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Eloísa Grifo | Research

Research

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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 problems 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 a general math audience article about symbolic powers, and I am writing lecture notes on symbolic powers (reader beware: these are under construction!). 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.

Papers




Talks and notes


a virtual talk about symbolic powers I gave at MSRI
Semester long course notes on symbolic powers
from a course I taught at UNL in Spring 2022.

For shorter notes, see my CIMAT lectures

english version   versión en español   versão em português

BRIDGES notes, aimed at advanced undergraduates:

Lecture notes     Problem list     Day 1     Day 2     Day 3

Here are other notes, videos, and slides from 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-2140355.


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