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 for "Summer@ICERM 2018: Low Dimensional Topology and Geometry"
Image credit: T. Aougab & J. Gaster

Program Details

2018 Proposed Research Project Topics
  • Self-intersection Number of Geodesics
  • Hausdorff Dimension and Hyperbolic Pair of Pants
  • Symmetries of Curve Graph Variants
  • Square Tilings
  • Coloring Problem for Curve and Arc Graphs
  • Curves Intersecting Each Other Twice
  • Navigating the Space of SL_2(C) Characters
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

Talks will be presented virtually or in-person as indicated in the schedule below.

  • Speaker
  • Poster Presenter
  • Attendee
  • Virtual Attendee
  • 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 - 9:00am EDTBreakfast11th Floor Collaborative Space 
9:00 - 10:00am EDTWelcome/ Meet & Greet121 S Main St, 11th Floor Lecture Hall 
10:00 - 12:00pm EDTScavenger Hunt Brown University Campus 
12:00 - 1:30pm EDTWelcome Lunch  
1:30 - 2:00pm EDTHuman Interactions11th Floor Lecture Hall 
2:00 - 3:30pm EDTMoira Chas' Experiences - Stony Brook University11th Floor Lecture Hall 
3:30 - 4:00pm EDTCoffee/ Tea Break11th Floor Collaborative Space 
4:00 - 5:00pm EDTMoira Chas' Experiences (Cont.)11th Floor Lecture Hall 
6:30 - 8:30pm EDTDinner Flatbread Company, 161 Cushing St, Providence, RI 02906, USA 
Tuesday, June 12, 2018
TimeEventLocationMaterials
8:15 - 9:00am EDTBreakfast11th Floor Collaborative Space 
9:00 - 10:30am EDTSurface geometry and topology- secretly covering spaces and fundamental groups - Tarik Aougab - Brown University & Jonah Gaster - University of Illinois11th Floor Lecture Hall 
10:30 - 11:00am EDTCoffee/ Tea Break11th Floor Collaborative Space 
11:00 - 12:00pm EDTSurface geometry and topology- secretly covering spaces and fundamental groups (cont.) - Tarik Aougab - Brown University & Jonah Gaster - University of Illinois11th Floor Lecture Hall 
12:00 - 2:00pm EDTLunch Break - On Brown's CampusVerney Woolley 
2:00 - 3:30pm EDTMobius transformations are generated by inversions & Inversions preserve distance - Jonah Gaster - University of Illinois11th Floor Lecture Hall 
3:30 - 4:00pm EDTCoffee/ Tea Break11th Floor Collaborative Space 
4:00 - 5:00pm EDTMatrices + hyperbolic geometry - All Organizers11th Floor Lecture Hall 
5:30 - 7:30pm EDTCrochet Lessons & Pizza - Moira Chas - Stony Brook University11th Floor Collaborative Space 
Wednesday, June 13, 2018
TimeEventLocationMaterials
8:15 - 9:00am EDTBreakfast11th Floor Collaborative Space 
9:00 - 10:30am EDTMoira Chas11th Floor Lecture Hall 
10:30 - 11:00am EDTCoffee/ Tea Break11th Floor Collaborative Space 
11:00 - 12:00pm EDTMoira Chas11th Floor Lecture Hall 
12:00 - 1:30pm EDTLunch BreakICERM 
1:30 - 3:30pm EDTBill Goldman11th Floor Lecture Hall 
3:30 - 4:00pm EDTCoffee/ Tea Break11th Floor Collaborative Space 
4:00 - 5:00pm EDTBill Goldman11th Floor Lecture Hall 
6:00 - 8:00pm EDTDinner Trinity Brewhouse, 186 Fountain St, Providence, RI 02903, USA 
Thursday, June 14, 2018
TimeEventLocationMaterials
9:00 - 10:30am EDTJonah Gaster11th Floor Lecture Hall 
