Seminars and Colloquia Schedule

Liquid-crystals are intermediate phases between solid and liquid states

Series
CDSNS Colloquium
Time
Monday, March 14, 2011 - 11:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Weishi Liu – University of Kansas –
They may flow like fluids but under constraints of mechanical energies from their crystal aspects. As a result, they exhibit very rich phenomena that grant them tremendous applications in modern technology. Based on works of Oseen, Z\"ocher, Frank and others, a continuum theory (not most general but satisfactory to a great extent) for liquid-crystals was formulated by Ericksen and Leslie in 1960s. We will first give a brief introduction to this classical theory and then focus on various important special settings in both static and dynamic cases. These special flows are rather simple for classical fluids but are quite nonlinear for liquid-crystals. We are able to apply abstract theory of nonlinear dynamical systems upon revealing specific structures of the problems at hands.

Inversion of the Born Series in Optical Tomography

Series
Applied and Computational Mathematics Seminar
Time
Monday, March 14, 2011 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
John Schotland – University of Michigan, Ann Arbor
The inverse problem of optical tomography consists of recovering thespatially-varying absorption of a highly-scattering medium from boundarymeasurements. In this talk we will discuss direct reconstruction methods forthis problem that are based on inversion of the Born series. In previouswork we have utilized such series expansions as tools to develop fast imagereconstruction algorithms. Here we characterize their convergence, stabilityand approximation error. Analogous results for the Calderon problem ofreconstructing the conductivity in electrical impedance tomography will alsobe presented.

Lecture series on the disjoint paths algorithm

Series
Graph Theory Seminar
Time
Monday, March 14, 2011 - 14:05 for 1 hour (actually 50 minutes)
Location
Skiiles 168
Speaker
Paul Wollan – School of Mathematics, Georgia Tech and University of Rome
This lecture will conclude the series. In a climactic finish the speaker will prove the Unique Linkage Theorem, thereby completing the proof of correctness of the Disjoint Paths Algorithm.

Skewloops, quadrics, and curvature

Series
Geometry Topology Seminar
Time
Monday, March 14, 2011 - 14:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Bruce Solomon – Indiana University –
A smooth loop in 3-space is skew if it has no pair of parallel tangent lines. With M.~Ghomi, we proved some years ago that among surfaces with some positive Gauss curvature (i.e., local convexity) the absence of skewloops characterizes quadrics. The relationship between skewloops and negatively curved surfaces has proven harder to analyze, however. We report some recent progress on that problem, including evidence both for and against the possibility that the absence of skewloops characterizes quadricsamong surfaces with negative curvature.

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).

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.

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".

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 –

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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).

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.

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.

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

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.

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.

A 2-nilpotent real section conjecture

Series
Algebra Seminar
Time
Thursday, March 17, 2011 - 15:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Kirsten Wickelgren – Harvard University
Grothendieck's anabelian conjectures say that hyperbolic curves over certain fields should be K(pi,1)'s in algebraic geometry. It follows that points on such a curve are conjecturally the sections of etale pi_1 of the structure map. These conjectures are analogous to equivalences between fixed points and homotopy fixed points of Galois actions on related topological spaces. This talk will start with an introduction to Grothendieck's anabelian conjectures, and then present a 2-nilpotent real section conjecture: for a smooth curve X over R with negative Euler characteristic, pi_0(X(R)) is determined by the maximal 2-nilpotent quotient of the fundamental group with its Galois action, as the kernel of an obstruction of Jordan Ellenberg. This implies that the set of real points equipped with a real tangent direction of the smooth compactification of X is determined by the maximal 2-nilpotent quotient of Gal(C(X)) with its Gal(R) action, showing a 2-nilpotent birational real section conjecture.

Canonical subgroups for p-divisible groups

Series
Algebra Seminar
Time
Thursday, March 17, 2011 - 16:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Joe Rabinoff – Harvard University
An elliptic curve over the integer ring of a p-adic field whose special fiber is ordinary has a canonical line contained in its p-torsion. This fact has many arithmetic applications: for instance, it shows that there is a canonical partially-defined section of the natural map of modular curves X_0(Np) -> X_0(N). Lubin was the first to notice that elliptic curves with "not too supersingular" reduction also contain a canonical order-p subgroup. I'll begin the talk by giving an overview of Lubin and Katz's theory of the canonical subgroup of an elliptic curve. I'll then explain one approach to defining the canonical subgroup of any abelian variety (even any p-divisible group), and state a very general existence result. If there is time I'll indicate the role tropical geometry plays in its proof.

A one-dimensional dynamical system with random switching

Series
SIAM Student Seminar
Time
Friday, March 18, 2011 - 13:00 for 1 hour (actually 50 minutes)
Location
Skiles 246
Speaker
Tobias Hurth – School of Mathematics, Georgia Tech
We will study a simple dynamical system with two driving vector fields on the unit interval. The driving vector fields point to opposite directions, and we will follow the trajectory induced by one vector field for a random, exponentially distributed, amount of time before switching to the regime of the other one. Thanks to the simplicity of the system, we obtain an explicit formula for its invariant density. Basically exploiting analytic properties of this density, we derive versions of the law of large numbers, the central limit theorem and the large deviations principle for our system. If time permits, we will also discuss some ideas on how to prove existence of invariant densities, both in our one-dimensional setting and for more general systems with random switching. The talk will rely to a large extent on my Master's thesis I wrote last year under the guidance and supervision of Yuri Bakhtin.