Home Teaching CV
Eloísa Grifo | Research

Research

My research interests lie in commutative algebra and homological algebra. I am interested in applying homological algebra, characteristic p techniques, and p-derivations to different questions in commutative algebra. I have worked on questions that relate to infinite free resolutions, DG algebras, thick subcategories of $$D(R)$$, local cohomology, and symbolic powers. I wrote my PhD thesis under the supervision of Craig Huneke, on the containment problem for symbolic and ordinary powers of ideals over regular rings.

Talks and notes

• Here is video of a virtual talk about symbolic powers I gave at MSRI

• Notes on symbolic powers:
Written for the Escuela de otoño de Àlgebra Conmutativa at CIMAT in November 2019 organized by Luis Núñez-Betancourt and Abraham Martín del Campo.

• Older notes on symbolic powers

Written 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.

• Here are other notes, videos, and slides from some talks I have given.

• Software

I often use Macaulay2 in my research, and I have contributed to a few Macaulay2 packages, some of which you can find on my GitHub page.

• SpectralSequences
(developed with David Berlekamp, Adam Boocher, Nathan Grieve, Gregory G. Smith, and Thanh Vu)
This package comes with Macaulay2 version ≥ 1.10.
1. This is a Macaulay2 package that provides tools for effective computation of the pages and differentials in spectral sequences obtained from many kinds of filtered chain complexes.

• SymbolicPowers
(with contributions from Ben Drabkin, Alexandra Seceleanu, and Branden Stone)
Version 2.0 comes with Macaulay2 version $$\geqslant$$ 1.14.
This is a Macaulay2 package that provides tools for computing symbolic powers.

• ThickSubcategories
(with Janina Letz and Josh Pollitz)
Under construction; use with caution.
This is a Macaulay2 package that provides tools for computations related to thick subcategories of D(R); for example, it computes (or gives bounds for) levels of modules and complexes, and produces modules that are non-proxy small over non-ci quotients of polynomial rings.

• My research is supported by NSF grant DMS-2001445.

email: eloisa.grifo@ucr.edu