Seminars and Colloquia by Series

On the inertia set of a graph

Series
Graph Theory Seminar
Time
Monday, October 6, 2008 - 11:05 for 1.5 hours (actually 80 minutes)
Location
Skiles 255
Speaker
Hein van der Holst – University of Eindhoven
For an undirected graph G=(V,E) with V={1,...,n} let S(G) be the set of all symmetric n x n matrices A=[a_i,j] with a_i,j non-zero for distinct i,j if and only if ij is an edge. The inertia of a symmetric matrix is the triple (p_+,p_-,p_0), where p_+, p_-,p_0 are the number of positive, negative, and null eigenvalues respectively. The inverse inertia problem asks which inertias can be obtained by matrices in S(G). This problem has been studied intensively by Barrett, Hall, and Loewy. In this talk I will present new results on the inverse inertia problem, among them a Colin de Verdiere type invariant for the inertia set (this is the set of all possible inertias) of a graph, a formula for the inertia set of graphs with a 2-separation, and a formula for the inertia set of the join of a collection of graphs. The Colin de Verdiere type invariant for the inertia set is joint work with F. Barioli, S.M. Fallat, H.T. Hall, D. Hershkowitz, L. Hogben, and B. Shader, and the formula for the inertia set of the join of a collection of graphs is joint work with W. Barrett and H.T. Hall.

Maps and Branched Covers - Combinatorics, Geometry and Physics

Series
Combinatorics Seminar
Time
Friday, October 3, 2008 - 15:00 for 1 hour (actually 50 minutes)
Location
Skiles 255
Speaker
Ian Goulden – University of Waterloo
This is an expository account of recent work on the enumeration of maps (graphs embedded on a surface of arbitrary genus) and branched covers of the sphere.  These combinatorial and geometric objects can both be represented by permutation factorizations, in the which the subgroup generated by the factors acts transitively on the underlying symbols (these are called "transitive factorizations"). Various results and methods are discussed, including a number of methods from mathematical physics, such as matrix integrals and the KP hierarchy of integrable systems. A notable example of the results is a recent recurrence for triangulations of a surface of arbitrary genus obtained from the simplest partial differential equation in the KP hierarchy. The recurrence is very simple, but we do not know a combinatorial interpretation of it, yet it leads to precise asymptotics for the number of triangulations with n edges, of a surface of genus g.

Large N duality and integrable systems

Series
Geometry Topology Seminar
Time
Friday, October 3, 2008 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 269
Speaker
Tony Pantev – Dept of Mathematics, University of Penn
I will describe a framework which relates large N duality to the geometry of degenerating Calabi-Yau spaces and the Hitchin integrable system. I will give a geometric interpretation of the Dijkgraaf-Vafa large N quantization procedure in this context.

Perfect simulation of Matern Type III point processes

Series
Stochastics Seminar
Time
Thursday, October 2, 2008 - 15:00 for 1 hour (actually 50 minutes)
Location
Skiles 269
Speaker
Mark Huber – Departments of Mathematics and Statistical Sciences, Duke University
Spatial data are often more dispersed than would be expected if the points were independently placed. Such data can be modeled with repulsive point processes, where the points appear as if they are repelling one another. Various models have been created to deal with this phenomenon. Matern created three algorithms that generate repulsive processes. Here, Matérn Type III processes are used to approximate the likelihood and posterior values for data. Perfect simulation methods are used to draw auxiliary variables for each spatial point that are part of the type III process.

Geometry and Topology in Fluid Mechanics

Series
School of Mathematics Colloquium
Time
Thursday, October 2, 2008 - 11:00 for 1 hour (actually 50 minutes)
Location
Skiles 269
Speaker
John Etnyre – School of Mathematics, Georgia Tech
Describe the trajectories of particles floating in a liquid. This is a surprisingly difficult problem and attempts to understand it have involved many diverse techniques. In the 60's Arold, Marsden, Ebin and others began to introduce topological techniques into the study of fluid flows. In this talk we will discuss some of these ideas and see how they naturally lead to the introduction of contact geometry into the study of fluid flows. We then consider some of the results one can obtain from this contact geometry perspective. For example we will show that for a sufficiently smooth steady ideal fluid flowing in the three sphere there is always some particle whose trajectory is a closed loop that bounds an embedded disk, and that (generically) certain steady Euler flows are (linearly) unstable.

Geometry and Topology in Fluid Mechanics

Series
School of Mathematics Colloquium
Time
Thursday, October 2, 2008 - 11:00 for 1 hour (actually 50 minutes)
Location
Skiles 269
Speaker
John Etnyre – School of Mathematics, Georgia Tech
Describe the trajectories of particles floating in a liquid. This is a surprisingly difficult problem and attempts to understand it have involved many diverse techniques. In the 60's Arold, Marsden, Ebin and others began to introduce topological techniques into the study of fluid flows. In this talk we will discuss some of these ideas and see how they naturally lead to the introduction of contact geometry into the study of fluid flows. We then consider some of the results one can obtain from this contact geometry perspective. For example we will show that for a sufficiently smooth steady ideal fluid flowing in the three sphere there is always some particle whose trajectory is a closed loop that bounds an embedded disk, and that (generically) certain steady Euler flows are (linearly) unstable.

A Friendly Introduction to Constraint Programming

Series
ACO Student Seminar
Time
Wednesday, October 1, 2008 - 13:30 for 2 hours
Location
ISyE Executive Classroom
Speaker
Daniel Dadush – ACO, Georgia Tech
Constraint Programming is a powerful technique developed by the Computer Science community to solve combinatorial problems. I will present the model, explain constraint propagation and arc consistency, and give some basic search heuristics. I will also go through some illustrative examples to show the solution process works.

Knots, continued fractions and DNA

Series
Research Horizons Seminar
Time
Wednesday, October 1, 2008 - 12:00 for 1 hour (actually 50 minutes)
Location
Skiles 255
Speaker
Roland van der Veen – University of Amsterdam
In this introduction to knot theory we will focus on a class of knots called rational knots. Here the word rational refers to a beautiful theorem by J. Conway that sets up a one to one correspondence between these knots and the rational numbers using continued fractions. We aim to give an elementary proof of Conway's theorem and discuss its application to the study of DNA recombination. No knowledge of topology is assumed.

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