Dylan Peifer

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Contact

djp282@cornell.edu

Department of Mathematics
120 Malott Hall
Cornell University
Ithaca, NY 14853-4201 USA

Page last updated 08 Sep 2019.

About Me

I am a sixth 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.

Curriculum Vitae

Teaching

Current - Fall 2019

I am a recitation TA for MATH 2940 Linear Algebra for Engineers. My sections are

and my office hours are Th 3:30-5:30pm in Thurston 102. You can find more information about the course, including the handouts I use in recitation, on our Canvas page.

Previous

Research

My primary research interests are in computational algebra, particularly efficient algorithms to compute Gröbner bases. In the past I have 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. An algorithm for enumerating difference sets. Journal of Software for Algebra and Geometry 9 (2019), 35-41.
  2. 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.
  3. 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)
  4. 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.
  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)

Other Presentations

  1. Reinforcement Learning in Buchberger's Algorithm, CACAO Seminar, UC Davis, April 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.
  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 not distributed with a standard install of GAP, but the latest release (2.3.0) is 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.

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.

projecteuler