non-normal
subgroup has a normalizer which is maximal. For p-groups it is shown
that the index in G of the center of G is at most 16 when p=2 and at
most p^3 when p is odd. We also prove a structural theorem for
general groups with maximal normalizers (MN-groups) and show that a
solvable MN-group has many of the same properties as a nilpotent
MN-group.
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Friday, April 24
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Minor Oral
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Time: 2:00pm-3:00pm
Location: Eads, Room 103
Host: Prof. Renato Feres
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Speaker: Joshua Brady
Department of Mathematics, Washington University in St. Louis
Title: The Euler-Poincaré equations and the geometry of the Averaged
Euler equations in fluid dynamics
Abstract: The Euler-Poincaré equations are an alternative way to look
at the reduced dynamics of a system. After the work of Marsden,
Ratiu, and Shkoller we will see how solutions to the Averaged Euler
equations in fluid flow correspond to the geodesics of a volume
preserving diffeomorphism group.
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Friday, April 24
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Colloquium
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Tea: 2:30-3:00pm,Cupples I, Room 199
Talk: 3:00-4:00pm, Lounderman, Room 461
Host: Prof. Xiang Tang
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Speaker: Professor Yuri Berest
Department of Mathematics, Cornell University
Title: Ideals of Rings of Differential Operators
Abstract: Linear differential operators play a fundamental role in many areas of
mathematics and mathematical physics. In algebraic geometry, given a
complex variety X, there is a canonical way to define the algebra D(X) of
(global, linear) differential operators on X. If X is smooth, D(X) can be
viewed
as a natural quantization of the ring O(T^*X) of regular functions on the
cotangent
bundle of X. For example, in the simplest case when X is the affine line,
O(T^*X) is isomorphic to the polynomial ring C[x,y], while D(X) to the Weyl
algebra A_1(C) = C/([d/dx, x]-1) of ordinary differential operators
with polynomial coefficients.
This talk will be concerned with understanding the structure of ideals of
D(X), their moduli spaces and the action of automorphisms of D(X) on these
moduli spaces. First, as a motivation, we will list several questions from
analysis of PDEs, mathematical physics and geometry which lead (rather
surprisingly)
to this problem. Then we will discuss our simplest example: the Weyl algebra
A_1(C),
in which case we will construct the moduli spaces of ideals quite
explicitly,
in terms of matrices satisfying some simple equations. In the main part of
talk, we will explain how to generalize this construction to an arbitrary
smooth
curve using some recent ideas from noncommutative geometry. Finally, time
permitting, we will present some results and conjectures for higher
dimensional varieties.
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Monday, April 27
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Thesis Defense
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Time: 11:00am-1:00pm
Location: Cupples I, Room 199
Host: Prof. John Shareshian
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Speaker: Jonathan Browder
Department of Mathematics, Washington University in St. Louis
Title: Proper Group Actions and the Face Structure of Simplicial
Complexes
Abstract: The f-vector of a simplicial complex lists the number of
faces the complex has in each dimension; one of the central questions
of geometric combinatorics is that of classifying the f-vectors of
various classes of simplicial complexes. We will discuss a complete
characterization of the f-vectors of Cohen-Macaulay complexes having
certain restriction on the faces (these being motivated by the study
of complexes with certain types of symmetry). We will also discuss
some connections between these questions, representation theory, and
algebraic geometry.
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Wednesday, April 29
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Major Oral
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Time: 12:00-1:00pm
Location: Cupples I, Room 199
Host: Prof. Renato Feres
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Speaker: Joshua Brady
Department of Mathematics, Washington University in St. Louis
Title: The Riemannian geometry of volume preserving diffeomorphism
groups
Abstract: In fluid dynamics, volume preserving diffeomorphism groups
arise as the proper setting in which to study incompressible fluids.
In exploring possible ways to model turbulence an interesting metric
has come up. We will investigate the Riemannian geometry of a volume
preserving diffeomorphism group endowed with this metric.
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Thursday, April 30
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Thesis Defense
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Time: 10:00-12:00pm
Location: Cupples I, Room 199
Host: Prof. Nan Lin
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Speaker: Ruibin Xi
Department of Mathematics, Washington University in St. Louis
Title: Statistical Aggregation: Theory and Applications
Abstract: Due to their size and complexity, massive data sets bring many
computational challenges for statistical analysis, such as overcoming
the memory limitation and improving computational efficiency of
traditional statistical methods. The statistical aggregation strategy is
developed to conquer such challenges posed by massive data sets. The
statistical aggregation partitions the entire data set into smaller
subsets, compresses each subset into certain low-dimensional summary
statistics and aggregates the summary statistics to approximate the
statistics of interest. The resulted statistics from aggregation are
required to be asymptotically equivalent to the statistics of interest.
I will apply the statistical aggregation to two large families of
estimators, estimating equation (EE) estimators and U-statistics,
develop their compression-aggregation schemes and show that the
statistical aggregation tremendously reduces
their computational burden while maintaining their efficiency. I further
apply the statistical aggregation to U-statistic based estimating
equations and propose new estimating equations that need much less
computational time but give asymptotically equivalent estimators.
Applications of the statistical aggregation to data cubes will also be
discussed.
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MAY 2009
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Friday, May 1
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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 Guido Weiss
Department of Mathematics, Washington University in St. Louis
Title: Locally compact Abelian Groups and the Action of the Zac Transform
Abstract: This third lecture will extend the material of the previous lectures to the setting of Locally Compact Abelian groups.
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AUGUST 2009
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Tuesday, August 4
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Thesis Defense
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Time: 10:00-12:00pm
Location: Cupples I, Room 199
Host: Profs. Guido Weiss and Edward Wilson
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Speaker: Bob Houska
Department of Mathematics, Washington University in St. Louis
Title: Frames, Composite Wavelets, and Shearlets
Abstract: One-dimensional wavelet systems have enjoyed a great deal of
success in
applications. This success is due, in large part, to the plentiful
existence of compactly supported and smooth one-dimensional scaling
functions.
Traditional wavelet systems have been used quite successfully in
higher-dimensional applications as well. However, the geometric structure
present in dimensions two and higher is significantly more complex than
that present in dimension one, and there are several important
multi-dimensional applications for which traditional wavelet systems are
too geometrically simplistic. In response to this deficiency, the more
geometrically diverse composite wavelet systems were recently introduced
by Guo, Labate, Weiss, and Wilson.
A particular type of composite wavelet system - the shearlet system - has
been shown by the above mentioned authors to outperform traditional
wavelet systems in several important multi-dimensional applications.
Despite these positive results, however, shearlet systems have one major
drawback - essentially no useful shearlet scaling functions exist. We will
discuss several results of this variety.
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