Collaborative mathematical research for undergraduate students
We had an amazing first in-person meeting at the JMM. Thank you everyone who came and presented results.
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!
Welcome the new Vietnam Polymath REU! We are excited to find ways to collaborate with you.
The following is for the summer of 2023. It will be updated for 2024 later on.
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 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.)
2023 Mentors and Projects
Ricardo Baptista (Caltech) is working on scalable algorithms for probabilistic modeling and Bayesian inference.
At the 2023 Polymath Jr, Ricardo will c0-run a project in machine learning, probably related to optimal transport or topics in covariance estimation. More information to appear.
Anurag Bishnoi (TU Delft, The Netherlands) is working in Extremal Combinatorics, Finite Geometry, and Algebraic Graph Theory.
At the 2023 Polymath Jr, Anurag will run a combinatorial project about covering grids with hyperplanes. For more details, click here.
At the 2023 Polymath Jr, Jyoti will run a software development project that is based around math education. More details to appear.
At the 2023 Polymath Jr, Ben will run a project on combinatorial representation theory. More detail to appear.
Caro Williams-Pierce (University of Maryland) is studying the design and evaluation of digital media for mathematical play using novel mathematical representations and interactions.
At the 2023 Polymath Jr, Caro will advise the math-education / software development project. More details to appear.
Johanna Franklin (Hofstra University) is working in computability theory and its applications to probability and analysis.
At the 2023 Polymath Jr, Johanna will run research ethics discussions and other activities.
Matthew Junge (CUNY) uses probability to describe natural phenomena. He is a regular mentor for the nyc discrete math REU
At the 2023 Polymath Jr., Matt will co-run a project in probability. More details to appear.
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.
At the 2023 Polymath Jr., Vincent will run a project in toy models of fluid equations for energy cascades in fluid flow. For more details, click here.
Jeffrey Meier (Western Washington University) studies manifold theory and knot theory in dimensions three and four.
At the 2023 Polymath Jr., Jeffery will co-run a project on invariants of ribbon knots. For more details, click here.
At the 2023 Polymath Jr, Steven will run projects in number theory, with a focus on elliptic curves and elementary number theory. For more details, click here.
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 2023 Polymath Jr, Victor will run a project about integral evaluation. More information to appear.
Eyvindur Ari Palsson (VirginiaTech) is working in Harmonic Analysis, Geometric Measure Theory, and
Combinatorics. He is regularly a mentor at the Williams SMALL REU.
At the 2023 Polymath Jr, Eyvindur will co-run a combinatorial project about distinct distances. For more information, click here.
Sherry Sarkar (Carnegie Mellon) is a PhD student working on approximation algorithms and combinatorics.
At the 2023 Polymath Jr, Sherry will be running an expository project on theoretical computer science. The goal is to produce well written surveys on recent progress in subfields such as approximation algorithms and combinatorial optimization.
Alexandra Seceleanu (University of Nebraska-Lincoln) is working in commutative algebra, with a geometric and computational flavor.
At the 2023 Polymath Jr, Alexandra will run a project about strength and symmetry of polynomials. For more details, click here.
At the 2023 Polymath Jr, Adam will co-run a combinatorial project about distinct distances. For more information, click here.
Si Tang (Lehigh University) is working in probability and mathematical biology.
At the 2023 Polymath Jr, Si will c0-run a project in probability. More details to appear.
Giulio Trigila (CUNY) is working in optimization, machine learning, applied probability and computational physics.
At the 2023 Polymath Jr, Giulio will c0-run a project in machine learning. More information to appear.
Nathan Wagner (Brown University) is working at the intersection of harmonic analysis, complex analysis, and operator theory.
At the 2023 Polymath Jr, Nathan will run a project on Hankel operators on Bergman spaces. For more information, click here.
Xianyi Zeng (Lehigh University) is working on numerical methods for partial differential equations and their applications in geological, mechanical, and biological problems.
At the 2023 Polymath Jr, Xianyi will run a project using analytical and computational methods to study a rod-chain system to model train derailment and their inherent mathematical instabilities.
At the 2023 Polymath Jr, Yunus will run a project about Toeplitz Operators on Bergman Spaces. For more information, see here.
Alex Zupan (University of Nebraska-Lincoln) is working in geometric topology, low-dimensional topology, and knot theory.
At the 2023 Polymath Jr, Alex will run a project on invariants of ribbon knots. For more details, click here.
Involved with the program but not mentoring in 2023.
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.
Seoyoung Kim (University of Göttingen). Kim supervised undergraduate research projects at Brown University and at the SMALL REU of Williams College. She is also part of the Girls sySTEM mentoring program for high school students in Ontario, Canada.
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 co-PI of the SDSU REU.
Marion Campisi (San Jose State University) is working in geometric topology, 3-dimensional manifolds, knot theory, and gerrymandering.
Enrique Treviño (Lake Forest College) is working in analytic and computational number theory. He is an editor in chief of the USAMO.
Cody Stockdale (Clemson University) works in analysis and particularly in harmonic analysis, operator theory, and complex variables.
Ananthnarayan Hariharan (IIT Bombay) is working in Commutative Algebra and Homological Algebra.
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.
In 2023, the program will run from June 20th to August 13th.
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 in-person 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 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.
Quotes from recent end-of-program surveys:
"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."
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 REU-style program during the summer of 2023, 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.
This website is for the summer of 2023. Information for the summer of 2024 will appear later on. The applications deadline will be April 1st
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.
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 email@example.com.
The Polymath Jr logo was made by Luisa Estrada. An additional logo is by Huiwen Lu.