Wednesday, September 24, 2008 - 12:00 , Location: Skiles 255 , Jeff Geronimo , School of Mathematics, Georgia Tech , Organizer:
A Turning point is where solutions to differential equations change behavior from exponential to oscillatory. In this region approximate solutions given by the powerful WKB method break down. In a series of paper in the 30's and 40's Langer developed a transformation (the Langer transformation) that allows the development of good approximate solutions (in terms of Airy functions) in the region of the Turning point I will discuss a discrete analog of this transformation and show how it leads to nice asymptotic formulas for various orthogonal polynomials.
Wednesday, September 17, 2008 - 12:00 , Location: Skiles 255 , Leonid Bunimovich , School of Mathematics, Georgia Tech , Organizer:
Dynamics of spatially extended systems is often described by Lattice Dynamical Systems (LDS). LDS were introduced 25 years ago independently by four physicists from four countries. Sometimes LDS themselves are quite relevant models of real phenomena. Besides, very often discretizations of partial differential equations lead to LDS. LDS consist of local dynamical systems sitting in the nodes of a lattice which interact between themselves. Mathematical studies of LDS started in 1988 and introduced a thermodynamic formalism for these spatially extended dynamical systems. They allowed to give exact definitions of such previously vague phenomena as space-time chaos and coherent structures and prove their existence in LDS. The basic notions and results in this area will be discussed. It is a preparatory talk for the next day colloquium where Dynamical Networks, i.e. the systems with arbitrary graphs of interactions, will be discussed.
Wednesday, September 10, 2008 - 12:00 , Location: Skiles 255 , Zhiwu Lin , School of Mathematics, Georgia Tech , Organizer:
A plasma is a gas of ionized particles. For a dilute plasma of very high temperature, the collisions can be ignored. Such situations occur, for example, in nuclear fusion devices and space plasmas. The Vlasov-Poisson and Vlasov-Maxwell equations are kinetic models for such collisionless plasmas. The Vlasov-Poisson equation is also used for galaxy evolution. I will describe some mathematical results on these models, including well-posedness and stability issues.
Wednesday, September 3, 2008 - 12:00 , Location: Skiles 255 , Robin Thomas , School of Mathematics, Georgia Tech , Organizer:
I will explain and prove a beautiful and useful theorem of Alon and Tarsi that uses multivariate polynomials to guarantee, under suitable hypotheses, the existence of a coloring of a graph. The proof method, sometimes called a Combinatorial Nullstellensatz, has other applications in graph theory, combinatorics and number theory.
Wednesday, August 27, 2008 - 12:00 , Location: Skiles 255 , Tom Trotter, Teena Carroll, Luca Dieci , School of Mathematics, Georgia Tech , Organizer:
* Dr. Trotter: perspective of the hiring committee with an emphasis on research universities. * Dr. Carroll: perspective of the applicant with an emphasis on liberal arts universities. * Dr. Dieci: other advice, including non-academic routes.
, Location: Skiles 006 , Leonid Bunimovich , School of Mathematics - Georgia Institute of Technology , Organizer:
Hosts: Amey Kaloti and Ricardo Restrepo
An efficient (arguably the most efficient) way to study and describe dynamical systems with complex behavior is to code their orbits. To do so one considers a partition (physicists call it coarse graining) of the space of states (phase space) of the systems and identify location of a point with an element of such partition where this point belongs. . By doing so one gets an unified description of dynamical systems in Differential equations, Number theory, probability theory, Combinatorics, etc. I'll present an introduction to this Symbolic dynamics for interacting dynamical systems (dynamical networks) and formulate some open problems.This talk will also serve as a preparatory one for the next day Math Colloquium.