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.

- November 20, 2020

Jack Jeffries (University of Nebraska-Lincoln)

TBA - December 4, 2020

Benjamin Briggs (University of Utah)

The friendship between commutative algebra and rational homotopy theory

- November 6, 2020

Alessandra Costantini (UCR)

Combinatorial Commutative Algebra II

talk notes

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. - October 30, 2020

Alessandra Costantini (UCR)

Combinatorial Commutative Algebra I

talk notes (see also notes from a related previous talk)

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. - October 23, 2020

Adam Boocher (University of San Diego)

What are Betti Numbers?

talk notes part 1 and part 2

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. - October 16, 2020

Eloísa Grifo (UCR)

Betti numbers and free resolutions notes

Abstract: 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

Organizational meeting

- commalg, a website with conference listing and updates from the commutative algebra community
- Fellowship of the Ring, a worldwide virtual commutative algebra seminar hosted by MSRI
- Commutative and Homological Algebra Market Presentations, a virtual commutative algebra seminar with talks by graduate students and young researchers
- Macaulay2, a commutative algebra software
- Macaulay2 online, a way to run Macaulay2 without installing it
- Recent arXiv papers in Commutative Algebra
- Virtual seminar on recent connections between algebra, geometry, and combinatorics