Organizing Committee
- Susanna Fishel
Arizona State University - Pamela E. Harris
Williams College - Gordon Rojas Kirby
Arizona State University
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.

Program Details
- 2022 Proposed Research Topics
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- Invariant and Prime Parking Sequences
- Statistics on parking functions and their generalizations
- Connection to posets and graph theory, algebraic structures, and discrete geometry
- Important Notes
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- 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*
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- $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
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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
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Cara Bennett
Georgia Institute of Technology
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Steven Bradt
Arizona State University
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Josephine Brooks
University of Toronto
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Lucas Chaves Meyles
University of California, Los Angeles
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Douglas Chen
Johns Hopkins University
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Michael Dougherty
Swarthmore College
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Jennifer Elder
Rockhurst University
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Susanna Fishel
Arizona State University
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Pamela E. Harris
Williams College
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Max Hlavacek
UC berkeley
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Richter Jordaan
MIT
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Zoe Markman
Swarthmore College
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Lucy Martinez
Rutgers University
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Juan Carlos Martinez Mori
Cornell University
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Ava Mock
Wellesley College
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Alejandro Morales
University of Massachusetts, Amherst
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Eric Pabón-Cancel
University of Puerto Rico, Mayagüez Campus
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Eva Reutercrona
Pacific Lutheran University
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Gordon Rojas Kirby
Arizona State University
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Sophie Rubenfeld
Hamilton College
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Gabriel Sargent
University of Notre Dame
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Sam Sehayek
University of California, Santa Barbara
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Ethan Spingarn
Amherst College
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Izah Tahir
Georgia Institute of Technology
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Bianca Teves
Haverford College
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Steve Trettel
Stanford University
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Robin Truax
Stanford University
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Amanda Verga
Trinity College
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Andres Vindas Melendez
University of California, Berkeley
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Susan Wang
Mount Holyoke College
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Juliet Whidden
Vassar College
Summer Schedule
Monday, June 13, 2022
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8:00 - 8:45 am EDTBreakfast -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.
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8:45 - 9:15 am EDTCheck In11th Floor Collaborative Space
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9:15 - 9:30 am EDTWelcome10th Floor Collaborative Space (Office 1015 Side)
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10:00 am - 12:00 pm EDTScavenger HuntScavenger Hunt - Brown University, Providence, RI 02912, USA
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12:00 - 1:30 pm EDTWelcome LunchWorking Lunch - 10th Floor Collaborative Space (Office 1015 Side)
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2:00 - 3:00 pm EDTGoals of Summer+Community agreement10th Floor Collaborative Space
- Susanna Fishel, Arizona State University
- Gordon Rojas Kirby, Arizona State University
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3:00 - 4:30 pm EDTPython and Sage introTutorial - 10th Floor Collaborative Space
- Juan Carlos Martinez Mori, Cornell University
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3:00 - 3:30 pm EDTCoffee Break11th Floor Collaborative Space
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4:30 - 6:00 pm EDTReception11th Floor Collaborative Space
Tuesday, June 14, 2022
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10:00 - 11:00 am EDTLecture- posets,perms10th Floor Collaborative Space
- Jennifer Elder, Rockhurst University
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11:00 am - 12:00 pm EDTProblem Session10th Floor Collaborative Space
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12:00 - 2:00 pm EDTLunch/Free Time
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2:00 - 3:00 pm EDTLecture- posets,perms10th Floor Collaborative Space
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3:00 - 3:30 pm EDTCoffee Break11th Floor Collaborative Space
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3:00 - 4:30 pm EDTProblem Session10th Floor Collaborative Space
Wednesday, June 15, 2022
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10:00 - 11:00 am EDTLecture-Catalan, parking function10th Floor Collaborative Space
- Steven Bradt, Arizona State University
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11:00 am - 12:00 pm EDTProblem Session10th Floor Collaborative Space
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12:00 - 2:00 pm EDTLunch/Free Time
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2:00 - 3:00 pm EDTLecture-Catalan, parking function10th Floor Collaborative Space
- Steven Bradt, Arizona State University
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3:00 - 3:30 pm EDTCoffee Break11th Floor Collaborative Space
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3:00 - 4:30 pm EDTProblem Session10th Floor Collaborative Space
Thursday, June 16, 2022
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10:00 - 11:00 am EDTIntro to graph theory10th Floor Collaborative Space
- Max Hlavacek, UC berkeley
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11:00 am - 12:00 pm EDTProblem Session10th Floor Collaborative Space
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12:00 - 2:00 pm EDTLunch/Free Time
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2:00 - 3:00 pm EDTIntro to chip firing10th Floor Collaborative Space
- Lucy Martinez, Rutgers University
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3:00 - 3:30 pm EDTCoffee Break11th Floor Collaborative Space
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3:00 - 4:30 pm EDTProblem Session10th Floor Collaborative Space
Friday, June 17, 2022
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10:00 - 11:00 am EDTHyperplanes10th Floor Collaborative Space
- Sam Sehayek, University of California, Santa Barbara
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11:00 am - 12:00 pm EDTProblem Session10th Floor Collaborative Space
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12:00 - 2:00 pm EDTLunch/Free Time
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2:00 - 3:00 pm EDTHyperplanes10th Floor Collaborative Space
- Sam Sehayek, University of California, Santa Barbara
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3:00 - 3:30 pm EDTCoffee Break11th Floor Collaborative Space
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3:00 - 4:30 pm EDTProblem Session10th Floor Collaborative Space
Monday, June 20, 2022
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3:00 - 3:30 pm EDTCoffee Break11th Floor Collaborative Space
Tuesday, June 21, 2022
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3:00 - 3:30 pm EDTCoffee Break11th Floor Collaborative Space
Wednesday, June 22, 2022
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3:00 - 3:30 pm EDTCoffee Break11th Floor Collaborative Space
Thursday, June 23, 2022
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3:00 - 3:30 pm EDTCoffee Break11th Floor Collaborative Space
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6:00 - 8:00 pm EDTGame Night- 11th Floor Collaborative Space
Friday, June 24, 2022
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2:00 - 3:00 pm EDTColloquium - Geometric combinatorics: an intro to Ehrhart theory11th 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.
