Friday Evening Lecture:
"Frodo meets Neo: Studying rings using matrices"
Colorado College
Abstract:
Recently, quotients of polynomial rings have been popping up in
unexpected places, such as the study of phylogenetic trees in
evolutionary biology and the game SET. We will start the talk with an
introduction to quotients of polynomial rings and motivate our study of
rings by introducing a few of these recent new uses for rings. A
powerful tool for studying such rings (and modules) is the minimal free
resolution. Minimal free resolutions in this context consist of a
sequence of maps given by matrices and we can give many examples. In
fact, there are algorithms for computing minimal free resolutions, but
describing the structure based only on data from the ideal can be
difficult and many of the results combine algebra, topology and
combinatorics. We conclude with recent results and open questions on
the structure of the minimal free resolution of certain quotient rings,
including results by undergraduates.
