Title:  Group Presentations and a Geometric Approach to Infinite Groups

Time:  Friday,  4:00 PM - 5:00 PM

Abstract: A group presentation is a method for describing a mathematical group. It consists of one or more generators where each member of the group can be written as a product of the powers of these generators and a set of relations, each of which gives a particular relationship between the generators. In many cases, group presentations give an excellent way of systematically listing the group elements. They are also important in many problems arising in algebraic topology. A fundamental question is, by looking at the presentation, can one determine if the group is infinite or finite? A geometric approach to this question will be introduced and illustrated by examples.

Bio:  Vince received his B.S. in Mathematics from the University of Notre Dame and spent five years in Africa as a Peace Corps volunteer teaching math. After 5 more years teaching at a high school in Connecticut, he went to graduate school and obtained a Ph.D. in Mathematics at the University of Michigan. He taught at Union College for three years and then at Keene State College for 30 years before retiring in 2021. Since then, he has taught part-time at Keene State College and Mt. Holyoke College. Over the last 20 years, he has mentored students reading math journal articles to find and investigate potential research questions. Students always give a conference talk on their work; eight projects have led to publications. He is currently working with students on five different research projects.