Organizing Committee
- John Doyle
Louisiana Tech University - Benjamin Hutz
Saint Louis University - Bianca Thompson
Westminster College - Adam Towsley
Rochester Institute of Technology
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
Talks will be presented virtually or in-person as indicated in the schedule below.
- Speaker
- Poster Presenter
- Attendee
- Virtual 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
Time | Event | Location | Materials |
---|---|---|---|
8:15 - 9:00am EDT | Registration and Breakfast - ICERM 121 South Main Street, Providence RI 02903 | 10th Floor | |
9:00 - 10:00am EDT | Meet and Greet | 10th Floor | |
10:00 - 12:00pm EDT | Scavenger Hunt | Brown University, Providence, RI 02912, USA | |
12:00 - 1:30pm EDT | Welcome Lunch | 10th Floor | |
1:30 - 2:00pm EDT | Goals of Summer - Ben Hutz, Saint Louis University | 10th Floor | |
2:00 - 3:00pm EDT | Broad Overview of Arithemetic Dynamics - John Doyle, Louisiana Tech University | 10th Floor | |
3:00 - 3:30pm EDT | Coffee/ Tea Break | 10th Floor | |
3:30 - 5:00pm EDT | Dynamic Systems in Sage - Ben Hutz, St Louis University | 10th floor |
Tuesday, June 11, 2019
Time | Event | Location | Materials |
---|---|---|---|
9:00 - 10:30am EDT | Project Talk - Bianca Thompson, Westminster College | 10th Floor | |
10:30 - 11:00am EDT | Coffee/ Tea Break | 10th Floor | |
11:00 - 12:00pm EDT | Project Talk - Bianca Thompson, Westminster College | 10th Floor | |
12:00 - 1:30pm EDT | Lunch Break | ||
1:30 - 3:00pm EDT | Project Talk - Adam Towsley, Rochester Institute of Technology | 10th Floor | |
3:00 - 3:30pm EDT | Coffee/ Tea Break | 10th Floor | |
3:30 - 5:00pm EDT | Project Talk - Adam Towsley, Rochester Institute of Technology | 10th Floor |
Wednesday, June 12, 2019
Time | Event | Location | Materials |
---|---|---|---|
9:00 - 10:30am EDT | Project Talk - John Doyle, Louisiana Tech University | 10th Floor | |
10:30 - 11:00am EDT | Coffee/ Tea Break | 10th Floor | |
11:00 - 12:00pm EDT | Project Talk - John Doyle, Louisiana Tech University | 10th Floor | |
12:00 - 1:30pm EDT | Lunch Break | ||
1:30 - 3:00pm EDT | Project Talk - Ben Hutz, St Louis University | 10th Floor | |
3:00 - 3:30pm EDT | Coffee/ Tea Break | 10th Floor | |
3:30 - 5:00pm EDT | Project Talk - Ben Hutz, St Louis University | 10th Floor |
Thursday, June 13, 2019
Time | Event | Location | Materials |
---|---|---|---|
9:00 - 10:30am EDT | Sage Development | 10th Floor | |
10:30 - 11:00am EDT | Coffee/ Tea Break | 10th Floor | |
11:00 - 12:00pm EDT | Sage Development | 10th Floor | |
12:00 - 1:30pm EDT | Lunch Break | ||
1:30 - 3:00pm EDT | Group Interactions Discussion - Bianca Thompson, Westminster College | 10th Floor | |
3:00 - 3:30pm EDT | Coffee/ Tea Break | 10th Floor | |
3:30 - 5:00pm EDT | Introduction to Math Research - Ben Hutz, St Louis University | 10th Floor | |
5:00 - 5:00pm EDT | Ranked project lists due |
Friday, June 14, 2019
Time | Event | Location | Materials |
---|---|---|---|
9:00 - 10:30am EDT | Using Latex - Adam Towsley, Rochester Institute of Technology | 10th Floor | |
