Department Colloquium, Spring 2009
Colloquium Seminars Clec Lectures Public Lectures Distinguished Lectures

Schedule

Date
Speaker
Title
Friday, January 23, 3pm, MP3314 Z. Wang, Johns Hopkins university
(Host: Y. Lin)		 Semi-classical Spectral Invariants for Schrodinger Operators
Friday, January 30, 3pm, MP3314 Dongwen Qi, Georgia Southwestern
(Host: X. Xie)		 Some Properties of Irreducible, Infinite, Non-affine Coxeter Groups
Friday, February 6, 3pm, MP3314 Kostantin Oskolkov, University of South Carolina
(Host: S. Zheng)		 Schrodinger equation and Riemann’s “non-differentiable” function
Friday, February 13, 3pm, MP3314 Robert Raphael, Concordia University (Montreal)
(Host: F. Mynard)		 On commutative clean rings
Wednesday, February 25, 6pm,  Education Auditorium
DISTINGUISHED LECTURE 		C. Sogge,  Johns Hopkins University
(Host: S. Zheng)		 Blowup rates for eigenfunctions and quasimodes
Friday, February 27, 3pm, MP3314 C. Sogge,  Johns Hopkins University Abstract Strichartz estimates and existence theorems for nonlinear wave equations
Friday, March 6, 3pm, MP3314 Koffi B. Fadimba, University of South Carolina Aiken
(Host: B. Oluyede)		 The saturation equation: A fully discretized and linearized scheme
Friday, March 13, 3pm, MP3314 S. Dolecki, University of Burgundy  (France)
(Host: F. Mynard)		 Significance of the work of Guiseppe Peano (1858-1932)
SPRING BREAK
Thursday, March 26,  IT 1005, 5.30pm
CLEC Lecture (poster)		 James Keesling, University of Florida
(Host: F. Mynard)		 Biomathematics
Friday, March 27, 3pm, MP3314 James Keesling, University of Florida Attractors and Inverse Limits
Friday, April 3, 3pm, MP3314 Yi Li, University of Iowa
(Host: C. Zhao)		 Stability of Traveling Waves for Double Degenerate Fisher-Type Equations
Friday, April 10, 3pm, MP3314 Alexander Teplyaev, University of Connecticut
(Host: S. Ngai)		 Existence and uniqueness of diffusions and Laplacians on fractals
Friday, April 17, 3pm, MP3314 Xiangdong Xie, Georgia Southern U. The Volume Entropy Rigidity Conjecture
Friday, May 1st, 3pm, MP3314 Robert Taylor, Clemson University
(Host: B. Oluyede)		 Consistency and Validity of Dependent Bootstrapping in Finite Populations

to be announced

Details of Spring 2009 lectures

Friday, January 23, 3pm, MP3314

Speaker: Z. Wang, John Hopkins university

Title: Semi-classical Spectral Invariants for Schrodinger Operators

Abstract: click here.


 Friday, January 30, 3pm, MP3314

Speaker: Dongwen Qi, Georgia Southwestern

Title: Some Properties of Irreducible, Infinite, Non-affine Coxeter Groups

Abstract:
Coxeter groups arise in many parts of mathematics as groups generated by reflections, especially, from the semi-simple Lie theory.  A  Coxeter
group is typically defined in terms of generators and relations. The irreducibility  of a Coxeter group is defined by its presentation, which  also distinguishes when a Coxeter group is an infinite group and when it is affine or non-affine.
In this talk, we will illustrate the group theoretic differences between irreducible, infinite, affine Coxeter groups and irreducible, infinite, non-affine
Coxeter groups. It is shown that the center of any finite-index subgroup of an irreducible, infinite, non-affine Coxeter group is trivial and any finite-index subgroup cannot be expressed as a direct product of two subgroups. A unique decomposition theorem is established for any finite-index group of a class of Coxeter groups. It is also shown that the orbit of any element other than the identity under the conjugation action in a irreducible, infinite, non-affine  Coxeter group is an infinite set. An irreducible, infinite, affine Coxeter group does not posses any of the above properties. Our discussion also leads to the conclusion: An irreducible, infinite Coxeter group is affine if and only if it contains an abelian group of
finite index.

