Brown University, Institute for Computational and Experimental Research in Mathematics

Program ID: ICERM-SI2021 [#1006]
Program Title: Summer@ICERM: Undergraduate Summer Research Program: Computational Polygonal Billiards
Program Type: Undergraduate program
Program Location: Providence, Rhode Island 02912, United States [map] sort by distance
Subject Area: Mathematics
Application Deadline: 2021/02/14 11:59PMhelp popup finished (2020/10/06, finished 2021/06/17)
Program Description:    

*** this program has been closed and new applications are no longer accepted. ***

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SUMMER@ICERM: Undergraduate Summer Research Program at Brown University

"Computational Polygonal Billiards" from June 14 - August 6, 2021

Organizing Committee: Paul Apisa (Yale University), Diana Davis (Phillips Exeter Academy), Samuel Lelièvre (Université Paris-Sud)

The eight-week Summer@ICERM 2021 program is designed for a select group of 18-22 undergraduate scholars. It comes with a $3,570 stipend. Providence, RI room, board, and travel funding provided for in-person programming, pandemic permitting.

The faculty advisers will present a variety of research projects on the theme of computational polygonal billiards and flat surfaces. This overarching theme will allow participants to use the theory of flat surfaces, along with the computational tools of pre-existing free software including Sage packages, to work on open problems in the field. Faculty will also guide the development of free software for flat surfaces. Students will be assigned to one or more research groups before the program begins and will be expected to do background reading before the program starts. During the program, students will work with faculty advisors to ensure they have the background understanding necessary to work on the problems. Students will also learn programming skills and computational techniques, including using Sage.

Throughout the eight-week program, students will work on their projects in groups of two to four, supervised by faculty advisors and aided by teaching assistants. Students will meet daily, give regular talks about their findings, attend mini-courses, guest talks, and professional development seminars, and will acquire skills in free software development. Students will learn how to collaborate mathematically, working closely in their teams to write up their research into a paper.

2021 Proposed Research Topics
  • Project 1: The Finite Blocking Problem
  • Project 2: Square-Tiled Surfaces
  • Project 3: Periodic Points on Veech Surfaces
  • Project 4: Periodic Billiard Paths

ICERM provides an excellent research environment. Students, faculty, and TAs will have access to ICERM’s computer facilities and specialized software. ICERM staff will provide logistical support for students and will help build community through fun activities and events.

More program details are available at

Funding Includes:

  • $3,570 stipend
  • Providence, RI room, board, and travel funding provided for in-person programming, pandemic permitting. (Brown University students who choose not to live in ICERM provided housing will waive dorm and meal funding.)


  • Applicants must be matriculating undergraduate students at the time of the start of Summer@ICERM 2021.
  • Funding is available for a very small number of students who are not US citizens or permanent residents. 

Students must apply via by February 14, 2021, to receive full consideration. ICERM will begin making offers between late February and early March 2021. 

ICERM is committed to fostering a diverse and inclusive academic global community; as an EEO/AA employer, Brown considers applicants for employment without regard to, and does not discriminate on the basis of, gender, sex, sexual orientation, gender identity, national origin, age, race, protected veteran status, disability, or any other legally protected status.

Application Materials Required:
Submit the following items online at this website to complete your application:
Further Info:
email address
Brown University/ICERM
Box 1995
Providence, RI 02912