Organizing Committee
Abstract

Imagine spending eight-weeks on the beautiful Brown University campus in historic Providence, RI, working in a small team setting to solve mathematical research problems developed by faculty experts in their fields.

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 with support for travel within the U.S., room and board paid, plus a $3,570 stipend*.

The 2019 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 interdisciplinary research projects on the theme of Computational Arithmetic Dynamics. This overarching theme will allow participants to utilize theory and computation from algebra, number theory, and algebraic geometry. Faculty will also guide the development of open-source computational tools for dynamical systems in Sage as well as work on a database of dynamical systems.

The faculty will begin the program with brief introductory talks. Throughout the eight-week program, students will work on assigned 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, professional development seminars, and will acquire skill in open-source software development. Students will learn how to collaborate mathematically, working closely in their teams to write up their research into a poster and/or paper by the end of the program.

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

Program Details

2019 Proposed Research Project Topics
  • Classification of Preperiodic Graphs
  • Automorphisms of Rational Functions
  • Post-Critically Finite Maps
  • Randomness over Finite Fields
Important Notes
  • Applicants must be matriculating undergraduate students at the time of the start of Summer@ICERM 2019.
  • Funding is available for 2-3 students who are not US citizens or permanent residents.
Funding Includes*
  • $3,570 stipend
  • Dormitory housing
  • Meal plan
  • Travel support within the U.S.
  • Fun events
  • *Brown students who choose not to live in the dorm will waive the dorm, meal, and travel funding.

Confirmed Speakers & Participants

  • Speaker
  • Poster Presenter
  • Attendee
  • Heidi Benham
    Western Oregon University
  • Talia Blum
    Massachusetts Institute of Technology
  • Julia Cai
    Yale University
  • Jasmine Camero
    California State University, Fullerton
  • Anna Chlopecki
    University of Illinois at Urbana-Champaign
  • John Doyle
    Louisiana Tech University
  • Alexander Galarraga
    Swarthmore College
  • Brandon Gontmacher
    Stony Brook University
  • Meghan Grip
    University of Rochester
  • Benjamin Hutz
    Saint Louis University
  • Trevor Hyde
    University of Michigan
  • Grayson Jorgenson
    Florida State University
  • Colby Kelln
    University of Michigan
  • Juliano Levier-Gomes
    Westminster College
  • Chieh-mi Lu
    California State University San Marcos
  • Joey Lupo
    Amherst College
  • Leopold Mayer
    Lawrence University
  • Junwen Peng
    University of Rochester
  • Emily Rachfal
    Kenyon College
  • Olivia Schwager
    Muhlenberg College
  • Alex Shearer
    Pacific Lutheran University
  • Srinjoy Srimani
    Brown University
  • Henry Talbott
    Brown University
  • Bianca Thompson
    Westminster College
  • Matt Torrence
    Gettysburg College
  • Adam Towsley
    Rochester Institute of Technology
  • Max Weinreich
    Brown University
  • Shuofeng Xu
    Colby College
  • Eric Zhu
    Georgia Institute of Technology

