The Story of the Alternating Sign Matrix Conjecture

Thursday, March 19, 2009

Speaker: Dave Bressoud

Title: The Story of the Alternating Sign Matrix Conjecture

Abstract: What is the role of proof in mathematics? Most of the
time, the search for proof is less about establishing truth than it is about
exploring unknown territory. In finding a route from what is known to the
result one believes is out there, the mathematician often encounters
unexpected insights into seemingly unrelated problems. I will illustrate
this point with an example of recent research into a generalization of the
permutation matrix known as the "alternating sign matrix." This is a story
that began with Charles Dodgson (aka Lewis Carroll), matured at the
Institute for Defense Analysis (now the Center for Communications Research),
drew in researchers from combinatorics, analysis, and algebra. The problem
ultimately was solved with insights from statistical mechanics.