## Seminars and Colloquia by Series

Wednesday, September 14, 2011 - 12:05 , Location: Skiles 005. , Rafael De La Llave , Georgia Tech. , Organizer:
Starting in the 30's Physicists were concerned with the problem of motion of dislocations or the problem of deposition of materials over a periodic structure. This leads naturally to a variational problem (minimizing the energy). One wants to know very delicate properties of the minimizers, which was a problem that Morse was studying at the same time. The systematic mathematical study of these problems started in the 80's with the work of Aubry and Mather who developed the basis to deal with very subtle problems. The mathematics that have become useful include dynamical systems, partial differential equations, calculus of variations and numerical analysis. Physical intuition also helps. I plan to explain some of the basic questions and, perhaps illustrate some of the results.
Wednesday, April 20, 2011 - 12:00 , Location: Skiles 006 , , School of Mathematics - Georgia Institute of Technology , Organizer:

Hosts: Amey Kaloti and Ricardo Restrepo

Fourier series provide a way of writing almost any signal as a superposition of pure tones, or musical notes.  But this representation is not local, and does not reflect the way that music is actually generated by instruments playing individual notes at different times.  We will discuss time-frequency representations, which are a type of local Fourier representation of signals.  This gives us a mathematical model for representing music.  While the model is crude for music, it is in fact apowerful mathematical representation that has appeared widely throughout mathematics (e.g., partial differential equations), physics (e.g., quantum mechanics), and engineering (e.g., time-varying filtering).  We ask one very basic question: are the notes in this representation linearly independent?  This seemingly trivial question leads to surprising mathematical difficulties.
Wednesday, April 13, 2011 - 12:05 , Location: Skiles 005 , Maria Westdickenberg , Georgia Tech , Organizer:
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
Wednesday, April 6, 2011 - 12:05 , Location: Skiles 006 , , School of Mathematics - Georgia Institute of Technology , Organizer:

Hosts: Amey Kaloti and Ricardo Restrepo

By means of examples, I will illustrate the connection between orthogonal hypergeometric polynomials which satisfy interesting spectral and self-dual properties and representations of Lie algebras.
Wednesday, March 30, 2011 - 12:00 , Location: Skiles 006 , , School of Mathematics - Georgia Institute of Technology , Organizer:

Hosts: Amey Kaloti and Ricardo Restrepo.

In this talk we will connect several different areas of mathematical analysis: complex analysis, harmonic analysis and functiontheory all in the hopes of gaining a better understanding of Carleson measures for certain classes of function spaces.
Wednesday, March 16, 2011 - 12:05 , Location: Skiles 006 , Sung Ha Kang , Georgia Tech , , Organizer:
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.
Wednesday, March 9, 2011 - 12:00 , Location: Skiles 006 , , ISYE - Georgia Institute of Technology , Organizer:

Hosts: Amey Kaloti and Ricardo Restrepo

This talk gives an overview of the mathematics of service processes, with a focus on several problems I have been involved in. In many service environments, resources are shared and delays arise as a result; examples include bank tellers, data centers, hospitals, the visa/mortgage application process.I will discuss some frequently employed mathematical tools in this area. Since randomness is inherent to many service environments, I will focus on stochastic processes and stochastic networks.
Wednesday, March 2, 2011 - 12:00 , Location: Skiles 006 , , School of Mathematics - Georgia Institute of Technology , Organizer:
An elliptic curve is the set of solutions to a cubic equation in two variables and it has a natural group structure---you can add two points to get another.  I'll explain why this is so, give some examples of the different types of groups that can arise (depending on the ground field), and mention some recent results on curves with many points.  The are some nice thesis problems in this area which will be discussed in a follow-up talk later this semester in the algebra seminar.
Wednesday, February 16, 2011 - 12:05 , Location: Skiles 006 , Sergio Almada Monter , Georgia Tech , Organizer:
In this talk the general setting for stochastic perturbation for dynamical systems is given. Recent research direction are given for the case in which the perturbation is non-linear. This is a generalization of the well known theory of Freidling Wentzell and Large deviations, which will be summarized during the talk.As always pizza and drinks will be served. Hosts: Amey Kaloti and Ricardo Restrepo.
Wednesday, February 2, 2011 - 12:05 , Location: Skiles 006 , John Etnyre , Georgia Tech , , Organizer:
Four dimensions is unique in many ways. For examplen-dimensional Euclidean space has a unique smooth structure if andonly if n is not equal to four. In other words, there is only one wayto understand smooth functions on R^n if and only if n is not 4. Thereare many other way that smooth structures on 4-dimensional manifoldsbehave in surprising ways. In this talk I will discuss this and I willsketch the beautiful interplay of ideas (you got algebra, analysis andtopology, a little something for everyone!) that go into proving R^4has more that one smooth structure (actually it has uncountably manydifferent smooth structures but that that would take longer toexplain).