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3:00 - 3:30 pm EDTCoffee Break11th Floor Collaborative Space
Monday, June 27, 2022
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3:00 - 3:30 pm EDTCoffee Break11th Floor Collaborative Space
Tuesday, June 28, 2022
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3:00 - 3:30 pm EDTCoffee Break11th Floor Collaborative Space
Wednesday, June 29, 2022
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3:00 - 3:30 pm EDTCoffee Break11th Floor Collaborative Space
Thursday, June 30, 2022
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3:00 - 3:30 pm EDTCoffee Break11th Floor Collaborative Space
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6:00 - 8:00 pm EDTGame Night- 10th Floor Collaborative Space
Friday, July 1, 2022
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2:00 - 2:45 pm EDTPattern avoidance in Parking FunctionsVirtual
- 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.)
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3:00 - 3:30 pm EDTCoffee Break11th Floor Collaborative Space
Monday, July 4, 2022
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3:00 - 3:30 pm EDTCoffee Break11th Floor Collaborative Space
Tuesday, July 5, 2022
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3:00 - 3:30 pm EDTCoffee Break11th Floor Collaborative Space
Wednesday, July 6, 2022
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4:00 - 6:00 pm EDTIce Cream SocialCoffee Break - 11th Floor Collaborative Space
Thursday, July 7, 2022
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3:00 - 3:30 pm EDTCoffee Break11th Floor Collaborative Space
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6:00 - 8:00 pm EDTGame Night- 11th Floor Collaborative Space
Friday, July 8, 2022
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3:00 - 3:45 pm EDTColloquium - Geometry and Poincare Conjecture11th Floor Lecture Hall
- Steve Trettel, Stanford University
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3:00 - 3:30 pm EDTCoffee Break11th Floor Collaborative Space
Monday, July 11, 2022
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3:00 - 3:30 pm EDTCoffee Break11th Floor Collaborative Space
Tuesday, July 12, 2022
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3:00 - 3:30 pm EDTCoffee Break11th Floor Collaborative Space
Wednesday, July 13, 2022
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3:00 - 3:30 pm EDTCoffee Break11th Floor Collaborative Space
Thursday, July 14, 2022
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3:00 - 3:30 pm EDTCoffee Break11th Floor Collaborative Space
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6:00 - 8:00 pm EDTGame Night- 11th Floor Collaborative Space
Friday, July 15, 2022
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3:00 - 3:30 pm EDTCoffee Break11th Floor Collaborative Space
Monday, July 18, 2022
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3:00 - 3:30 pm EDTCoffee Break11th Floor Collaborative Space
Tuesday, July 19, 2022
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3:00 - 3:30 pm EDTCoffee Break11th Floor Collaborative Space
Wednesday, July 20, 2022
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3:00 - 3:30 pm EDTCoffee Break11th Floor Collaborative Space
Thursday, July 21, 2022
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3:00 - 3:30 pm EDTCoffee Break11th Floor Collaborative Space
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6:00 - 8:00 pm EDTGame Night- 11th Floor Collaborative Space
Friday, July 22, 2022
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3:00 - 3:30 pm EDTCoffee Break11th Floor Collaborative Space
Monday, July 25, 2022
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3:00 - 3:30 pm EDTCoffee Break11th Floor Collaborative Space
Tuesday, July 26, 2022
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3:00 - 3:30 pm EDTCoffee Break11th Floor Collaborative Space
Wednesday, July 27, 2022
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3:00 - 3:30 pm EDTCoffee Break11th Floor Collaborative Space
Thursday, July 28, 2022
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3:00 - 3:30 pm EDTCoffee Break11th Floor Collaborative Space
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6:00 - 8:00 pm EDTGame Night- 11th Floor Collaborative Space
Friday, July 29, 2022
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3:00 - 3:30 pm EDTCoffee Break11th Floor Collaborative Space
Monday, August 1, 2022
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3:00 - 3:30 pm EDTCoffee Break11th Floor Collaborative Space
Tuesday, August 2, 2022
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3:00 - 3:30 pm EDTCoffee Break11th Floor Collaborative Space
Wednesday, August 3, 2022
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3:00 - 3:30 pm EDTCoffee Break11th Floor Collaborative Space
Thursday, August 4, 2022
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3:00 - 3:30 pm EDTCoffee Break11th Floor Collaborative Space
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6:00 - 8:00 pm EDTGame Night- 11th Floor Collaborative Space
Friday, August 5, 2022
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3:00 - 3:30 pm EDTCoffee Break11th 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 .
ICERM local time in Providence, RI is Eastern Daylight Time (UTC-4). Would you like to switch back to ICERM time or choose a different custom timezone?