Summer@ICERM 2021: Computational Polygonal Billiards

Institute for Computational and Experimental Research in Mathematics (ICERM)

https://icerm.brown.edu/summerug/2021/
June 14, 2021 - August 6, 2021
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

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