Wednesday, January 23, 2013 - 12:05 , Location: Skiles 005 , Doug Ulmer , Georgia Tech, School of Math , Organizer: Robert Krone
I will review a little bit of the theory of algebric curves, which essentialy amounts to studying the zero set of a two-variable polynomial. There are several amazing facts about the number of points on a curve when the ground field is finite. (This particular case has many applications to cryptography and coding theory.) An open problem in this area is whether there exist "supersingular" curves of every genus. (I'll explain the terminology, which has something to do with having many points or few points.) A new project I have just started should go some way toward resolving this question.
Wednesday, January 16, 2013 - 12:05 , Location: Skiles 005 , Hao Min Zhou , Georgia Tech, School of Math , Organizer: Robert Krone
In this talk, I will use the shortest path problem as an example to illustrate how one can use optimization, stochastic differential equations and partial differential equations together to solve some challenging real world problems. On the other end, I will show what new and challenging mathematical problems can be raised from those applications. The talk is based on a joint work with Shui-Nee Chow and Jun Lu. And it is intended for graduate students.
Tuesday, January 15, 2013 - 12:00 , Location: Skiles 005 , Dr. Joseph Rabinoff , School of Mathematics , firstname.lastname@example.org , Organizer:
Wednesday, December 5, 2012 - 12:05 , Location: Skiles 005 , Heinrich Matzinger , Georgia Tech, School of Math , Organizer: Robert Krone
The question of the asymptotic order of magnitude of the fluctuation of the Optimal Alignment Score of two random sequences of length n has been open for decades. We prove a relation between that order and the limit of the rescaled optimal alignment score considered as a function of the substitution matrix. This allows us to determine the asymptotic order of the fluctuation for many realistic situations up to a high confidence level.
Wednesday, November 28, 2012 - 12:05 , Location: Skiles 005 , Guillermo Goldsztein , Georgia Tech, School of Math , Organizer: Robert Krone
I will describe a class of mathematical models of composites and polycrystals. The problems I will describe two research projects that are well suited for graduate student interested in learning more about this area of research.
Wednesday, November 14, 2012 - 12:05 , Location: Skiles 005 , Matt Baker , Georgia Tech, School of Math , Organizer: Robert Krone
I will discuss how one can solve certain concrete problems in number theory, for example the Diophantine equation 2x^2 + 1 = 3^m, using p-adic analysis. No previous knowledge of p-adic numbers will be assumed. If time permits, I will discuss how similar p-adic analytic methods can be used to prove the famous Skolem-Mahler-Lech theorem: If a_n is a sequence of complex numbers satisfying some finite-order linear recurrence, then for any complex number b there are only finitely many n for which a_n = b.
Wednesday, November 7, 2012 - 12:05 , Location: Skiles 005 , Santosh Vempala , Georgia Tech, College of Computing , Organizer: Robert Krone
The hyperplane conjecture of Kannan, Lovasz and Simonovits asserts that the isoperimetric constant of a logconcave measure (minimum surface to volume ratio over all subsets of measure at most half) is approximated by a halfspace to within an absolute constant factor. I will describe the motivation, implications and some developments around the conjecture and an approach to resolving it (which does not seem entirely ridiculous).
Wednesday, October 31, 2012 - 12:05 , Location: Skiles 005 , John Etnyre , Georgia Tech, School of Math , Organizer: Robert Krone
Contact geometry is a beautiful subject that has important interactions with topology in dimension three. In this talk I will give a brief introduction to contact geometry and discuss its interactions with Riemannian geometry. In particular I will discuss a contact geometry analog of the famous sphere theorem and more generally indicate how the curvature of a Riemannian metric can influence properties of a contact structure adapted to it.
Wednesday, October 24, 2012 - 12:05 , Location: Skiles 005 , Brett Wick , Georgia Tech: School of Math , Organizer: Robert Krone
In this talk we will connect functional analysis and analytic function theory by studying the compact linear operators on Bergman spaces. In particular, we will show how it is possible to obtain a characterization of the compact operators in terms of more geometric information associated to the function spaces. We will also point to several interesting lines of inquiry that are connected to the problems in this talk. This talk will be self-contained and accessible to any mathematics graduate student.
Wednesday, October 17, 2012 - 12:05 , Location: Skiles 005 , Mohammad Ghomi , Georgia Tech - School of Math , Organizer: Robert Krone
One of the most outstanding problems in differential geometry is concerned with flexibility of closed surface in Euclidean 3-space: Is it possible to continuously deform a smooth closed surface without changing its intrinsic metric structure? In this talk I will give a quick survey of known results in this area, which is primarily concerned with convex surfaces, and outline a program for studying the general case.