Wednesday, April 10, 2013 - 12:05 , Location: Skiles 005 , Christine Heitsch , Georgia Institute of Technology, School of Mathematics , email@example.com , Organizer:
A 1986 article with this title, written by M. Zuker and published by the AMS, outlined several major challenges in the area. Stating the folding problem is simple; given an RNA sequence, predict the set of (canonical, nested) base pairs found in the native structure. Yet, despite significant advances over the past 25 years, it remains largely unsolved. A fundamental problem identified by Zuker was, and still is, the "ill-conditioning" of discrete optimization solution approaches. We revisit some of the questions this raises, and present recent advances in considering multiple (sub)optimal structures, in incorporating auxiliary experimental data into the optimization, and in understanding alternative models of RNA folding.
Wednesday, March 27, 2013 - 12:05 , Location: Skiles 005 , Plamen Iliev , Georgia Tech, School of Math , Organizer: Robert Krone
In the last few years many problems of mathematical and physical interest, which may not be Hamiltonian or even dynamical, were solved using techniques from integrable systems. I will review some of these techniques and their connections to some open research problems.
Wednesday, March 6, 2013 - 12:05 , Location: Skiles 005 , Greg Blekherman , Georgia Tech, School of Math , Organizer: Robert Krone
I will discuss algebraic (sums of squares based) certificates for nonnegativity of polynomials and their use in optimization. Then I will discuss some recent results on degree bounds and state some open questions.
Wednesday, February 13, 2013 - 12:05 , Location: Skiles 005 , Michael Lacey , Georgia Tech, School of Math , Organizer: Robert Krone
I'll introduce the Hilbert transform in a natural way justifying it as a canonical operation. In fact, it is such a basic operation, that it arises naturally in a range of settings, with the important complication that the measure spaces need not be Lebesge, but rather a pair of potentially exotic measures. Does the Hilbert transform map L^2 of one measure into L^2 of the other? The full characterization has only just been found. I'll illustrate the difficulties with a charming example using uniform measure on the standard 1/3 Cantor set.
From microscopic to macroscopic: some consideration on a simple model for a gas in or out of equilibriumWednesday, February 6, 2013 - 12:05 , Location: Skiles 005 , Federico Bonetto , Georgia Tech, School of Math , Organizer: Robert Krone
The derivation of the properties of macroscopic systems (e.g. the air in a room) from the motions and interactions of their microscopic constituents is the principal goal of Statistical Mechanics. I will introduce a simplified model of a gas (the Kac model). After discussing its relation with more realistic models, I'll present some known results and possible extension.
Wednesday, January 30, 2013 - 12:05 , Location: Skiles 005 , Howie Weiss , Georgia Tech, School of Math , Organizer: Robert Krone
After some brief comments about the nature of mathematical modeling in biology and medicine, we will formulate and analyze the SIR infectious disease transmission model. The model is a system of three non-linear differential equations that does not admit a closed form solution. However, we can apply methods of dynamical systems to understand a great deal about the nature of solutions. Along the way we will use this model to develop a theoretical foundation for public health interventions, and we will observe how the model yields several fundamental insights (e.g., threshold for infection, herd immunity, etc.) that could not be obtained any other way. At the end of the talk we will compare the model predictions with data from actual outbreaks.
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.