Organizing Committee
Abstract

The Summer@ICERM faculty advisers will present a variety of research projects on the combinatorics of parking functions. This overarching theme will allow participants to study and analyze parking functions by leveraging computational techniques and theory. Faculty will also guide the development of open-source computational tools for analyzing parking functions and their statistics, with time devoted to creating a database of parking functions and their generalizations.

Throughout the eight-week program, 18-22 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.

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Program Details

2022 Proposed Research Topics
  • Invariant and Prime Parking Sequences
  • Statistics on parking functions and their generalizations
  • Connection to posets and graph theory, algebraic structures, and discrete geometry
Detailed Project Descriptions (PDF)
Important Notes
  • Applicants must be matriculating undergraduate students at the time of the start of Summer@ICERM 2022.
  • Funding is available for 2-3 students who are not US citizens or permanent residents.
Funding Includes*
  • $3,800 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, 2022 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
  • Cara Bennett
    Georgia Institute of Technology
  • Steven Bradt
    Arizona State University
  • Josephine Brooks
    University of Toronto
  • Lucas Chaves Meyles
    University of California, Los Angeles
  • Douglas Chen
    Johns Hopkins University
  • Michael Dougherty
    Swarthmore College
  • Jennifer Elder
    Rockhurst University
  • Susanna Fishel
    Arizona State University
  • Pamela E. Harris
    Williams College
  • Max Hlavacek
    UC berkeley
  • Richter Jordaan
    MIT
  • Zoe Markman
    Swarthmore College
  • Lucy Martinez
    Rutgers University
  • Juan Carlos Martinez Mori
    Cornell University
  • Ava Mock
    Wellesley College
  • Alejandro Morales
    University of Massachusetts, Amherst
  • Eric Pabón-Cancel
    University of Puerto Rico, Mayagüez Campus
  • Eva Reutercrona
    Pacific Lutheran University
  • Gordon Rojas Kirby
    Arizona State University
  • Sophie Rubenfeld
    Hamilton College
  • Gabriel Sargent
    University of Notre Dame
  • Sam Sehayek
    University of California, Santa Barbara
  • Ethan Spingarn
    Amherst College
  • Izah Tahir
    Georgia Institute of Technology
  • Bianca Teves
    Haverford College
  • Steve Trettel
    Stanford University
  • Robin Truax
    Stanford University
  • Amanda Verga
    Trinity College
  • Andres Vindas Melendez
    University of California, Berkeley
  • Susan Wang
    Mount Holyoke College
  • Juliet Whidden
    Vassar College

