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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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MARCH 2009
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Wednesday, March 4
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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 Jimin Ding
Department of Mathematics, Washington University in St. Louis
Title: Introduction of Joint modeling of survival and Longitudinal data
Abstract: Survival analysis and longitudinal data analysis are two specific
fields in traditional statistics. However, in biomedical and clinical
studies, observed longitudinal covariates often are subject to disease,
death or censoring. Further, the hazard rate of survival is affected by the
underlying longitudinal process. In this talk, I will introduce how the
joint modeling approach link the two processes together and model them
simultaneously to correct the estimation bias and improve the efficiency.
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Thursday, March 5
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Kirk Lecture
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Time:Tea:4:00-4:30pm
Talk:4:30-5:30pm
Location: Cupples I, Room 199
Host: Prof. John Shareshian
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Speaker: Professor Robin Hartshorne
Department of Mathematics, University of California, Berkeley
Title: Non-Euclidean triangles, a problem of Euler, and K3 surfaces
Abstract: The problem of finding right triangles with sides of rational length in
hyperbolic geometry turns out to be equivalent to a problem from Euler's
Algebra about differences of squares. The modern interpretation leads to
the study of rational points on algebraic K3 surfaces.
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Tuesday, March 10
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Algebraic Geometry Seminar
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Time: 3:00-4:30pm
Location: Eads, Room 215
Host: Prof. Mohan Kumar
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Speaker: Professor A. Prabhakar Rao
Department of Mathematics, University of Missouri, St. Louis
Title: Hartshorne's proof of Lichtenbaum's conjecture.
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Monday, March 16
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Minor 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: Tame and Wild Automorphisms in Three Variables
Abstract: It is well known that all automorphisms of a polynomial ring in
two variables over a field are tame. In 1972, Nagata produced an example
over three variables and conjectured that it was wild (not tame).
Shestakov and Umirbaev proved in 2003 that it is indeed wild. We will
give a broad outline of their proof, and delve in to a special case to get a feel for their methods.
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Monday, March 16
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Analysis Seminar
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Time:4:00-5:00pm
Location: Cupples I, Room 199
Host: Prof. John McCarthy
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Speaker: Jan-Fredrik Olsen
Department of Mathematics, Norwegian University of Science and Technology, Trondheim
Title: The Boundary Behaviour of a Class of Modified Zeta Functions
Abstract: Click here to view the abstract.
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Monday, March 16
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Dissertation Defense
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Time:5:00-7:00pm
Location: Cupples I, Room 199
Host: Prof. Albert Baernstein
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Speaker: James Gill
Department of Mathematics, Washington University in St. Louis
Title: Functions of finite distortion in the plane and a lower bound for
the weak-type constant of the Beurling-Ahlfors transform
Abstract: We will briefly describe a series of results on the
regularity of maps of finite distortion in the plane. These maps are
solutions to the Beltrami equation, a PDE which relates the analytic
and anti-analytic derivatives of a complex valued function on a
domain in the plane. We will also discuss a lower bound for the
weak-type constant of the Beurling-Ahlfors transform, which is
important singular integral operator used in solving the Beltrami
equation.
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Tuesday, March 17
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Senior Honors Thesis Presentation
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Time:11:00-12:00pm
Location: Cupples I, Room 199
Host: Prof. John Shareshian
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Speaker: Renee Short
Department of Mathematics, Washington University in St. Louis
Title: On the Row Sums of the Character Tables of GL(2,F)
Abstract: In this paper we investigate the irreducible
representations of GL(2,F)
where F is a finite field. We then explore the behavior of the row
sums
of the character table, in particular which rows sum to zero.
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Wednesday, March 18
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Geometry and Topology Seminar
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Time:3:00-4:00pm
Location: Cupples I, Room 199
Host: Prof. Rachel Roberts and Prof. Xiang Tang
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Speaker: Professor Xiang Tang
Department of Mathematics, Washington University in St. Louis
Title: Introduction to Jones Polynomial
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Wednesday, March 18
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Senior Honors Thesis Presentation
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Time:3:00-4:00pm
Location: Cupples I, Room 115
Host: Prof. John McCarthy
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Speaker: Vivek Kulkarni
Department of Mathematics, Washington University in St. Louis
Title: An Introduction to the Optimality of Diseases
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Wednesday, March 18
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Graduate Student Seminar
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CANCELLED
Time:4:00-5:00pm
Location: Cupples I, Room 199
Host: Prof. Steven Krantz
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Rescheduled April 22, 2009
Speaker: Professor Nan Lin
Department of Mathematics, Washington University in St. Louis
Title: TBA
Abstract: TBA
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Thursday, March 19
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Dissertation Defense
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Time:2:30-3:30pm
Location: Cupples I, Room 199
Host: Prof. Steven Krantz
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Speaker: Bennett Standeven
Department of Mathematics, Washington University in St. Louis
Title: The Role of First Order Logic in Complex Analysis of Several
Variables
Abstract:Over any complex variety V, there may be defined an algebra of locally
holomorphic functions OO(V). The first-order properties of these algebras
remain largely unstudied, although BHRFOCI is an extensive study of
such algebras in one complex variable.
Just as the algebra of germs at a point plays an important role in the study
of multivariable complex analysis, the first-order theory of this algebra
should play an important role in a study of the first-order theories of
other holomorphic function algebras.
