Seminars and Colloquia Schedule

Theory and applications of fractal transformations

Series
Analysis Seminar
Time
Monday, September 27, 2010 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 255
Speaker
Michael Barnsley – Department of Mathematics, Australian National University
Let A and B be attractors of two point-fibred iterated function systems with coding maps f and g. A transformations from A into B can be constructed by composing a branch of the inverse of f with g. I will outline the shape of the theory of such transformations, which are termed "fractal" because their graphs are typically of non-integer dimension. I will also describe the remarkable geometry of these transformations when the generating iterated functions systems are projective. Finally, I will show how they can be used to provide new insights into dynamical systems and also how they can be used to manipulate, filter, process and efficiently store digital images, and how they can be used in image synthesis, leading to applications in the visual arts.

HOMFLY-PT polynomial and Legendrian links in the solid torus

Series
Geometry Topology Seminar
Time
Monday, September 27, 2010 - 15:45 for 1 hour (actually 50 minutes)
Location
Skiles 269
Speaker
Dan Rutherford – Duke University

This is the first talk in the Emory-Ga Tech-UGA joint seminar. The second talk will follow at 5.

A smooth knot in a contact 3-manifold is called Legendrian if it is always tangent to the contact planes. In this talk, I will discuss Legendrian knots in R^3 and the solid torus where knots can be conveniently viewed using their `front projections'. In particular, I will describe how certain decompositions of front projections known as `normal rulings' (introduced by Fuchs and Chekanov-Pushkar) can be used to give combinatorial descriptions for parts of the HOMFLY-PT and Kauffman polynomials. I will conclude by discussing recent generalizations to Legendrian solid torus links. It is usual to identify the `HOMFLY-PT skein module' of the solid torus with the ring of symmetric functions. In this context, normal rulings can be used to give a knot theory description of the standard scalar product determined by taking the Schur functions to form an orthonormal basis.

Surgery Formulas and Heegaard Floer Homology of Mapping Tori

Series
Geometry Topology Seminar
Time
Monday, September 27, 2010 - 17:00 for 1 hour (actually 50 minutes)
Location
Skiles 269
Speaker
Evan Fink – University of Georgia

This is the second talk in the Emory-Ga Tech-UGA joint seminar. The first talk will begin at 3:45.

There are many conjectured connections between Heegaard Floer homology and the various homologies appearing in low dimensional topology and symplectic geometry. One of these conjectures states, roughly, that if \phi is a diffeomorphism of a closed Riemann surface, a certain portion of the Heegaard Floer homology of the mapping torus of \phi should be equal to the Symplectic Floer homology of \phi. I will discuss how this can be confirmed when \phi is periodic (i.e., when some iterate of \phi is the identity map). I will recall how a mapping torus can be realized via Dehn surgery; then, I will sketch how the surgery long exact triangles of Heegaard Floer homology can be distilled into more direct surgery formulas involving knot Floer homology. Finally, I'll say a few words about what actually happens when you use these formulas for the aforementioned Dehn surgeries: a "really big game of tic-tac-toe".

Turbulence: a walk on the wild side

Series
PDE Seminar
Time
Tuesday, September 28, 2010 - 15:00 for 1 hour (actually 50 minutes)
Location
Skiles 255
Speaker
Prof. Predrag Cvitanović – Physics, Georgia Institute of Technology –
In the world of moderate Reynolds number, everyday turbulence of fluids flowing across planes and down pipes a velvet revolution is taking place. Experiments are almost as detailed as the numerical simulations, DNS is yielding exact numerical solutions that one dared not dream about a decade ago, and dynamical systems visualization of turbulent fluid's state space geometry is unexpectedly elegant. We shall take you on a tour of this newly breached, hitherto inaccessible territory. Mastery of fluid mechanics is no prerequisite, and perhaps a hindrance: the talk is aimed at anyone who had ever wondered why - if no cloud is ever seen twice - we know a cloud when we see one? And how do we turn that into mathematics? (Joint work with J. F. Gibson)

Analytification is the Limit of All Tropicalizations

Series
Tropical Geometry Seminar
Time
Wednesday, September 29, 2010 - 10:05 for 1 hour (actually 50 minutes)
Location
Skiles 114
Speaker
Ye Luo – Georgia Tech
We introduce extended tropicalizations for closed subvarieties of toric varieties and show that the analytification of a quasprojective variety over a nonarchimedean field is naturally homeomorphic to the inverse limit of the tropicalizations of its quasiprojective embeddings. This talk is based on a paper of Sam Pyane with the same title.

