Organizing Committee
Abstract

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.

This program is partially funded by a grant from the National Security Agency.

Image for "Summer@ICERM 2021: Computational Polygonal Billiards"
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 MathPrograms.org. Applications submitted by February 14, 2021 will receive full consideration.

Confirmed Speakers & Participants

Talks will be presented virtually or in-person as indicated in the schedule below.

  • Speaker
  • Poster Presenter
  • Attendee
  • Virtual Attendee
  • Paul Apisa
    University of Michigan
  • Jessica Bennett
    Brown University
  • Madeline Brandt
    Brown University
  • Kelly Chen
    MIT
  • Ahmed Zawad Chowdhury
    MIT
  • Mei Rose Connor
    Stony Brook University
  • Catherine Cui
    Harvard
  • Elaine Danielson
    University of Florida
  • Diana Davis
    Phillips Exeter Academy
  • Samuel Everett
    University of Colorado, Boulder
  • Sam 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
  • Caroline Klivans
    Brown University
  • Destine Lee
    Columbia University
  • Samuel Lelièvre
    Université Paris-Saclay
  • Vanessa Lin
    UNC
  • Kathryn Lindsey
    Boston College
  • Aidan Mager
    University of Washington
  • Alba Málaga Sabogal
    Université de Lorraine
  • Olga Romaskevich
    Free-lance mathematician
  • Richard Schwartz
    Brown University
  • Sunrose Shrestha
    Wesleyan University
  • Zachary Steinberg
    Amherst College
  • Chenyang Sun
    Williams College
  • Cameron Thomas
    Morehouse College
  • Bena Tshishiku
    Brown University
  • Hamilton Wan
    Yale
  • Jane Wang
    Indiana University

