Time

Oct 18 2012 - 1:50pm - 2:45 pm

Location

MA 105

Speaker

James B. Wilson (Colorado State University)

Abstract

Interesting geometric constructions arise from multiplications without zero-divisors, for example projective planes, generalized quadrangles, etc. Such products are also responsible for groups with unlikely behavior, such as having all nontrivial conjugacy classes of the same size.  Yet, there do not seem to be many examples of finite products without zero-divisors (i.e., nonsingular bilinear maps).  In this talk, I will discuss joint work with T. Miyazaki of Trinity College, in which we prove that a positive logarithmic proportion of all finite bilinear maps are nonsingular.  So, the exotic-seeming constructions in geometry and algebra are actually common.  The proof is a surprising application of theoretical computer science, particularly the study of NP-complete problems.  In fact, we see how a game of mine-sweeper is a cleverly disguised instance of a nonsingular product, proving that nonsingular products are child's play.