Eloísa Grifo | Talk notes

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Eloísa Grifo | Talk notes

Notes on symbolic powers

Here is video of a talk on symbolic powers I gave at the Fellowship of the ring, the virtual Worldwide Commutative Algebra Seminar, hosted by MSRI.

I've written several sets of lecture notes on symbolic powers. All of these are drafts and are highly likely to contain typos.

Notes directed at advanced commutative algebra graduate students:
The following are notes I wrote for a semester long course on symbolic powers at the University of Nebrask—Lincoln:

Main symbolic powers notes
These are likely to still contain typos, but these are the most up-to-date notes I have written on the subject.

I have also written shorter notes for week-long courses. The notes below were written for the Escuela de otoño de Àlgebra Conmutativa at CIMAT in November 2019 organized by Luis Núñez-Betancourt and Abraham Martín del Campo, and earlier for the RTG Advanced Mini-course in Commutative Algebra at the University of Utah in May 2018, organized by Anurag K. Singh and Srikanth B. Iyengar. The older version of my notes on symbolic powers is no longer kept updated, so I'd recommend reading the newer version below. While the CIMAT lectures were delivered in spanish, the main version of the notes is the English version, and the others are more or less translations of the English version.

english version versión en español versão em português

Notes directed at advanced undergraduates:
These are the materials for the lecture series I gave at BRIDGES, a conference aimed towards early graduate students and advanced undergraduate students interested in representation theory, number theory, and commutative algebra, hosted by the University of Utah AWM student chapter. These lectures assumed only a first course in algebra, and no commutative algebra background.

Lecture notes Problem list Day 1 Day 2 Day 3

Other videos from research talks

Symbolic powers in mixed characteristic, at the ICERM workshop D-modules, Group Actions, and Frobenius: Computing on Singularities

Symbolic powers in mixed characteristic
in
BIRS workshop on advances in mixed char
May 10, 2022

Symbolic powers in mixed characteristic
in
Special Month On Singularities & K-Stability
June 6, 2021

Differential powers in mixed characteristic
in
Special Session on differential operators in algebraic geometry and commutative algebra at the 2021 MCA
July 16, 2021