Summer Schedule

Monday, June 14, 2021
  • 9:00 - 10:30 am EDT
    Welcome Summer@ICERM
    Welcome - Virtual
    • Paul Apisa, University of Michigan
    • Diana Davis, Phillips Exeter Academy
    • Brendan Hassett, ICERM/Brown University
    • Samuel Lelièvre, Université Paris-Saclay
  • 10:30 - 11:30 am EDT
    Morning Lecture
    Virtual
  • 11:30 am - 1:00 pm EDT
    Lunch/Free Time
    Virtual
  • 1:00 - 2:00 pm EDT
    Problem Session
    Virtual
  • 2:00 - 2:15 pm EDT
    Coffee Break
    Virtual
  • 2:30 - 3:30 pm EDT
    Sage Training
    Seminar - Virtual
  • 3:30 - 4:00 pm EDT
    Coffee Break
    Virtual
  • 4:00 - 5:00 pm EDT
    Afternoon Lecture
    Virtual
  • 7:30 - 9:30 pm EDT
    Game Night
    - Virtual
Tuesday, June 15, 2021
  • 10:30 - 11:30 am EDT
    Morning Lecture
    Virtual
  • 11:30 am - 1:00 pm EDT
    Lunch/Free Time
    Virtual
  • 1:00 - 2:00 pm EDT
    Problem Session
    Virtual
  • 2:00 - 2:15 pm EDT
    Coffee Break
    Virtual
  • 2:30 - 3:30 pm EDT
    Sage Training
    Virtual
  • 3:30 - 4:00 pm EDT
    Coffee Break
    Virtual
  • 4:00 - 5:00 pm EDT
    Afternoon Lecture
    Virtual
  • 7:30 - 9:30 pm EDT
    Movie Night
    - Virtual
Wednesday, June 16, 2021
  • 10:30 - 11:30 am EDT
    Morning Lecture
    Virtual
  • 11:30 am - 1:00 pm EDT
    Lunch/Free Time
    Virtual
  • 1:00 - 2:00 pm EDT
    Problem Session
    Virtual
  • 2:00 - 2:15 pm EDT
    Coffee Break
    Virtual
  • 2:30 - 3:30 pm EDT
    Sage Training
    Virtual
  • 3:30 - 4:00 pm EDT
    Coffee Break
    Virtual
  • 4:00 - 5:00 pm EDT
    Afternoon Lecture
    Virtual
Thursday, June 17, 2021
  • 9:00 - 10:00 am EDT
    Group Walk from student residence (optional)
    External Event - Virtual
  • 10:30 - 11:30 am EDT
    Morning Lecture
    Virtual
  • 11:30 am - 1:00 pm EDT
    Lunch/Free Time
    Virtual
  • 1:00 - 2:00 pm EDT
    Problem Session
    Virtual
  • 2:00 - 2:15 pm EDT
    Coffee Break
    Virtual
  • 2:30 - 3:30 pm EDT
    Sage Training
    Virtual
  • 3:30 - 4:00 pm EDT
    Coffee Break
    Virtual
  • 4:00 - 5:00 pm EDT
    Afternoon Lecture
    Virtual
  • 7:30 - 9:30 pm EDT
    Game Night
    - Virtual
Friday, June 18, 2021
  • 9:00 - 10:00 am EDT
    Group Walk from student residence (optional)
    External Event - Virtual
  • 10:30 - 11:30 am EDT
    Morning Lecture
    Virtual
  • 11:30 am - 1:00 pm EDT
    Lunch/Free Time
    Virtual
  • 1:00 - 2:00 pm EDT
    Problem Session
    Virtual
  • 2:00 - 2:15 pm EDT
    Coffee Break
    Virtual
  • 2:30 - 3:30 pm EDT
    Sage Training
    Virtual
  • 3:30 - 4:00 pm EDT
    Coffee Break
    Virtual
  • 4:00 - 5:00 pm EDT
    Afternoon Lecture
    Virtual
  • 5:30 - 6:30 pm EDT
    Iterated Function Systems
    Virtual
    • Kathryn Lindsey, Boston College
    Abstract
    Simple operations on the plane can give rise to beautiful and intricate patterns. "Iterated function systems" are a simple mechanism through which complicated behaviors can arise. I will show examples of iterated function systems, and discuss how they are related to some of my ongoing research in dynamical systems.
Friday, June 25, 2021
  • 10:00 - 10:45 am EDT
    Regular polygons 1
    Virtual
  • 11:00 - 11:45 am EDT
    Convex presentations
    Virtual
  • 1:00 - 1:45 pm EDT
    Language complexity 1
    Virtual
  • 2:00 - 2:45 pm EDT
    Language complexity 2
    Virtual
  • 3:00 - 3:45 pm EDT
    Colloquium: TBD
    Virtual
    • Bena Tshishiku, Brown University
Monday, June 28, 2021
  • 10:00 - 10:45 am EDT
    Periodic Points
    Virtual
  • 11:00 - 11:45 am EDT
    Exploring orbit closures
    Virtual
  • 1:00 - 1:45 pm EDT
    Dilation surfaces 1
    Tutorial - Virtual
  • 2:00 - 2:45 pm EDT
    Dilation surfaces 2
    Tutorial - Virtual
  • 3:00 - 3:45 pm EDT
    15-minute student talks
    Virtual
Tuesday, June 29, 2021
  • 10:00 - 10:45 am EDT
