Seminars and Colloquia by Series

3-Connected Minor Minimal Non-Projective Planar Graphs with an Internal 3-Separation

Series
Graph Theory Seminar
Time
Thursday, March 17, 2011 - 12:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Arash Asadi – Math, GT
The property that a graph has an embedding in projective plane is closed under taking minors. So by the well known theorem of Robertson and Seymour, there exists a finite list of minor-minimal graphs, call it L, such that a given graph G is projective planar if and only if G does not contain any graph isomorphic to a member of L as a minor. Glover, Huneke and Wang found 35 graphs in L, and Archdeacon proved that those are all the members of L. In this talk we show a new strategy for finding the list L. Our approach is based on conditioning on the connectivity of a member of L. Assume G is a member of L. If G is not 3-connected then the structure of G is well understood. In the case that G is 3-connected, the problem breaks down into two main cases, either G has an internal separation of order three or G is internally 4-connected . In this talk we find the set of all 3-connected minor minimal non-projective planar graphs with an internal 3-separation. This is joint work with Luke Postle and Robin Thomas.

Geometric complexity and topological rigidity

Series
School of Mathematics Colloquium
Time
Thursday, March 17, 2011 - 11:05 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Guoliang Yu – Vanderbilt University –
In this talk, I will introduce a notion of geometric complexity  to study topological rigidity of manifolds. This is joint work with Erik Guentner and Romain Tessera. I will try to make this talk accessible to graduate students and non experts.

Title: Wannier transform for aperiodic solids

Series
Math Physics Seminar
Time
Wednesday, March 16, 2011 - 16:30 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Jean Bellissard – Georgia Tech
The motivation is to compute the spectral properties of the Schrodinger operator describing an electron in a quasicrystal. The talk will focus on the case of the Fibonacci sequence (one dimension), to illustrate the method. Then the Wannier transform will be defined. It will be shown that the Hamiltonian can be seen as a direct integral over operators with discrete spectra, in a way similar to the construction of band spectra for crystal. A discussion of the differences with crystal will conclude this talk.This is joint work with Giuseppe De Nittis and Vida Milani

Scattering for the cubic Klein Gordon equation in two space dimensions

Series
Analysis Seminar
Time
Wednesday, March 16, 2011 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Betsy Stovall – UCLA
We will discuss a proof that finite energy solutions to the defocusing cubicKlein Gordon equation scatter, and will discuss a related result in thefocusing case. (Don't worry, we will also explain what it means for asolution to a PDE to scatter.) This is joint work with Rowan Killip andMonica Visan.

Introduction to variational image segmentation

Series
Research Horizons Seminar
Time
Wednesday, March 16, 2011 - 12:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Sung Ha Kang – Georgia Tech –
This talk is an introduction to using variational approaches for image reconstruction and segmentation. This talk will start with Total Variation minimization (TV) model and discuss Mumford-Shah and Chan-Vese model for image segmentation. I will mainly focus on multiphase segmentation and its extensions.

2-dimensional TQFTs and Frobenius Algebras

Series
Geometry Topology Student Seminar
Time
Wednesday, March 16, 2011 - 11:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Alan Diaz – Georgia Tech
( This will be a continuation of last week's talk. )An n-dimensional topological quantum field theory is a functor from the category of closed, oriented (n-1)-manifolds and n-dimensional cobordisms to the category of vector spaces and linear maps. Three and four dimensional TQFTs can be difficult to describe, but provide interesting invariants of n-manifolds and are the subjects of ongoing research. This talk focuses on the simpler case n=2, where TQFTs turn out to be equivalent, as categories, to Frobenius algebras. I'll introduce the two structures -- one topological, one algebraic -- explicitly describe the correspondence, and give some examples.

Dynamic modeling of proteins: physical basis for molecular evolution

Series
Mathematical Biology Seminar
Time
Wednesday, March 16, 2011 - 11:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Dr. Yi Mao – NIMBioS –

Please Note: http://www.nimbios.org/press/MaoFeature

Dynamic modeling of a coarse-grained elastic protein modelprovides an effective way of exploring the relationship between protein structure and function. In particular functionally important residues are identified by a variety of computational methods based on the fluctuation analysis. The results from the modeling provide great insights into how random mutagenesis of proteins can give rise to desired property (protein engineering of bioluminescence system) and how molecular physics constrains evolutionary pathways of proteins (emergence of drug resistance behaviors inHIV-1 protease).

It pays to do the right thing: Incentive mechanisms for Societal Networks

Series
ACO Seminar
Time
Tuesday, March 15, 2011 - 16:30 for 1 hour (actually 50 minutes)
Location
Klaus 2443
Speaker
Balaji Prabhakar – Stanford University
Why did kamikaze pilots wear helmets? Why does glue not stick to the inside of the bottle? Why is lemonade made with artificial flavor but dishwashing liquid made with real lemons? How can I avoid traffic jams and be paid for it? While the first three are some of life's enduring questions, the fourth is the subject of a traffic decongestion research project at Stanford University. In this talk, I will briefly describe this project and, more generally, discuss incentive mechanisms for Societal Networks--- networks which are vital for a society's functioning; for example, transportation, energy, healthcare and waste management. I will talk about incentive mechanisms and experiments for reducing road congestion, pollution and energy use, and for improving "wellness" and good driving habits. Some salient themes are: using low-cost sensing technology to make societal networks much more efficient, using price as a signal to co-ordinate individual behavior, and intelligently "throwing money at problems".

Commutator Stories

Series
PDE Seminar
Time
Tuesday, March 15, 2011 - 11:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Prof. Peter Constantin – Department of Mathematics, University of Chicago –
I'll talk about a couple of commutator estimates and their role in the proofs of existence and uniqueness of solutions of active scalar equations with singular integral constitutive relations like the generalized SQG and Oldroyd B models.

Post-critically finite polynomials

Series
Algebra Seminar
Time
Monday, March 14, 2011 - 15:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Patrick Ingram – University of Waterloo
In classical holomorphic dynamics, rational self-maps of the Riemann sphere whose critical points all have finite forward orbit under iteration are known as post-critically finite (PCF) maps. A deep result of Thurston shows that if one excludes examples arising from endomorphisms of elliptic curves, then PCF maps are in some sense sparse, living in a countable union of zero-dimensional subvarieties of the appropriate moduli space (a result offering dubious comfort to number theorists, who tend to work over countable fields). We show that if one restricts attention to polynomials, then the set of PCF points in moduli space is actually a set of algebraic points of bounded height. This allows us to give an elementary proof of the appropriate part of Thurston's result, but it also provides an effective means of listing all PCF polynomials of a given degree, with coefficients of bounded algebraic degree (up to the appropriate sense of equivalence).

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