Mathematics faculty and graduate students are invited to attend the PhD Preliminary Examination of Seth Ireland.

Advisor:  Dr. Chris Peterson

Co-Advisor:  Dr. Renzo Cavalieri

Committee:  Dr. Maria Gillespie, Dr. Sarath Sreedharan

Title:  w-Stable Ideals

Abstract:  Strongly stable ideals are a class of monomial ideals which correspond exactly to generic initial ideals in characteristic zero. Strongly stable ideals can be completely described in terms of their Borel generators, a subset of the monomial generators of the ideal. Many computations on strongly stable ideals can be done using only the Borel generators. In a weighted polynomial ring, we define and study a subset of strongly stable ideals which we call w-stable ideals that share many desirable formal properties of strongly stable ideals. In particular, for these ideals, we define objects analogous to Borel generators which we call $w$-Borel generators.