    Regular polygons 2
    Virtual
  • 11:00 - 11:45 am EDT
    Blocking
    Virtual
  • 1:00 - 1:45 pm EDT
    Language complexity 1
    Virtual
  • 2:00 - 2:45 pm EDT
    Language complexity 2
    Virtual
  • 3:00 - 3:45 pm EDT
    Equity in mathematics
    Professional Development - Virtual
Wednesday, June 30, 2021
  • 10:00 - 10:45 am EDT
    Regular Polygons 2
    Virtual
  • 11:00 - 11:45 am EDT
    Convex presentations
    Virtual
  • 1:00 - 1:45 pm EDT
    Periodic points
    Virtual
  • 2:00 - 2:45 pm EDT
    Exploring orbit closures
    Virtual
  • 3:00 - 3:45 pm EDT
    Updates from groups D1, D2, R1, R2, B
    Group Presentations - Virtual
Thursday, July 1, 2021
  • 10:00 - 10:45 am EDT
    Regular polygons 2
    Virtual
  • 11:00 - 11:45 am EDT
    Blocking
    Virtual
  • 1:00 - 1:45 pm EDT
    Dilation surfaces 1
    Tutorial - Virtual
  • 2:00 - 2:45 pm EDT
    Dilation surfaces 2
    Tutorial - Virtual
  • 3:00 - 3:45 pm EDT
    Updates from groups L1, L2, P, E, C
    Group Presentations - Virtual
Friday, July 2, 2021
  • 10:00 - 10:45 am EDT
    Colloquium: The farthest point map on the regular dodecahedron.
    11th Floor Lecture Hall
    • Richard Schwartz, Brown University
    Abstract
    Alice and Bob are 2 points on the surface of the regular dodecahedron, equipped with its path metric. They want to get away from each other, so Alice moves to the point farthest away from Bob. Then Bob moves to the point farthest away from Alice (in her new location). And so on. Where do Alice and Bob go? In this talk I will explain how this game leads to a piecewise bi-rational map on the surface of the regular dodecahedron whose omega limit set is the boundary of a certain tiling by 180 convex quadrilaterals. I'll illustrate all this with computer demos, and explain how I used the computer to help prove the result.
  • 11:00 - 11:45 am EDT
    Convex presentations
    Virtual
  • 1:00 - 1:45 pm EDT
    Language complexity 1
    Virtual
  • 2:00 - 2:45 pm EDT
    Language complexity 2
    Virtual
  • 3:00 - 3:45 pm EDT
    Regular polygons 1
    Virtual
Tuesday, July 6, 2021
  • 10:00 - 10:45 am EDT
    Regular polygons 2
    Virtual
  • 11:00 - 11:45 am EDT
    Blocking
    Virtual
  • 1:00 - 1:45 pm EDT
    Language complexity 1
    Virtual
  • 2:00 - 2:45 pm EDT
    Language complexity 2
    Virtual
  • 3:00 - 3:45 pm EDT
    Professional Development: Imposter syndrome
    Professional Development - Virtual
Wednesday, July 7, 2021
  • 10:00 - 10:45 am EDT
    Regular polygons 2
    Virtual
  • 11:00 - 11:45 am EDT
    Convex presentations
    Virtual
  • 1:00 - 1:45 pm EDT
    Periodic points
    Virtual
  • 2:00 - 2:45 pm EDT
    Exploring orbit closures
    Virtual
  • 3:00 - 3:45 pm EDT
    Updates from Groups D1, D2, R1, R2, B
    Group Presentations - Virtual
Thursday, July 8, 2021
  • 10:00 - 10:45 am EDT
    Regular polygons 2
    Virtual
  • 11:00 - 11:45 am EDT
    Blocking
    Virtual
  • 1:00 - 1:45 pm EDT
    Dilation surfaces 1
    Virtual
  • 2:00 - 2:45 pm EDT
    Dilation surfaces 2
    Virtual
  • 3:00 - 3:45 pm EDT
    Updates from groups L1, L2, P, E, C
    Group Presentations - Virtual
Friday, July 9, 2021
  • 10:00 - 10:45 am EDT
    Regular polygons 1
    Virtual
  • 11:00 - 11:45 am EDT
    Convex presentations
    Virtual
  • 1:00 - 1:45 pm EDT
    Language complexity 1
    Virtual
  • 2:00 - 2:45 pm EDT
    Language complexity 2
    Virtual
  • 3:00 - 3:45 pm EDT
    Colloquium: Tropical Geometry of Curves
    11th Floor Lecture Hall
    • Madeline Brandt, Brown University
    Abstract
    Tropical geometry is a new and exciting field of math which creates a link between algebraic geometry and combinatorics. As a result of this connection, surprising insights have developed in both areas. In this talk, I will show you how to carry out the tropicalization process for curves. This takes in an algebraic curve, and associates to it a metric graph. Even in this low-dimensional case, it is not easy to state a general algorithm. We will explore this through examples.
