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 $3,000 stipend*.

The Summer@ICERM 2012 program is designed for a select group of 10-12 undergraduate scholars. Students in the 2012 program worked in small groups of two or three, supervised by a faculty advisor and aided by a teaching assistant. The faculty advisors described a variety of enticing open questions in geometry and in dynamical systems of geometric origin.

Topics discussed included Euclidean, hyperbolic and projective geometry, iteration of geometric constructions, and mathematical billiards. A variety of activities around these research themes allowed participants to engage in collaborative research, communicate and examine their findings in formal and informal settings, and report-out their findings with a finished product.

Image for "Summer@ICERM 2012: Geometry and Dynamics"
Summer@ICERM 2012 Participants: Front row, l-r: Dmitri Gekhtman, Desislava Nikolov, Julienne LaChance, Clara Redwood, Amy Nesky. Middle row, l-r: Kevin Casto, Diana Davis, Pat Hooper, In-Jee Jeong, Ian Alevy. Back row, l-r: Tarik Aougab, Sergei Tabachnikov, Andrew Kimball, Emmanuel Tsukerman, Francisc Bozgan, Yilong Yang, Hai Bin Chang, Katherine Engelman
Image: R. Schwartz

"Perfectly organized research program, projects were very accessible and we had the chance to have real progress on our research. Professors were very helpful and the meetings were very useful. ICERM looks wonderful and it is a great place to do research."
-- Summer@ICERM 2012 Participant

"I enjoyed the program thoroughly; it was well organized and would highly recommend it!"
-- Summer@ICERM 2012 Participant

"I loved the workspace. It was particularly stimulating and exciting to work there. I also enjoyed the varied exposure to different topics by the different advisors and TA's, and the fact that they were easily approachable and willing to help at all times."
-- Summer@ICERM 2012 Participant

Program Details

2012 Research Project Topics

In this Research Program, the faculty organizers stressed open questions which were accessible via mathematical methods available to undergraduates. In addition, participants were expected to be able to gain intuition into some of these problems via computer experimentation and visualization.

Funding Includes
  • $3,000 stipend
  • Dormitory housing
  • Meal plan
  • Travel support within U.S.
  • Access to fun local events

Confirmed Speakers & Participants

  • Speaker
  • Poster Presenter
  • Attendee
  • Virtual Attendee
  • Ian Alevy
    Brown University
  • Tarik Aougab
    Brown University
  • Tom Banchoff
    Brown University
  • Francisc Bozgan
    Center of Mathematical Statistics/UCLA
  • Kevin Castro
    Brown University
  • HaiBin Chang
    National University of Singapore
  • Feng Chen
    Brown University
  • Jeangoudoux Clothilde
    Université Pierre et Marie Curie (Paris VI)
  • Constantine Dafermos
    Brown University
  • Diana Davis
    Northwestern University
  • Nadejda Drenska
    Brown University
  • Katherine Engelman
    Bryn Mawr College
  • Dmitri Gekhtman
    Harvard University
  • Vivian Healey
    Brown University
  • Pat Hooper
    City College of New York
  • In-Jee Jeong
    Princeton University
  • Daniel Johnson
    Brown University
  • Richard Kenyon
    Brown University
  • Andrew Kimball
    Western Carolina University
  • Ariah Klages-Mundt
    Amherst College
  • Caroline Klivans
    Brown University
  • Joe Klobusicky
    Brown University
  • Sarah Koch
    University of Michigan, Ann Arbor
  • Julienne LaChance
    Rensselaer Polytechnical Institute
  • Benjamin LeVeque
    Brown University
  • Caglayan Llyas
    Université Pierre et Marie Curie (Paris VI)
  • Cressot Loic
    Université Pierre et Marie Curie (Paris VI)
  • Yvon Maday
    Brown University
  • Elizabeth Makrides
    Brown University
  • Moreau Martin
    Université Pierre et Marie Curie (Paris VI)
  • Sarah Mohajeri
    Université Pierre et Marie Curie (Paris VI)
  • Amy Nesky
    University of Michigan
  • Desislava Nikolov
    Stellenbosch University
  • Ndiaye Pape
    Université Pierre et Marie Curie (Paris VI)
  • Loriot Paul
    Université Pierre et Marie Curie (Paris VI)
  • Chukiat Phonsom
    Brown University
  • Clara Redwood
    Reed College
  • Labady Rudy-Angele
    Université Pierre et Marie Curie (Paris VI)
  • Richard Schwartz
    Brown University
  • Laura Slivinski
    Brown University
  • Alex St. Laurent
    Brown University
  • Walter Strauss
    Brown University
  • Xiang Sun
    Brown University
  • Sergei Tabachnikov
    ICERM and Penn State
  • Lejeune Thibault
    Université Pierre et Marie Curie (Paris VI)
  • France Thibaut
    Université Pierre et Marie Curie (Paris VI)
  • Emmanuel Tsukerman
    University of California, Berkeley
  • Martin Ulirsch
    Fields Institute for Research in Mathematical Sciences
  • Cedric Villani
    Université de Lyon II
  • Mantchala Vincateish
    Université Pierre et Marie Curie (Paris VI)
  • Xu Wallon
    Université Pierre et Marie Curie (Paris VI)
  • Yilong Yang
    Brown University
  • Zuhal Yildirim
    Brown University

