Collaborative mathematical research for undergraduate students

Polymath Jr.

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Click here for results from the summer of 2020 and the summer of 2021.
 

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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!

  • Welcome the new Vietnam Polymath REU! We are excited to find ways to collaborate with you. 

 

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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.

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-2218374.  

 

(The full details are provided below.)
 

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2022 Mentors and Projects (Still updating)

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Ricardo Baptista (MIT) is working on scalable algorithms for probabilistic modeling and Bayesian inference.

At the 2022 Polymath Jr, Ricardo will c0-run a project in machine learning. More information to appear.

 

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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 2022 Polymath Jr, Zhanar will run a project on TBD

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Anurag Bishnoi (TU Delft, The Netherlands) is working in Extremal Combinatorics, Finite Geometry, and Algebraic Graph Theory.

At the 2022 Polymath Jr, Anurag will co-run the special Ramsey theory project. For more information, see here.

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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.

At the 2022 Polymath Jr, Ben will run a project on lattice models. For more information, click here.

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Marion Campisi (San Jose State University) is working in geometric topology, 3-dimensional manifolds, knot theory, and gerrymandering.

At the 2022 Polymath Jr, Marion will run a project on combinatorial knot theory. Further details will follow soon.

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Johanna Franklin (Hofstra University) is working in computability theory and its applications to probability and analysis.

At the 2022 Polymath Jr, Franklin will run a project in mathematical logic. For more information, click here.

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Luis David Garcia Puente (Colorado College) 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.

At the 2022 Polymath Jr, Luis will co-run the special Ramsey theory project. For more information, see here.

Ananthnarayan Hariharan (I.I.T Bombay) is working in Commutative Algebra and Homological Algebra. 

At the 2022 Polymath Jr, Ananth will run a project in commutative algebra. More details to appear.

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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. 

At the 2022 Polymath Jr, Steven will run a project in number theory. For more information, see here.

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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 2022 Polymath Jr, Victor will run a project on integral evaluation. More information to appear.

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Natasha Morrison (University of Victoria, Canada) is working in extremal, probabilistic and additive combinatorics.

At the 2022 Polymath Jr, Natasha will co-run the special Ramsey theory project. For more information, see here.

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Giulio Trigila (CUNY) is working in optimization, machine learning, applied probability and computational physics.

At the 2022 Polymath Jr, Giulio will c0-run a project in machine learning. More information to appear.

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Adam Sheffer (CUNY) is working in combinatorial geometry and additive combinatorics. He is running the NYC Discrete Math REU.

 

At the 2022 Polymath Jr, Adam will co-run the special Ramsey theory project. For more information, see here​.

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Cody Stockdale (Clemson University) works in analysis and particularly in harmonic analysis, operator theory, and complex variables.

At the 2022 Polymath Jr, Cody will run a project in harmonic analysis. For more information, see here.

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Yunus Zeytuncu (University of Michigan-Dearborn) is working in complex analysis. He is running the UM-Dearborn REU in Mathematical Analysis.

At the 2022 Polymath Jr, Yunus will run a project ellipses, numerical range, Hardy spaces, and Poncelet's theorem. Further details will follow soon.

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Alex Zupan (University of Nebraska-Lincoln) is working in geometric topology, low-dimensional topology, and knot theory.

At the 2022 Polymath Jr, Alex will run a project on Symmetric union presentations for ribbon links. For more information, click here.

Involved with the program but not mentoring in 2022.

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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. 

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Seoyoung Kim (Queen's University). 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.

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Pat Devlin (Yale University) is working in probabilistic and extremal combinatorics. He has been a mentor and coordinator of Yale's SUMRY REU program.

Alexandra Seceleanu (University of Nebraska-Lincoln) is working in commutative algebra, with a geometric and computational flavor.  

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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 a research mentor at the SDSU REU.

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Eric Rowland (Hofstra University) studies arithmetic properties of integer sequences that arise in combinatorial settings.

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Enrique Treviño (Lake Forest College) is working in analytic and computational number theory. He is an editor in chief of the USAMO.

 

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 20th to August 14th

  • 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. 

  • 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. 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 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 2022, 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.

We no longer accept applications to the 2022 program

  • Applications are submitted through mathprograms.org

  • 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 adam.sheffer@baruch.cuny.edu

The Polymath Jr logo was made by Luisa Estrada. An additional logo is by Huiwen Lu.

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