10:30 - 11:00am EDTCoffee/ Tea Break11th Floor Collaborative Space 
11:00 - 12:00pm EDTJonah Gaster11th Floor Lecture Hall 
12:00 - 1:30pm EDTLunch Break  
1:30 - 3:30pm EDTTarik Aougab11th Floor Lecture Hall 
3:30 - 4:00pm EDTCoffee/ Tea Break11th Floor Collaborative Space 
4:00 - 5:00pm EDTTarik Aougab11th Floor Lecture Hall 
Friday, June 15, 2018
TimeEventLocationMaterials
9:00 - 10:30am EDTGroup Project Discussions11th Floor Lecture Hall 
10:30 - 11:00am EDTCoffee/ Tea Break11th Floor Collaborative Space 
11:00 - 12:00pm EDTGroup Project Discussions11th Floor Lecture Hall 
12:00 - 1:30pm EDTLunch Break  
1:30 - 3:30pm EDTGroup Project Assignments11th Floor Lecture Hall 
3:30 - 4:00pm EDTCoffee/ Tea Break11th Floor Collaborative Space 
4:00 - 5:00pm EDTGroup Project Assignments11th Floor Lecture Hall 
Monday, June 18, 2018
TimeEventLocationMaterials
10:00 - 12:00pm EDTColoring Problem for Curve and Arc Graphs - Group Meeting10th Floor Classroom 
1:30 - 3:30pm EDTSymmetries of Curve Graph Variants - Group Meeting10th Floor Classroom 
1:30 - 3:30pm EDTHausdorff Dimension and Hyperbolic Pair of Pants - Group Meeting11th Floor Conference Room 
Tuesday, June 19, 2018
TimeEventLocationMaterials
10:00 - 12:00pm EDTSelf-intersection Number of Geodesics11th Floor Conference Room 
10:00 - 12:00pm EDTNavigating the Space of SL_2(C) Characters 10th Floor Classroom 
1:30 - 3:30pm EDTSquare Tilings10th Floor Classroom 
1:30 - 3:30pm EDTCurves Intersecting Each Other Twice11th Floor Conference Room 
Wednesday, June 20, 2018
TimeEventLocationMaterials
10:00 - 12:00pm EDTOrganizers Meeting 11th floor Conference Room 
1:30 - 3:30pm EDTGroup Activity10th Floor Collaborative Space 
Thursday, June 21, 2018
TimeEventLocationMaterials
10:00 - 12:00pm EDTHausdorff Dimension and Hyperbolic Pair of Pants10th Floor Classroom 
10:00 - 12:00pm EDTSymmetries of Curve Graph Variants11th Floor Conference Room 
1:30 - 3:30pm EDTColoring Problem for Curve and Arc Graphs10th Floor Classroom 
Friday, June 22, 2018
TimeEventLocationMaterials
10:00 - 12:00pm EDTSquare Tilings11th Floor Conference Room 
10:00 - 12:00pm EDTCurves Intersecting Each Other Twice10th Floor Classroom 
1:30 - 3:30pm EDTSelf-intersection Number of Geodesics11th Floor Conference Room 
1:30 - 3:30pm EDTNavigating the Space of SL_2(C) Characters 10th Floor Classroom 
Tuesday, June 26, 2018
TimeEventLocationMaterials
10:00 - 12:00pm EDTSelf-intersection Number of Geodesics11th Floor Conference Room 
10:00 - 12:00pm EDTNavigating the Space of SL_2(C) Characters 10th Floor Classroom 
1:30 - 3:30pm EDTSquare Tilings10th Floor Classroom 
1:30 - 3:30pm EDTCurves Intersecting Each Other Twice10th floor collaborative space (near office 1001) 
3:30 - 4:00pm EDTCoffee/ Tea Break11th Floor Collaborative Space 
Wednesday, June 27, 2018
TimeEventLocationMaterials
8:45 - 10:45am EDTGroup Activity10th Floor Collaborative Space 
10:00 - 12:00pm EDTOrganizers Meeting 11th floor Conference Room 
3:30 - 4:00pm EDTCoffee/ Tea Break11th Floor Collaborative Space 
4:30 - 6:00pm EDTSummer Student Theoretical Physics Research Session Visit10th Floor Collaborative Space 
