Seminars and Colloquia by Series

Wednesday, November 11, 2009 - 12:00 , Location: Skiles 171 , Jean Bellissard , School of Mathematics, Georgia Tech , , Organizer:
An assembly of atoms in a solid phase will be described through the notion of Delone sets and related to tilings. The Hull and the tiling space wiill be defined. It will be shown that the tiling space and the Hull can be constructed through an inverse limit of CW-complexes built out of the tiles and of the local patches. From then various cohomologies can be defined and allow to distinguish between these atomic distributions. The question of whether these topological invariant can be seen in experiments will be addressed.
Wednesday, November 4, 2009 - 12:00 , Location: Skiles 171 , Leonid Bunimovich , School of Mathematics, Georgia Tech , , Organizer:
Dynamical systems theory is concerned with systems that change in time (where time can be any semigroup). However, it is quite rare that one can find the solutions for such systems or even a "sizable" subset of such solutions. An approach motivated by this fact, that goes back to Poincaré, is to study instead partitions of the (phase) space M of all states of a dynamical system and consider the evolution of the elements of this partition (instead of the evolution of points of M). I'll explain how the objects in the title appear, some relations between them, and formulate a few general as well as more specific open problems suitable for a PhD thesis in dynamical systems, mathematical biology, graph theory and applied and computational mathematics. This talk will also serve to motivate and introduce to the topics to be given in tomorrow's colloquium.
Wednesday, October 28, 2009 - 12:00 , Location: Skiles 171 , Igor Belegradek , School of Mathematics, Georgia Tech , , Organizer:
The Soul Theorem, proved by Cheeger and Gromoll forty year ago, reveals a beautiful structure of noncompact complete manifolds of nonnegative curvature. In the talk I will sketch a proof of the Soul Theorem, and relate it to my current work on moduli spaces of nonnegatively curved metrics.
Wednesday, October 21, 2009 - 12:00 , Location: Skiles 171 , Doron Lubinsky , School of Mathematics, Georgia Tech , , Organizer:
Orthogonal polynomials are an important tool in many areas of pure and applied mathematics. We outline one application in random matrix theory. We discuss generalizations of orthogonal polynomials such as the Muntz orthogonal polynomials investigated by Ulfar Stefansson. Finally, we present some conjectures about biorthogonal polynomials, which would be a great Ph.D. project for any interested student.
Wednesday, October 14, 2009 - 12:00 , Location: Skiles 171 , Sung Ha Kang , School of Mathematics, Georgia Tech , , Organizer:
Image segmentation has been widely studied, specially since Mumford-Shah functional was been proposed. Many theoretical works as well as numerous extensions have been studied rough out the years. This talk will focus on introduction to these image segmentation functionals.  I will start with the review of Mumford-Shah functional and discuss Chan-Vese model.  Some new extensions will be presented at the end.
Wednesday, October 7, 2009 - 12:00 , Location: Skiles 171 , Stavros Garoufalidis , School of Mathematics, Georgia Tech , , Organizer:
In linear algebra classes we learn that a symmetic matrix with real entries has real eigenvalues. But many times we deal with nonsymmetric matrices that we want them to have real eigenvalues and be stable under a small perturbation. In the 1930's totally positive matrices were discovered in mechanical problems of vibtrations, then lost for over 50 years. They were rediscovered in the 1990's as esoteric objects in quantum groups and crystal bases. In the 2000's these matrices appeared in relation to Teichmuller space and its quantization. I plan to give a high school introduction to totally positive matrices.
Wednesday, September 30, 2009 - 12:00 , Location: Skiles 171 , Brett Wick , School of Mathematics, Georgia Tech , , Organizer:
 In the last 10 years there has been a resurgence of interest in questions about certain spaces of analytic functions. In this talk we will discuss various advances in the study of these spaces of functions and highlight questions of current interest in analytic function theory. We will give an overview of recent advances in the Corona Problem, bilinear forms on spaces of analytic functions, and highlight some methods to studying these questions that use more discrete techniques. 
Wednesday, September 23, 2009 - 12:00 , Location: Skiles 171 , Stavros Garoufalidis , Georgia Tech School of Mathematics , , Organizer:
Dodgson (the author of Alice in Wonderland) was an amateur mathematician who wrote a book about determinants in 1866 and gave a copy to the queen. The queen dismissed the book and so did the math community for over a century. The Hodgson Condensation method resurfaced in the 80's as the fastest method to compute determinants (almost always, and almost surely). Interested about Lie groups, and their representations? In crystal bases? In cluster algebras? In alternating sign matrices? OK, how about square ice? Are you nuts? If so, come and listen.
Wednesday, September 16, 2009 - 12:00 , Location: Skiles 171 , William T. Trotter , School of Mathematics, Georgia Tech , , Organizer:

(joint work with Csaba Biro, Dave Howard, Mitch Keller and Stephen Young. Biro and Young finished their Ph.D.'s at Georgia Tech in 2008. Howard and Keller will graduate in spring 2010)

Motivated by questions in algebra involving what is called "Stanley" depth, the following combinatorial question was posed to us by Herzog: Given a positive integer n, can you partition the family of all non-empty subsets of {1, 2, ..., n} into intervals, all of the form [A, B] where |B| is at least n/2. We answered this question in the affirmative by first embedding it in a stronger result and then finding two elegant proofs. In this talk, which will be entirely self-contained, I will give both proofs. The paper resulting from this research will appear in the Journal of Combinatorial Theory, Series A.
Wednesday, September 9, 2009 - 12:00 , Location: Skiles 171 , Ernie Croot , School of Mathematics, Georgia Tech , , Organizer:
Additive combinatorics is a relatively new field, with many diverse and exciting research programmes.  In this talk I will discuss two of these programmes -- the continuing development of sum-product inequalities, and the unfolding progress on arithmetic progressions -- along with some new results proved by me and my collaborators.  Hopefully I will have time to mention some nice research problems as well.