Summer Schedule

Monday, June 13, 2022
  • 8:00 - 8:45 am EDT
    Breakfast -
    Breakfast - 10th Floor Collaborative Space
    Abstract
    For Undergraduate Researchers - come to the 11th floor of 121 South Main Street to check in prior to breakfast on the 10th floor.
  • 8:45 - 9:15 am EDT
    Check In
    11th Floor Collaborative Space
  • 9:15 - 9:30 am EDT
    Welcome
    10th Floor Collaborative Space (Office 1015 Side)
  • 10:00 am - 12:00 pm EDT
    Scavenger Hunt
    Scavenger Hunt - Brown University, Providence, RI 02912, USA
  • 12:00 - 1:30 pm EDT
    Welcome Lunch
    Working Lunch - 10th Floor Collaborative Space (Office 1015 Side)
  • 2:00 - 3:00 pm EDT
    Goals of Summer+Community agreement
    10th Floor Collaborative Space
    • Susanna Fishel, Arizona State University
    • Gordon Rojas Kirby, Arizona State University
  • 3:00 - 4:30 pm EDT
    Python and Sage intro
    Tutorial - 10th Floor Collaborative Space
    • Juan Carlos Martinez Mori, Cornell University
  • 3:00 - 3:30 pm EDT
    Coffee Break
    11th Floor Collaborative Space
  • 4:30 - 6:00 pm EDT
    Reception
    11th Floor Collaborative Space
Tuesday, June 14, 2022
  • 10:00 - 11:00 am EDT
    Lecture- posets,perms
    10th Floor Collaborative Space
    • Jennifer Elder, Rockhurst University
  • 11:00 am - 12:00 pm EDT
    Problem Session
    10th Floor Collaborative Space
  • 12:00 - 2:00 pm EDT
    Lunch/Free Time
  • 2:00 - 3:00 pm EDT
    Lecture- posets,perms
    10th Floor Collaborative Space
  • 3:00 - 3:30 pm EDT
    Coffee Break
    11th Floor Collaborative Space
  • 3:00 - 4:30 pm EDT
    Problem Session
    10th Floor Collaborative Space
Wednesday, June 15, 2022
  • 10:00 - 11:00 am EDT
    Lecture-Catalan, parking function
    10th Floor Collaborative Space
    • Steven Bradt, Arizona State University
  • 11:00 am - 12:00 pm EDT
    Problem Session
    10th Floor Collaborative Space
  • 12:00 - 2:00 pm EDT
    Lunch/Free Time
  • 2:00 - 3:00 pm EDT
    Lecture-Catalan, parking function
    10th Floor Collaborative Space
    • Steven Bradt, Arizona State University
  • 3:00 - 3:30 pm EDT
    Coffee Break
    11th Floor Collaborative Space
  • 3:00 - 4:30 pm EDT
    Problem Session
    10th Floor Collaborative Space
Thursday, June 16, 2022
  • 10:00 - 11:00 am EDT
    Intro to graph theory
    10th Floor Collaborative Space
    • Max Hlavacek, UC berkeley
  • 11:00 am - 12:00 pm EDT
    Problem Session
    10th Floor Collaborative Space
  • 12:00 - 2:00 pm EDT
    Lunch/Free Time
  • 2:00 - 3:00 pm EDT
    Intro to chip firing
    10th Floor Collaborative Space
    • Lucy Martinez, Rutgers University
  • 3:00 - 3:30 pm EDT
    Coffee Break
    11th Floor Collaborative Space
  • 3:00 - 4:30 pm EDT
    Problem Session
    10th Floor Collaborative Space
Friday, June 17, 2022
  • 10:00 - 11:00 am EDT
    Hyperplanes
    10th Floor Collaborative Space
    • Sam Sehayek, University of California, Santa Barbara
  • 11:00 am - 12:00 pm EDT
    Problem Session
    10th Floor Collaborative Space
  • 12:00 - 2:00 pm EDT
    Lunch/Free Time
  • 2:00 - 3:00 pm EDT
    Hyperplanes
    10th Floor Collaborative Space
    • Sam Sehayek, University of California, Santa Barbara
  • 3:00 - 3:30 pm EDT
    Coffee Break
    11th Floor Collaborative Space
  • 3:00 - 4:30 pm EDT
    Problem Session
    10th Floor Collaborative Space
Monday, June 20, 2022
  • 3:00 - 3:30 pm EDT
    Coffee Break
    11th Floor Collaborative Space
Tuesday, June 21, 2022
  • 3:00 - 3:30 pm EDT
    Coffee Break
    11th Floor Collaborative Space
Wednesday, June 22, 2022
  • 3:00 - 3:30 pm EDT
    Coffee Break
    11th Floor Collaborative Space
Thursday, June 23, 2022
  • 3:00 - 3:30 pm EDT
    Coffee Break
    11th Floor Collaborative Space
  • 6:00 - 8:00 pm EDT
    Game Night
    - 11th Floor Collaborative Space
Friday, June 24, 2022
  • 2:00 - 3:00 pm EDT
    Colloquium - Geometric combinatorics: an intro to Ehrhart theory
    11th Floor Lecture Hall
    • Andres Vindas Melendez, University of California, Berkeley
    Abstract
    Geometric combinatorics is an area of mathematics concerned with counting properties of geometric objects described by a finite set of building blocks. Polytopes are geometric objects that can be formed by taking the convex hull of finitely many points. When extracting combinatorial information from geometric objects, a natural approach is to subdivide the combinatorial object into smaller, more accessible pieces. In the case of polytopes a natural approach is to triangulate the polytope into simplices or parallelepipeds. The Ehrhart polynomial of a lattice polytope P encodes the number of integer lattice points in dilates of P, and the h*-polynomial of P is the numerator of the accompanying generating function. In this talk I will present background on polytopes, lattice-point enumeration, and share my favorite family of polytopes. I will conclude the talk with some open problems.
