## Seminars and Colloquia by Series

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).
Tuesday, January 25, 2011 - 12:00 , Location: Skiles 006 , , School of Mathematics - Georgia Institute of Technology , Organizer:

Hosts: Amey Kaloti and Ricardo Restrepo

I will state two different inequalities which are poorly understood, even utterly mysterious. They are stated purely in terms of conditional expectations over dyadic intervals. Motivations and connections carry one into the area of Furstenberg's multilinear ergodic averages.
Wednesday, January 19, 2011 - 12:00 , Location: Skiles 006 , , MIT - Mathematics , Organizer:

Hosts: Amey Kaloti and Ricardo Restrepo

Gauge theory is a beautiful subject that studies the space of connections on a vector bundle.  It is also the natural language in which theories of particle physics are formulated.  In fact, the word "gauge" has its origins in electromagnetism, and in this talk, we explore the basic geometric objects of gauge theory and show how one explicitly recovers the classical Maxwell's equations as a special case of the equations of gauge theory .  Next, generalizing Maxwell's equations to a nonabelian" setting, we obtain the Yang-Mills equations, which describe the electroweak force in nature. Surprisingly, these equations were used by Simon Donaldson in the 1980s to prove spectacular results for the topology of smooth four-manifolds. We conclude this talk by describing some of the beautiful geometry and analysis behind gauge theory that goes into the work of Donaldson (for which we awarded a Fields Medal), and time permitting, we hope to say a bit about other gauge-theoretic applications to low-dimensional topology, for instance, instanton Floer homology.
Wednesday, December 8, 2010 - 12:00 , Location: Skiles 171 , , School of Mathematics - Georgia Institute of Technology , Organizer:

Hosts: Yao Li and Ricardo Restrepo

Ulam's problem has to do with finding asymptotics, as $n \to +\infy$, for the length of the longest increasing subsequence of a random permutation of \$\{1, .., n\}. I'll survey its history, its solutions and various extensions emphasizing progresses made at GaTech.
Wednesday, December 1, 2010 - 12:00 , Location: Skiles 171 , , School of Mathematics - Georgia Institute of Technology , Organizer:

Hosts: Yao Li and Ricardo Restrepo

Suppose you want to stir a pot of soup with several spoons.  What is the most efficient way to do this?  Thurston's theory of surface homeomorphisms gives us a concrete way to analyze this question.  That is, to each mixing pattern we can associate a real number called the entropy.  We'll start from scratch with a simple example, state the Nielsen-Thurston classification of surface homeomorphisms, and give some open questions about entropies of surface homeomorphisms.
Wednesday, November 10, 2010 - 12:00 , Location: Skiles 171 , , CEISMC and School of Mathematics , Organizer:

Hosts: Yao Li and Ricardo Restrepo.

Dr. Millman is the Director of the Center for Education Integrating Science, Mathematics & Computing (CEISMC) and professor of mathematics at the Georgia Institute of Technology. He is a first hand expert in mathematics education and K-12 mathematics teacher education. Complementing the previous panel discussion on jobs in academia and industry, Dr. Milman will lead the discussion on teaching jobs.
Wednesday, November 3, 2010 - 12:00 , Location: Skiles 171 , , School of Mathematics - Georgia Institute of Technology , Organizer:

Hosts: Yao Li and Ricardo Restrepo

Modern Economic Theory is largely based on the concept of Nash Equilibrium. In its simplest form this is an essentially statics notion. I'll introduce a simple model for the origin of money (Kiotaki and Wright, JPE 1989) and use it to introduce a more general (dynamic) concept of Nash Equilibrium and my understanding of its relation to Dynamical Systems Theory and Statistical Mechanics.