Collaborative mathematical research for undergraduate students
Polymath Jr.
Past results: 2020, 2021, 2022.
Recent events: 2023 Boston, 2024 San Francisco, 2025 will be in Seattle.
News:

Congratulations to our 2020 Distinct distances group for winning a Young Researchers award! This $1,000 award is for publications by authors under 35, while they were under 25!
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The Program
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.
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Each project consists of 1525 undergraduates, a main mentor, and graduate students and postdocs as additional mentors. The 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 DMS2218374.
(Many more details are provided below.)
2024 Mentors and Projects (Almost final)
Jyoti Arora founded NotABot Studio at Silicone Valley. This company developments mathematical games with Augmented Reality and Artificial Intelligence.
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At the 2024 Polymath Jr, Jyoti will run a software development project that is based around math education. More details to appear.
Ricardo Baptista (Caltech) is working on scalable algorithms for probabilistic modeling and Bayesian inference.
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At the 2024 Polymath Jr, Ricardo will run a project in machine learning. See here for more information.
Lisa Berger (Stony Brook) is working in algebraic number theory.
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In the 2024 Polymath Jr program, Lisa will run several projects on the geometry and arithmetic of a special collection of highly symmetric Riemann surfaces. We expect projects to have entry points for students with various backgrounds in mathematics.
Zhanar Berikkyzy (Fairfield University) is working in combinatorics. She is the director of the Summer Math Research Program at Fairfield.
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In the 2024 Polymath Jr program, Zhanar will run a project in the intersection of analysis, algebra, and combinatorics. More details to appear.
Mikil Foss (University of NebraskaLincoln) works on variational problems related to partial differential equations, integral equations, and continuum mechanics.
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At the 2024 Polymath Jr, Mikil will run a project on nonlocal models. See here for more details.
Johanna Franklin (Hofstra University) is working in computability theory and its applications to probability and analysis.
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At the 2024 Polymath Jr, Johanna will run research ethics discussions and other activities.
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Timothy Goldberg (LenoirRhyne University) Works in differential geometry, specifically symplectic geometry. His recent research is primarily motivated by work with students, often in the area of recreational mathematics.
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At the 2024 Polymath Jr, Timothy will run a project on games and finite geometry.
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Daniel P. Johnston (Trinity College) is working in graph theory and combinatorics.
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At the 2024 Polymath Jr, Daniel will run a project on TBD.
Jeffrey Meier (Western Washington University) studies manifold theory and knot theory in dimensions three and four.
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At the 2024 Polymath Jr, Jeffrey will run a project on 3 and 4dimensional topology. More details to appear.
Steven Miller (Williams College) is working in analytic number theory, random matrix theory, and probability. He has been the director of the SMALL REU program for over a decade.
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At the 2024 Polymath Jr, Steven will run projects in number theory, More details to appear.
Saadeddine Mneimneh (CUNY) researches applications of mathematical modeling and algorithmic techniques to problems such as scheduling, load balancing, and computational biology.
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At the 2024 Polymath Jr, Saad will run a project on algorithms. For more details, see here.
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Lisa Naples (Fairfield University) is working in Geometry of measures / Analysis on Metric Spaces.
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In the 2024 Polymath Jr program, Zhanar will run a project in the intersection of analysis, algebra, and combinatorics. More details to appear.
M.Tip Phaovibul (AwesomeMath) is working in analytic, probabilistic, and computational number theory. He is also associated editor of USA(J)MO.
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In the 2024 Polymath Jr program, M.Tip will run a project in number theory. More details to appear.
Geremias Polanco (Smith College) is working primarily in analytic number theory, but this has led him also into the interplay with algebraic combinatorics.
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In the 2024 Polymath Jr program, Geremias will run a project in number theory. More details to appear.
Petronela Radu (University of NebraskaLincoln) is working in Partial Differential Equations, Continuum Mechanics, Peridynamics, Integral Equations, and Calculus of Variations
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At the 2024 Polymath Jr, Petronela will run a project on nonlocal models. See here for more details.
Puck Rombach (University of Vermont) is working in structural and extremal graph theory, matroids, algorithms, and complexity.
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At the 2024 Polymath Puck will run a project on TBD.
Lauren Rose (Bard) is working in Algebraic combinatorics, Commutative algebra, and Discrete Geometry. She is the founder of several mathematical outreach programs.
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At the 2024 Polymath Jr, Lauren will run a project on games and finite geometry. More details to appear.
Alexandra Seceleanu (University of NebraskaLincoln) is working in commutative algebra, with a geometric and computational flavor.
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At the 2024 Polymath Jr, Alexandra will run a project about commutative algebra. See here for more details.
Adam Sheffer (CUNY) is working in combinatorial geometry and additive combinatorics. He is running the NYC Discrete Math REU.
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At the 2024 Polymath Jr, Adam will organize the program, but will not run a project.
Giulio Trigila (CUNY) is working in optimization, machine learning, applied probability and computational physics.
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At the 2024 Polymath Jr, Giulio will run a project in machine learning. See here for more information.
Nathan Wagner (Brown University) is working at the intersection of harmonic analysis, complex analysis, and operator theory.
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In the 2024 Polymath Jr, Nathan will run a project in analysis. More details to appear.
Daniel van Wyk (Fairfield University) is working in in the research sphere of operator algebras.
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In the 2024 Polymath Jr program, Daniel will run a project in the intersection of analysis, algebra, and combinatorics. More details to appear.
Yunus Zeytuncu (University of MichiganDearborn) is working in complex analysis. He is running the UMDearborn REU in Mathematical Analysis.
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At the 2024 Polymath Jr, Yunus will run a project about complex analysis. More details to appear.
Alex Zupan (University of NebraskaLincoln) is working in geometric topology, lowdimensional topology, and knot theory.
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At the 2024 Polymath Jr, Alex will run a project on 3 and 4dimensional topology. More details to appear.
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Involved with the program but not mentoring in 2024.
Vincent Martinez (CUNY) is working in the analysis of partial differential equations arising in fluid dynamics and on the problem of parameter estimation in dynamical systems. He is currently running the CUNY Directed Reading Program.
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Pat Devlin (Swarthmore) is working in probabilistic and extremal combinatorics. He has been a mentor and coordinator of Yale's SUMRY REU program.
Matthew Junge (CUNY) uses probability to describe natural phenomena. He is a regular mentor for the NYC discrete math REU.
Enrique Treviño (Lake Forest College) is working in analytic and computational number theory. He is an editor in chief of the USAMO.
Christopher O'Neill (San Diego State University) is O'Neill is working in the intersection of commutative algebra, discrete optimization, and semigroup theory, using methods from algebraic and enumerative combinatorics. He is the coPI of the SDSU REU.
Eric Rowland (Hofstra University) studies arithmetic properties of integer sequences that arise in combinatorial settings. He also creates highly popular mathematical YouTube videos.
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Marion Campisi (San Jose State University) is working in geometric topology, 3dimensional manifolds, knot theory, and gerrymandering.
Ananthnarayan Hariharan (IIT Bombay) is working in Commutative Algebra and Homological Algebra.
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Anurag Bishnoi (TU Delft, The Netherlands) is working in â€‹Extremal Combinatorics, Finite Geometry, and Algebraic Graph Theory.
Cody Stockdale (Clemson University) works in analysis and particularly in harmonic analysis, operator theory, and complex variables.
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Kira Adaricheva (Hofstra University) is working in universal algebra, lattice theory, and convex geometries.
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Ben Brubaker (University of Minnesota) is working in analytic number theory and representation theory. He has been a mentor at the UMN REU program, as well as the program coordinator.
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.
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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.
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The research projects.â€‹
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In 2024, the program will run from June 17th to August 11th.