Monday, July 12, 2021
  • 10:00 - 10:45 am EDT
    Periodic points
    Virtual
  • 11:00 - 11:45 am EDT
    Exploring orbit closures
    Virtual
  • 1:00 - 1:45 pm EDT
    Dilation surfaces 1
    Virtual
  • 2:00 - 2:45 pm EDT
    Dilation surfaces 2
    Virtual
  • 3:00 - 3:45 pm EDT
    15-minute student talks
    Lightning Talks - Virtual
Tuesday, July 13, 2021
  • 10:00 - 10:45 am EDT
    Regular polygons 2
    Virtual
  • 11:00 - 11:45 am EDT
    Blocking
    Virtual
  • 1:00 - 1:45 pm EDT
    Language complexity 1
    Virtual
  • 2:00 - 2:45 pm EDT
    Language complexity 2
    Virtual
  • 3:00 - 3:45 pm EDT
    Professional Development: Graduate School
    Professional Development - Virtual
Wednesday, July 14, 2021
  • 9:00 - 9:45 am EDT
    Math Opportunities at the National Security Agency
    Virtual
    • Amanda Carr, NSA Commercial Engagement Center
  • 10:00 - 10:45 am EDT
    Regular polygons 2
    Virtual
  • 11:00 - 11:45 am EDT
    Convex presentations
    Virtual
  • 1:00 - 1:45 pm EDT
    Periodic points
    Virtual
  • 2:00 - 2:45 pm EDT
    Exploring orbit closures
    Virtual
  • 3:00 - 3:45 pm EDT
    Updates from groups D1, D2, R1, R2, B
    Group Presentations - Virtual
Thursday, July 15, 2021
  • 10:00 - 10:45 am EDT
    Regular polygons 2
    Virtual
  • 11:00 - 11:45 am EDT
    Blocking
    Virtual
  • 1:00 - 1:45 pm EDT
    Dilation surfaces 1
    Virtual
  • 2:00 - 2:45 pm EDT
    Dilation surfaces 2
    Virtual
  • 3:00 - 3:45 pm EDT
    Updates from groups L1, L2, P, E, C
    Group Presentations - Virtual
Friday, July 16, 2021
  • 10:00 - 10:45 am EDT
    Regular polygons 1
    Virtual
  • 11:00 - 11:45 am EDT
    Convex presentations
    Virtual
  • 1:00 - 1:45 pm EDT
    Language complexity 1
    Virtual
  • 2:00 - 2:45 pm EDT
    Language complexity 2
    Virtual
  • 8:00 - 9:00 pm EDT
    Colloquium: Tiling billiards, or good morning from Russia
    Virtual
    • Olga Romaskevich, Free-lance mathematician
    Abstract
    At the moment, I am traveling through Russia and preparing an exhibition project about Russian women in mathematics called МАТЕМАТИКА (https://matematika.mathematiquesvagabondes.fr/). I will share with you some news about this project, directly from Novosibirsk!
    On the math side, I will speak about tiling billiards. This is a class of dynamical systems that model the movement of light in heterogeneous media with refraction coefficient equal to -1. Its mathematical exploration started around five years ago, and a lot is yet to discover. I will mostly speak about two tilings, billiards on which we understand the best: triangle and cyclic quadrilateral periodic tilings. I will focus on new ideas that give a simple proof of a so-called Tree Conjecture for these two tilings, formulated by Baird-Smith, Davis, Fromm and Iyer in 2017. This Conjecture says that for a periodic trajectory on a tiling, it passes by all the tiles crossed by the domain it bounds (you can check it for two examples given on the Figures and think of why it is called the Tree Conjecture!).
    As a (hopefully, pleasant) homework before the talk, I invite you to watch a video by Ofir David on the subject called Refraction tilings (https://www.youtube.com/watch?v=t1r1cO1V35I) that illustrates some of the key features of triangle tiling billiard dynamics.
Monday, July 19, 2021
  • 10:00 - 10:45 am EDT
    Periodic points
    Virtual
  • 11:00 - 11:45 am EDT
    Exploring orbit closures
    Virtual
  • 1:00 - 1:45 pm EDT
    Dilation surfaces 1
    Virtual
  • 2:00 - 2:45 pm EDT
    Dilation surfaces 2
    Virtual
  • 3:00 - 3:45 pm EDT
    15-minute student talks
    Virtual
Tuesday, July 20, 2021