  • 3:00 - 3:30 pm EDT
    Coffee Break
    11th Floor Collaborative Space
Monday, June 27, 2022
  • 3:00 - 3:30 pm EDT
    Coffee Break
    11th Floor Collaborative Space
Tuesday, June 28, 2022
  • 3:00 - 3:30 pm EDT
    Coffee Break
    11th Floor Collaborative Space
Wednesday, June 29, 2022
  • 3:00 - 3:30 pm EDT
    Coffee Break
    11th Floor Collaborative Space
Thursday, June 30, 2022
  • 3:00 - 3:30 pm EDT
    Coffee Break
    11th Floor Collaborative Space
  • 6:00 - 8:00 pm EDT
    Game Night
    - 10th Floor Collaborative Space
Friday, July 1, 2022
  • 2:00 - 2:45 pm EDT
    Pattern avoidance in Parking Functions
    Virtual
    • Virtual Speaker
    • Ayo Adeniran, Colby College
    Abstract
    Parking functions have been well-studied in combinatorics. We extend the classical definition of patterns in permutations to parking functions. In particular, we study parking functions that avoid permutations of length 3. A number of well-known combinatorial sequences arise in our analysis, and this talk will highlight several enumeration results and conjectures. This project is joint work with Lara Pudwell(Valparaiso U.)
  • 3:00 - 3:30 pm EDT
    Coffee Break
    11th Floor Collaborative Space
Monday, July 4, 2022
  • 3:00 - 3:30 pm EDT
    Coffee Break
    11th Floor Collaborative Space
Tuesday, July 5, 2022
  • 3:00 - 3:30 pm EDT
    Coffee Break
    11th Floor Collaborative Space
Wednesday, July 6, 2022
  • 4:00 - 6:00 pm EDT
    Ice Cream Social
    Coffee Break - 11th Floor Collaborative Space
Thursday, July 7, 2022
  • 3:00 - 3:30 pm EDT
    Coffee Break
    11th Floor Collaborative Space
  • 6:00 - 8:00 pm EDT
    Game Night
    - 11th Floor Collaborative Space
Friday, July 8, 2022
  • 3:00 - 3:45 pm EDT
    Colloquium - Geometry and Poincare Conjecture
    11th Floor Lecture Hall
    • Steve Trettel, Stanford University
  • 3:00 - 3:30 pm EDT
    Coffee Break
    11th Floor Collaborative Space
Monday, July 11, 2022
  • 3:00 - 3:30 pm EDT
    Coffee Break
    11th Floor Collaborative Space
Tuesday, July 12, 2022
  • 3:00 - 3:30 pm EDT
    Coffee Break
    11th Floor Collaborative Space
Wednesday, July 13, 2022
  • 3:00 - 3:30 pm EDT
    Coffee Break
    11th Floor Collaborative Space
Thursday, July 14, 2022
  • 3:00 - 3:30 pm EDT
    Coffee Break
    11th Floor Collaborative Space
  • 6:00 - 8:00 pm EDT
    Game Night
    - 11th Floor Collaborative Space
Friday, July 15, 2022
  • 3:00 - 3:30 pm EDT
    Coffee Break
    11th Floor Collaborative Space
Monday, July 18, 2022
  • 3:00 - 3:30 pm EDT
    Coffee Break
    11th Floor Collaborative Space
Tuesday, July 19, 2022
  • 3:00 - 3:30 pm EDT
    Coffee Break
    11th Floor Collaborative Space
Wednesday, July 20, 2022
  • 3:00 - 3:30 pm EDT
    Coffee Break
    11th Floor Collaborative Space
Thursday, July 21, 2022
  • 3:00 - 3:30 pm EDT
    Coffee Break
    11th Floor Collaborative Space
  • 6:00 - 8:00 pm EDT
    Game Night
    - 11th Floor Collaborative Space
Friday, July 22, 2022
  • 3:00 - 3:30 pm EDT
    Coffee Break
    11th Floor Collaborative Space
Monday, July 25, 2022
  • 3:00 - 3:30 pm EDT
    Coffee Break
    11th Floor Collaborative Space
Tuesday, July 26, 2022
  • 3:00 - 3:30 pm EDT
    Coffee Break
    11th Floor Collaborative Space
Wednesday, July 27, 2022
  • 3:00 - 3:30 pm EDT
    Coffee Break
    11th Floor Collaborative Space
Thursday, July 28, 2022
  • 3:00 - 3:30 pm EDT
    Coffee Break
    11th Floor Collaborative Space
  • 6:00 - 8:00 pm EDT
    Game Night
    - 11th Floor Collaborative Space
Friday, July 29, 2022
  • 3:00 - 3:30 pm EDT
    Coffee Break
    11th Floor Collaborative Space
Monday, August 1, 2022
  • 3:00 - 3:30 pm EDT
    Coffee Break
    11th Floor Collaborative Space
Tuesday, August 2, 2022
  • 3:00 - 3:30 pm EDT
    Coffee Break
    11th Floor Collaborative Space
Wednesday, August 3, 2022
  • 3:00 - 3:30 pm EDT
    Coffee Break
    11th Floor Collaborative Space
Thursday, August 4, 2022
  • 3:00 - 3:30 pm EDT
    Coffee Break
    11th Floor Collaborative Space
  • 6:00 - 8:00 pm EDT
    Game Night
    - 11th Floor Collaborative Space
Friday, August 5, 2022
  • 3:00 - 3:30 pm EDT
    Coffee Break
    11th Floor Collaborative Space

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

All event times are listed in .

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 2021: Computational Polygonal Billiards
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