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 $3,500 stipend*.

The 2018 Summer@ICERM program at Brown University is an eight-week residential program designed for a select group of 16-20 undergraduate scholars from around the world.

The faculty advisers will present a variety of research projects that are interdisciplinary and represent areas in low-dimensional topology, hyperbolic geometry, dynamics, and combinatorics. Student researchers will have the opportunity to explore theoretical problems at the intersections of these subfields, and to help design software packages for visualizing and experimenting with the building blocks of hyperbolic and affine geometry.

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, and professional development seminars, practice coding, and learn Tex. Students will learn how to collaborate mathematically, and they will work closely in their teams to write up their research into a poster and/or paper by the end of the program.

ICERM provides an excellent research environment, and the students and their faculty and TA mentors will have access to shared offices and collaborative space throughout the institute. They also will have access to ICERM’s computer facilities and specialized software. ICERM staff will provide logistical support for students and will help build community through fun activities and events.

Image credit: T. Aougab & J. Gaster

Program Details

2018 Proposed Research Project Topics
  • Curves on surfaces
  • Triangulations of 3-manifolds
  • Dynamics of Character Varieties
  • Visualization of Geometric Structures
Important Notes
  • Applicants must be matriculating undergraduate students at the time of the start of Summer@ICERM 2018.
  • Funding is available for a very small number of students who are not US citizens or permanent residents.
Funding Includes
  • $3,500 stipend
  • Dormitory housing
  • Meal plan
  • Travel support within U.S.
  • Fun events
  • Brown students who choose not to live in the dorm will waive the dorm, meal, and travel funding.
Deadlines
February 16, 2018 (for all non-Brown University students)

All non-Brown students must apply via MathPrograms.org by this date in order to receive full consideration. ICERM will begin making offers to non-Brown students between late February and early March 2018.

January 15, 2018 (for all Brown University Students)

Brown University students must apply for Summer@ICERM by emailing their interest to Professor Tarik Aougab, the I-Team faculty sponsor running this program. Up to six Brown students will be selected to participate, and Professor Aougab must submit the final list of Brown students to the UTRA selection committee by January 15, 2018. The I-Team UTRA Awards will be announced to the Brown student applicants on February 1, 2018.

Confirmed Speakers & Participants

  • Tarik Aougab
    Brown University
  • Jean-Philippe Burelle
    CNRS-IHES
  • Francisco Castaneda
    Instituto Tecnologico Autonomo de Mexico (ITAM)
  • Yassin Chandran
    University of California, Santa Barbara
  • Moira Chas
    Stony Brook University
  • Zichen Cui
    Reed College
  • Charles Daly
    University of Maryland
  • Ajeet Gary
    University of Maryland
  • Jonah Gaster
    McGill University
  • William Goldman
    University of Maryland
  • Isnayni Hadi
    California State University, Northridge
  • Paige Helms
    University of California Riverside
  • Ian Hill
    James Madison University
  • Jae Young Kim
    Brown University
  • Max Lahn
    Brown University
  • Jonghyun Lee
    Brown University
  • Miguel Lopez
    Boston University
  • Marissa Loving
    University of Illinois at Urbana- Champaign
  • Aisha Mechery
    Bryn Mawr College
  • William Menasco
    University at Buffalo
  • Simran Nayak
    Brown University
  • John Oakley
    Concordia University Texas
  • Emily Rexer
    Emory University
  • Zoe Riell
    Smith College
  • Jenny Rustad
    University of Maryland
  • Roberta Shapiro
    Rutgers University
  • Brandis Whitfield
    Brandeis Universiy
  • Yang Xiao
    Brown University
  • Alex Xu
    University of California, Santa Barbara