  • 10:00 - 10:45 am EDT
    Regular polygons 2
    Virtual
  • 11:00 - 11:45 am EDT
    Blocking
    Virtual
  • 1:00 - 1:45 pm EDT
    Language complexity 1
    Virtual
  • 2:00 - 2:45 pm EDT
    Language complexity 2
    Virtual
  • 3:00 - 3:45 pm EDT
    Professional Development: The GRE
    Professional Development - Virtual
Wednesday, July 21, 2021
  • 10:00 - 10:45 am EDT
    Regular polygons 2
    Virtual
  • 11:00 - 11:45 am EDT
    Convex presentations
    Virtual
  • 1:00 - 1:45 pm EDT
    Periodic Points
    Virtual
  • 2:00 - 2:45 pm EDT
    Exploring orbit closures
    Virtual
  • 3:00 - 3:45 pm EDT
    Updates from groups D1, D2, R1, R2, B
    Group Presentations - Virtual
Thursday, July 22, 2021
  • 10:00 - 10:45 am EDT
    Regular Polygons 2
    Virtual
  • 10:00 - 10:45 am EDT
    sage-flatsurf demo
    Virtual
    • Pat Hooper, City College of New York
  • 11:00 - 11:45 am EDT
    Blocking
    Virtual
  • 1:00 - 1:45 pm EDT
    Dilation surfaces 1
    Virtual
  • 2:00 - 2:45 pm EDT
    Dilation surfaces 2
    Virtual
  • 3:00 - 3:45 pm EDT
    Updates from groups L1, L2, P, E, C
    Group Presentations - Virtual
Friday, July 23, 2021
  • 10:00 - 10:45 am EDT
    Regular Polygons 1
    Virtual
  • 11:00 - 11:45 am EDT
    Convex Presentations
    Virtual
  • 1:00 - 1:45 pm EDT
    Language Complexity 1
    Virtual
  • 2:00 - 2:45 pm EDT
    Language Complexity 2
    Virtual
  • 3:00 - 3:45 pm EDT
    Colloquium: Chasing polyhedral flat tori with diplotori
    Virtual
    • Alba Málaga Sabogal, Université de Lorraine
    Abstract
    A general flat torus can be obtained by abstractly identifying the opposite sides of a parallelogram. However, actually gluing the opposite sides of a paper parallelogram in euclidean space, is a horse of a different color.+ In this talk, I will talk about one possible answer to this question: folding the paper, origami-style. More precisely, we will be looking into polyhedral embeddings of flat tori. This is joint work with Samuel Lelièvre (Orsay) and Pierre Arnoux (Marseille).
Monday, July 26, 2021
  • 10:00 - 10:45 am EDT
    Periodic Points
    Virtual
  • 11:00 - 11:45 am EDT
    Exploring orbit closures
    Virtual
  • 1:00 - 1:45 pm EDT
    Dilation surfaces 1
    Virtual
  • 2:00 - 2:45 pm EDT
    Dilation surfaces 2
    Virtual
Tuesday, July 27, 2021
  • 10:00 - 10:45 am EDT
    Regular polygons 2
    Virtual
  • 11:00 - 11:45 am EDT
    Blocking
    Virtual
  • 1:00 - 1:45 pm EDT
    Language complexity 1
    Virtual
  • 2:00 - 2:45 pm EDT
    Language complexity 2
    Virtual
  • 3:00 - 3:45 pm EDT
    Professional Development: The paper submission process
    Professional Development - Virtual
Wednesday, July 28, 2021
  • 10:00 - 10:45 am EDT
    Regular polygons 2
    Virtual
  • 11:00 - 11:45 am EDT
    Convex presentations
    Virtual
  • 1:00 - 1:45 pm EDT
    Periodic points
    Virtual
  • 2:00 - 2:45 pm EDT
    Exploring orbit closures
    Virtual
  • 3:00 - 3:45 pm EDT
    Updates from groups D1, D2, R1, R2, B
    Group Presentations - Virtual
Thursday, July 29, 2021
  • 9:15 - 10:15 am EDT
    Ethics I
    10th Floor Classroom
    • Brendan Hassett, ICERM/Brown University
  • 10:00 - 10:45 am EDT
    Regular polygons 2
    Virtual
  • 11:00 - 11:45 am EDT
    Blocking
    Virtual
  • 1:00 - 1:45 pm EDT
    Dilation surfaces 1
    Virtual
  • 2:00 - 2:45 pm EDT
    Dilation surfaces 2
    Virtual
  • 3:00 - 3:45 pm EDT
    Updates from groups L1, L2, P, E, C
    Group Presentations - Virtual
Friday, July 30, 2021
  • 9:15 - 10:15 am EDT
    Ethics II
    10th Floor Classroom
    • Brendan Hassett, ICERM/Brown University
  • 10:00 - 10:45 am EDT
    Regular polygons 1
    Virtual
  • 11:00 - 11:45 am EDT
    Convex presentations
    Virtual
  • 1:00 - 1:45 pm EDT
    Language complexity 1
    Virtual
  • 2:00 - 2:45 pm EDT
