Organizing Committee

Imagine creating career-building connections between peers, near peers (graduate students and postdocs), and academic professionals.

Imagine spending your summer in a fun, memorable, and intellectually stimulating environment.

Now, imagine having this experience while being paid a $3,570 stipend. (Providence, RI room, board, and travel funding provided for in-person programming, pandemic permitting.)

The 2021 Summer@ICERM program at Brown University is an eight-week residential program designed for a select group of 18-22 undergraduate scholars.

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.

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A billiard trajectory on a regular pentagon, with a two coloring
The "Gothic" translation surface
A polygon for which a candle placed at one indicated point does not illuminate the other indicated point

Program Details

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
Detailed Project Descriptions (PDF)
Important Notes
  • Applicants must be matriculating undergraduate students at the time of the start of Summer@ICERM 2021.
  • Funding is available for 2-3 students who are not US citizens or permanent residents.
Funding Includes*
  • $3,570 stipend
  • Providence, RI room, board, and travel funding provided for in-person programming, pandemic permitting. (Brown students who choose not to live in the dorm will waive ICERM provided housing and meal funding.)
To Apply

Applications accepted via Applications submitted by February 14, 2021 will receive full consideration.

Confirmed Speakers & Participants

  • Speaker
  • Poster Presenter
  • Attendee
  • Virtual Attendee
  • Paul Apisa
    University of Michigan
  • Jessica Bennett
    Brown University
  • Kelly Chen
  • Ahmed Zawad Chowdhury
  • Mei Rose Connor
    Stony Brook University
  • Catherine Cui
  • Elaine Danielson
    University of Florida
  • Diana Davis
    Phillips Exeter Academy
  • Samuel Everett
    University of Colorado, Boulder
  • Samuel Freedman
    Brown University
  • Victor Ginsburg
    Pennsylvania State University
  • Brin Harper
    Massachusetts Institute of Technology
  • Paige Helms
    University of Washington
  • Paul Kielstra
    Harvard University
  • Veronica Kirgios
    Notre Dame
  • Destine Lee
    Columbia University
  • Samuel Lelièvre
    Université Paris-Saclay
  • Vanessa Lin
  • Aidan Mager
    University of Washington
  • Sunrose Shrestha
    Tufts University
  • Zachary Steinberg
    Amherst College
  • Chenyang Sun
    Williams College
  • Cameron Thomas
    Morehouse College
  • Hamilton Wan
  • Jane Wang
    Indiana University
  • Hanna Yang

Other Summer@ICERM Events

Summer@ICERM 2012: Geometry and Dynamics
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Summer@ICERM 2013: Geometry and Dynamics
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Summer@ICERM 2014: Polygons and Polynomials
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Summer@ICERM 2015: Computational Dynamics and Topology
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Summer@ICERM 2016: Dynamics and Stochastics
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Summer@ICERM 2017: Topological Data Analysis
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Summer@ICERM 2018: Low Dimensional Topology and Geometry
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Summer@ICERM 2019: Computational Arithmetic Dynamics
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