Summer Schedule

Monday, June 11, 2018
TimeEventLocationMaterials
8:15 - 9:00Breakfast11th Floor Collaborative Space 
9:00 - 10:00Welcome/ Meet & Greet121 S Main St, 11th Floor Lecture Hall 
10:00 - 12:00Scavenger Hunt Brown University Campus 
12:00 - 1:30Welcome Lunch  
1:30 - 2:00Human Interactions11th Floor Lecture Hall 
2:00 - 3:30Moira Chas' Experiences - Stony Brook University11th Floor Lecture Hall 
3:30 - 4:00Coffee/ Tea Break11th Floor Collaborative Space 
4:00 - 5:00Moira Chas' Experiences (Cont.)11th Floor Lecture Hall 
6:30 - 8:30Dinner Flatbread Company, 161 Cushing St, Providence, RI 02906, USA 
Tuesday, June 12, 2018
TimeEventLocationMaterials
8:15 - 9:00Breakfast11th Floor Collaborative Space 
9:00 - 10:30Surface geometry and topology- secretly covering spaces and fundamental groups - Tarik Aougab - Brown University & Jonah Gaster - University of Illinois11th Floor Lecture Hall 
10:30 - 11:00Coffee/ Tea Break11th Floor Collaborative Space 
11:00 - 12:00Surface geometry and topology- secretly covering spaces and fundamental groups (cont.) - Tarik Aougab - Brown University & Jonah Gaster - University of Illinois11th Floor Lecture Hall 
12:00 - 2:00Lunch Break - On Brown's CampusVerney Woolley 
2:00 - 3:30Mobius transformations are generated by inversions & Inversions preserve distance - Jonah Gaster - University of Illinois11th Floor Lecture Hall 
3:30 - 4:00Coffee/ Tea Break11th Floor Collaborative Space 
4:00 - 5:00Matrices + hyperbolic geometry - All Organizers11th Floor Lecture Hall 
5:30 - 7:30Crochet Lessons & Pizza - Moira Chas - Stony Brook University11th Floor Collaborative Space 
Wednesday, June 13, 2018
TimeEventLocationMaterials
8:15 - 9:00Breakfast11th Floor Collaborative Space 
9:00 - 10:30Moira Chas11th Floor Lecture Hall 
10:30 - 11:00Coffee/ Tea Break11th Floor Collaborative Space 
11:00 - 12:00Moira Chas11th Floor Lecture Hall 
12:00 - 1:30Lunch BreakICERM 
1:30 - 3:30Bill Goldman11th Floor Lecture Hall 
3:30 - 4:00Coffee/ Tea Break11th Floor Collaborative Space 
4:00 - 5:00Bill Goldman11th Floor Lecture Hall 
6:00 - 8:00Dinner Trinity Brewhouse, 186 Fountain St, Providence, RI 02903, USA 
Thursday, June 14, 2018
TimeEventLocationMaterials
9:00 - 10:30Jonah Gaster11th Floor Lecture Hall 
10:30 - 11:00Coffee/ Tea Break11th Floor Collaborative Space 
11:00 - 12:00Jonah Gaster11th Floor Lecture Hall 
12:00 - 1:30Lunch Break  
1:30 - 3:30Tarik Aougab11th Floor Lecture Hall 
3:30 - 4:00Coffee/ Tea Break11th Floor Collaborative Space 
4:00 - 5:00Tarik Aougab11th Floor Lecture Hall 
Friday, June 15, 2018
TimeEventLocationMaterials
9:00 - 10:30Group Project Discussions11th Floor Lecture Hall 
10:30 - 11:00Coffee/ Tea Break11th Floor Collaborative Space 
11:00 - 12:00Group Project Discussions11th Floor Lecture Hall 
12:00 - 1:30Lunch Break  
1:30 - 3:30Group Project Assignments11th Floor Lecture Hall 
3:30 - 4:00Coffee/ Tea Break11th Floor Collaborative Space 
4:00 - 5:00Group Project Assignments11th Floor Lecture Hall 
Monday, June 18, 2018
TimeEventLocationMaterials
10:00 - 12:00Coloring Problem for Curve and Arc Graphs - Group Meeting10th Floor Classroom 
1:30 - 3:30Symmetries of Curve Graph Variants - Group Meeting10th Floor Classroom 
1:30 - 3:30Hausdorff Dimension and Hyperbolic Pair of Pants - Group Meeting11th Floor Conference Room 
Tuesday, June 19, 2018
TimeEventLocationMaterials
10:00 - 12:00Self-intersection Number of Geodesics11th Floor Conference Room 
10:00 - 12:00Navigating the Space of SL_2(C) Characters 10th Floor Classroom 
1:30 - 3:30Square Tilings10th Floor Classroom 
1:30 - 3:30Curves Intersecting Each Other Twice11th Floor Conference Room 
Wednesday, June 20, 2018
TimeEventLocationMaterials
10:00 - 12:00Organizers Meeting 11th floor Conference Room 
1:30 - 3:30Group Activity10th Floor Collaborative Space 
Thursday, June 21, 2018
TimeEventLocationMaterials
