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.
    Summer@ICERM 2019: Computational Arithmetic Dynamics

    Summer 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.

    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 the MAA "Outstanding Poster Award" at JMM 2020

    **Recipient of an MAA "Honorable Mention" at JMM 2020

    Publications

    • Julia Cai, Benjamin Hutz, Leo Mayer, Max Weinreich, Automorphism Groups of Endomorphisms of $\mathbb{P}^1 (\bar{\mathbb{F}}_p)$, cai2022automorphism:2003.12113, 2022.
    • Brandon Gontmacher, Benjamin Hutz, Grayson Jorgenson, Srinjoy Srimani, Simon Xu, Automorphism loci for degree 3 and degree 4 endomorphisms of the projective line, gontmacher2021automorphism:2007.15483, 2021.
    • Heidi Benham, Alexander Galarraga, Benjamin Hutz, Joey Lupo, Wayne Peng, Adam Towsley, New Normal Forms For Degree Three Polynomials and Rational Functions, benham2022new:2001.06164, 2022.
    • Anna Chlopecki, Juliano Levier-Gomes, Wayne Peng, Alex Shearer, Adam Towsley, Permutation polynomials: iteration of shift and inversion maps over finite fields, chlopecki2021permutation:1910.12928, 2021.
    • Talia Blum, John R. Doyle, Trevor Hyde, Colby Kelln, Henry Talbott, Max Weinreich, Dynamical moduli spaces and polynomial endomorphisms of configurations, blum2021dynamical:2108.10777, 2021.
    • Heidi Benham, Alexander Galarraga, Benjamin Hutz, Joey Lupo, Wayne Peng, Adam Towsley, Integrality and Thurston Rigidity for Bicritical PCF Polynomials, benham2022integrality:2212.02558, 2022.