Shier, Douglas R. (Clemson University)

Topics:

Procedures and Paradoxes in Voting
Voting procedures are a way of translating our individual preferences into preferences for a larger group. This talk discusses several voting schemes that have been proposed as well as some potential pitfalls that can occur in trying to design an "ideal" voting method. (Elementary)

Measuring the Homogeneity of Surfaces: A Network Model
A problem that arises in several applied areas is ensuring that particles are spread homogeneously over a given surface. This issue occurs in several technological, biological, and geological applications. We discuss a network model, and spanning trees for this network, which can be used to study this problem. (Elementary)

Mathematical Approaches to the Ranking of Athletic Teams
In a variety of sports, such as collegiate basketball, teams need to be ranked as a basis for inclusion in post-season tournaments. If we are given the won-loss-tie histories of the teams in a league, how can one determine ranking in an unbiased manner? We present one useful approach that defines the strength of a team in terms of the strengths of the teams it has beaten. (Elementary)

Some Excursions in Network Modeling
Our modern technological world provides ample evidence of networks, such as computer networks, transportation networks, and power distribution networks. What are more intriguing are those conceptual (rather than physical) networks that are lurking just beneath the surface of seemingly innocent problems. In this expository talk, we will first review some fundamental concepts related to shortest paths (and its associated dual problem). These ideas will be applied to some interesting problems that arise in apparently unrelated domains: specifically, artificial intelligence (temporal reasoning) and decision analysis (ranking procedures). (Intermediate)

Background:

• A.B. Applied Mathematics - Harvard University
• Ph.D. Operations Research - London School of Economics

Currently, Professor in the Mathematical Sciences Department, Clemson University. Formerly, Mathematician with the Center for Applied Mathematics, National Bureau of Standards, Gaithersburg, Maryland; and Professor of Operations Research, College of William and Mary. Served as Associate Editor for the journals Operations Research, Operations Research Letters, Management Science, and the INFORMS Journal on Computing. Currently Editor-in-Chief of Networks. Author of papers involving network optimization, reliability, discrete mathematics, and mathematical modeling.