10:00 - 12:00Hausdorff Dimension and Hyperbolic Pair of Pants10th Floor Classroom 
10:00 - 12:00Symmetries of Curve Graph Variants11th Floor Conference Room 
1:30 - 3:30Coloring Problem for Curve and Arc Graphs10th Floor Classroom 
Friday, June 22, 2018
TimeEventLocationMaterials
10:00 - 12:00Square Tilings11th Floor Conference Room 
10:00 - 12:00Curves Intersecting Each Other Twice10th Floor Classroom 
1:30 - 3:30Self-intersection Number of Geodesics11th Floor Conference Room 
1:30 - 3:30Navigating the Space of SL_2(C) Characters 10th Floor Classroom 
Tuesday, June 26, 2018
TimeEventLocationMaterials
10:00 - 12:00Self-intersection Number of Geodesics11th Floor Conference Room 
10:00 - 12:00Navigating the Space of SL_2(C) Characters 10th Floor Classroom 
1:30 - 3:30Square Tilings10th Floor Classroom 
1:30 - 3:30Curves Intersecting Each Other Twice10th floor collaborative space (near office 1001) 
3:30 - 4:00Coffee/ Tea Break11th Floor Collaborative Space 
Wednesday, June 27, 2018
TimeEventLocationMaterials
8:45 - 10:45Group Activity10th Floor Collaborative Space 
10:00 - 12:00Organizers Meeting 11th floor Conference Room 
3:30 - 4:00Coffee/ Tea Break11th Floor Collaborative Space 
4:30 - 6:00Summer Student Theoretical Physics Research Session Visit10th Floor Collaborative Space 
Thursday, June 28, 2018
TimeEventLocationMaterials
10:00 - 12:00Hausdorff Dimension and Hyperbolic Pair of Pants11th Floor Conference Room 
10:00 - 12:00Symmetries of Curve Graph Variants10th Floor Classroom 
1:30 - 3:30Coloring Problem for Curve and Arc Graphs10th Floor Classroom 
3:30 - 4:00Coffee/ Tea Break11th Floor Collaborative Space 
Friday, June 29, 2018
TimeEventLocationMaterials
10:00 - 12:00Curves Intersecting Each Other Twice10th Floor Classroom 
10:00 - 12:00Square Tilings11th Floor Conference Room 
1:30 - 3:30Navigating the Space of SL_2(C) Characters 10th Floor Classroom 
1:30 - 3:30Self-intersection Number of Geodesics11th Floor Conference Room 
3:30 - 4:00Coffee/ Tea Break11th Floor Collaborative Space 
Monday, July 2, 2018
TimeEventLocationMaterials
10:00 - 12:00Coloring Problem for Curve and Arc Graphs - Group Meeting10th Floor Classroom 
1:30 - 3:30Hausdorff Dimension and Hyperbolic Pair of Pants - Group Meeting11th Floor Conference Room 
1:30 - 3:30Symmetries of Curve Graph Variants - Group Meeting10th Floor Classroom 
3:30 - 4:00Coffee/ Tea Break11th Floor Collaborative Space 
Tuesday, July 3, 2018
TimeEventLocationMaterials
10:00 - 12:00Self-intersection Number of Geodesics11th Floor Conference Room 
10:00 - 12:00Navigating the Space of SL_2(C) Characters 10th Floor Classroom 
1:30 - 3:30Curves Intersecting Each Other Twice10th floor collaborative space (near office 1001) 
1:30 - 3:30Square Tilings10th Floor Classroom 
3:30 - 4:00Coffee/ Tea Break11th Floor Collaborative Space 
Thursday, July 5, 2018
TimeEventLocationMaterials
10:00 - 12:00Hausdorff Dimension and Hyperbolic Pair of Pants11th Floor Conference Room 
10:00 - 12:00Symmetries of Curve Graph Variants10th Floor Classroom 
1:30 - 3:30Coloring Problem for Curve and Arc Graphs10th Floor Classroom 
3:30 - 4:00Coffee/ Tea Break11th Floor Collaborative Space 
Friday, July 6, 2018
TimeEventLocationMaterials
10:00 - 12:00Square Tilings11th Floor Conference Room 
1:30 - 3:30Navigating the Space of SL_2(C) Characters 10th Floor Classroom 
1:30 - 3:30Self-intersection Number of Geodesics11th Floor Conference Room 
3:30 - 4:00Coffee/ Tea Break11th Floor Collaborative Space 
Monday, July 9, 2018
TimeEventLocationMaterials
10:00 - 12:00Coloring Problem for Curve and Arc Graphs - Group Meeting10th Floor Classroom 
1:30 - 3:30Hausdorff Dimension and Hyperbolic Pair of Pants - Group Meeting11th Floor Conference Room 
1:30 - 3:30Symmetries of Curve Graph Variants - Group Meeting10th Floor Classroom 
3:30 - 4:00Coffee/ Tea Break11th Floor Collaborative Space 
