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SIAM SAGA - Seminar on Applied Geometry and Algebra
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Date: Tuesday, January 12, 2021 at 11:00am EST (5:00pm CET)

Speaker: Sonja Petrović, Illinois Institute of Technology

Title: Random Monomial Ideals

Abstract: Joint work with Jesus A. De Loera, Lily Silverstein, Despina Stasi, Dane Wilburne. Inspired by the study of random graphs and simplicial complexes, and motivated by the need to understand average behavior of ideals, we propose and study probabilistic models of random monomial ideals. We prove theorems about the probability distributions, expectations and thresholds for events involving monomial ideals with given Hilbert function, Krull dimension, first graded Betti numbers, and present several experimentally-backed conjectures about regularity, projective dimension, strong genericity, and Cohen Macaulayness of random monomial ideals. The models for monomial ideals can be used as a basis for generating other types of algebraic objects, and proving existence of desired properties. The talk will feature a tasting of ongoing work in both of these directions.

Moderator: Jose Israel Rodriguez, University of Wisconsin, Madison
Feb 9, 2021 11:00 AM
Mar 9, 2021 11:00 AM
Apr 13, 2021 11:00 AM
May 11, 2021 11:00 AM
Jun 8, 2021 11:00 AM
Jul 13, 2021 11:00 AM
Aug 10, 2021 11:00 AM
Sep 14, 2021 11:00 AM
Oct 12, 2021 11:00 AM
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Speakers

Sonja Petrović
Associate Professor @Illinois Institute of Technology
I am an Associate Professor in the Department of Applied Mathematics, College of Computing, at Illinois Institute of Technology. I am a member of the statistics, discrete math, and computational math research groups. My research is in nonlinear algebra and nonlinear statistics. I develop, analyze, and apply statistical models for discrete relational data such as networks. I also study randomized algorithm approaches to computational algebra problems whose expected runtimes are much lower than the well-known worst-case complexity bounds, develop probabilistic models to study average and extreme behavior of algebraic objects, and use machine learning to predict and improve the behavior of algebraic computations. Prior to joining IIT in 2013, I was on faculty at Penn State Statistics.