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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 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.

Papers




Talks and notes

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

Notes on symbolic powers:

  • BRIDGES notes, aimed at advanced undergraduates:

    Lecture notes     Problem list     Day 1     Day 2     Day 3

  • CIMAT notes, aimed at commutative algebra graduate students:

  • english version   versión en español   versão em português


    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