Summer Schedule

Monday, June 18, 2012
TimeEventLocationMaterials
9:00 - 9:30am EDTSummer@ICERM Non-Brown Student Meet & Greet  
9:30 - 10:00am EDTNon-Brown Student Orientation  
10:00 - 11:30am EDTAll Summer@ICERM students orientation  
11:30 - 1:00pm EDTICERM Welcome Lunch11th Floor Collaborative Space 
1:00 - 4:00pm EDTIntroductions11th Floor Lecture Hall 
Tuesday, June 19, 2012
TimeEventLocationMaterials
9:00 - 12:00pm EDTResearch Topic Introductions11th Floor Lecture Hall 
12:00 - 1:30pm EDTBreak for Free Lunch  
1:30 - 3:00pm EDTResearch Topic Introductions11th Floor Lecture Hall 
3:00 - 3:30pm EDTCoffee/Tea Break11th Floor Collaborative Space 
Wednesday, June 20, 2012
TimeEventLocationMaterials
8:30 - 12:30pm EDTBEARCORE TrainingMedical Education Building - 222 Richmond Street, Providence RI 
2:30 - 3:00pm EDTIT Tutorial - Isani Cayetano, ICERM11th Floor Lecture Hall 
3:00 - 3:30pm EDTCoffee/Tea Break11th Floor Collaborative Space 
Thursday, June 21, 2012
TimeEventLocationMaterials
9:00 - 12:00pm EDTResearch Topic Introductions11th Floor Lecture Hall 
1:30 - 3:00pm EDTProblem Discussions11th Floor Lecture Hall  
3:00 - 3:30pm EDTCoffee/Tea Break11th Floor Collaborative Space 
Friday, June 22, 2012
TimeEventLocationMaterials
9:00 - 12:00pm EDTResearch Topic Introductions11th Floor Lecture Hall 
1:30 - 3:00pm EDTForm Research Groups11th Floor Lecture Hall 
3:00 - 3:30pm EDTCoffee/Tea Break11th Floor Collaborative Space 
Monday, June 25, 2012
TimeEventLocationMaterials
9:30 - 11:00am EDTThe JAVA programming language - Pat Hooper, City College of New York11th Floor Lecture Hall 
3:00 - 3:30pm EDTCoffee/Tea Break11th Floor Collaborative Space 
Tuesday, June 26, 2012
TimeEventLocationMaterials
9:30 - 11:00am EDTMathematical graphics - Pat Hooper, City College of New York11th Floor Lecture Hall 
3:00 - 3:30pm EDTCoffee/Tea Break11th Floor Collaborative Space 
Wednesday, June 27, 2012
TimeEventLocationMaterials
10:00 - 11:00am EDTWorking Seminar11th Floor Lecture Hall 
11:00 - 12:30pm EDTSquare grids, double lattice PETS, and renormalization - Rich Schwartz, Brown University11th Floor Lecture Hall 
3:00 - 3:30pm EDTCoffee/Tea Break11th Floor Collaborative Space 
Thursday, June 28, 2012
TimeEventLocationMaterials
9:30 - 11:00am EDTCreating interactive programs - Pat Hooper, City College of New York11th Floor Lecture Hall 
3:00 - 3:30pm EDTCoffee/Tea Break11th Floor Collaborative Space 
Friday, June 29, 2012
TimeEventLocationMaterials
9:30 - 11:00am EDTSharing programs with others - Pat Hooper, City College of New York11th Floor Lecture Hall 
3:00 - 3:30pm EDTCoffee/Tea Break11th Floor Collaborative Space 
Monday, July 2, 2012
TimeEventLocationMaterials
10:00 - 11:00am EDTIntroduction to Complex Dynamics - Sarah Koch, Harvard University11th Floor Lecture Hall 
3:00 - 3:30pm EDTCoffee/Tea Break11th Floor Collaborative Space 
Tuesday, July 3, 2012
TimeEventLocationMaterials
10:00 - 11:00am EDTIntroduction to Complex Dynamics - Sarah Koch, Harvard University11th Floor Lecture Hall 
3:00 - 3:30pm EDTCoffee/Tea Break11th Floor Collaborative Space 
Thursday, July 5, 2012
