Peter Gibbons Memorial Lecture Series: The Combinatorics at the Heart of the Problem
Speaker: Charles Colbourn, Arizona State University
When: Refreshments at 5.30pm, lecture starts at 6.00pm.
Charlie Colbourn is Professor of Computer Science and Engineering at Arizona State University in Tempe. He has authored about three hundred refereed journal papers and three books and has graduated 18 Ph.D. students. He was a fellow student with Peter Gibbons at the University of Toronto and includes Peter among his many co-authors.
Colbourn's research employs combinatorial mathematics and algorithms to address problems in diverse areas including software testing, networking (optical, wireless, wireline), computational molecular biology, communications and information theory and experimental design. He develops deep combinatorial results with real applications.
Synopsis: Simple relationships among objects are often used to characterize the structures built from them. For example, the relation between points and lines in a drawing, or nodes and links in a network, determines the possible structures that arise. When these relationships are constrained to follow well-defined rules, natural questions arise: Is there any structure obeying the constraints? If yes, how many are there? Of those, which is the "best" as measured by some criterion? These are the central questions of combinatorics.
As a discipline, combinatorics has evolved from a set of disjointed topics and parlour tricks into a thriving field with deep results. Yet from the outset its development has been driven by the frequency with which understanding and solving a practical problem means finding the combinatorics at the heart of the problem. More remarkable is the diversity of practical problems in which one type of combinatorial object arises. Whether designing software test cases, compressing files, designing a statistical experiment, designing reliable circuits, transmitting signals on a noisy channel, or identifying diseased members of a population, the combinatorics at the heart is essentially the same. Understanding the underlying combinatorics seems crucial; mathematical tools are indispensable for this, but algorithmic and computational developments have led both to wider application and to deeper theory.
Peter Gibbons excelled at communicating the insights gained to students and colleagues alike. He was a stalwart supporter and leader of his discipline, his department, and his university. His scientific work spanned combinatorics and graph theory - building algorithmic tools, developing new theory, and applying these results in many different ways. In this talk, using Peter's work as a guide we explore the process of finding the combinatorics at the heart of a problem, and the process of carrying that back to the driving application. And in the process we celebrate the life of a friend.