Department of Mathematical Sciences
| Colloquium | Seminars | Clec Lectures | Public Lectures | Distinguished Lectures |
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| Friday, August 28, 3pm, MP3314 | Xiangdong
Xie, Georgia Southern University |
Isoperimetric Inequalities in Group Theory |
| Friday, September 4, 3pm, MP3314 | Frederic Mynard, Georgia
Southern University |
Splitting Group Topologies on Function Spaces |
| Friday, September 11, 3pm, MP3314 | Laszlo Szekely,
University of South Carolina (Host: H.Wang) |
Phylogenetic Combinatorics |
| Friday, September 18, 3pm, MP3314 | Matthew Boylan,
University of South Carolina (Host: A. Sills) |
Modular Forms and Partitions |
| Friday,
September 25, 3pm, MP3314 |
No talk this week |
No talk this week |
| Friday, October 2, 3pm, MP3314 | No talk this week | No talk this week |
| Friday, October 9, 3pm, MP3314 | Alexander Stokolos, Georgia Southern University | A gentle
introduction in the Bellman Function technique I |
| Monday, October 12, 5pm, MP3314 | Francis Jordan,
Queensborough College, CUNY (Host: F. Mynard) |
Coincidence of
function space topologies |
| Friday, October 23,
3pm,
MP3314 |
Alexander Stokolos, Georgia Southern University | A gentle introduction in the Bellman Function technique II |
| Friday, October 30, 3pm, MP3314 | Benjamin Dodson, University of California,
Riverside (Host: S. Zheng) |
The
I-method and global well-posedness for the defocusing nonlinear
Schrodinger equation |
| Friday, November 6, 3pm, MP3314 | Timothy
Goldberg, Cornell University (Host: Y. Lin) |
Hamiltonian actions on integral Kahler manifolds |
| Friday, November 13, 3pm, MP3314 | Ling Lan, Medical College of Georgia (Host: C. Champ) |
Nonparametric estimation of waiting time distribution functions and other characteristics of multi-state models |
| Friday, November 20, 3pm, MP3314 | Nages Shanmugalingam, University of Cincinnati (Host: X. Xie) |
Geometric consequences of BV
extension property |
| Friday, December 4, 3pm, MP3314 | Alina Iacob, Georgia Southern University | TBA |
Details of Fall 2009 lectures
Friday, November 20, 3pm, MP3314Speaker: Nages Shanmugalingam, University of Cincinnati
Title: Geometric consequences of BV extension property
Abstract: Functions of bounded variation, or BV functions,
are useful in measuring surface areas of nice enough Borel
sets. The theory of BV functions is used for example in
image processing and in some PDEs governing blistering of
paint surfaces under intense heat. Burago and Mazya gave
a characterization of BV extension domains in terms of
extendability of sets with finite perimeter as sets with
controlled "minimal" surface extensions outside the domain.
While this is a simpler criterion than the criterion of
BV extension, it is in general not so simple to verify.
We will explain a simple geometric criterion for planar
BV extension domains.
Friday, November 13, 3pm, MP3314
Speaker: Ling Lan, Medical College of Georgia
TITLE: Nonparametric estimation of waiting time distribution functions and other characteristics of multi-state models
ABSTRACT: As a type of multivariate survival data, multi-state models have a wide range of applications, notably in cancer and infectious disease progression studies. Neither empirical nor rate based (Kaplan-Meier) calculations are possible using current status data when each subject is inspected only once during the entire study period. In this talk, I will present a novel nonparametric approach using a fractional at-risk set, for calculation of state occupation probabilities as well as distribution functions of state entry and exit times, using isotonic regression and kernel smoothing. Based on the fractional at-risk set method, we also construct nonparametric estimators of state waiting time distribution functions in a Markov multi-state model using current status data. This is a particularly difficult problem since neither the entry nor the exit times of a given state are directly observed. Detailed simulation studies will be presented in support of our estimators. We also illustrate our methods using a pubertal development data set obtained from the NHANES III.