    Language complexity 2
    Virtual
  • 3:00 - 3:45 pm EDT
    Colloquium: TBD
    10th Floor Classroom
    • Caroline Klivans, Brown University
Monday, August 2, 2021
  • 10:00 - 10:45 am EDT
    Periodic points
    Virtual
  • 11:00 - 11:45 am EDT
    Exploring orbit closures
    Virtual
  • 1:00 - 1:45 pm EDT
    Dilation surfaces 1
    Virtual
  • 2:00 - 2:45 pm EDT
    Dilation surfaces 2
    Virtual
  • 3:00 - 3:45 pm EDT
    15-minute student talks
    Group Presentations - Virtual
Tuesday, August 3, 2021
  • 10:00 - 10:45 am EDT
    Regular polygons 2
    Virtual
  • 11:00 - 11:45 am EDT
    Blocking
    Virtual
  • 1:00 - 1:45 pm EDT
    Language complexity 1
    Virtual
  • 2:00 - 2:45 pm EDT
    Language complexity 2
    Virtual
Wednesday, August 4, 2021
  • 10:00 - 10:45 am EDT
    Regular polygons 2
    Virtual
  • 11:00 - 11:45 am EDT
    Convex presentations
    Virtual
  • 1:00 - 1:45 pm EDT
    Periodic points
    Virtual
  • 2:00 - 2:45 pm EDT
    Exploring orbit closures
    Virtual
  • 3:00 - 3:45 pm EDT
    Updates from groups D1, D2, R1, R2, B
    Group Presentations - Virtual
Thursday, August 5, 2021
  • 10:00 - 10:45 am EDT
    Regular polygons 2
    Virtual
  • 11:00 - 11:45 am EDT
    Blocking
    Virtual
  • 1:00 - 1:45 pm EDT
    Dilation surfaces 1
    Virtual
  • 2:00 - 2:45 pm EDT
    Dilation surfaces 2
    Virtual
  • 3:00 - 3:12 pm EDT
    Hecke Eigenforms to Flat Atlases
    Group Presentations - 11th Floor Lecture Hall
    • Ahmed Zawad Chowdhury, MIT
    • Elaine Danielson, University of Florida
    • Aidan Mager, University of Washington
    • Hamilton Wan, Yale
  • 3:13 - 3:25 pm EDT
    Closed Geodesics on Dilation Surfaces
    Group Presentations - 11th Floor Lecture Hall
    • Catherine Cui, Harvard
    • Victor Ginsburg, Pennsylvania State University
    • Veronica Kirgios, Notre Dame
    • Vanessa Lin, UNC
  • 3:26 - 3:38 pm EDT
    Hyperbolic Staircases: Periodic paths on (2n + 1)-gons
    Group Presentations - 11th Floor Lecture Hall
    • Mei Rose Connor, Stony Brook University
    • Paul Kielstra, Harvard University
    • Zachary Steinberg, Amherst College
    • Chenyang Sun, Williams College
  • 3:39 - 3:51 pm EDT
    Periodic Orbits of AAffine Interval Exchange Transformations
    Group Presentations - 11th Floor Lecture Hall
    • Kelly Chen, MIT
    • Zachary Steinberg, Amherst College
    • Cameron Thomas, Morehouse College
  • 3:52 - 4:04 pm EDT
    Language Complexity of Billiards
    Group Presentations - 11th Floor Lecture Hall
    • Jessica Bennett, Brown University
    • Catherine Cui, Harvard
    • Elaine Danielson, University of Florida
    • Veronica Kirgios, Notre Dame
  • 4:05 - 4:10 pm EDT
    Coffee Break
    11th Floor Lecture Hall
  • 4:11 - 4:23 pm EDT
    The J-invariant as a tool for detecting Veech Surfaces and the Combinatorics of Lattice Hexagons
    Group Presentations - 11th Floor Lecture Hall
    • Mei Rose Connor, Stony Brook University
    • Brin Harper, Massachusetts Institute of Technology
    • Hamilton Wan, Yale
    • Hanna Yang, MIT
  • 4:24 - 4:36 pm EDT
    Long and Short Trajectories in the Double Pentagon
    Group Presentations - 11th Floor Lecture Hall
    • Samuel Everett, University of Colorado, Boulder
    • Vanessa Lin, UNC
    • Aidan Mager, University of Washington
  • 4:37 - 4:49 pm EDT
    Blocking and Periodic Points on Veech Surfaces
    Group Presentations - 11th Floor Lecture Hall
    • Jessica Bennett, Brown University
    • Ahmed Zawad Chowdhury, MIT
    • Samuel Everett, University of Colorado, Boulder
    • Destine Lee, Columbia University
  • 4:50 - 5:02 pm EDT
    Towards the Asymptotic Language Complexity of the Regular Hexagon
    Group Presentations - 11th Floor Lecture Hall
    • Paul Kielstra, Harvard University
    • Chenyang Sun, Williams College
    • Cameron Thomas, Morehouse College