Tuesday, July 10, 2018
TimeEventLocationMaterials
10:00 - 12:00Navigating the Space of SL_2(C) Characters 10th Floor Classroom 
10:00 - 12:00Self-intersection Number of Geodesics11th Floor Conference Room 
1:30 - 3:30Curves Intersecting Each Other Twice10th floor collaborative space (near office 1001) 
1:30 - 3:30Square Tilings10th Floor Collaborative Space 
3:30 - 4:00Coffee/ Tea Break11th Floor Collaborative Space 
Wednesday, July 11, 2018
TimeEventLocationMaterials
10:00 - 12:00Organizers Meeting 11th floor Conference Room 
3:00 - 3:30Coffee/ Tea Break11th Floor Collaborative Space 
3:30 - 4:30Billiards and Translation Surfaces - Jenny Rustad, University of Maryland10th Floor Classroom
Thursday, July 12, 2018
TimeEventLocationMaterials
10:00 - 12:00Hausdorff Dimension and Hyperbolic Pair of Pants11th Floor Conference Room 
10:00 - 12:00Symmetries of Curve Graph Variants10th Floor Classroom 
1:30 - 3:30Coloring Problem for Curve and Arc Graphs10th Floor Classroom 
3:15 - 3:45Coffee/ Tea Break11th Floor Collaborative Space 
3:45 - 4:30Neutral Networks - Eli Grigsby, Boston College10th Floor Classroom 
Friday, July 13, 2018
TimeEventLocationMaterials
10:00 - 12:00Square Tilings11th Floor Conference Room 
2:00 - 3:00A basic Thurston contribution - the meaning of wall paper symmetry- orbifolds - Dennis Sulllivan, CUNY & Stony Brook University11th Floor Lecture Hall
3:30 - 4:00Coffee/ Tea Break11th Floor Collaborative Space 
Monday, July 16, 2018
TimeEventLocationMaterials
10:00 - 12:00Coloring Problem for Curve and Arc Graphs - Group Meeting10th Floor Classroom 
1:30 - 3:30Hausdorff Dimension and Hyperbolic Pair of Pants - Group Meeting11th Floor Conference Room 
1:30 - 3:30Symmetries of Curve Graph Variants - Group Meeting10th Floor Classroom 
3:30 - 4:00Coffee/ Tea Break11th Floor Collaborative Space 
Tuesday, July 17, 2018
TimeEventLocationMaterials
10:00 - 12:00Self-intersection Number of Geodesics11th Floor Conference Room 
10:00 - 12:00Navigating the Space of SL_2(C) Characters 10th Floor Classroom 
1:30 - 3:30Curves Intersecting Each Other Twice10th floor collaborative space (near office 1001) 
1:30 - 3:30Square Tilings10th Floor Collaborative Space 
3:30 - 4:00Coffee/ Tea Break11th Floor Collaborative Space 
Wednesday, July 18, 2018
TimeEventLocationMaterials
10:00 - 12:00Organizers Meeting 11th floor Conference Room 
2:30 - 3:00Coffee/ Tea Break11th Floor Collaborative Space 
3:00 - 3:45Graduate School Experience - Marissa Loving- University of Illinois at Urbana- Champaign11th Floor Lecture Hall 
4:00 - 5:00Grad School Panel - Marissa Loving - University of Illinois at Urbana- Champaign; Sunny Xiao- Brown University; Jenny Rustad- University of Maryland; and Charles Daly, University of Maryland11th Floor Lecture Hall 
6:00 - 8:00Night of Games and Knitting11th Floor Collaborative Space 
Thursday, July 19, 2018
TimeEventLocationMaterials
10:00 - 12:00Symmetries of Curve Graph Variants10th Floor Classroom 
10:00 - 12:00Hausdorff Dimension and Hyperbolic Pair of Pants11th Floor Conference Room 
1:30 - 3:30Coloring Problem for Curve and Arc Graphs10th Floor Classroom 
3:15 - 3:45Coffee/ Tea Break11th Floor Collaborative Space 
3:45 - 4:45Gauss Bonnet Theorem - Charles Daly, University of Maryland11th Floor Lecture Hall 
Friday, July 20, 2018
TimeEventLocationMaterials
10:00 - 12:00Square Tilings11th Floor Conference Room 
1:30 - 3:30Navigating the Space of SL_2(C) Characters 10th Floor Classroom 
1:30 - 3:30Self-intersection Number of Geodesics11th Floor Conference Room 
3:30 - 3:45Group Photo11th Floor Collaborative Space 
3:45 - 4:30Coffee/ Tea Break11th Floor Collaborative Space 
Monday, July 23, 2018
TimeEventLocationMaterials
10:00 - 12:00Coloring Problem for Curve and Arc Graphs - Group Meeting10th Floor Classroom 
1:30 - 3:00Symmetries of Curve Graph Variants - Group Meeting10th Floor Classroom 