Friday, November 6, 3pm, MP3314
Speaker: Timothy Goldberg, Cornell University
TITLE: Hamiltonian actions on integral Kahler manifolds
ABSTRACT:
A Hamiltonian action of a compact and connected Lie group on a compact
and connected symplectic manifold determines a convex polytope, called
the moment polytope, which often encodes much useful information about
the Hamiltonian action. If the group is abelian, i.e. a torus, then
the moment polytope can be determined easily by knowing the fixed
points of the action. Unfortunately, there is generally no such
simple description for non‑abelian actions, except in special cases.
One such special case is when the symplectic manifold is integral Kahler and the action is by holomorphic transformations. Here, the
moment polytope can be constructed from group representations related
to the Hamiltonian action. In this talk, I will present this
description of the moment polytope and describe how it has been used
by various geometers, including myself, to obtain results about moment
polytopes associated to various algebraic subsets of the Kahler
manifold.
Friday, October 30, 3pm, MP3314
Speaker: Benjamin Dodson, University of California, Riverside
Title: The I-method and global well-posedness for the defocusing nonlinear Schrodinger equation
Abstract: click here
Monday, October 12, 5pm, MP3314
Speaker: Francis Jordan, Queensborough College, CUNY
Title: Coincidence of function space topologies
Abstract: We consider conditions under which the compact‑open, Isbell, or natural (finest splitting) topologies on the set of
continuous real‑valued functions on a space coincide. To this end, we consider the natural topology on the set of upper semicontinuous set‑valued functions and give a concrete description of its open sets. This description allows us to give a number examples of function spaces where the compact‑open, Isbell, and natural topologies do or do not agree. We show that $\real$‑concordance and local compactness coincide for metric spaces. We find the an example of a non‑locally compact space X for which the compact‑open and and natural topologies on C(X,R) coincide (R=the real numbers). Also, under some set‑theoretical hypotheses, we find an example of a space X were the Isbell and natural topologies coincide on C(X,R), but the Isbell topology is not the compact‑open topology.
paper is here
Friday, October 9, 3pm, MP3314
Speaker: Alexander Stokolos, Georgia Southern University
Title: A gentle introduction in the Bellman Function techniqueAbstract: I will explain how the Bellman Function methodology is
working on examples of Young, Hoelder and Hardy-Littlewood-Doob inequlaities.
The last one is a joint result with Leonid Slavin and Vasily Vasyunin.
Friday, September 18, 3pm, MP3314
Speaker: Matthew Boylan, University of South Carolina
Title: Modular forms and partitions
Abstract: Classical modular forms play important roles in several
different areas of mathematics. These include, for example, arithmetic
geometry (elliptic curves, L-functions, Wiles' proof of Fermat's Last
Theorem), algebraic number theory (class numbers, singular moduli), Lie
theory, representation theory, and mathematical physics. In this talk, I
will discuss the role that modular forms play in recent work on the
ordinary partition function, p(n). The function p(n) counts the number
of ways to write the integer n as a sum of integers <= n. As such, it is
a fundamental and much-studied object in additive and combinatorial
number theory.
Friday, September 11, 3pm, MP3314
Speaker: Laszlo Szekely, University of South Carolina
Title: Phylogenetic Combinatorics
Abstract: Phylogeny reconstruction is a major problem in biology.
Biomolecular sequences (DNA, purine‑pyrimidine, amino
acid sequences) provide objective data for phylogeny
reconstruction.
Stochastic models try to describe biomolecular sequence
evolution through mutations. As a consequence, reconstruction
of model trees can happen "with high probability" (whp) at best.
I will discuss two complexities of phylogeny reconstruction,
the computational complexity and the sequence length needed for
phylogeny reconstruction whp in the Cavender‑Farris‑Neyman
model. I will also discuss whether verification of a phylogenetic
tree is any easier than phylogeny reconstruction.
Friday, September 4, 3pm, MP3314
Speaker: Frederic Mynard, Georgia Southern University
Title: Splitting Group Toplogies on Function Spaces
Abstract: pdf
Friday, August 28, 3pm, MP3314
Speaker: Xiangdong Xie, Georgia Southern University
Title: Isoperimetric Inequalities in Group Theory
Abstract: TBA
.
| Spring 2009 | |
Please direct questions or comments regarding the colloquium to Xiangdong Xie