## Seminars and Colloquia by Series

Series: Other Talks
Friday, February 20, 2009 - 15:00 , Location: Skiles 269 , Igor Belegradek , School of Mathematics, Georgia Tech , Organizer: Igor Belegradek
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.
Friday, February 20, 2009 - 15:00 , Location: Skiles 255 , Ernie Croot , School of Mathematics, Georgia Tech , Organizer: Prasad Tetali
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.
Friday, February 20, 2009 - 15:00 , Location: Skiles 268 , Sergio Almada , School of Mathematics, Georgia Tech , Organizer:
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.
Friday, February 20, 2009 - 15:00 , Location: Skiles 269 , Igor Belegradek , Ga Tech , Organizer: John Etnyre
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.
Friday, February 20, 2009 - 12:30 , Location: Skiles 269 , Ke Yin , School of Mathematics, Georgia Tech , Organizer:
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).
Thursday, February 19, 2009 - 15:00 , Location: Skiles 269 , Heinrich Matzinger , School of Mathematics, Georgai Tech , Organizer: Heinrich Matzinger
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
Thursday, February 19, 2009 - 12:05 , Location: Skiles 255 , Peter Horak , University of Washington, Tacoma , Organizer: Robin Thomas
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.
Thursday, February 19, 2009 - 11:00 , Location: Skiles 269 , Amigo Garcia , Miguel Hernández University, Spain , Organizer: Guillermo Goldsztein
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.
Wednesday, February 18, 2009 - 13:30 , Location: ISyE Executive Classroom , Linji Yang , CS, Georgia Tech , Organizer: Annette Rohrs
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.
Wednesday, February 18, 2009 - 12:00 , Location: Skiles 255 , Matt Baker , School of Mathematics, Georgia Tech , Organizer:
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.