10:30 - 11:00am EDT | Coffee/ Tea Break | 10th Floor | |
11:00 - 12:00pm EDT | Group Project Assignments | 10th Floor | |
12:00 - 1:30pm EDT | Lunch Break | ||
1:30 - 3:00pm EDT | Group Project Meetings | 10th Floor | |
3:00 - 3:30pm EDT | Coffee/ Tea Break | 10th Floor | |
3:30 - 5:00pm EDT | Group Project Working Time | 10th Floor |
Monday, June 17, 2019
Time | Event | Location | Materials |
---|---|---|---|
9:00 - 12:00pm EDT | Group Project Meetings | 10th Floor Collaborative Space | |
3:00 - 3:30pm EDT | Coffee/ Tea Break | 10th Floor |
Tuesday, June 18, 2019
Time | Event | Location | Materials |
---|---|---|---|
9:30 - 10:30am EDT | Algebraic Geometry 101 - Max Weinreich, Brown University | 10th Floor Collaborative Space | |
3:00 - 3:30pm EDT | Coffee/ Tea Break | 10th Floor |
Wednesday, June 19, 2019
Thursday, June 20, 2019
Time | Event | Location | Materials |
---|---|---|---|
9:00 - 12:00pm EDT | Sage Development | 10th Floor Collaborative Space | |
3:00 - 3:30pm EDT | Coffee/ Tea Break | 10th Floor |
Friday, June 21, 2019
Time | Event | Location | Materials |
---|---|---|---|
9:30 - 11:00am EDT | Group Presentations | 10th Floor Collaborative Space | |
3:00 - 3:30pm EDT | Coffee/ Tea Break | 10th Floor |
Monday, June 24, 2019
Time | Event | Location | Materials |
---|---|---|---|
9:00 - 12:00pm EDT | Group Project Meetings | 10th Floor Collaborative Space | |
3:00 - 3:30pm EDT | Coffee/ Tea Break | 10th Floor |
Tuesday, June 25, 2019
Time | Event | Location | Materials |
---|---|---|---|
3:00 - 3:30pm EDT | Coffee/ Tea Break | 10th Floor |
Wednesday, June 26, 2019
Time | Event | Location | Materials |
---|---|---|---|
9:30 - 10:30am EDT | An introduction to height functions - Wayne Peng, University of Rochester | 10th Floor Collaborate Space | |
3:00 - 3:30pm EDT | Coffee/ Tea Break | 10th Floor |
Thursday, June 27, 2019
Time | Event | Location | Materials |
---|---|---|---|
3:00 - 3:30pm EDT | Coffee/ Tea Break | 10th Floor |
Friday, June 28, 2019
Monday, July 1, 2019
Time | Event | Location | Materials |
---|---|---|---|
9:00 - 12:00pm EDT | Group Project Meetings | 11th Floor Lecture Hall | |
3:00 - 3:30pm EDT | Coffee/ Tea Break | 10th Floor |
Tuesday, July 2, 2019
Time | Event | Location | Materials |
---|---|---|---|
10:30 - 11:30am EDT | Building telescopes for mathematicians. - Andrew Sutherland, MIT | 11th Floor Lecture Hall | |
3:00 - 3:30pm EDT | Coffee/ Tea Break | 10th Floor |
Wednesday, July 3, 2019
Friday, July 5, 2019
Time | Event | Location | Materials |
---|---|---|---|
3:00 - 3:30pm EDT | Coffee/ Tea Break | 10th Floor |
Monday, July 8, 2019
Time | Event | Location | Materials |
---|---|---|---|
3:00 - 3:30pm EDT | Coffee/ Tea Break | 10th Floor |
Tuesday, July 9, 2019
Wednesday, July 10, 2019
Time | Event | Location | Materials |
---|---|---|---|
9:30 - 10:30am EDT | Rachel Locke, National Security Agency | 11th Floor Lecture Hall | |
2:00 - 3:00pm EDT | Ethics II | 11th Floor Lecture Hall | |
3:00 - 3:30pm EDT | Coffee/ Tea Break | 10th Floor |