1:30 - 3:00Hausdorff Dimension and Hyperbolic Pair of Pants - Group Meeting11th Floor Conference Room 
3:00 - 3:30Coffee/ Tea Break11th Floor Collaborative Space 
3:30 - 4:30Total positivity and ping-pong in projective space - Jean-Philippe Burelle - IHES10th Floor Collaborative Space 
Tuesday, July 24, 2018
TimeEventLocationMaterials
10:00 - 12:00Self-intersection Number of Geodesics11th Floor Conference Room 
10:00 - 12:00Navigating the Space of SL_2(C) Characters 10th Floor Classroom 
1:30 - 3:30Square Tilings - Bill Menasco- University of Buffalo10th Floor Collaborative Space 
1:30 - 3:30Curves Intersecting Each Other Twice10th floor collaborative space (near office 1001) 
3:30 - 4:00Coffee/ Tea Break11th Floor Collaborative Space 
Wednesday, July 25, 2018
TimeEventLocationMaterials
11:00 - 12:00TBD - Moon Duchin - Tufts University10th Floor Collaborative Space 
2:00 - 4:00Organizers Meeting 11th floor Conference Room 
3:00 - 3:30Coffee/ Tea Break11th Floor Collaborative Space 
Thursday, July 26, 2018
TimeEventLocationMaterials
10:00 - 11:00Hausdorff Dimension and Hyperbolic Pair of Pants11th Floor Conference Room 
10:00 - 11:00Symmetries of Curve Graph Variants10th Floor Classroom 
1:30 - 3:30Coloring Problem for Curve and Arc Graphs10th Floor Classroom 
3:00 - 3:30Coffee/ Tea Break11th Floor Collaborative Space 
3:30 - 4:30Brown University's Mathematics Graduate Program Info Session - Tom Goodwillie- Brown University10th Floor Collaborative Space 
Friday, July 27, 2018
TimeEventLocationMaterials
10:00 - 12:00Square Tilings10th Floor Classroom 
1:30 - 2:30Navigating the Space of SL_2(C) Characters 10th Floor Classroom 
1:30 - 2:30Self-intersection Number of Geodesics11th Floor Conference Room 
2:30 - 3:00Coffee/ Tea Break11th Floor Collaborative Space 
3:00 - 4:00Women in Math - Moira Chas - Stony Brook University10th Floor Collaborative Space 
4:00 - 5:00Diversity and Inclusion in grad school/mathematics - Marissa Loving, University of Illinois at Urbana- Champaign; Sunny Xiao, Brown University; Tarik Aougab- Brown University10th Floor Collaborate Space 
Monday, July 30, 2018
TimeEventLocationMaterials
3:15 - 3:45Coffee/ Tea Break11th Floor Collaborative Space 
3:45 - 4:15Incompressible Surfaces in 4-Punctured Sphere Bundles - Sunny Xiao, Brown University11th Floor Lecture Hall 
4:15 - 4:45Least Dilatation of Pure Surface Braids - Marissa Loving, University of Illinois at Urbana- Champaign11th Floor Lecture Hall 
Tuesday, July 31, 2018
TimeEventLocationMaterials
3:30 - 4:00Coffee/ Tea Break11th Floor Collaborative Space 
Wednesday, August 1, 2018
TimeEventLocationMaterials
10:30 - 10:45Group Photo11th Floor Collaborative Space 
11:00 - 11:45Group 7: Visualizing Cubic Moduli Spaces11th Floor Lecture Hall 
2:00 - 2:45Group 2: Hausdorff Dimension of the Limit Set of Hyperbolic Pair of Pants11th Floor Lecture Hall 
3:00 - 3:45Group 1: Length and Self-intersection Number of Geodesics in Hyperbolic Surfaces11th Floor Lecture Hall 
3:45 - 4:15Coffee/ Tea Break11th Floor Collaborative Space 
4:30 - 5:30Diversity and Inclusion in grad school/mathematics continued - Marissa Loving, University of Illinois at Urbana- Champaign; Sunny Xiao, Brown University; Tarik Aougab- Brown University10th Floor Collaborate Space 
Thursday, August 2, 2018
TimeEventLocationMaterials
10:00 - 10:45Group 3: Automorphism Group of the k-Curve Graph11th Floor Lecture Hall 
11:00 - 11:45Group 4: Minimally Intersecting Filling Pair Origamis11th Floor Lecture Hall 
2:00 - 2:45Group 5: Super Farey Graphs11th Floor Lecture Hall 
3:00 - 3:45Group 6: Complete Algebraic Two-Systems on the Surface of Genus 211th Floor Lecture Hall 
3:45 - 4:15Coffee/ Tea Break11th Floor Collaborative Space 
Friday, August 3, 2018
TimeEventLocationMaterials
1:30 - 2:00Coffee/ Tea Break11th Floor Collaborative Space 