Friday, February 6, 3pm, MP3314

Speaker: Kostantin Oskolkov, University of South Carolina

Title: Schrodinger equation and Riemann’s “non-differentiable” function


Abstract: click here.


Friday, February 13, 3pm, MP3314

Speaker: Robert Raphael, Concordia University (Montreal)

Title: On commutative clean rings


Abstract:
A commutative ring with identity is called clean if each element is the sum of an idempotent and a unit. We explain why this class is natural to study. Several classes of familiar classes of commutative rings are examined and we show why each is, or is not, clean.
We discuss the preservation of the clean property under some basic constructions and prove an embedding theorem.
Lastly we give applications to rings of the form C(X) where X is a Tychonoff space.
The talk is based on research published jointly with W. D. Burgess of the University of Ottawa. The papers are available the following website. www.mathstat.uottawa.ca/~wburgess/pubs.htm

DISTINGUISHED LECTURE
Wednesday, February 25, 6pm, Education auditorium

Speaker: C. Sogge,  Johns Hopkins University

Title: Blowup rates for eigenfunctions and quasimodes

Abstract:
 We study size estimates for eigenfunctions and quasimodes on compact Riemannian manifolds with and without boundary.  We are interested in when these functions blowup at the maximal possible rate as measured by $L^p$ rates as their energy goes to infinity.  We wish to characterize what sort of geometries must be present for maximal blowup and conversely what geometries lead to sub-maximal blowup rates.  This is joint work with John Toth and Steve Zelditch and with Hart Smith.

Friday, February 27, 3pm, MP3314

Speaker: C. Sogge,  Johns Hopkins University

Title: Abstract Strichartz estimates and existence theorems for nonlinear wave equations


Abstract:
We shall show how local energy decay estimates for certain linear wave equations involving compact perturbations of the standard Laplacian lead to optimal global existence theorems for the corresponding small amplitude nonlinear wave equations with power nonlinearities. To achieve this goal, at least for spatial dimensions $n=3$ and 4, we shall show how the aforementioned linear decay estimates can be combined with ``abstract Strichartz" estimates for the free wave equation to prove corresponding estimates for the perturbed wave equation when $n\ge3$. As we shall see, we are only partially successful in the latter endeavor when the dimension is equal to two, and therefore, at present, our applications to nonlinear wave equations in this case are limited.

Friday, March 6, 3pm, MP3314

Speaker: Koffi B. Fadimba, University of South Carolina Aiken

Title: The saturation equation: A fully discretized and linearized scheme


Abstract: click here.


Friday, March 13, 3pm, MP3314

Speaker: Szymon Dolecki, University of Burgundy

Title: Significance of the work of Guiseppe Peano (1858-1932)


Abstract:
In 2008 mathematics celebrated the 150th anniversary of the birth of Giuseppe Peano, as well as the 100th anniversary of the last (fifth) edition of Formulario Mathematico. Peano gave foundational contributions to various branches of mathematics: logic, formal language of mathematics, set theory, arithmetic, infinitesimal calculus, tangency, differentiability, Grassmann geometric calculus, derivative of measures, definition of surface area, general topology,  optimization, ordinary differential equations, convexity. Nowadays, many of these contributions are attributed to others authors, who rediscovered them often much later.

Thursday, March 26, IT 1005, 5.30pm
CLEC Lecture
Speaker: James Keesling, University of Florida

Title: Biomathematics


Abstract:
This lecture will show some of the ways that  mathematics has played a role in advances in biology.  In some cases simple mathematics can profoundly influence our understanding.  In some cases, sophisticated mathematical models are necessary to  explain certain biological phenomena.   We will discuss models in epidemiology, vectored diseases, morphogenesis, and insect pheromones with many biological examples.


