Collaborative mathematical research for undergraduate students

Polymath REU

The Program

Due to the pandemic, many students are stuck at home without a summer research program. The aim of the Polymath REU program is to provide research opportunities for such students. 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.
 

Projects and Mentors

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. 

Kira's Polymath REU project will study convex geometries. More details can be found on this page.

Ben Brubaker (University of Minnesota) is working in analytic number theory and representation theory. He has been a mentor at the UMN REU program and is currently coordinating the program.

 

Ben will be running projects on combinatorial representation theory. An example of one such project can be found on this page.

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

Pat will be mentoring students in research involving games on finite graphs, and examples can be found on this page.

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. 

Steven's Polymath REU projects are "Walking to Infinity on Special Sequences" and "Zeckendorf Games." More details can be found on this page.

Vic Reiner (University of Minnesota)

is working in algebraic combinatorics. He has been the founder and director of the UMN REU program.
 

Vic will run a project related to the combinatorics of q-binomial coefficients and a certain commutative ring.  It is the main problem discussed in this blog post and in this arXiv preprint

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

Alexandra's polymath project "Monomials, convex bodies, and optimization" is briefly described on this page.

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

At the Polymath REU, Adam will run a research project about the Erdős distinct distances problem. More details can be found on this page.

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

Yunus's Polymath REU projects are "Rearrangement of series" and "Bergman projection, Toeplitz operators, and Geometry." More details can be found on this page.

More Details

Click on the pdf file for a program description. 

The goal of the original polymath project is to solve problems by forming a collaboration between many mathematicians . This is done via a dedicated wiki site. This project involves longstanding open problems and some of the world's leading mathematicians. 

The Polymath REU program focuses on more modest open problems 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 research part of the program begins June 22nd and ends August 15th. Different projects may have slightly different dates.

  • Work on the projects is done on a website that requires a user and password. Unlike the original polymath project, the projects and progress are not publicly available.

  • Each project includes a document that describes the problems and the background. The main mentor may also hold a zoom lecture to introduce the project.

  • The website would include a platform for collaborative work (either a wiki or a message board).

  • In addition to the main mentor, most projects also include graduate students or postdocs as additional mentors. 

  • Having zoom meetings with and without the mentors is encouraged.

  • Resulting manuscripts would be signed by the pseudo-name Polymath REU, with a list of all participants included. This may not seem optimal, since students who made significant progress should get credit for that. However, these students could ask for a reference letter from the project’s main mentor. This letter would state the contributions the student made to the project and possibly more.

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 U.S. hours.

  • Participation is free but no funding is provided to the participants. 

  • The participants must be undergraduate students. The program is not open to high-school students and to people who already hold a bachelor's degree.

  • If you participate in an REU-style program during the summer of 2020, 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 June 10th. The rolling applications were cancelled. Acceptance messages would be sent a few days after the deadline. 

  • Applications are submitted through mathprograms.org. In particular, please apply on the program's page.

  • 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 any additional questions or comments, please contact Adam Sheffer at adam.sheffer@baruch.cuny.edu

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