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Graded Expectations:  An Invitation to Probabilistic Commutative Algebra

Matthew Stamps, Yale-NUS College
Wednesday, October 24, 2018 - 3:30pm
PDL C-401
Matt Stamps Picture

This talk will explore a connection between seemingly unrelated families of graphs, integer sequences, and numerical invariants of) polynomial rings, specifically threshold graphs, anti-lecture hall compositions, and Betti numbers of quotients of polynomial rings with 2-linear resolutions.  I will introduce these three families of objects, describe an explicit one-to-one-to-one correspondence between them, and elucidate some preliminary consequences of said correspondence.  Most notably, I will make use of a well-studied random model for threshold graphs to calculate expected values (and properties) of Betti numbers and anti-lecture hall compositions.  No prior knowledge of commutative algebra will be assumed; all of the essential ideas will be illustrated with concrete examples.  This is joint work with Alexander Engström and Christian Go.

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