Final Projects

Final Student Presentations
  • "Length and Self-intersection Number of Geodesics in Hyperbolic Surfaces" by I. Hadi, B. Whitfield, and A. Xu
  • "Hausdorff Dimension of the Limit Set of Hyperbolic Pair of Pants" by F. Castaneda and I. Hill
  • "Automorphism Group of the k-Curve Graph" by Y. Chandran, R. Oakley, and R. Shapiro
  • "Minimally Intersecting Filling Pair Origamis" by Z. Cui, A. Gary, P. Helms, and T. Kim
  • "Super Farey Graphs" by M. Lopez, E. Rexer, and Z. Riell
  • "Complete Algebraic Two-Systems on the Surface of Genus 2" by M. Lahn, A. Mechery, and S. Nayak
  • "Visualizing Cubic Moduli Spaces" by A. Gary and J. Lee

Other Summer@ICERM Events

Summer@ICERM 2012: Geometry and Dynamics
Summer@ICERM 2013: Geometry and Dynamics
Summer@ICERM 2014: Polygons and Polynomials
Summer@ICERM 2015: Computational Dynamics and Topology
Summer@ICERM 2016: Dynamics and Stochastics
Summer@ICERM 2017: Topological Data Analysis
Summer@ICERM 2019: Computational Arithmetic Dynamics