Summer Schedule

Monday, June 10, 2019
TimeEventLocationMaterials
8:15 - 9:00Registration and Breakfast - ICERM 121 South Main Street, Providence RI 0290310th Floor 
9:00 - 10:00Meet and Greet10th Floor 
10:00 - 12:00Scavenger HuntBrown University, Providence, RI 02912, USA 
12:00 - 1:30Welcome Lunch10th Floor 
1:30 - 2:00Goals of Summer - Ben Hutz, Saint Louis University10th Floor 
2:00 - 3:00Broad Overview of Arithemetic Dynamics - John Doyle, Louisiana Tech University10th Floor 
3:00 - 3:30Coffee/ Tea Break10th Floor 
3:30 - 5:00Dynamic Systems in Sage - Ben Hutz, St Louis University10th floor 
Tuesday, June 11, 2019
TimeEventLocationMaterials
9:00 - 10:30Project Talk - Bianca Thompson, Westminster College10th Floor 
10:30 - 11:00Coffee/ Tea Break10th Floor 
11:00 - 12:00Project Talk - Bianca Thompson, Westminster College10th Floor 
12:00 - 1:30Lunch Break  
1:30 - 3:00Project Talk - Adam Towsley, Rochester Institute of Technology10th Floor 
3:00 - 3:30Coffee/ Tea Break10th Floor 
3:30 - 5:00Project Talk - Adam Towsley, Rochester Institute of Technology10th Floor 
Wednesday, June 12, 2019
TimeEventLocationMaterials
9:00 - 10:30Project Talk - John Doyle, Louisiana Tech University10th Floor 
10:30 - 11:00Coffee/ Tea Break10th Floor 
11:00 - 12:00Project Talk - John Doyle, Louisiana Tech University10th Floor 
12:00 - 1:30Lunch Break  
1:30 - 3:00Project Talk - Ben Hutz, St Louis University10th Floor 
3:00 - 3:30Coffee/ Tea Break10th Floor 
3:30 - 5:00Project Talk - Ben Hutz, St Louis University10th Floor 
Thursday, June 13, 2019
TimeEventLocationMaterials
9:00 - 10:30Sage Development10th Floor 
10:30 - 11:00Coffee/ Tea Break10th Floor 
11:00 - 12:00Sage Development10th Floor 
12:00 - 1:30Lunch Break  
1:30 - 3:00Group Interactions Discussion - Bianca Thompson, Westminster College10th Floor 
3:00 - 3:30Coffee/ Tea Break10th Floor 
3:30 - 5:00Introduction to Math Research - Ben Hutz, St Louis University10th Floor 
5:00 - 5:00Ranked project lists due  
Friday, June 14, 2019
TimeEventLocationMaterials
9:00 - 10:30Using Latex - Adam Towsley, Rochester Institute of Technology10th Floor 
10:30 - 11:00Coffee/ Tea Break10th Floor 
11:00 - 12:00Group Project Assignments10th Floor 
12:00 - 1:30Lunch Break  
1:30 - 3:00Group Project Meetings10th Floor 
3:00 - 3:30Coffee/ Tea Break10th Floor 
3:30 - 5:00Group Project Working Time10th Floor 
Monday, June 17, 2019
TimeEventLocationMaterials
9:00 - 12:00Group Project Meetings10th Floor Collaborative Space 
3:00 - 3:30Coffee/ Tea Break10th Floor 
Tuesday, June 18, 2019
TimeEventLocationMaterials
9:30 - 10:30Algebraic Geometry 101 - Max Weinreich, Brown University10th Floor Collaborative Space 
3:00 - 3:30Coffee/ Tea Break10th Floor 
Wednesday, June 19, 2019
TimeEventLocationMaterials
10:30 - 11:30What is a p-adic Mandelbrot set? - Jacqueline Anderson, Bridgewater State University10th Floor Collaborative Space
2:00 - 3:00Dynamical Moduli Spaces - John Doyle, Louisiana Tech University10th Floor Collaborative Space 
3:00 - 3:30Coffee/ Tea Break10th Floor 
Thursday, June 20, 2019
TimeEventLocationMaterials
9:00 - 12:00Sage Development10th Floor Collaborative Space 
3:00 - 3:30Coffee/ Tea Break10th Floor 
Friday, June 21, 2019
TimeEventLocationMaterials
9:30 - 11:00Group Presentations10th Floor Collaborative Space 