Notes and slides from research talks

Symbolic powers in mixed characteristic (BIRS workshop on advances in mixed char, 05/10/2022)
Cohomological Support Varieties (CA+ at Iowa State, 05/01/2022, and KUMUNU at UNL, 05/08/2022)
Symbolic powers (Combinatorial Algebra meets Algebraic Combinatorics at the Fields Institute, 01/23/2022)
Symbolic powers in mixed characteristic (ICERM workshop D-modules, Group Actions, and Frobenius: Computing on Singularities, 08/12/2021)
Differential powers in mixed characteristic (Special session on Differential operators in CA and AG at the Mathematical Congress of the Americas, 07/16/2021)
Symbolic powers in mixed characteristic (Special Month On Singularities & K-Stability 06/07/2021)
Test modules for the complete intersection property (Notre Dame AG/CA Seminar 04/27/2021)
Test modules for the complete intersection property (Special Session on Commutative Algebra at the Cincinnati Virtual AMS Sectional Meeting.)
Constructing non-proxy small modules (Special Session on Commutative Algebra at the Brown Virtual AMS Sectional Meeting)
Symbolic Powers (Mulheres Matemáticas: uma tarde de encontro)
Constructing non-proxy small modules (UNL Commutative Algebra Seminar)
Constructing non-proxy small modules (Special Session on Homological Methods in Algebra at the Virtual Fall AMS Sectional Meeting 2020)
Symbolic Powers, stable containments, and degree bounds — these notes correspond to the video above (Fellowship of the ring, worldwide seminar)
Symbolic Powers and the (stable) containment problem (Bern/Fribourg/Neuchâtel InterCity Seminar)
Symbolic Powers (Tulane University Colloquium)
Symbolic Powers and the (stable) containment problem (Tulane University Algebra and Combinatorics Seminar)
Symbolic Powers (University of Nebraska — Lincoln Colloquium)
A stable version of Harbourne's Conjecture (University of Illinois at Chicago Commutative Algebra Seminar)
Symbolic powers and Two versions of Harbourne's Conjecture (2 part talk) (University of Nebraska — Lincoln Commutative Algebra Seminar)
A stable version of Harbourne's Conjecture (University of Utah Commutative Algebra Seminar)
Symbolic powers and the (stable) containment problem (University of Wisconsin Madison Algebra and Algebraic Geometry Seminar)
A Fedder-type criterion over Gorenstein rings (Morgantown Algebra Days)
Symbolic powers and the containment problem (Central Michigan Algebra and Combinatorics Seminar)
Symbolic powers (UC Riverside Colloquium and Oklahoma State Colloquium)
A Fedder-type criterion over Gorenstein rings and symbolic powers (Oberwolfach Workshop on Singularities and Homological Aspects of Commutative Algebra)
A stable version of Harbourne's Conjecture (Special Session on Symbolic and regular powers of ideals at the CMS Winter Meeting 2018)
Symbolic powers of ideals defining F-pure rings (Special Session on Advances in Commutative Algebra at the Ann Arbor AMS Meeting 2018)
Symbolic powers and free resolutions (Special Session on Commutative Algebra and complexity at the Ann Arbor AMS Meeting 2018)
A stable version of Harbourne's Conjecture (MFO Mini-workshop on Asymptotic invariants of homogeneous ideals 2018)
Homological algebra vs symbolic powers (KUMUNUjr 2018)
Applying homological algebra to a problem on symbolic powers (Boston AMS Meeting Special Session on Homological Methods in Commutative Algebra)
Symbolic powers and the containment problem (Special Session on Commutative Algebra at the Portland AMS Meeting)
Symbolic powers and the containment problem (PhD thesis defense)
The Zariski-Nagata theorem in mixed characteristic (AMS Sectional Meeting in Ohio, Special Session in Commutative and Combinatorial Algebra)
Symbolic powers: the Containment Problem and Harbourne's Conjecture (Joint Math Meetings, Special Session in Commutative Algebra in All Characteristics)
Symbolic powers and differential operators (George Mason University Combinatorics, Algebra and Geometry Seminar)
Symbolic powers and the Containment Problem (University of Kansas Algebra Seminar)
Symbolic powers and the Containment Problem (2 hour talk) (University of South Carolina Algebraic Geometry Seminar)
Symbolic powers and differential operators (New Mexico State University Algebra Seminar)
A stable version of Harbourne's Conjecture (AMS sectional meeting in Orlando, Florida, Special Session on Commutative Algebra)
A stable version of Harbourne's Conjecture (AMS sectional meeting in Denton, Texas, Special Session on Commutative Algebra)
Symbolic powers of ideals defining F-pure rings (AMS sectional meeting in New York, New York, Special Session on Commutative Algebra)
Symbolic powers of ideals defining F-pure rings (University of Utah Commutative Algebra Seminar)
Symbolic powers of ideals defining F-pure rings (AMS sectional meeting in Charleston, SC, Special Session on Commutative Algebra)
Symbolic powers in characteristic p (2 hour talk) (University of Nebraska — Lincoln Commutative Algebra Seminar)
Symbolic powers (Clemson University Algebra and Discrete Math Seminar)
Symbolic powers of ideals defining F-pure rings (University of Michigan Commutative Algebra Seminar)

Notes and slides from expository talks and talks directed at undergraduates

A story of algebra vs geometry (UCR Graduate Open House, November 2020)
Frobenius or: how I learned to stop worrying and love characteristic p (BIKES, University of Utah Commutative Algebra Student Seminar, January 2020)
Symbolic powers and a story of algebra vs geometry (Undergraduate Research Symposium, UIC, November 2019)
Symbolic powers (University of Michigan Graduate Student Commutative Algebra Seminar, Winter of 2019)
Slicing a square pizza (University of Michigan Math Club, Winter of 2019)
An introduction to singularities in characteristic p: Frobenius is your friend (Reading course on singularities organized by Devlin Mallory at UMich in the Fall of 2018)

email: grifo@unl.edu | Office: 339 Avery Hall