Seminars and Colloquia by Series

Introduction to metric and comparison geometry

Series
Geometry Topology Working Seminar
Time
Friday, February 20, 2009 - 15:00 for 2 hours
Location
Skiles 269
Speaker
Comparison geometry studies Riemannian manifolds with a given curvature bound. This minicourse is an introduction to volume comparison (as developed by Bishop and Gromov), which is fundamental in understanding manifolds with a lower bound on Ricci curvature. Prerequisites are very modest: we only need basics of Riemannian geometry, and fluency with fundamental groups and metric spaces. The second (2 hour) lecture is about Gromov-Hausdorff convergence, which provides a natural framework to studying degenerations of Riemannian metrics.

Sums and products in C[x]

Series
Combinatorics Seminar
Time
Friday, February 20, 2009 - 15:00 for 1 hour (actually 50 minutes)
Location
Skiles 255
Speaker
Ernie CrootSchool of Mathematics, Georgia Tech
In this work (joint with Derrick Hart), we show that there exists a constant c > 0 such that the following holds for all n sufficiently large: if S is a set of n monic polynomials over C[x], and the product set S.S = {fg : f,g in S}; has size at most n^(1+c), then the sumset S+S = {f+g : f,g in S}; has size \Omega(n^2). There is a related result due to Mei-Chu Chang, which says that if S is a set of n complex numbers, and |S.S| < n^(1+c), then |S+S| > n^(2-f(c)), where f(c) -> 0 as c -> 0; but, there currently is no result (other than the one due to myself and Hart) giving a lower bound of the quality >> n^2 for |S+S| for a fixed value of c. Our proof combines combinatorial and algebraic methods.

Coupling in ergodic problems for Stochastic Navier-Stokes

Series
Probability Working Seminar
Time
Friday, February 20, 2009 - 15:00 for 1 hour (actually 50 minutes)
Location
Skiles 268
Speaker
Sergio AlmadaSchool of Mathematics, Georgia Tech
The talk is based on a paper by Kuksin, Pyatnickiy, and Shirikyan. In this paper, the convergence to a stationary distribution is established by partial coupling. Here, only finitely many coordinates in the (infinite-dimensional) phase space participate in the coupling while the dynamics takes care of the other coordinates.

Introduction to basic governing equations of fluid dynamics

Series
SIAM Student Seminar
Time
Friday, February 20, 2009 - 12:30 for 2 hours
Location
Skiles 269
Speaker
Ke YinSchool of Mathematics, Georgia Tech
In this introductory talk, I am going to derive the basic governing equations of fluid dynamics. Our assumption are the three physical principles: the conservation of mass, Newton's second law, and the conservation of energy. The main object is to present Euler equations (which characterize inviscid flow) and Navier-Stokes equations (which characterize viscid flow).

Optimal alignments and sceneries

Series
Stochastics Seminar
Time
Thursday, February 19, 2009 - 15:00 for 1 hour (actually 50 minutes)
Location
Skiles 269
Speaker
Heinrich MatzingerSchool of Mathematics, Georgai Tech
We explore the connection between Scenery Reconstruction and Optimal Alignments. We present some new algorithms which work in practise and not just in theory, to solve the Scenery Reconstruction problem

Tiling R^n by unit cubes

Series
Graph Theory Seminar
Time
Thursday, February 19, 2009 - 12:05 for 1.5 hours (actually 80 minutes)
Location
Skiles 255
Speaker
Peter HorakUniversity of Washington, Tacoma
Tiling problems belong to the oldest problems in whole mathematics. They attracted attention of many famous mathematicians. Even one of the Hilbert problems is devoted to the topic. The interest in tilings by unit cubes originated with a conjecture raised by Minkowski in 1908. In this lecture we will discuss the conjecture, and other closely related problems.

Molecular topology - Applying graph theory to health science

Series
School of Mathematics Colloquium
Time
Thursday, February 19, 2009 - 11:00 for 1 hour (actually 50 minutes)
Location
Skiles 269
Speaker
Amigo GarciaMiguel Hernández University, Spain
Molecular topology is an application of graph theory to fields like chemistry, biology and pharmacology, in which the molecular structure matters. Its scope is the topological characterization of molecules by means of numerical invariants, called topological indices, which are the main ingredient of the molecular topological models. These models have been instrumental in the discovery of new applications of naturally occurring molecules, as well as in the design of synthetic molecules with specific chemical, biological or pharmacological properties. The talk will focus on pharmacological applications.

Random Walk Sampling - Examples & Techniques for Bounding Mixing Tim

Series
ACO Student Seminar
Time
Wednesday, February 18, 2009 - 13:30 for 2 hours
Location
ISyE Executive Classroom
Speaker
Linji YangCS, Georgia Tech
In this talk I will give an introduction of the Markov Chain Monte Carlo Method, which uses markov chains to sample interesting combinatorial objects such as proper colorings, independent sets and perfect matchings of a graph. I will introduce methods such as Couplings and Canonical Paths which have been widely used to analyze how many steps Markov Chains needs to go (mixing time) in order to get a sufficiently random combinatorial object. I will also give a brief survey of some recent results in the sampling of colorings.

Kirchhoff's matrix-tree theorem revisited

Series
Research Horizons Seminar
Time
Wednesday, February 18, 2009 - 12:00 for 1 hour (actually 50 minutes)
Location
Skiles 255
Speaker
Matt BakerSchool of Mathematics, Georgia Tech
I will give a modern bijective proof of Kirchhoff's classical theorem relating the number of spanning trees in a graph to the Laplacian matrix of the graph. The proof will highlight some analogies between graph theory and algebraic geometry.

Traveling fronts in disordered media

Series
PDE Seminar
Time
Tuesday, February 17, 2009 - 15:05 for 1.5 hours (actually 80 minutes)
Location
Skiles 255
Speaker
Andrej ZlatošUniversity of Chicago
We study generalized traveling front solutions of reaction-diffusion equations modeling flame propagation in combustible media. Although the case of periodic media has been studied extensively, until very recently little has been known for general disordered media. In this talk we will address questions of existence, uniqueness, and stability of traveling fronts in this framework.