Mathematical Sciences Research Institute

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MSRI-UP 2020: Branched Covers of Curves June 13, 2020 - July 26, 2020
Parent Program: --
Location: MSRI: Online/Virtual
Organizers Federico Ardila (San Francisco State University), LEAD Duane Cooper (Morehouse College), Maria Franco (Queensborough Community College (CUNY); MSRI - Mathematical Sciences Research Institute), Rebecca Garcia (Sam Houston State University), Edray Goins (Pomona College), Suzanne Weekes (Worcester Polytechnic Institute)

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The MSRI Undergraduate Program (MSRI--UP) is a comprehensive summer program designed for undergraduate students who have completed two years of university-level mathematics courses and would like to conduct research in the mathematical sciences.  The main objective of the MSRI-UP is to identify talented students, especially those from underrepresented groups, who are interested in mathematics and make available to them meaningful research opportunities, the necessary skills and knowledge to participate in successful collaborations, and a community of academic peers and mentors who can advise, encourage and support them through a successful graduate program.

The theme of the 2020 MSRI-UP is “Branched Covers of Curves" and the research leader is Dr. Edray Goins, Professor of Mathematics at Pomona College. The research program will focus on Galois Theory of curves, i.e. the realization of certain finite groups as the symmetries of maps from one curve to another.  Students will work on a variety of problems ranging from the explicit construction of covers for a given group to visualizing such covers as exotic surfaces which are self-intersections of the sphere and the torus.  The research groups will focus on Belyi maps, Dessin d’Enfants, Origami, and Shabat polynomials; while working in a variety of areas such as Galois theory, monodromy groups, number theory, and Riemann surfaces. 

Students must have completed at least one proof-based mathematics course before the summer.  Students who have taken an abstract algebra course will find it useful, though this is not required to be admitted to the program.

General Description

During the summer, each of the 18 student participants will:

  • participate in the mathematics research program under the direction of Prof. Edray Goins of Pomona College, a post-doc and two graduate students
  • complete a research project done in collaboration with other MSRI-UP students
  • give a presentation and write a technical report on his/her research project
  • attend a series of colloquium talks given by leading researches in their fields
  • attend workshops aimed at developing skills and techniques needed for research careers in the mathematical sciences and
  • learn techniques that will maximize a student's likelihood of admissions to graduate programs as well as the likelihood of winning fellowships
  • receive a $3600 stipend, lodging, meals and round trip travel to Berkeley, CA.

After the summer, each student will:

  • have an opportunity to attend a national mathematics or science conference where students will present their research
  • be part of a network of mentors that will provide continuous advice in the long term as the student makes progress in his/her studies
  • be contacted regarding future research opportunities

Application Materials

Applications for MSRI-UP 2020 are now open on the National Science Foundation's REU Common Application.  Due to funding restrictions, only U.S. citizens and permanent residents are eligible to apply, and the program cannot accept foreign students regardless of funding.  In addition, students who have already graduated or will have graduated with a bachelor's degree by August 31, 2020 are not eligible to apply.  Applications submitted by February 15, 2020 will receive full consideration. (Applications submitted after February 15, 2020 but by March 1, 2020 may still be considered in a second round of acceptances.) We expect to begin making offers for participation in late February or early March.

A complete application consists of the following:

Common Application Requirements:

1. Personal Statement (5,000 characters) describing your academic and career goals and how the REU program will help you achieve these goals.  

2. Resume or CV

3. College transcript

4. Contact information for two referencesPlease designate two Faculty References; these should be someone from whom you have taken a class or with whom you have done independent mathematical or scientific work. The people you identify as the Faculty Reference on the website will be notified to fill out an on-line form . Although the person will be notified automatically by email, it is the student's responsibility to make sure the letter is uploaded on time. 

MSRI-UP Specific Application Requirements:

1. Additional Statement (limit 2,500 characters) sharing any further information that will help us get a complete picture of you as a potential participant in MSRI-UP. Please address the origins of your interest in mathematics and science, any experiences (school-related and otherwise) that have particularly stimulated you, any obstacles you have faced along the way, and your experience collaborating with and supporting your peers, particularly those from groups underrepresented in mathematics. Students from 2-Year Institutions: If you are currently attending a two-year institution, please describe your plans for transferring to a four-year institution.

2. Description of Previous Summer / Research Experiences.
Please list and give a brief description of all mathematics or science research or summer programs (high school or college), if any, in which you have participated. (Students who have not participated in any programs previously are encouraged to apply.)

3. List of Mathematics/Science Courses Taken with Grades.
Please list all mathematics and science courses taken, starting with the most recent.  State the Course Number, Course Title, Term Taken, Grade Received, and Institution where you took the course.
Example: MATH 201, Calculus 1, Spring 2015, B+, Carolina Community College 

For additional information, please contact the on-site director for the 2020 MSRI-UP.

The directors of MSRI-UP are:

Funding provided by:


Previous Years:

Primary Mathematics Subject Classification No Primary AMS MSC
Secondary Mathematics Subject Classification No Secondary AMS MSC
Schedule, Notes/Handouts & Videos
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Jul 24, 2020
10:00 AM - 10:15 AM
  Opening Remarks
10:15 AM - 11:00 AM
  Computing Monodromy of Toroidal Belyi Pairs
Rebecca Lopez (Marist College), Chidera Okenwa (University of California, Berkeley)
11:00 AM - 11:45 AM
  Visualizing Toroidal Belyi Pairs
Deion Elzie (California State Polytechnic University), Mikaela Nishida (Pomona College), Cameron Thomas (Morehouse College)
11:45 AM - 01:00 PM
01:00 PM - 01:45 PM
  Automorphism Groups and Monodromy of Classical Modular Curves
Samuel Heard (University of Oklahoma), Fabian Ramirez (Sonoma State University), Vanessa Sun (Macaulay Honors College at Hunter College, CUNY)
01:45 PM - 02:30 PM
  Explicit Constructions of Finite Groups as Monodromy Groups
Ra-Zakee Muhammad (Pomona College), Javier Santiago (University of Puerto Rico), Eyob Tsegaye (Stanford University)
02:30 PM - 03:15 PM
03:15 PM - 04:00 PM
  Dessin d'Enfants from Cartographic Groups
Nicholas Arosemena (Morehouse College), Yaren Euceda (University of Minnesota, Twin Cities), Ashly Powell (University of the Virgin Islands)
04:00 PM - 04:45 PM
  To and From 2-Generated Groups and Origamis: Starting from Square One
Sarai Gonzalez (Eastern University), Elisa Rodriguez (Ursinus College ), William Sablan (University of Guam)
04:45 PM - 05:00 PM
  Closing Remarks