Collaborative mathematical research for undergraduate students
Polymath Jr.

Past results: 2020, 2021, 2022, 2023
Recent events: 2023 Boston, 2024 San Francisco, 2025 Seattle.

News:​
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Due to the mathprograms.org issue, the application deadline is now April 8.
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We gradually update the website for 2025. The program will run June 16 - August 3.
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The Program
Our goal is to provide research opportunities to every undergraduate who wishes to explore advanced mathematics. This online 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 15-25 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 DMS-2218374.
(Many more details are provided below.)


2025 Mentors and Projects (under construction)

Sam Adriaensen (Vrije Universiteit Brussel and Worcester Polytechnic Institute) is working finite geometry and its connection to algebraic graph theory and coding theory.
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At the 2025 Polymath Jr, Sam will run a combinatorics project titled The Hat Guessing Number of a Graph.​​​

Gessica Alecci (Politecnico di Torino, Italy) is working in number theory, cryptography, commutative algebra, ring theory, and algebraic geometry
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At the 2025 Polymath Jr, Gessica will run a project on TBD.​​​

Ricardo Baptista (Caltech) is working on scalable algorithms for probabilistic modeling and Bayesian inference.
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At the 2025 Polymath Jr, Baptista will co-run the machine learning group.

Anurag Bishnoi (TU Delft, The Netherlands) is working in ​Extremal Combinatorics, Finite Geometry, and Algebraic Graph Theory.
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At the 2025 Polymath Jr, Anurag will run a combinatorics project titled The Hat Guessing Number of a Graph.​​​

Aseel Farhat (University of Virginia) is an applied analysis mathematician, specializing in partial differential equations (PDEs) arising in fluid dynamics.​
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At the 2025 Polymath Jr, Aseel will run a project on TBD.​​​

Mikil Foss (University of Nebraska-Lincoln) works on variational problems related to partial differential equations, integral equations, and continuum mechanics.
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At the 2025 Polymath Jr, Mikil will run a project on non-local models. More details to appear.


Johanna Franklin (Hofstra University) is working in computability theory and its applications to probability and analysis.
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At the 2025 Polymath Jr, Johanna will run research ethics discussions and other activities.
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Timothy Goldberg (Lenoir-Rhyne University) studies finite geometry and combinatorial design theory, related to recreational mathematics. Most of his research is motivated by work with students.
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At the 2025 Polymath Jr, Timothy will run a project on Games and Finite Geometry​​​

Amanda Harsy (Lewis University) works in geometric group theory, linear algebra, statistics, and data science. She mentored research in REU-style programs at ICERM and Lewis University.
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At the 2025 Polymath Jr, Amanda will run the project Predictive Modeling and Analysis of Sports Using Linear Algebra-based Models. For more information, click here.





Sean Howe (University of Utah) works on arithmetic and algebraic geometry, representation theory, and number theory. He also runs a pre-REU program.
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At the 2025 Polymath Jr, Sean will run a project on random matrices and representation theory.
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More mentors to appear! Will we have a project about turning potatoes into gold?​​
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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At the 2025 Polymath Jr, Vincent will run a project on TBD.
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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 2025 Polymath Jr, Steven will run projects in number theory and probability.
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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At the 2025 Polymath Jr program, M.Tip will run projects about integer partitions and aboutk-Color Rubrics and other mathematical toys. More details to appear.

Petronela Radu (University of Nebraska-Lincoln) is working in Partial Differential Equations, Continuum Mechanics, Peridynamics, Integral Equations, and Calculus of Variations
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At the 2025 Polymath Jr, Petronela will run a project on non-local models. More details to appear.

More mentors to appear! Will we check if there are eyes or more legs in the world?






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 2025 Polymath Jr, Lauren will run a project on Games and Finite Geometry.
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 2025 Polymath Jr, Adam will run project about Ramsey numbers. For more details, click here.
Cara Jill Sulyok (Lewis University) is working in development of mathematical models to answer questions in biology and medicine. She mentored research in REU-style programs at ICERM and Lewis University.
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At the 2025 Polymath Jr, Cara will run project about TBD.
Giulio Trigila (CUNY) is working in optimization, machine learning, applied probability and computational physics.
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At the 2025 Polymath Jr, Giulio will run a project in machine learning.
Nathan Wagner (Brown University) is working at the intersection of harmonic analysis, complex analysis, and operator theory.
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At the 2025 Polymath Jr, Nathan will run a project about Experimental Mathematics and AI Approaches (with a focus on analysis). For more details click here.
Yunus Zeytuncu (University of Michigan-Dearborn) is working in complex analysis. He is running the UM-Dearborn REU in Mathematical Analysis.
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At the 2025 Polymath Jr, Yunus will run a project about Experimental Mathematics and AI Approaches (with a focus on analysis). For more details click here.

Alex Zupan (University of Nebraska-Lincoln) is working in geometric topology, low-dimensional topology, and knot theory.
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At the 2025 Polymath Jr, Alex will run a project in topology.
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Involved with the organization but not mentoring in 2025.

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.


Pat Devlin (Swarthmore) is working in probabilistic and extremal combinatorics. He has been a mentor and coordinator of Yale's SUMRY REU program.
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Alexandra Seceleanu (University of Nebraska-Lincoln) 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.
Many More Details
The goal of the original polymath project is to solve problems by forming an 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.​
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In 2025, the program will run June 16 - August 3.
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This is an online program. For work purposes, we rely on a dedicated wiki server, Discord severs, overleaf, Zoom, and more.
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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.
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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 in-person math conferences.
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In addition to the main mentor, each project includes additional mentors. These are usually graduate students, but also postdocs and experienced undergraduates.
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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.
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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.
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Quotes from recent end-of-program surveys:​​
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"My favorite part was reading the literature and collecting data that would support or contradict our conjectures."
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"My favorite part were the people in the program."
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"I really enjoyed the freedom I had to research what interested me the most within my project."
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"My favorite part was thinking up crazy concepts and bringing it up in discussion and having people not dismiss you outright."
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"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."
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"While not being a big contributor to the group, I had fun learning what I could and challenging myself with the exercises."
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"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."​
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Applying to the program.
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Acceptance is not automatic. However, the program is open to the majority of undergraduates having experience with writing mathematical proofs.
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There are no citizenship restrictions and the participants could be anywhere in the world. Online meetings are likely to follow US hours.
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Participation is free but no funding is provided for participants. We fund some participants who travel conferences to present their results.
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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.
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Students who are before their first college term are asked to explain in detail how they already have experience with writing mathematical proofs.
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Students who just graduated college will receive higher priority if they do not have previous research experience (or have unusual circumstances).
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If you participate in an REU-style 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. Applications for the summer of 2025 are now open. The deadline is April 8, and may be changed to a later date.
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Applications are submitted through mathprograms.org. (Check for programs under Williams College.)
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In mathprograms, under "year" and "month", please make sure to state the expected date (or past date) when you graduate(d) your undergraduate degree.
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State the institution of your undergraduate degree.
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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.)
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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.
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A reference letter from at least one math professor is required.
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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.
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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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