Applied Algebra Seminar: Statistical Commutative Algebra

Seminar | April 6 | 5:15-6:15 p.m. | 891 Evans Hall

 Jesus De Loera, University of California, Davis

 Department of Mathematics

Randomness is an important algorithmic tool in algebra and analysis. Monomial ideals play a key role in computational commutative algebra, and they give a strong link to algebraic combinatorics e.g., through Stanley-Reisner ideals of simplicial complexes. Inspired by results on random graphs and random simplicial complexes, we develop a theory of random monomial ideals. We present theorems about the probability distributions, expectations and thresholds for events of monomial ideals with given Hilbert function, Krull dimension, first graded Betti numbers. We also discuss conjectures about regularity, depth, and Cohen-Macaulayness. Our new results are joint with Sonja Petrovic, Despina Stasi, Lily Silverstein, Dane Wilburne.