Thursday, June 28, 2018
TimeEventLocationMaterials
10:00 - 12:00pm EDTHausdorff Dimension and Hyperbolic Pair of Pants11th Floor Conference Room 
10:00 - 12:00pm EDTSymmetries of Curve Graph Variants10th Floor Classroom 
1:30 - 3:30pm EDTColoring Problem for Curve and Arc Graphs10th Floor Classroom 
3:30 - 4:00pm EDTCoffee/ Tea Break11th Floor Collaborative Space 
Friday, June 29, 2018
TimeEventLocationMaterials
10:00 - 12:00pm EDTCurves Intersecting Each Other Twice10th Floor Classroom 
10:00 - 12:00pm EDTSquare Tilings11th Floor Conference Room 
1:30 - 3:30pm EDTNavigating the Space of SL_2(C) Characters 10th Floor Classroom 
1:30 - 3:30pm EDTSelf-intersection Number of Geodesics11th Floor Conference Room 
3:30 - 4:00pm EDTCoffee/ Tea Break11th Floor Collaborative Space 
Monday, July 2, 2018
TimeEventLocationMaterials
10:00 - 12:00pm EDTColoring Problem for Curve and Arc Graphs - Group Meeting10th Floor Classroom 
1:30 - 3:30pm EDTHausdorff Dimension and Hyperbolic Pair of Pants - Group Meeting11th Floor Conference Room 
1:30 - 3:30pm EDTSymmetries of Curve Graph Variants - Group Meeting10th Floor Classroom 
3:30 - 4:00pm EDTCoffee/ Tea Break11th Floor Collaborative Space 
Tuesday, July 3, 2018
TimeEventLocationMaterials
10:00 - 12:00pm EDTSelf-intersection Number of Geodesics11th Floor Conference Room 
10:00 - 12:00pm EDTNavigating the Space of SL_2(C) Characters 10th Floor Classroom 
1:30 - 3:30pm EDTCurves Intersecting Each Other Twice10th floor collaborative space (near office 1001) 
1:30 - 3:30pm EDTSquare Tilings10th Floor Classroom 
3:30 - 4:00pm EDTCoffee/ Tea Break11th Floor Collaborative Space 
Thursday, July 5, 2018
TimeEventLocationMaterials
10:00 - 12:00pm EDTHausdorff Dimension and Hyperbolic Pair of Pants11th Floor Conference Room 
10:00 - 12:00pm EDTSymmetries of Curve Graph Variants10th Floor Classroom 
1:30 - 3:30pm EDTColoring Problem for Curve and Arc Graphs10th Floor Classroom 
3:30 - 4:00pm EDTCoffee/ Tea Break11th Floor Collaborative Space 
Friday, July 6, 2018
TimeEventLocationMaterials
10:00 - 12:00pm EDTSquare Tilings11th Floor Conference Room 
1:30 - 3:30pm EDTNavigating the Space of SL_2(C) Characters 10th Floor Classroom 
1:30 - 3:30pm EDTSelf-intersection Number of Geodesics11th Floor Conference Room 
3:30 - 4:00pm EDTCoffee/ Tea Break11th Floor Collaborative Space 
Monday, July 9, 2018
TimeEventLocationMaterials
10:00 - 12:00pm EDTColoring Problem for Curve and Arc Graphs - Group Meeting10th Floor Classroom 
1:30 - 3:30pm EDTHausdorff Dimension and Hyperbolic Pair of Pants - Group Meeting11th Floor Conference Room 
1:30 - 3:30pm EDTSymmetries of Curve Graph Variants - Group Meeting10th Floor Classroom 
3:30 - 4:00pm EDTCoffee/ Tea Break11th Floor Collaborative Space 
Tuesday, July 10, 2018
TimeEventLocationMaterials
10:00 - 12:00pm EDTNavigating the Space of SL_2(C) Characters 10th Floor Classroom 
10:00 - 12:00pm EDTSelf-intersection Number of Geodesics11th Floor Conference Room 
1:30 - 3:30pm EDTCurves Intersecting Each Other Twice10th floor collaborative space (near office 1001) 