Thursday, July 11, 2019
Time | Event | Location | Materials |
---|---|---|---|
3:00 - 3:30pm EDT | Coffee/ Tea Break | 10th Floor |
Friday, July 12, 2019
Time | Event | Location | Materials |
---|---|---|---|
3:00 - 3:30pm EDT | Coffee/ Tea Break | 10th Floor |
Monday, July 15, 2019
Time | Event | Location | Materials |
---|---|---|---|
3:00 - 3:30pm EDT | Coffee/ Tea Break | 10th Floor |
Tuesday, July 16, 2019
Wednesday, July 17, 2019
Time | Event | Location | Materials |
---|---|---|---|
3:00 - 3:30pm EDT | Coffee/ Tea Break | 10th Floor |
Thursday, July 18, 2019
Time | Event | Location | Materials |
---|---|---|---|
3:00 - 3:30pm EDT | Coffee/ Tea Break | 10th Floor |
Friday, July 19, 2019
Time | Event | Location | Materials |
---|---|---|---|
3:00 - 3:30pm EDT | Coffee/ Tea Break | 10th Floor |
Monday, July 22, 2019
Time | Event | Location | Materials |
---|---|---|---|
9:30 - 10:30am EDT | Graduate Student Panel | 10th Floor Collaborative Space | |
3:00 - 3:30pm EDT | Coffee/ Tea Break | 10th Floor |
Wednesday, July 24, 2019
Time | Event | Location | Materials |
---|---|---|---|
3:00 - 3:30pm EDT | Coffee/ Tea Break | 10th Floor |
Thursday, July 25, 2019
Time | Event | Location | Materials |
---|---|---|---|
1:00 - 3:00pm EDT | Off Site Visit to AMS | 201 Charles St, Providence, RI 02904, USA | |
3:00 - 3:30pm EDT | Coffee/ Tea Break | 10th Floor |
Friday, July 26, 2019
Time | Event | Location | Materials |
---|---|---|---|
1:30 - 1:45pm EDT | Group Photo | 10th Floor at the stairwell | |
3:00 - 3:30pm EDT | Coffee/ Tea Break | 10th Floor |
Monday, July 29, 2019
Time | Event | Location | Materials |
---|---|---|---|
3:00 - 3:30pm EDT | Coffee/ Tea Break | 10th Floor | |
7:00 - 10:00pm EDT | Summer@ICERM Game Night | 10th Floor Collaborative |
Tuesday, July 30, 2019
Time | Event | Location | Materials |
---|---|---|---|
3:00 - 3:30pm EDT | Coffee/ Tea Break | 10th Floor |
Wednesday, July 31, 2019
Time | Event | Location | Materials |
---|---|---|---|
3:00 - 3:30pm EDT | Coffee/ Tea Break | 10th Floor |
Thursday, August 1, 2019
Time | Event | Location | Materials |
---|---|---|---|
3:00 - 3:30pm EDT | Cake & Coffee/ Tea Break | 10th Floor |
Friday, August 2, 2019
Time | Event | Location | Materials |
---|---|---|---|
8:45 - 9:20am EDT | Summer@ICERM Presentations | Digital Scholarship Lab, 1st floor of the Rockefeller Library | |
9:20 - 9:50am EDT | Periodic points for Lattès maps over finite fields - Mentors: Bianca Thompson, Trevor Hyde Students: Jasmine Camero, Fiona Lu, Eric Zhu | Digital Scholarship Lab, 1st floor of the Rockefeller Library | |
10:00 - 10:30am EDT | Dynamical statistics over finite fields break - Mentors: Adam Towsley, Wayne Peng Students: Anna Chlopecki, Juliano Levier-Gomes, Alex Shearer | Digital Scholarship Lab, 1st floor of the Rockefeller Library | |
10:30 - 10:50am EDT | Break | ||
10:50 - 11:20am EDT | Classification of rational preperiodic structures - Mentors: John Doyle, Bianca Thompson, Grayson Jorgenson Students: Meghan Grip, Emily Rachfal, Olivia Schwager, Matt Torrence | Digital Scholarship Lab, 1st floor of the Rockefeller Library | |
