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Projects
Welcome to the projects page. Below is a rough division of topics for the workshop based on interests given during registration. Please add your name to the project you would like to work on. If you are interested in working on a project that is not listed, feel free to add it to the list.
As we get closer to the workshop, initial leaders will be identified for each group. At this time, groups will be able to scope out the work for the workshop and larger groups should split into smaller, more focused groups.
Given a reductive group acting linearly on a polynomial ring, the ring of invariants is a finitely generated algebra. One may wish to find an explicit generating set for a ring of invariants, compute its Hilbert series, or provide bounds on the degrees of the generators. The Macaulay2 package InvariantRing implements algorithms for finite groups. This project will focus on implementing some of the available algorithms for reductive groups; this includes the general algorithm of Derksen-Kemper, as well as more specialized algorithms for tori, Hilbert series, and Reynolds operators of semisimple groups.
- Francesca Gandini (Leader)
- Michael Perlman
- Fred Galetto
- Luigi Ferraro
- Matthew Mastroeni
- Hang Huang
- Ha Thi Thu Hien
Currently there is a single package dealing with statistics in Macaulay2, Markov. This package constructs Markov ideals, arising from Bayesian networks in Statistics. Due to the development of Algebraic Statistics, a new package would be useful in order to consolidate and extend methods to calculate Maximum Likelihood Estimate degree for specific ideals and varieties; enhance and refine homotopy continuation methods for different parametrizations of statistical models.
- Jose Israel Rodriguez (Leader)
- Marc Harkonen (Leader)
- Fatemeh Tarashi
- Benjamin Hollering
- Aida Maraj
- Joseph Skelton
Coding theory is a branch of information theory that was originally developed to reliably transmit information through a noisy communication channel. Interesting parameters, such as dimension and length , of certain families of codes are related to dimension and degree of certain algebraic varieties, which can be studied using methods of computational commutative algebra. Another important concept is the minimum distance, which is related to the number of errors that can be corrected when the information is transmitted. This notion was generalized to graded ideals in which allows to find lower bounds for minimum distance using Gröbner bases and Hilbert functions. The goal of this project is to review the existing literature for procedures and algorithms that can be coded and distributed as a package to streamline future computations in coding theory using Macaulay2.
- Hiram López (Leader)
- Nathan Nichols
- Delio Jaramillo
- Ivan Soprunov
- Matt Perkins
- Eduardo Camps
- Asiyeh Rafieipour
- German Vera Martínez
- Henry Chimal Dzul
- Taylor Ball
- Gregory G. Smith (Leader)
- Diane Maclagan (Leader)
- Ritvik Ramkumar
- Mahrud Sayrafi
- Rachel Webb
- Jay Yang
- Matthew Faust
- Anton Leykin (Leader)
- Justin Chen
- Kelly Maluccio
- Leah Gold
- Hasan Mahmood
A package that uses external optimization software (SCIP) to speed up some algebraic computations in M2, and add some additional functions related to enumerating monomial ideals with particular properties (fixed Hilbert function, Betti numbers, etc.).
- Lily Silverstein (Leader)
- Radoslav Zlatev
- Nathaniel Welty
- Courtney Gibbons
A package for interacting with Toric Quiver Varieties and the associated flow polytopes.
- Mary Barker (Leader)
- Gwyneth Whieldon
- Erika Pirnes
- Maryam Nowroozi
- Sankhaneel Bisui
- Michael Burr (Leader)
- Elise Walker
- Tim Duff
FastLinAlg is a for computing (applications of) function field linear algebra more quickly in certain settings. This package needs some development as it is still experimental. It provides functionality for doing certain linear algebra operations in function fields quickly.
- Karl Schwede (Leader)
- Zhan Jiang
- Jay White
- Thai Nguyen
- Sarasij Maitra
- Andrew Tawfeek
Numerical Certification (alpha-theory, interval arithmetic for certifying roots of polynomial systems)
- Kisun Lee (Leader)
- Thomas Yahl
- Dylan Peifer (Leader)
- Daoji Huang