Seminars and Colloquia by Series

FoSoM Panel Discussion

Series
Other Talks
Time
Thursday, April 14, 2011 - 16:00 for 3 hours
Location
Skiles 005
Speaker
Math Alumni – School of Mathematics, Georgia Tech

Please Note: Refreshments will be served at 3:30.

The Friends of the School of Mathematics present a panel discussion on "Non-Academic Careers: Opportunities and Challenges for Students" A distinguished panel of alumni of the School will present their views on opportunities and challenges for students as they prepare for non-academic careers. The panelists will also answer questions from the audience. Graduate students and undergraduate majors in Mathematics are especially encouraged to attend.

Rumor Processes on $\bb{N}$

Series
Stochastics Seminar
Time
Thursday, April 14, 2011 - 15:00 for 1 hour (actually 50 minutes)
Location
Skiles 171
Speaker
Fabio Machado – USP san paulo Brazil
We study four discrete time stochastic systems on $\bbN$ modelingprocesses of rumour spreading. The involved individuals can eitherhave an active ora passive role, speaking up or asking for the rumour. The appetite inspreading or hearing the rumour is represented by a set of randomvariables whose distributionsmay depend on the individuals. Our goal is to understand - based on those randomvariables distribution - whether the probability of having an infiniteset of individuals knowing the rumour is positive or not.

On Steinberg's Conjecture: 3-coloring certain planar graphs

Series
Graph Theory Seminar
Time
Thursday, April 14, 2011 - 12:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Peter Whalen – Math, GT
Steinberg's Conjecture states that any planar graph without cycles of length four or five is three colorable. Borodin, Glebov, Montassier, and Raspaud showed that planar graphs without cycles of length four, five, or seven are three colorable and Borodin and Glebov showed that planar graphs without five cycles or triangles at distance at most two apart are three colorable. We prove a statement similar to both of these results: that any planar graph with no cycles of length four through six or cycles of length seven with incident triangles distance exactly two apart are three colorable. Special thanks to Robin Thomas for substantial contributions in the development of the proof.

Sequential Minimum Energy Designs: From Nano Experiments to Global Optimization

Series
School of Mathematics Colloquium
Time
Thursday, April 14, 2011 - 11:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Jeff Wu – ISyE GATech
Motivated by a problem in the synthesis of nanowires, a sequential space filling design, called Sequential Minimum Energy Design (SMED), is proposed for exploring and searching for the optimal conditions in complex black-box functions. The SMED is a novel approach to generate designs that are model independent, can quickly carve out regions with no observable nanostructure morphology, allow for the exploration of complex response surfaces, and can be used for sequential experimentation. It can be viewed as a sequential design procedure for stochastic functions and a global optimization procedure for deterministic functions. The basic idea has been developed into an implementable algorithm, and guidelines for choosing the parameters of SMED have been proposed. Convergence of the algorithm has been established under certain regularity conditions. Performance of the algorithm has been studied using experimental data on nanowire synthesis as well as standard test functions.(Joint work with V. R. Joseph, Georgia Tech and T. Dasgupta, Harvard U.)

Noisy heteroclinic networks and sequential decision making.

Series
Math Physics Seminar
Time
Wednesday, April 13, 2011 - 16:30 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Yuri Bakhtin – Georgia Tech
I will talk about sequential decision making models based ondiffusion along heteroclinic networks of dynamical systems, i.e.,multiple saddle-type equilibrium points connected by heteroclinicorbits. The goal is to give a precise description of the asymptoticbehavior in the limit of vanishing noise.In particular, I will interpret exit times for stochastic dynamics asdecision making times and give a result on their asymptotic behavior.I will report on extensive data on decision making in no a priori biassetting obtained in a psychology experiment that I ran with JoshuaCorrell (University of Chicago),and compare the data with my theoretical results. I will also showthat the same kind of limiting distribution for exit times appears innonequilibrium models of statistical mechanics.

On the uniqueness sets in the Bergmann-Fock space

Series
Analysis Seminar
Time
Wednesday, April 13, 2011 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Mishko Mitkovski – School of Mathematics, Georgia Tech
It is well known that, via the Bargmann transform, the completeness problems for both Gabor systems in signal processing and coherent states in quantum mechanics are equivalent to the uniqueness set problem in the Bargmann-Fock space. We introduce an analog of the Beurling-Malliavin density to try to characterize these uniqueness sets and show that all sets with such density strictly less than one cannot be uniqueness sets. This is joint work with Brett Wick.

Weierstrass points on the Drinfeld modular curve X_0(\mathfrak{p})

Series
Algebra Seminar
Time
Wednesday, April 13, 2011 - 13:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Christelle Vincent – University of Wisconsin Madison
For q a power of a prime, consider the ring \mathbb{F}_q[T]. Due to the many similarities between \mathbb{F}_q[T] and the ring of integers \mathbb{Z}, we can define for \mathbb{F}_q[T] objects that are analogous to elliptic curves, modular forms, and modular curves. In particular, for \mathfrak{p} a prime ideal in \mathbb{F}_q[T], we can define the Drinfeld modular curve X_0(\mathfrak{p}), and study the reduction modulo \mathfrak{p} of its Weierstrass points, as is done in the classical case by Rohrlich, and Ahlgren and Ono. In this talk we will present some partial results in this direction, defining all necessary objects as we go. The first 20 minutes should be accessible to graduate students interested in number theory.

Towards a rigorous upper bound for a scaling problem in thermal convection

Series
Research Horizons Seminar
Time
Wednesday, April 13, 2011 - 12:05 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Maria Westdickenberg – Georgia Tech
Hot fluid expands. Expansion makes a fluid ``parcel'' lighter, causing it to rise. Cold, dense patches of fluid sink. And there we have the thermally induced motion of a fluid sitting on a hot plate... A longstanding open problem in applied analysis is the scaling of the Nusselt number (with respect to the Rayleigh number or, equivalently, system height) in thermal convection. The goal is a fundamental understanding of the effect of buoyancy-induced convection on heat transport in chaotic systems. The commonly held belief that the Nusselt number scales like (Ra)^(1/3) has eluded analytical proof for decades. We will describe the nature of the questions involved, the way that they can be framed (and reframed) mathematically, and the partial successes so far, including a recent preprint by Otto and Seis and a work in progress by the same authors

Navier-Stokes solver using Green's functions

Series
PDE Seminar
Time
Tuesday, April 12, 2011 - 11:00 for 1 hour (actually 50 minutes)
Location
Skiles 255
Speaker
Prof. Divakar Viswanath – University of Michigan –
The incompressible Navier-Stokes equations provide an adequate physical model of a variety of physical phenomena. However, when the fluid speeds are not too low, the equations possess very complicated solutions making both mathematical theory and numerical work challenging. If time is discretized by treating the inertial term explicitly, each time step of the solver is a linear boundary value problem. We show how to solve this linear boundary value problem using Green's functions, assuming the channel and plane Couette geometries. The advantage of using Green's functions is that numerical derivatives are replaced by numerical integrals. However, the mere use of Green's functions does not result in a good solver. Numerical derivatives can come in through the nonlinear inertial term or the incompressibility constraint, even if the linear boundary value problem is tackled using Green's functions. In addition, the boundary value problem will be singularly perturbed at high Reynolds numbers. We show how to eliminate all numerical derivatives in the wall-normal direction and to cast the integrals into a form that is robust in the singularly perturbed limit. [This talk is based on joint work with Tobasco].

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