Seminars and Colloquia by Series

Two weight inequality for the Hilbert transform

Series
Research Horizons Seminar
Time
Tuesday, March 2, 2010 - 12:00 for 1 hour (actually 50 minutes)
Location
Skiles 255
Speaker
Michael Lacey – School of Math, Georgia Tech

Please Note: Hosted by: Huy Huynh and Yao Li

The Hilbert transform is a foundational transform, with deep connections to electrical charge, and analyticity. The `two weight inequality for the Hilbert transform' concerns the most general setting in which the Hilbert transform admits a (weighted) L^2 inequality. We will give a couple of (surprising?) ways that this question arises. And we will indicate the surprise that is behind the recent description of all setting in which the two weight inequality holds.

Markov Chain Mixing with Applications

Series
Research Horizons Seminar
Time
Tuesday, February 23, 2010 - 12:00 for 1 hour (actually 50 minutes)
Location
Skiles 255
Speaker
Prasad Tetali – Professor, School of Mathematics and School of Computer Science

Please Note: Hosted by: Huy Huynh and Yao Li

Sampling from and approximately counting the size of a large set of combinatorial structures has contributed to a renaissance in research in finite Markov chains in the last two decades. Applications are wide-ranging from sophisticated card shuffles, deciphering simple substitution ciphers (of prison inmates in the California state prison), estimating the volume of a high-dimensional convex body, and to understanding the speed of Gibbs sampling heuristics in statistical physics. More recent applications include rigorous estimates on J.M. Pollard's (1979) classical Rho and Kangaroo algorithms for the discrete logarithm problem in finite cyclic groups. The lecture will be a brief (mostly self-contained) introduction to the Markov Chain Monte Carlo (MCMC) methodology and applications, and will include some open problems.

Orthogonal Polynomials and their Ph.D. Theses

Series
Research Horizons Seminar
Time
Tuesday, February 16, 2010 - 12:00 for 1 hour (actually 50 minutes)
Location
Skiles 255
Speaker
Doron Lubinsky – School of Mathematics, Georgia Tech

Please Note: Hosted by: Huy Huynh and Yao Li

Orthogonal Polynomials and their generalizations have a great many applications in areas ranging from signal processing to random matrices to combinatorics. We outline a few of the connections, and present some possible Ph. D Problems

A Probabilistic Technique for Finding Almost Periods in Additive Combinatorics

Series
Research Horizons Seminar
Time
Tuesday, February 9, 2010 - 12:00 for 1 hour (actually 50 minutes)
Location
Skiles 255
Speaker
Ernie Croot – School of Math, Georgia Tech

Please Note: Hosted by: Huy Huynh and Yao Li

Olof Sisask and myself have produced a new probabilistic technique for finding `almost periods' of convolutions of subsets of finite groups. In this talk I will explain how this has allowed us to give (just recently) new bounds on the length of the longest arithmetic progression in a sumset A+A.

The arithmetic of dynamical systems

Series
Research Horizons Seminar
Time
Tuesday, February 2, 2010 - 12:00 for 1 hour (actually 50 minutes)
Location
Skiles 255
Speaker
Matt Baker – School of Math, Georgia Tech

Please Note: Hosted by: Huy Huynh and Yao Li

I will discuss some theorems and conjectures in the relatively new field of arithmetic dynamics, focusing in particular on some methods from number theory which can be used to study the orbits of points in algebraic dynamical systems.

Variational problems involving area (continued)

Series
Research Horizons Seminar
Time
Tuesday, January 26, 2010 - 12:00 for 1 hour (actually 50 minutes)
Location
Skiles 255
Speaker
John McCuan – School of Math, Georgia Tech

Please Note: Hosted by: Huy Huynh and Yao Li

In the preceeding talk, I outlined a framework for variational problems and some of the basic tools and results. In this talk I will attempt describe several problems of current interest.

Variational problems involving area.

Series
Research Horizons Seminar
Time
Wednesday, December 2, 2009 - 12:00 for 1 hour (actually 50 minutes)
Location
Skiles 171
Speaker
John McCuan – School of Mathematics, Georgia Tech –
I will describe several geometrical problems that arise from the minimization of some sort of integral functional and the basic relation between such minimization and partial differential equations. Then I will make some further comments on my favorite kind of such problems, namely those that have something to do with minimizing area of surfaces under various side conditions.

Panel Discussion with Students About the Hiring Process.

Series
Research Horizons Seminar
Time
Wednesday, November 18, 2009 - 12:00 for 1 hour (actually 50 minutes)
Location
Skiles 269
Speaker
Drs. Ulmer, Harrell, and Wick – School of Mathematics, Georgia Tech
The Research Horizons seminar this week will be a panel discussion on the academic job market for mathematicians. The discussion will begin with an overview by Doug Ulmer of the hiring process, with a focus on the case of research-oriented universities. The panel will then take questions from the audience. Professor Wick was hired last year at Tech, so has recently been on the students' side of the process. Professor Harrell has been involved with hiring at Tech for many years and can provide a perspective on the university side of the process.

Topological aspects in the theory of aperiodic solids and tiling spaces

Series
Research Horizons Seminar
Time
Wednesday, November 11, 2009 - 12:00 for 1 hour (actually 50 minutes)
Location
Skiles 171
Speaker
Jean Bellissard – School of Mathematics, Georgia Tech –
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.

Dynamical Systems, Graphs, Entropies, Dynamical Networks, and Statistical Mechanics

Series
Research Horizons Seminar
Time
Wednesday, November 4, 2009 - 12:00 for 1 hour (actually 50 minutes)
Location
Skiles 171
Speaker
Leonid Bunimovich – School of Mathematics, Georgia Tech –
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.

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