Dylan Peifer

About Me

I am a seventh year graduate student in mathematics at Cornell University. My advisor is Michael Stillman and my research area is computational algebra. I grew up in Weaverville, North Carolina and spent my undergraduate years in Northfield, Minnesota at Carleton College, where I majored in mathematics, minored in Russian language, and took many courses in physics. In the past I have been a vegetable gardener, ballroom dancer, temporary Muscovite, ultimate frisbee player, mountain biker, clarinetist/saxophonist, math contest participant, and many others. Outside of math, I currently occupy myself with programming and running.

CV/Resume

Teaching

Current - Fall 2020

I am not currently teaching.

Previous

• Spring 2020 - MATH 2940 Linear Algebra for Engineers
• Fall 2019 - MATH 2940 Linear Algebra for Engineers
• Spring 2019 - MATH 2940 Linear Algebra for Engineers
• Fall 2018 - MATH 2940 Linear Algebra for Engineers (Head TA)
• Spring 2018 - MATH 1920 Multivariable Calculus for Engineers
• Fall 2017 - MATH 1920 Multivariable Calculus for Engineers
• Fall 2016 - MATH 1920 Multivariable Calculus for Engineers (Head TA)
• Fall 2015 - MATH 1920 Multivariable Calculus for Engineers
• Spring 2015 - MATH 1106 Calculus for the Life and Social Sciences
• Fall 2014 - MATH 1910 Calculus for Engineers

Research

My primary research interests are in computational algebra, where I am particularly interested in efficient algorithms to compute Gröbner bases. My current thesis work involves applying reinforcement learning to improving heuristics in Buchberger's algorithm for computing a Gröbner basis. In my research I am a frequent user and contributer to the open-source computer algebra system Macaulay2.

In the past I studied the arc algebra, a generalization of the Kauffman bracket skein algebra, under the direction of Helen Wong. I also studied Hadamard difference sets while at the 2013 San Diego State University Mathematics REU .

Publications

A current list of preprints can always be found on arXiv.

1. Dylan Peifer, Michael Stillman, and Daniel Halpern-Leistner. Learning selection strategies in Buchberger's algorithm. In Proceedings of the 37th International Conference on Machine Learning (ICML 2020).
2. Dylan Peifer. An algorithm for enumerating difference sets. Journal of Software for Algebra and Geometry 9 (2019), 35-41.
3. Omar A. AbuGhneim, Dylan Peifer, and Ken W. Smith. All (96, 20, 4) difference sets and related structures. Bulletin of the Institute of Combinatorics and its Applications 85 (2019), 44-59.
4. Martin Bobb, Stephen Kennedy, Dylan Peifer, and Helen Wong. Roger and Yang's Kauffman bracket arc algebra is finitely generated. Journal of Knot Theory and its Ramifications 25:6 (2016)
5. Martin Bobb, Stephen Kennedy, Dylan Peifer, and Helen Wong. Presentations of Roger and Yang's Kauffman bracket arc algebra. Involve, a Journal of Mathematics 9:4 (2016), 689-698.

Conference Presentations

1. Reinforcement Learning in Buchberger's Algorithm (poster), Summer School on Randomness and Learning in Non-Linear Algebra, Max Planck Institute for Mathematics in the Sciences, Leipzig, July 2019. (poster)
2. All (96, 20, 4) Difference Sets, Joint Mathematics Meetings, San Diego, January 2018. (slides)
3. An Algorithm for Enumerating Difference Sets, Binghamton University Graduate Conference in Algebra and Topology, Binghamton University, October 2017. (slides)
4. Generators of the Arc Algebra, Binghamton University Graduate Conference in Algebra and Topology, Binghamton University, November 2015. (slides)
5. A Finite Set of Generators for the Arc Algebra, Joint Mathematics Meetings, San Antonio, January 2015. (slides)
6. Difference Set Transfers (poster), Joint Mathematics Meetings, Baltimore, January 2014. (poster)
7. Difference Set Transfers, Northfield Undergraduate Mathematics Symposium, St. Olaf College, October 2013. (slides)

Invited Presentations

1. Learning Selection Strategies in Buchberger's Algorithm, Nonlinear Algebra and Statistics Seminar, Illinois Tech, October 2020. (slides)
2. Learning Selection Strategies in Buchberger's Algorithm, Seminar in Symbolic-Numeric Computing, CUNY Graduate Center, October 2019. (slides, video)
3. Reinforcement Learning in Buchberger's Algorithm, CACAO Seminar, UC Davis, April 2019. (slides)

Other Presentations

1. Policy Gradient, Olivetti Club, Cornell University, December 2019.
2. Q-Learning, Olivetti Club, Cornell University, March 2019.
3. Signature Gröbner Bases, Olivetti Club, Cornell University, November 2018.
4. Selection Strategies in Buchberger's Algorithm, Olivetti Club, Cornell University, April 2018. (notes)
5. The LLL Algorithm, Olivetti Club, Cornell University, October 2017.
6. The F₄ Algorithm, MATH 6140 Final Presentations, Cornell University, May 2017. (notes, slides)
7. Hidden Field Equations, Olivetti Club, Cornell University, March 2017.
8. The Gröbner Walk, Olivetti Club, Cornell University, October 2016.
9. Hadamard Difference Sets, Olivetti Club, Cornell University, April 2016. (notes)
10. The Arc Algebra of a Surface, Math Comps Gala, Carleton College, May 2014. (slides)

Projects

Enumerating Difference Sets

The DifSets package is a GAP package implementing an algorithm for enumerating all difference sets up to equivalence in a group. The package is distributed with a standard install of GAP 4.11.0 and later. The latest release (2.3.1) is also free to download here, and additional progress and updates can be found on GitHub. Installing the package allows one to perform exhuastive searches or get access to the results of the successful searches of 1006 of the 1032 groups of order less than 100 performed by the package.

The Gröbner Walk

The GroebnerWalk package is a Macaulay2 package implementing the Gröbner walk algorithm for computing Gröbner bases. The package is distributed with a standard install of Macaulay2 1.11 and later. The latest release (1.0.0) is also free to download here, and additional progress and updates can be found on GitHub.

FGLM

The FGLM package is a Macaulay2 package implementing the FGLM algorithm for computing Gröbner bases of zero-dimensional ideals. The package is distributed with a standard install of Macaulay2 1.14 and later. The latest release (1.0.0) is also free to download here, and additional progress and updates can be found on GitHub.

Puzzles

I initially became interested in mathematics through math competitions, and I continue to enjoy solving puzzles related to math or programming. Puzzles I've recently been working on include those from Project Euler, Jane Street, FiveThirtyEight, and IBM Research.