This is a seminar in Commutative Algebra, primarily aimed at graduate students who do not yet have a strong background on the subject. Rather than having traditional research talks, our main goal is to introduce the audience to the field; the talks will survey results, techniques and ideas in current commutative algebra research.
In Fall 2020, all talks are happening on zoom; if you'd like to attend, please contact us.
Fall 2020 schedule
November 20, 2020
Jack Jeffries (University of Nebraska-Lincoln)
December 4, 2020
Benjamin Briggs (University of Utah)
The friendship between commutative algebra and rational homotopy theory
Abstract: This is the second of three talks aiming to understand how to use combinatorial properties to understand free resolutions and Betti numbers of ideals in a polynomial ring. In the first part of the talk I will explain how to use combinatorics to understand free resolutions of squarefree monomial ideals, and of monomial ideals that are not square free. If time allows, I will also explain how you can construct ideals generated by monomials or by squarefree monomials starting from any homogeneous ideal.
Abstract: This is the first of three talks aiming to understand how to use combinatorial properties to understand free resolutions and Betti numbers of ideals in a polynomial ring. I will describe free resolutions of ideals generated by monomials, and in particular by squarefree monomials. I will also explain how you can construct ideals generated by monomials or by squarefree monomials starting from any homogeneous ideal.
Abstract: In this talk I'll give lots of examples illustrating what betti numbers say about ideals in a polynomial ring. We will also
talk about conjectures for lower bounds for betti numbers including recent work with Derrick Wigglesworth.
A (minimal) free resolution of a finitely generated module M describes its generators, relations, the relations among the relations, etc, and contains lots of geometric and algebraic information about a module. In this talk, we will give a friendly introduction to free resolutions and construct several examples.
October 9, 2020
Eloísa Grifo (UCR)
What is Commutative Algebra and what will this seminar be about? notes
October 2, 2020
commalg, a website with conference listing and updates from the commutative algebra community