Spring 2007 GSS Schedule
Organizers: Robert Beeler and Jeremy Lyle
| Date | Speaker | Topic | Abstract |
|---|---|---|---|
| January 22 | John Chrispell | An Introduction to Latex | TeX, created by Donald E. Knuth, is a high quality way of typesetting
mathematical notation and ordinary text. LaTeX documents are created
using a markup language much like html. In this talk, I will start from
scratch, and show how to create a document using TeXnicCenter. Potential
talk topics will include:
|
| January 29 | Stacey Faulkenberg
and Christine Kraft |
Some helpful software for linear and nonlinear programming | We will present and solve a linear program in LINDO, Matlab, SAS/OR, and CPLEX. We will briefly discuss the differences in the packages. We will also present and solve a non-linear program in Matlab, Maple, SAS/OR, and CPLEX. We will post the code so that everyone may use it as a starting point for their programming. Please come to learn and make suggestions! |
| February 5 | Jobby Jacob | An Algorithm for the Single-Source Unsplittable Flow Problem | Let G=(V,E) be a capacitated directed graph with single source
s and k terminals t_1, t_2,...,t_k with demands d_1,d_2,...,d_k respectively. The objective for the single source unspittable flow problem is to unsplittably route every demand on a single path from s to the corresponding terminal without violating the capacities.
In (1) the authors propose an algorithm which will compute an unsplittable flow satisfying the demands such that the total flow through any edge exceeds its capacity by at most the maximum demand provided the necessary cut condition is satisfied. For the graphs in which all the capacities are at least the maximum demand, the algorithm will therefore obtain an unsplittable flow with congestion at most 2. We will also see how all demands can be routed unsplittably in 5 rounds, as well as some results in maximizing the total demand satisfied unsplittably. [1] Yefim Dinitz, Naveen Garg and Michel Goemans, On the Single-Source Unsplittable Flow Problem, Combinatorica, 19:17-41, 1999. |
| February 12 | Cancelled | ||
| March 5 | Jeremy Lyle | Dense Triangle-Free Graphs | What is the minimum degree for which a triangle-free graph must be bipartite? What is the minimum degree for which a triangle-free graph can have an arbitrarily large chromatic number? What happens in between? We consider the answers or partial answers to these questions. |
| March 19 | Spring Break | ||
| March 26 | Robert Beeler | Automorphic Decompositions of Graphs | |
| April 2 | Robert Beeler | Experiences on the Job Search | |
| April 16 | Timur Milgrom | Approximate Solutions to some Elliptic PDE's | An approximation of the Hilbert transform is established, for which we derive properties that are useful for solving linear PDEs and proving the existence of the solution of a system of non-linear PDEs. The approximation is applied to the Laplace equation and the limit is taken as the approximation parameter goes to zero which is compared to the exact solution. Finally, we give a proof of the existence of an approximate solution for a system of equations related to the vortex sheet without surface tension. |