What follows will focus on an axiomatic characterization of the theory,
carried as far as a proof of the Ruckert Nullstellensatz based on the
axioms. Several related results, including the Weierstrass theorems and the
theory of dimensions of ideals, will also be covered.
The use of first-order logic to prove such results makes it possible to
define algorithms to construct the entities guaranteed by the theorems, and
to place explicit bounds on their size or complexity.
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Thursday, March 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. Edward Wilson
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Speaker: Professor Robert Azencott
Department of Mathematics, University of Houston; École Normale Supérieure de France
Title: Random genetic evolution of cell populations and Large Deviations theory
Abstract: Genetic evolution of large cell populations such as viruses, bacteria, cancer cells, is governed by random dynamics involving mutations, reproduction, and selection. For such stochastic dynamics, reproduction growth rates define a fitness function on the space of cell genotypes, and population trajectories can be viewed as evolving in a "fitness landscape", where evolution mechanisms strongly favors high concentrations of genotypes with high fitness. Even quite simplified stochastic evolution models involving more than 2 genotypes cannot be "solved" explicitly, so that intensive Monte-Carlo simulations have become a natural tool in this context. But crucial evolutionary events can have extremely small occurence probability, and are then practically inaccessible to straightforward intensive simulations. A key example of such rare events is the random emergence of a new high fitness mutation and its rise to fixation (i.e. total population dominance).
Large Deviations Theory offers a powerful array of mathematical concepts and tools to analyze and quantify how specific rare events emerge in (discrete or continuous) dynamical systems perturbed by small random shocks. We will outline how large deviations "cost functionals" can be derived for trajectories of cell populations evolution. The most likely trajectory MLT realizing a specific very rare key biological event KBE can then be determined by solving a variational problem in path space. This enables the accurate evaluation of the occurence probability of KBE by highly accelerated Monte Carlo simulations where a "virtual" population is artificially forced to "follow" quite often the (usually very unlikely) trajectory MLT.
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Monday, March 23
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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: Baili Min
Department of Mathematics, Washington University in St. Louis
Title: Several Complex Variables
Abstract: This talk is a brief introduction to the analysis of several complex
variables. Unlike the generalization from $\mathbb{R}$ to
$\mathbb{R}^n$, we will see some new phenomena in $\mathbb{C}^n$,
such as the Hartogs extension phenomenon, zero sets of analytic
functions, biholomorphic mappings, etc. Some key concepts for this
subject will be introduced, including the domain of holomorphy,
pseudoconvexity, and so on.
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Tuesday, March 24
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Algebraic Geometry Seminar
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Time: 3:00-4:00pm
Location: Eads, Room 215
Host: Prof. Mohan Kumar
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Speaker: Professor David Wright
Department of Mathematics, Washington University in St. Louis
Title: Local Tameness of Polynomial Automorphisms
Abstract: We will sketch the proof of the following recently proved
theorem: If a polynomial automorphism is locally tame, it is stably
tame.
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Tuesday, March 24
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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. Gary Jensen
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Speaker: Professor Robert Osserman
Mathematical Sciences Research Institute
Title: An inverse problem in the calculus of variations, tube-like domains, and compressed catenaries
Abstract: The topics covered in this talk are all connected to an attempt to understand the mathematical underpinnings of the Gateway Arch. In general terms, the shape of the Arch is a polyhedral approximation to a piecewise-smooth surface that is the boundary of a tube-like domain centered on a compressed catenary curve. All these terms and the relations among them will be explained, along with their relevance to other features of the arch, such as the size and shape of the cross sections.
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Wednesday, March 25
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Lecture
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Time: 4:00-5:00pm
Location:
Steinberg Hall Auditorium
Host: Prof. Gary Jensen
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Speaker: Professor Robert Osserman
Mathematical Sciences Research Institute
Title: How the Arch got its Shape – A Just So Story
Abstract:
What is the shape of the Gateway Arch?
A parabola? No!
A catenary? No!
A “weighted catenary”? What does that mean?
And how did the Arch get its shape?
A sketch by Saarinen?
A model?
A mathematical equation?
A building code?
Lots of questions, many with surprising answers. Another case where the truth is harder to find, and stranger than the fiction that passes for fact.
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Monday, March 30
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Analysis Seminar
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Time: 4:00-5:00pm
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: The Dixmier trace of Bergman space Hankel operators
Abstract: Last year I talked about Hankel operators on the Bergman
space of the disk. This time I will discuss what happens for Bergman
spaces of multiply connected domains. The main topic will be the
general issue of how some results for function spaces on the disk
extend to function spaces on multiply connected domains.
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Tuesday, March 31
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Algebraic Geometry Seminar
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Time: 3:00-4:30pm
Location: Eads, Room 215
Host: Prof. Mohan Kumar
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Speaker: Professor G.V. Ravindra
Department of Mathematics, University of St. Louis, Missouri
Title: Chow group of 1-cycles on the moduli space of vector bundles of rank
2 over a curve
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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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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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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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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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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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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: Chunlin Fan
Department of Mathematics,
Washington University in St. Louis
Title: TBA
Abstract: TBA
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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: TBA
Abstract: TBA
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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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Tuesday, April 21
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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: Haley Abel
Department of Mathematics,
Washington University in St. Louis
Title: TBA
Abstract: TBA
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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: TBA
Abstract: TBA
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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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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 Yuri Berest
Department of Mathematics, Cornell University
Title: TBA
Abstract: TBA
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