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

Schedule

Date
Speaker
Title
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, MP3314

Speaker: 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 technique

 Abstract:   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


 
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Department Colloquium Archives
         Spring 2009

Please direct questions or comments regarding the colloquium to   Xiangdong Xie