1:30 - 3:30pm EDTSquare Tilings10th Floor Collaborative Space 
3:30 - 4:00pm EDTCoffee/ Tea Break11th Floor Collaborative Space 
Wednesday, July 11, 2018
TimeEventLocationMaterials
10:00 - 12:00pm EDTOrganizers Meeting 11th floor Conference Room 
3:00 - 3:30pm EDTCoffee/ Tea Break11th Floor Collaborative Space 
3:30 - 4:30pm EDTBilliards and Translation Surfaces - Jenny Rustad, University of Maryland10th Floor Classroom
Thursday, July 12, 2018
TimeEventLocationMaterials
10:00 - 12:00pm EDTHausdorff Dimension and Hyperbolic Pair of Pants11th Floor Conference Room 
10:00 - 12:00pm EDTSymmetries of Curve Graph Variants10th Floor Classroom 
1:30 - 3:30pm EDTColoring Problem for Curve and Arc Graphs10th Floor Classroom 
3:15 - 3:45pm EDTCoffee/ Tea Break11th Floor Collaborative Space 
3:45 - 4:30pm EDTNeutral Networks - Eli Grigsby, Boston College10th Floor Classroom 
Friday, July 13, 2018
TimeEventLocationMaterials
10:00 - 12:00pm EDTSquare Tilings11th Floor Conference Room 
2:00 - 3:00pm EDTA basic Thurston contribution - the meaning of wall paper symmetry- orbifolds - Dennis Sulllivan, CUNY & Stony Brook University11th Floor Lecture Hall
3:30 - 4:00pm EDTCoffee/ Tea Break11th Floor Collaborative Space 
Monday, July 16, 2018
TimeEventLocationMaterials
10:00 - 12:00pm EDTColoring Problem for Curve and Arc Graphs - Group Meeting10th Floor Classroom 
1:30 - 3:30pm EDTHausdorff Dimension and Hyperbolic Pair of Pants - Group Meeting11th Floor Conference Room 
1:30 - 3:30pm EDTSymmetries of Curve Graph Variants - Group Meeting10th Floor Classroom 
3:30 - 4:00pm EDTCoffee/ Tea Break11th Floor Collaborative Space 
Tuesday, July 17, 2018
TimeEventLocationMaterials
10:00 - 12:00pm EDTSelf-intersection Number of Geodesics11th Floor Conference Room 
10:00 - 12:00pm EDTNavigating the Space of SL_2(C) Characters 10th Floor Classroom 
1:30 - 3:30pm EDTCurves Intersecting Each Other Twice10th floor collaborative space (near office 1001) 
1:30 - 3:30pm EDTSquare Tilings10th Floor Collaborative Space 
3:30 - 4:00pm EDTCoffee/ Tea Break11th Floor Collaborative Space 
Wednesday, July 18, 2018
TimeEventLocationMaterials
10:00 - 12:00pm EDTOrganizers Meeting 11th floor Conference Room 
2:30 - 3:00pm EDTCoffee/ Tea Break11th Floor Collaborative Space 
3:00 - 3:45pm EDTGraduate School Experience - Marissa Loving- University of Illinois at Urbana- Champaign11th Floor Lecture Hall 
4:00 - 5:00pm EDTGrad 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 - 8:00pm EDTNight of Games and Knitting11th Floor Collaborative Space 
Thursday, July 19, 2018
TimeEventLocationMaterials
10:00 - 12:00pm EDTSymmetries of Curve Graph Variants10th Floor Classroom 
10:00 - 12:00pm EDTHausdorff Dimension and Hyperbolic Pair of Pants11th Floor Conference Room 
1:30 - 3:30pm EDTColoring Problem for Curve and Arc Graphs10th Floor Classroom 
3:15 - 3:45pm EDTCoffee/ Tea Break11th Floor Collaborative Space 
3:45 - 4:45pm EDTGauss Bonnet Theorem - Charles Daly, University of Maryland11th Floor Lecture Hall 
Friday, July 20, 2018
TimeEventLocationMaterials
10:00 - 12:00pm EDTSquare Tilings11th Floor Conference Room 
