Constructions in Combinatorial Commutative Algebra, Old and New

Department of Mathematics & Statistics

Dr. Justin Lyle
University of Arkansas

Constructions in Combinatorial
Commutative Algebra, Old and New

Thursday, March 25, 2021
11:00 am via ZOOM

This talk will overview some classical constructions in combinatorial commutative algebra, which provide a deep and profitable interplay between algebra, combinatorics, and topology. In particular, we will discuss the Stanley-Reisner correspondence which ties together the theories of simplicial complexes and squarefree monomial ideals in a polynomial ring, and classical results in this area. We then introduce higher nerve complexes of a simplicial complex, a new construction which extends the classical notion of a nerve complex, and demonstrate that their reduced homologies capture a wealth of algebraic information about the associated Stanley-Reisner ring. This talk is based on joint work with Dao, Doolittle, Duna, Goeckner, and Holmes and also on a
separate joint work with Holmes.

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