3:00 - 3:30Coffee/ Tea Break10th Floor 
Monday, June 24, 2019
TimeEventLocationMaterials
9:00 - 12:00Group Project Meetings10th Floor Collaborative Space 
3:00 - 3:30Coffee/ Tea Break10th Floor 
Tuesday, June 25, 2019
TimeEventLocationMaterials
3:00 - 3:30Coffee/ Tea Break10th Floor 
Wednesday, June 26, 2019
TimeEventLocationMaterials
9:30 - 10:30An introduction to height functions - Wayne Peng, University of Rochester10th Floor Collaborate Space 
3:00 - 3:30Coffee/ Tea Break10th Floor 
Thursday, June 27, 2019
TimeEventLocationMaterials
3:00 - 3:30Coffee/ Tea Break10th Floor 
Friday, June 28, 2019
TimeEventLocationMaterials
9:30 - 11:00Group Presentations10th Floor Collaborative Space 
2:00 - 3:00Potential Good Reduction and PCF Maps - Michelle Manes, University of Hawaii and NSF10th Floor Collaborative Space
3:00 - 3:30Coffee/ Tea Break10th Floor 
Monday, July 1, 2019
TimeEventLocationMaterials
9:00 - 12:00Group Project Meetings11th Floor Lecture Hall 
3:00 - 3:30Coffee/ Tea Break10th Floor 
Tuesday, July 2, 2019
TimeEventLocationMaterials
10:30 - 11:30Building telescopes for mathematicians. - Andrew Sutherland, MIT11th Floor Lecture Hall
3:00 - 3:30Coffee/ Tea Break10th Floor 
Wednesday, July 3, 2019
TimeEventLocationMaterials
11:00 - 12:00Existence of periodic points and Sharkovsky’s theorem - Trevor Hyde, University of Michigan11th Floor Lecture Hall
3:00 - 3:30Coffee/ Tea Break10th Floor 
Friday, July 5, 2019
TimeEventLocationMaterials
3:00 - 3:30Coffee/ Tea Break10th Floor 
Monday, July 8, 2019
TimeEventLocationMaterials
3:00 - 3:30Coffee/ Tea Break10th Floor 
Tuesday, July 9, 2019
TimeEventLocationMaterials
10:30 - 11:30Configurations of points on the Riemann Sphere - Rohini Ramadas, Brown University11th Floor Lecture Hall
2:00 - 3:00Ethics I11th Floor Lecture Hall 
3:00 - 3:30Coffee/ Tea Break10th Floor 
Wednesday, July 10, 2019
TimeEventLocationMaterials
9:30 - 10:30Rachel Locke, National Security Agency11th Floor Lecture Hall 
2:00 - 3:00Ethics II11th Floor Lecture Hall 
3:00 - 3:30Coffee/ Tea Break10th Floor 
Thursday, July 11, 2019
TimeEventLocationMaterials
3:00 - 3:30Coffee/ Tea Break10th Floor 
Friday, July 12, 2019
TimeEventLocationMaterials
3:00 - 3:30Coffee/ Tea Break10th Floor 
Monday, July 15, 2019
TimeEventLocationMaterials
3:00 - 3:30Coffee/ Tea Break10th Floor 
Tuesday, July 16, 2019
TimeEventLocationMaterials
9:00 - 10:00CCV Tutorial - Paul Hall, Center for Computation and Visualization at Brown University10th Floor Collaborative Space 
10:30 - 11:30Selected Topics in Arithmetic Dynamics - Joseph Silverman, Brown University10th Floor Collaborative Space
3:00 - 3:30Coffee/ Tea Break10th Floor 
Wednesday, July 17, 2019
TimeEventLocationMaterials
3:00 - 3:30Coffee/ Tea Break10th Floor 
Thursday, July 18, 2019
TimeEventLocationMaterials
3:00 - 3:30Coffee/ Tea Break10th Floor 
Friday, July 19, 2019
TimeEventLocationMaterials
3:00 - 3:30Coffee/ Tea Break10th Floor 
Monday, July 22, 2019
TimeEventLocationMaterials
9:30 - 10:30Graduate Student Panel10th Floor Collaborative Space 
3:00 - 3:30Coffee/ Tea Break10th Floor 
Wednesday, July 24, 2019
TimeEventLocationMaterials
3:00 - 3:30Coffee/ Tea Break10th Floor 
Thursday, July 25, 2019
TimeEventLocationMaterials
1:00 - 3:00Off Site Visit to AMS201 Charles St, Providence, RI 02904, USA 