Friday, March 27, 3pm, MP3314

Speaker: James Keesling, University of Florida

Title: Attractors and Inverse Limits

Abstract:
The study of attractors of dynamical systems is a central theme in dynamical systems.  Attractors determine the long-term behavior of a dynamical system.  Understanding these attractors allows us to see beyond the horizon.  They are used in studying weather patterns and turbulence among many other applications.
The structure of attractors has been determined for hyperbolic systems by Bob Williams.  His work completed an essential link in a program to understand hyperbolic dynamical systems outlined by Steve Smale.   The first part of the talk will give a brief history of this work. 
For non-hyperbolic systems, attractors are more complicated and not well-understood.   The last part of the talk will describe some recent research that shows promise of clarifying this case.
The talk will be accessible to non-specialists.
Friday, April 3, 3pm, MP3314

Speaker: Yi Li, University of Iowa

Title: Stability of Traveling Waves for Double Degenerate Fisher-Type Equations


Abstract:
This talk is concerned with the asymptotic stability of traveling wave solutions for double degenerate Fisher-type equations. By
detailed spectral analysis, each traveling front solution with non-critical speed is proved to be linearly exponentially stable in some exponentially weighted spaces. Further by Evans function method and detailed semi-group estimates, each traveling wave solution with non-critical speed is proved to be locally algebraically stable to perturbations in some appropriate polynomially weighted spaces.

Friday, April 10, 3pm, MP3314

Speaker: Alexander Teplyaev, University of Connecticut

Title: Existence and uniqueness of diffusions and Laplacians on fractals


Abstract:
The classical diffusion process was first studied by Einstein, and later a mathematical theory was developed by Wiener, Kolmogorov, Levy. One of the basic principles is that displacement in a small time is proportional to the square root of time. This law is related to the properties of the Gaussian transition density and the heat equation. Relatively recently Kusuoka, Fukushima, Kigami, Barlow, Bass, Perkins and others discovered that some fractals carry natural diffusion processes. These processes obey scaling laws that are different from the classical Gaussian diffusion, but are of so-called sub-Gaussian type. Moreover, in some situations the diffusion, and therefore the corresponding Laplace operator, are uniquely determined by the geometry of the space. Recently it was proved for Sierpinski carpets (a joint work with M. T. Barlow, R. F. Bass, T.
Kumagai).

Friday, April 17, 3pm, MP3314

Speaker: Xiangdong Xie, Georgia Southern University

Title: The Volume Entropy Rigidity Conjecture


Abstract:
Given a closed Riemannian manifold, one can consider the exponential growth rate of the volume of balls in the universal cover. Given a closed smooth manifold,  one can ask which Riemannian metric(s) minimizes the exponential growth rate among all Riemannian metrics having the same volume. The volume entropy rigidity conjecture claims that on a closed smooth manifold admitting a locally symmetric metric with nonpositive curvature, the exponential growth rate  is minimized by a  unique locally symmetric metric.  I will give a survey of this conjecture and related topics. 


Friday, May 1st, 3pm, MP3314

Speaker: Robert L. Taylor, Clemson University

Title: Consistency and Validity of Dependent Bootstrapping in Finite Populations

Abstract:
 
    The traditional bootstrap resamples with replacement from the original sample observations to form arrays of rowwise independent and identically distributed bootstrap random variables.  There are situations, for example, when sampling from finite populations, where resampling without replacement provides a more realistic bootstrap procedure and produces dependent bootstrap random variables.  The desired properties of consistency and asymptotic validity are shown to hold for certain nonparametric dependent bootstrap estimators.   In addition, it is shown that the smaller variation in dependent bootstrap estimators can be used to increase precision in some of the estimators.
Department Colloquium Archives

Please direct questions or comments regarding the colloquium to  Frederic Mynard