Mathematics, Computer Science and Statistics
The primary objective of the Department of Mathematics, Computer Science, & Statistics is to provide students with experiences in both theoretical and practical applications from one of three majors offered by the department.
Upcoming Seminar: Isoperimetric Profiles and Folner Functions of Groups
Nick Devin, Mathematics, Binghamton University
Friday, March 24, 2017 at 3:00 p.m. in Fitzelle Hall 205
The quintessential optimization problems in first-semester calculus involve maximizing the
area of a rectangular field given a fixed perimeter, or perhaps minimizing the perimeter given a fixed
area. We can generalize these question in several ways: What if the field can take on any shape? How
do we adapt the notions of area, perimeter, and optimization to different, more abstract mathematical
settings? In this talk, I will focus on a certain ”optimization” problem adapted to an algebraic setting–
namely, the Folner function of a finitely-generated amenable group. This function is a quasi-isometric
invariant of the group and, essentially, tells us how large a subset of the group must be in order to
have a small ”perimeter” in relation to its ”area.” We will look at several examples, talk about what
is known, and peer into what is unknown about Folner functions. Previous knowledge of group theory
will not be assumed.