3:00 - 3:30Coffee/ Tea Break10th Floor 
Friday, July 26, 2019
TimeEventLocationMaterials
1:30 - 1:45Group Photo10th Floor at the stairwell 
3:00 - 3:30Coffee/ Tea Break10th Floor 
Monday, July 29, 2019
TimeEventLocationMaterials
3:00 - 3:30Coffee/ Tea Break10th Floor 
7:00 - 10:00Summer@ICERM Game Night10th Floor Collaborative 
Tuesday, July 30, 2019
TimeEventLocationMaterials
3:00 - 3:30Coffee/ Tea Break10th Floor 
Wednesday, July 31, 2019
TimeEventLocationMaterials
3:00 - 3:30Coffee/ Tea Break10th Floor 
Thursday, August 1, 2019
TimeEventLocationMaterials
3:00 - 3:30Cake & Coffee/ Tea Break10th Floor 
Friday, August 2, 2019
TimeEventLocationMaterials
8:45 - 9:20Summer@ICERM PresentationsDigital Scholarship Lab, 1st floor of the Rockefeller Library 
9:20 - 9:50Periodic points for Lattès maps over finite fields - Mentors: Bianca Thompson, Trevor Hyde Students: Jasmine Camero, Fiona Lu, Eric ZhuDigital Scholarship Lab, 1st floor of the Rockefeller Library 
10:00 - 10:30Dynamical statistics over finite fields break - Mentors: Adam Towsley, Wayne Peng Students: Anna Chlopecki, Juliano Levier-Gomes, Alex ShearerDigital Scholarship Lab, 1st floor of the Rockefeller Library 
10:30 - 10:50Break  
10:50 - 11:20Classification of rational preperiodic structures - Mentors: John Doyle, Bianca Thompson, Grayson Jorgenson Students: Meghan Grip, Emily Rachfal, Olivia Schwager, Matt TorrenceDigital Scholarship Lab, 1st floor of the Rockefeller Library 
11:30 - 12:00Automorphism groups of rational maps char 0 - Mentors: Ben Hutz, Grayson Jorgenson, Max Weinreich Students: Julia Cai, Brandon Gontmacher, Leo Mayer, Srinjoy Srimani, Simon XuDigital Scholarship Lab, 1st floor of the Rockefeller Library 
12:00 - 1:30Break for Lunch  
1:30 - 2:00Automorphism groups of rational maps char p - Mentors: Ben Hutz, Grayson Jorgenson, Max Weinreich Students: Julia Cai, Brandon Gontmacher, Leo Mayer, Srinjoy Srimani, Simon XuDigital Scholarship Lab, 1st floor of the Rockefeller Library 
2:10 - 2:40Post-critically finite rational maps - Mentors: Ben Hutz, Adam Towsley, Wayne Peng Students: Joey Lupo, Alex Galarraga, Heidi BenhamDigital Scholarship Lab, 1st floor of the Rockefeller Library 
2:50 - 3:20Finite orbit sets for several polynomial maps - Mentors: Trevor Hyde, John Doyle, Max Weinreich Students: Talia Blum, Colby Kelln, Henry TalbottDigital Scholarship Lab, 1st floor of the Rockefeller Library 
3:30 - 4:00Coffee/ Tea Break  

Final Projects

Final Student Presentations
  • “Periodic points for Lattés maps over finite fields” by J. Camero, F. Lu, and E. Zhu
  • “Dynamical statistics over finite fields break” by A. Chlopecki, J. Levier-Gomes, and A. Shearer
  • “Classification of rational preperiodic structures” by M. Grip, E. Rachfal, O. Schwager, and M. Torrence
  • “Automorphism groups of rational maps char 0” by J. Cai, B. Gontmacher, L. Mayer, S. Srimani, and Simon Xu
  • “Automorphism groups of rational maps char p” by J. Cai, B. Gontmacher, L. Mayer, S. Srimani, and S. Xu
  • “Post-critically finite rational maps” by J. Lupo, A. Galarraga, H. Benham
  • “Finite orbit sets for several polynomial maps” by T. Blum, C. Kelln, and H. Talbott

Other Summer@ICERM Events

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