11:30 - 12:00pm EDT | Automorphism groups of rational maps char 0 - Mentors: Ben Hutz, Grayson Jorgenson, Max Weinreich Students: Julia Cai, Brandon Gontmacher, Leo Mayer, Srinjoy Srimani, Simon Xu | Digital Scholarship Lab, 1st floor of the Rockefeller Library | |
12:00 - 1:30pm EDT | Break for Lunch | ||
1:30 - 2:00pm EDT | Automorphism groups of rational maps char p - Mentors: Ben Hutz, Grayson Jorgenson, Max Weinreich Students: Julia Cai, Brandon Gontmacher, Leo Mayer, Srinjoy Srimani, Simon Xu | Digital Scholarship Lab, 1st floor of the Rockefeller Library | |
2:10 - 2:40pm EDT | Post-critically finite rational maps - Mentors: Ben Hutz, Adam Towsley, Wayne Peng Students: Joey Lupo, Alex Galarraga, Heidi Benham | Digital Scholarship Lab, 1st floor of the Rockefeller Library | |
2:50 - 3:20pm EDT | Finite orbit sets for several polynomial maps - Mentors: Trevor Hyde, John Doyle, Max Weinreich Students: Talia Blum, Colby Kelln, Henry Talbott | Digital Scholarship Lab, 1st floor of the Rockefeller Library | |
3:30 - 4:00pm EDT | Coffee/ 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
- Posters Presented at JMM 2020 in Denver, CO
-
- Unlikely Intersections and Portraits of Dynamical Semigroups (Colby Kelln, Talia Blum, and Henry Talbott)*
- Periodic Points for Latts maps over Finite Fields (Jasmine Camero, Fiona Lu, and Eric Zhu)**
- Characteristic 0 Automorphism Loci of the Moduli Space of Rational Functions (Brandon Gontmacher, Srinjoy Srimani, and Simon Xu)**
- Permutation Polynomials (Anna Chlopecki)**
- Rational Preperiodic Points of zd + c (Olivia Schwager, Emily Rachfal, and Matt Torrence)
- Explicit Description of Degree 3 Polynomials and an Algebraic Approach to a Special Case of Thurston Rigidity (Alexander Galarraga and Heidi Benham)
**Recipient of an MAA "Honorable Mention" at JMM 2020 - Papers
-
- B. Gontmacher, B. Hutz, G. Jorgenson, S. Srimani, and S. Xu. Automorphism loci for degree 3 and degree 4 endomorphisms of the projective line. arXiv:2007.15483
- J. Cai, B. Hutz, L. Mayer, and M. Weinreich. Automorphism Groups of Endomorphisms of ℙ1(𝔽¯p). arxiv:2003.12113
- H. Benham, A. Galarraga, B. Hutz, J. Lupo, W. Peng, and A. Towsley. Two New Normal Forms for Polynomial Endomorphisms of the Projective Line with Applications to Postcritically Finite Maps. arxiv:2001.06164
- A. Chlopecki, J. Levier-Gomes, W. Peng, A. Shearer, A. Towsley. Permutation polynomials: iteration of shift and inversion maps over finite fields. arxiv:1910.12928
- T. Blum, J. R. Doyle, T. Hyde, C. Kelln, H. Talbott, and M. Weinreich. Dynamical moduli spaces and polynomial endomorphisms of configurations. arxiv: 2108.10777
- J. R. Doyle, M. Grip, E. Rachfal, O. Schwager, and M. Torrence. Rational preperiodic graphs for polynomials of the form z^d + c. Awaiting submission.
- T. Blum, J. R. Doyle, T. Hyde, C. Kelln, H. Talbott, and M. Weinreich. Portrait spaces for dynamical semigroups. Awaiting submission.