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. Participants practice their presentation skills there, and later go to present their results at inperson math conferences.

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 researchrelated jobs.

You choose your level of involvement. It is completely fine to participate in the program parttime. 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.

Quotes from recent endofprogram surveys:â€‹â€‹

"My favorite part was reading the literature and collecting data that would support or contradict our conjectures."

"My favorite part were the people in the program."

"I really enjoyed the freedom I had to research what interested me the most within my project."

"My favorite part was thinking up crazy concepts and bringing it up in discussion and having people not dismiss you outright."

"This was my first research experience so it was also very nice to see how research is done and to contribute some results to it."

"While not being a big contributor to the group, I had fun learning what I could and challenging myself with the exercises."

"My favorite part was the presentation."
 "My favorite part of the program was having other people who were excited about math available to talk about math with."â€‹

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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. Online meetings are likely to follow US hours.

Participation is free but no funding is provided for participants. We fund some participants who travel conferences to present their results.

The participants must be undergraduate students. Students who start college next fall or graduate college this spring are eligible to apply, but may 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 will receive higher priority if they do not have previous research experience (or have unusual circumstances).


If you participate in an REUstyle program during the summer of 2024, 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.
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Application information. We do not accept additional applications for the summer 2024.

Applications are submitted through mathprograms.org. (Check for programs under Williams College.)

In mathprograms, under "year" and "month", please make sure to state the expected date (or past date) when you graduate(d) your undergraduate degree.

State the institution of your undergraduate degree.

Your application must make it clear that you have taken a mathematical proofs class. Other official programs that teach proof writing are also valid. (For example, a math circle.)

The cover letter can be very short. It is fine if it only includes your proof writing background. If you want, you are welcome to include any additional information: special circumstances, why you want to participate in the program, your background, or anything else.

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.
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For more information, see this article, published in the Notices of the American Mathematical Society.
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For any additional questions or comments, please contact Adam Sheffer at adam.sheffer@baruch.cuny.edu.
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The Polymath Jr logo was made by Luisa Estrada. An additional logo is by Huiwen Lu.
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