Network Models for Infectious Disease Dynamics

Series
Mathematical Biology Seminar
Time
Wednesday, September 29, 2010 - 11:00 for 1 hour (actually 50 minutes)
Location
Skiles 169
Speaker
Shweta Bansal – Center for Infectious Disease Dynamics, Penn State
Many infectious agents spread via close contact between infected and susceptible individuals. The nature and structure of interactions among individuals is thus of fundamental importance to the spread of infectious disease. Heterogeneities among host interactions can be modeled with contact networks, and analyzed using tools of percolation theory. Thus far, the field of contact network epidemiology has largely been focused on the impact of network structure on the progression of disease epidemics. In this talk, we introduce network models which incorporate feedback of the disease spread on network structure, and explore how this feedback limits the potential for future outbreaks. This has implications for seasonal diseases such as influenza, and supports the need for more adaptive public health policies in response to disease dynamics.

Applications of diffusion models to sequential decision making

Series
Research Horizons Seminar
Time
Wednesday, September 29, 2010 - 12:00 for 1 hour (actually 50 minutes)
Location
Skiles 171
Speaker
Yuri Bakhtin – School of Mathematics - Georgia Institute of Technology

Hosts: Yao Li and Ricardo Restrepo

I will consider mathematical models of decision making based on dynamics in the neighborhood of unstable equilibria and involving random perturbations due to small noise. I will report results on the vanishing noise limit for these systems, providing precise predictions about the statistics of decision making times and sequences of unstable equilibria visited by the process. Mathematically, the results are based on the analysis of random Poincare maps in the neighborhood of each equilibrium point. I will discuss applications to neuroscience and psychology along with some experimental data.

Analysis in constructions of low discrepancy sets

Series
Analysis Seminar
Time
Wednesday, September 29, 2010 - 16:30 for 1 hour (actually 50 minutes)
Location
Skiles 269
Speaker
Dmitriy Bilyk – University of South Carolina
Low discrepancy point distributions play an important role in many applications that require numerical integration. The methods of harmonic analysis are often used to produce new or de-randomize known probabilistic constructions. We discuss some recent results in this direction.

Introduction to infinite matroids

Series
Graph Theory Seminar
Time
Thursday, September 30, 2010 - 12:05 for 1 hour (actually 50 minutes)
Location
Skiles 114
Speaker
Luke Postle – Math, GT
Rota asked in the 1960's how one might construct an axiom system for infinite matroids. Among the many suggested answers were the B-matroids of Higgs. In 1978, Oxley proved that any infinite matroid system with the notions of duality and minors must be equivalent to B-matroids. He also provided a simpler mixed basis-independence axiom system for B-matroids, as opposed to the complicated closure system developed by Higgs. In this talk, we examine a recent paper of Bruhn et al that gives independence, basis, circuit, rank, and closure axiom systems for B-matroids. We will also discuss some open problems for infinite matroids.

A Stochastic Differential game for the inhomogeneous infinity-Laplace equation

Series
Stochastics Seminar
Time
Thursday, September 30, 2010 - 15:05 for 1 hour (actually 50 minutes)
Location
Skiles 002
Speaker
Amarjit Budhiraja – University of North Carolina at Chapel Hill
A two-player zero-sum stochastic differential game, defined in terms of an m-dimensional state process that is driven by a one-dimensional Brownian motion, played until the state exits the domain, is studied.The players controls enter in a diffusion coefficient and in an unbounded drift coefficient of the state process. We show that the game has value, and characterize the value function as the unique viscosity solution of an inhomogeneous infinity Laplace equation.Joint work with R. Atar.

Heegaard-Floer Theory by examples

Series
Geometry Topology Working Seminar
Time
Friday, October 1, 2010 - 14:00 for 2 hours
Location
Skiles 171
Speaker
John Etnyre and/or Amey Kaloti – Ga Tech
In this talk we will give an introduction of Heegaard-Floer theory through examples. By exploring several explicit examples we hope to show that various aspects of the definitions that seem complicated, really aren't too bad and it really is possible to work with these fairly abstract things. While this is technically a continuation of last weeks talk, we will review enough material so that this talk should be self contained.

The effects of small noise random perturbation for some problems without unique solutions.

Series
Probability Working Seminar
Time
Friday, October 1, 2010 - 15:05 for 1.5 hours (actually 80 minutes)
Location
Skiles 249
Speaker
Sergio Almada – School of Math, Georgia Tech
We consider the small noise perturbation (in the Ito sense) of a one dimensional ODE. We study the case in which the ODE has not unique solution, but the SDE does. A particular setting of this sort is studied and the properties of the solution are obtained when the noise level vanishes. We relate this to give an example of a 1-dimensional transport equation without uniqueness of weak solution. We show how by a suitable random noise perturbation, the stochastic equation is well posed and study what the limit is when the noise level tends to zero.