All event times are listed in ICERM local time in Providence, RI (Eastern Daylight Time / UTC-4).

All event times are listed in .

Final Projects

Final Student Presentations
  • "Hecke Eigenforms to Flat Atlases" by Zawad Chowdhury, Elaine Danielson, Aidan Mager, HamiltonWan
  • "Closed Geodesics on Dilation Surfaces" by Catherine Cui, Victor Ginsburg, Veronica Kirgios, Vanessa Lin
  • "Hyperbolic Staircases: Periodic paths on (2n + 1)-gons" by Mei Rose Connor, Michael Kielstra, Zachary Steinberg, Chenyang Sun
  • "Periodic Orbits of Affine Interval Exchange Transformations" by Kelly Chen, Zachary Steinberg, Cameron Thomas
  • "Language Complexity of Billiards" by Jessica Bennett1, Catherine Cui, Elaine Danielson, Veronica Kirgios
  • "The J-invariant as a tool for detecting Veech Surfaces and the Combinatorics of Lattice Hexagons" by Mei Rose Connor, Brin Harper, Hamilton Wan, Hanna Yang
  • "Long and Short Trajectories in the Double Pentagon" by Sam Everett, Vanessa Lin, Aidan Mager
  • "Blocking and Periodic Points on Veech Surfaces" by Jessica Bennett, Zawad Chowdhury, Sam Everett, Destine Lee
  • "Towards the Asymptotic Language Complexity of the Regular Hexagon" by Michael Kielstra, Chenyang Sun, Cameron Thomas
Read more about each project

Posters Presented at JMM 2022
  • Computing periodic points on Veech surfaces (Zawad Chowdhury, Samuel Everett, and Destine Lee)
  • Constructing Translation Surfaces from Hecke Eigenforms (Paul Apisa, Zawad Chowdhury, Elaine Danielson, Paige Helms, Aidan Mager, and Hamilton Ji Wan)
  • Hyperbolic Staircases: Periodic Paths on 2g + 1-gons (Mei Rose Connor, Diana Davis, Paige Helms, Michael Kielstra, Samuel Lelievre, Chenyang Sun, and Zachary Steinberg)
  • Periodic Orbits of Affine Interval Exchange Transformations (Kelly Chen, Zachary Steinberg, Cameron Thomas, and Jane Wang)
  • The Finite Blocking Problem on Cyclic Covers of the Regular Octagon (Jessica Bennett, and Destine Lee)
  • Towards a Classification of Veech 12-Gons and Trapezoidal Unfoldings (Paul Apisa, Brin Harper, Hamilton Ji Wan, and Hanna Yang)
  • Towards the Language Complexity of the Regular Hexagon (Diana Davis, Michael Kielstra, Samuel Lelievre, Sunrose Thapa Shrestha, Chenyang Sun, Cameron Thomas, and Jane Wang)

Publications

  • Zawad Chowdhury, Samuel Everett, Samuel Freedman, Destine Lee, Computing Periodic Points on Veech Surfaces, 2021, .
  • Samuel Everett, Vanessa Lin, Aidan Mager, Long and Short Periodic Billiard Trajectories in the Regular Pentagon, 2021, .
  • Mei Rose Connor, Diana Davis, Paige Helms, Samuel Lelièvre, Michael Kielstra, Zachary L. Steinberg, Chenyang Sun, Hyperbolic Staircases: Periodic Paths on 2g+1-gons, 2021, .

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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Summer@ICERM 2022: Computational Combinatorics
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