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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.

Series: SIAM Student Seminar

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).

Series: Stochastics Seminar

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

Series: Graph Theory Seminar

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.

Series: School of Mathematics Colloquium

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.

Series: ACO Student Seminar

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.

Series: Research Horizons Seminar

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.

Series: PDE Seminar

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.

Series: CDSNS Colloquium

Permutation entropy was introduced as a complexity measure of time series. Formally, it replaces the symbol blocks in the definition of Shannon entropy by the so-called ordinal patterns –a digest of the ups-and-downs along a finite orbit in a totally ordered state space. Later, this concept was extended to self maps of n-dimensional intervals, in metric and topological versions. It can be proven that, under some assumptions, the metric and topological permutation entropy coincide with their corresponding conventional counterparts. Besides its use as an entropy estimator, permutation entropy has found some interesting applications. We will talk about the detection of determinism in noisy time series, and the recovery of the control parameter from the symbolic sequences of a unimodal map (which allows to cryptanalize some chaotic ciphers).

Series: Geometry Topology Seminar

I will discuss a couple of applications of transverse knot theory to the classification of contact structures and braid theory. In particular I will make the statement "transverse knots classify contact structures" precise and then prove it (if we have time). I will also discuss how progress on two of Orevkov's questions concerning quasi-positive knots that have implications for Hilbert's 16th problem.