Sponsored by the Rutgers University Department of Mathematics and the
Center for Discrete Mathematics and Theoretical Computer Science (DIMACS)
Title: Algorithms in Combinatorial Design Theory
Speaker: Ilias Kotsireas, Wilfrid Laurier University
Date: Thursday, February 2, 2006 5:00pm
Location: Hill Center, Room 705, Rutgers University, Busch Campus, Piscataway, NJ
Many existence problems in Combinatorial Design Theory are directly amenable to algebraic formulations that enable the application of powerful computational algebra and metaheuristic methods. The application of computational algebra methods, often aided by supercomputing, reveals important combinatorial and group theoretic structural information on the varieties associated with combinatorial designs. The application of metaheuristic methods, such as genetic algorithms for instance, allows the construction of designs of large orders.
These ideas lead to some interesting consequences in Coding Theory, such as the construction of new self-dual codes with larger minimal distances. One of the practical outcomes of these projects is the deployment of several combinatorial designs databases, integrated in the Magma Computer Algebra System developed in Sydney. In this talk I will discuss specific examples of applications and new results, as well as future research perspectives.