Juliette Bruce

I frequently enjoy programming, most often working in either Macaulay2, MatLab, or HTML/CSS/Bootstrap, however, I also have (limited) experience with Python and Sage. A few of the more substantive projects I have worked are listed below.


VirtualResolutions - A package for Macualay2


While graded minimal free resolutions are useful for studying quasicoherent sheaves over projective space, when working over a product of projective spaces or, more generally, over smooth projective toric varieties, graded minimal free resolutions over the Cox ring seem too restricted by algebraic structure that is in some sense unimportant geometrically. By allowing a limited amount of homology, virtual resolutions, first introduced by Berkesch, Erman, and Smith (see arXiv:1703.07631), offer a more flexible alternative for studying toric subvarieties when compared to minimal graded free resolutions.

This Macaulay2 package provides tools for constructing and studying virtual resolutions for products of projective spaces. In particular, it implements a number of the methods for constructing virtual resolutions for products of projective spaces as introduced by Berkesch, Erman, and Smith. It contains methods for constructing curves in \(\mathbb{P}^1\times\mathbb{P}^2\) as these are a natural source for interesting virtual resolutions. This is a joint project with Ayah Almousa, Michael C. Loper, and Mahrud Sayrafi.



Publication:
Firing Bandits: Optimizing Crowdfunding. L. Jain, K. Jamieson. ICML 2018.


SchurVeronses - A package for Macualay2


Using a combination of high throughput high perfomance computing and sparse numerical linear algebra Daniel Erman, Steve Goldstein, and I managed to compute the syzygies of \(\mathbb{P}^{2}\)under the \(d\)-uple Veronese embedding for a number of values of \(d\). See arxiv:1711.03513. In addition, much of the data generated from these computations (graded Betti numbers, multigraded Betti numbers, Schur functor decompositions, etc.) is currently available online via syzygydata.com. The goal of this package is to make this data more accessible and easy to use by providing a way to access it via Macaulay2.



Publication:
Firing Bandits: Optimizing Crowdfunding. L. Jain, K. Jamieson. ICML 2018.


TestIdeals - A package for Macualay2


TestIdeals is a package for the Macaulay2 package focused on computing test ideals and related objects useful in the study of of F-singularities. This is done by constructing functions to efficently compute the Frobenious root of an ideal, as introducted in by Blickle-Mustata-Smith. This package was co-authored with Erin Bela, Alberto F. Boix, Drew Ellingson, Daniel Hernandez, Zhibek Kadyrsizova, Mordechai Katzman, Mordechai Katzman, Matthew Mastroeni, Maral Mostafazadehfard, Marcus Robinson, Karl Schwede, Dan Smolkin, Pedro Teixeira, and Emily Witt.



Publication:
The TestIdeals package for Macaulay2. L. Jain, K. Jamieson. ICML 2018.

  • TestIdeals
    A Macaulay2 Pacakge

  • FThresholds
    A Macaulay2 Pacakge

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