1:30 - 3:30pm EDTNavigating the Space of SL_2(C) Characters 10th Floor Classroom 
1:30 - 3:30pm EDTSelf-intersection Number of Geodesics11th Floor Conference Room 
3:30 - 3:45pm EDTGroup Photo11th Floor Collaborative Space 
3:45 - 4:30pm EDTCoffee/ Tea Break11th Floor Collaborative Space 
Monday, July 23, 2018
TimeEventLocationMaterials
10:00 - 12:00pm EDTColoring Problem for Curve and Arc Graphs - Group Meeting10th Floor Classroom 
1:30 - 3:00pm EDTSymmetries of Curve Graph Variants - Group Meeting10th Floor Classroom 
1:30 - 3:00pm EDTHausdorff Dimension and Hyperbolic Pair of Pants - Group Meeting11th Floor Conference Room 
3:00 - 3:30pm EDTCoffee/ Tea Break11th Floor Collaborative Space 
3:30 - 4:30pm EDTTotal positivity and ping-pong in projective space - Jean-Philippe Burelle - IHES10th Floor Collaborative Space 
Tuesday, July 24, 2018
TimeEventLocationMaterials
10:00 - 12:00pm EDTSelf-intersection Number of Geodesics11th Floor Conference Room 
10:00 - 12:00pm EDTNavigating the Space of SL_2(C) Characters 10th Floor Classroom 
1:30 - 3:30pm EDTSquare Tilings - Bill Menasco- University of Buffalo10th Floor Collaborative Space 
1:30 - 3:30pm EDTCurves Intersecting Each Other Twice10th floor collaborative space (near office 1001) 
3:30 - 4:00pm EDTCoffee/ Tea Break11th Floor Collaborative Space 
Wednesday, July 25, 2018
TimeEventLocationMaterials
11:00 - 12:00pm EDTTBD - Moon Duchin - Tufts University10th Floor Collaborative Space 
2:00 - 4:00pm EDTOrganizers Meeting 11th floor Conference Room 
3:00 - 3:30pm EDTCoffee/ Tea Break11th Floor Collaborative Space 
Thursday, July 26, 2018
TimeEventLocationMaterials
10:00 - 11:00am EDTHausdorff Dimension and Hyperbolic Pair of Pants11th Floor Conference Room 
10:00 - 11:00am EDTSymmetries of Curve Graph Variants10th Floor Classroom 
1:30 - 3:30pm EDTColoring Problem for Curve and Arc Graphs10th Floor Classroom 
3:00 - 3:30pm EDTCoffee/ Tea Break11th Floor Collaborative Space 
3:30 - 4:30pm EDTBrown University's Mathematics Graduate Program Info Session - Tom Goodwillie- Brown University10th Floor Collaborative Space 
Friday, July 27, 2018
TimeEventLocationMaterials
10:00 - 12:00pm EDTSquare Tilings10th Floor Classroom 
1:30 - 2:30pm EDTNavigating the Space of SL_2(C) Characters 10th Floor Classroom 
1:30 - 2:30pm EDTSelf-intersection Number of Geodesics11th Floor Conference Room 
2:30 - 3:00pm EDTCoffee/ Tea Break11th Floor Collaborative Space 
3:00 - 4:00pm EDTWomen in Math - Moira Chas - Stony Brook University10th Floor Collaborative Space 
4:00 - 5:00pm EDTDiversity 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 - 3:45pm EDTCoffee/ Tea Break11th Floor Collaborative Space 
3:45 - 4:15pm EDTIncompressible Surfaces in 4-Punctured Sphere Bundles - Sunny Xiao, Brown University11th Floor Lecture Hall 
4:15 - 4:45pm EDTLeast Dilatation of Pure Surface Braids - Marissa Loving, University of Illinois at Urbana- Champaign11th Floor Lecture Hall 
Tuesday, July 31, 2018
TimeEventLocationMaterials
3:30 - 4:00pm EDTCoffee/ Tea Break11th Floor Collaborative Space 
Wednesday, August 1, 2018
TimeEventLocationMaterials
