Our goal is to provide research opportunities to every undergraduate who wishes to explore advanced mathematics. The program consists of research projects in a variety of mathematical topics and runs in the spirit of the Polymath Project. Each project is mentored by an active researcher with experience in undergraduate mentoring.
Each project consists of 20-30 undergraduates, a main mentor, and additional mentors (usually graduate students). This group works towards solving a research problem and writing a paper. Each participant decides what they wish to obtain from the program, and participates accordingly.
The program is partially supported by NSF award DMS-2113535.
(The full details are provided below.)
2021 Mentors and Projects
Zhanar Berikkyzy (Fairfield University) is working in combinatorics, graph theory, and applications. She co-organizes the Summer Math Research program at Fairfield University.
At the 2021 Polymath Jr., Zhanar will run a project on anti-Ramsey multiplicities of graphs. For more information, see here.
At the 2021 Polymath Jr., Ben will run a project on equating functions on polytopes, with connections to representation theory. For more information see here.
Marion Campisi (San Jose State University) is working in geometric topology, 3-dimensional manifolds, knot theory, and gerrymandering.
At the 2021 Polymath Jr., Marion will run a project on minimal conformations of lattice knots and links. For more information see here.
At the 2021 Polymath Jr., Pat will run a project on Erdos-Ko-Rado problems in extremal combinatorics. For more information see here.
Johanna Franklin (Hofstra University) is working in computability theory and its applications to probability and analysis.
At the 2021 Polymath Jr., Johanna will run a project on applications of probability to abstract strategy games. For more information, see here.
At the 2021 Polymath Jr., Seoyoung will run a project about Diophantine m-tuples and elliptic curves. For more information, see here.
At the 2021 Polymath Jr., Steven will run two groups: one on Benford's Law of digit bias (theory and applications), and one on Number Theory. For more information, see here and also this introductory video.
Victor Moll (Tulane University) is working in special functions, number theory, and symbolic computation. He has been mentoring undergraduate research projects for over 20 years.
At the 2021 Polymath Jr., Victor will run a project on evaluation of integrals. For more information, see here.
Christopher O'Neill (San Diego State University) is working in the intersection of commutative algebra, discrete optimization, and semigroup theory, using methods from algebraic and enumerative combinatorics. He is a research mentor at the SDSU REU.
Eric Rowland (Hofstra University) studies arithmetic properties of integer sequences that arise in combinatorial settings.
At the 2021 Polymath Jr., Eric will run a combinatorics project on words that avoid repetitions. For more information, see here.
Alexandra Seceleanu (University of Nebraska-Lincoln) is working in commutative algebra, with a geometric and computational flavor.
At the 2021 Polymath Jr., Alexandra will run a project on computational algebra. For more information, see here.
At the 2021 Polymath Jr., Adam will run an additive combinatorics project about polynomial expanders. For more information, see here.
Zoran Šunić (Hofstra University) is interested in Groups, Graphs, Spaces, Dynamics, Algorithms, and Languages.
At the 2021 Polymath Jr., Zoran will run a project on Schreier graphs of self-similar groups. For more information, click here.
At the 2021 Polymath Jr., Yunus will run a project on ellipses, Blaschke products, and numerical range. For more information, see here.
Alex Zupan (University of Nebraska-Lincoln) is working in geometric topology, low-dimensional topology, and knot theory.
At the 2021 Polymath Jr., Alex will run a project on the tabulation of knotted surfaces in dimension four. For more information, see here.
Involved with the program but not mentoring in 2021.
Kira Adaricheva (Hofstra University) is working in universal algebra, lattice theory, and convex geometries. Her undergraduate research mentoring led to published papers in a variety of topics.
Luis David Garcia Puente (Sam Houston State University) is working in algebraic statistics, algebraic combinatorics, applied and computational algebraic geometry, and combinatorial commutative algebra. He has been mentoring undergraduate research projects for over 20 years, including as the research mentor of the 2016 MSRI-UP.
Many More Details
The goal of the original polymath project is to solve problems by forming a online collaboration between many mathematicians. This is done via a dedicated wiki site. This involves longstanding open problems and some of the world's leading mathematicians.
The Polymath Jr. program is an undergraduate version of the polymath project. It focuses on more modest open problems, usually ones that do not require significant background. However, these problems are still of interest to the research community and the results should be published in a research journal.
The research projects.
The program will run from June 21st to August 15th.
This is an online program. For work purposes, we rely on a dedicated wiki server, Discord severs, overleaf, Zoom, and more.
The first week is dedicated to learning about the various projects. Towards the end of that week, you rank the projects that you are interested in.
The final weekend is an online conference where each group presents their work.
In addition to the main mentor, each project includes additional mentors. These are usually graduate students, but also postdocs and experienced undergraduates.
- We encourage the participants to have as much interaction as possible. This includes regular work meetings, but also social meetings (for example, to play games).
All project participants who were active throughout the program have their name on the paper (sometimes under the pen name Poly Mathews Jr., with the actual names as a footnote). This may seem unfair for students who made significant progress. However, these students can get a strong letter of recommendation from the main mentor. Such a letter is usually much more important when applying to graduate school or research-related jobs.
You choose your level of involvement. It is completely fine to participate in the program part-time. Many participants may not make research breakthroughs, and that's fine. You can contribute by helping with the website, by helping with the writing, by organizing social events, and more. You can also participate in a minor way, just to get a first impression of how research looks like.
Work on the projects is done on non-public websites. Unlike the original polymath project, the projects and progress are not publicly available.
Applying to the program.
Acceptance is not automatic. However, the program is open to the majority of undergraduates having experience with writing mathematical proofs.
There are no citizenship restrictions and the participants could be anywhere in the world. However, online meetings are likely to follow US hours.
Participation is free but no funding is provided for participants.
The participants must be undergraduate students. Students who start college next fall or graduate college this spring are eligible to apply, but would receive lower priority.
Students who are before their first college term are asked to explain in detail how they already have experience with writing mathematical proofs.
Students who just graduated college are only eligible if they do not have previous research experience (or have unusual circumstances).
If you participate in an REU-style program during the summer of 2021, we highly recommend not to join this one. Being part of two programs will most likely get you to perform badly in both. If you insist, please provide a letter from the other program stating that they approve this.
The applications deadline is April 1st. Acceptance messages would be sent at most two weeks after the deadline.
In your application, state the institution where you are currently an undergraduate, an estimated month and year of graduation, and that you have taken a mathematical proofs class. A reference letter from at least one math professor is required.
You may include any additional information that you wish, such as a CV, additional letters, and previous research. However, these are not necessary to get into the program.
There is no need to state which project you are interested in.
For more information, see this article, published in the Notices of the American Mathematical Society.
For any additional questions or comments, please contact Adam Sheffer at firstname.lastname@example.org.