10:30 - 10:45am EDTGroup Photo11th Floor Collaborative Space 
11:00 - 11:45am EDTGroup 7: Visualizing Cubic Moduli Spaces11th Floor Lecture Hall 
2:00 - 2:45pm EDTGroup 2: Hausdorff Dimension of the Limit Set of Hyperbolic Pair of Pants11th Floor Lecture Hall 
3:00 - 3:45pm EDTGroup 1: Length and Self-intersection Number of Geodesics in Hyperbolic Surfaces11th Floor Lecture Hall 
3:45 - 4:15pm EDTCoffee/ Tea Break11th Floor Collaborative Space 
4:30 - 5:30pm EDTDiversity 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 - 10:45am EDTGroup 3: Automorphism Group of the k-Curve Graph11th Floor Lecture Hall 
11:00 - 11:45am EDTGroup 4: Minimally Intersecting Filling Pair Origamis11th Floor Lecture Hall 
2:00 - 2:45pm EDTGroup 5: Super Farey Graphs11th Floor Lecture Hall 
3:00 - 3:45pm EDTGroup 6: Complete Algebraic Two-Systems on the Surface of Genus 211th Floor Lecture Hall 
3:45 - 4:15pm EDTCoffee/ Tea Break11th Floor Collaborative Space 
Friday, August 3, 2018
TimeEventLocationMaterials
1:30 - 2:00pm EDTCoffee/ 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
Posters Presented at JMM 2019 in Baltimore, MD
  • Automorphisms of the k-curve graph* (Yassin Chandran, Roberta Shapiro, and Rob Oakley)
  • The Hausdorff Dimension of the Limit Set of a Pair of Pants (Ian Hill and Francisco Castaneda)
  • Combinatorics of k-Farey Graphs* (Miguel Lopez)
  • SL(2;Z) Action on Quadratic Differentials (Paige Helms)
  • Algebraic k-Systems of Curves* (Maxie Lahn and Aisha Mechery)
  • Monotonicity of Length of Closed Geodesics Given Self-Intersection Number (Isnayni Hadi, Brandis Whitfield and Alex Xu)
*Recipient of the MAA "Outstanding Poster Award" at JMM 2019
Papers

Publications

  • Charles Daly, Jonah Gaster, Max Lahn, Aisha Mechery, Simran Nayak, Algebraic k-systems of curves, arXiv:1911.08469, 2020.
  • Jonah Gaster, Miguel Lopez, Emily Rexer, Zoë Riell, Yang Xiao, Combinatorics of \textdollark\textdollar-Farey graphs, Rocky Mountain Journal of Mathematics 50 (2020) no. 1.
  • Shuchi Agrawal, Tarik Aougab, Yassin Chandran, Marissa Loving, J. Robert Oakley, Roberta Shapiro, Yang Xiao, Automorphisms of the k-curve graph, arXiv:1912.07666, 2023.

Other Summer@ICERM Events

Summer@ICERM 2012: Geometry and Dynamics
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Summer@ICERM 2013: Geometry and Dynamics
Image for "Summer@ICERM 2013: Geometry and Dynamics"
Summer@ICERM 2014: Polygons and Polynomials
Image for "Summer@ICERM 2014: Polygons and Polynomials"
Summer@ICERM 2015: Computational Dynamics and Topology
Image for "Summer@ICERM 2015: Computational Dynamics and Topology"
Summer@ICERM 2016: Dynamics and Stochastics
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Summer@ICERM 2017: Topological Data Analysis
Image for "Summer@ICERM 2017: Topological Data Analysis"
Summer@ICERM 2019: Computational Arithmetic Dynamics
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Summer@ICERM 2021: Computational Polygonal Billiards
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Summer@ICERM 2022: Computational Combinatorics
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