TimeEventLocationMaterials
10:00 - 11:00am EDTIntroduction to Complex Dynamics - Sarah Koch, Harvard University11th Floor Lecture Hall 
3:00 - 3:30pm EDTCoffee/Tea Break11th Floor Collaborative Space 
Friday, July 6, 2012
TimeEventLocationMaterials
10:00 - 11:00am EDTIntroduction to Complex Dynamics - Sarah Koch, Harvard University11th Floor Lecture Hall 
3:00 - 3:30pm EDTCoffee/Tea Break11th Floor Collaborative Space 
Monday, July 9, 2012
TimeEventLocationMaterials
3:00 - 3:30pm EDTCoffee/Tea Break11th Floor Collaborative Space 
Tuesday, July 10, 2012
TimeEventLocationMaterials
3:00 - 3:30pm EDTCoffee/Tea Break11th Floor Collaborative Space 
Wednesday, July 11, 2012
TimeEventLocationMaterials
9:30 - 12:00pm EDTWorking Seminar11th Floor Lecture Hall 
2:00 - 3:00pm EDTBuilding polyhedra by self-assembly - Govind Menon, Brown University11th Floor Lecture Hall 
3:00 - 3:30pm EDTCoffee/Tea Break11th Floor Collaborative Space 
Thursday, July 12, 2012
TimeEventLocationMaterials
3:00 - 3:30pm EDTCoffee/Tea Break11th Floor Collaborative Space 
Friday, July 13, 2012
TimeEventLocationMaterials
3:00 - 3:30pm EDTCoffee/Tea Break11th Floor Collaborative Space 
Monday, July 16, 2012
TimeEventLocationMaterials
9:30 - 11:00am EDTIntroduction to Hyperbolic Geometry - Jeff Brock, ICERM, Brown University11th Floor Lecture Hall 
3:00 - 3:30pm EDTCoffee/Tea Break11th Floor Collaborative Space 
Tuesday, July 17, 2012
TimeEventLocationMaterials
9:30 - 11:00am EDTIntroduction to Hyperbolic Geometry - Jeff Brock, ICERM, Brown University11th Floor Lecture Hall 
3:00 - 3:30pm EDTYellow Pig Day Celebration11th Floor Collaborative Space 
Wednesday, July 18, 2012
TimeEventLocationMaterials
2:00 - 3:00pm EDTGeometric Discrepancy Theory - Jill Pipher, ICERM11th Floor Lecture Hall 
3:00 - 3:05pm EDTSummer@ICERM Group Photo11th Floor Lecture Hall 
3:05 - 3:35pm EDTCoffee/Tea Break11th Floor Collaborative Space 
Thursday, July 19, 2012
TimeEventLocationMaterials
9:30 - 11:00am EDTIntroduction to Hyperbolic Geometry - Jeff Brock, ICERM, Brown University11th Floor Lecture Hall 
3:00 - 3:30pm EDTCoffee/Tea Break11th Floor Collaborative Space 
Friday, July 20, 2012
TimeEventLocationMaterials
10:00 - 11:00am EDTIntroduction to Hyperbolic Geometry - Jeff Brock, ICERM, Brown University11th Floor Lecture Hall 
3:00 - 3:30pm EDTCoffee/Tea Break11th Floor Collaborative Space 
Monday, July 23, 2012
TimeEventLocationMaterials
10:00 - 11:30am EDTPresentations11th Floor Lecture Hall 
3:00 - 3:30pm EDTCoffee/Tea Break11th Floor Collaborative Space 
Tuesday, July 24, 2012
TimeEventLocationMaterials
10:00 - 11:30am EDTPresentations11th Floor Lecture Hall 
3:00 - 3:30pm EDTCoffee/Tea Break11th Floor Collaborative Space 
Wednesday, July 25, 2012
TimeEventLocationMaterials
2:00 - 3:00pm EDTSnakes and ladders - Bjorn Sandstede, Brown University, ICERM11th Floor Lecture Hall 
3:00 - 3:30pm EDTCoffee/Tea Break11th Floor Collaborative Space 
Thursday, July 26, 2012
TimeEventLocationMaterials
10:00 - 11:30am EDTPresentations11th Floor Lecture Hall 
3:00 - 3:30pm EDTCoffee/Tea Break11th Floor Collaborative Space 
Friday, July 27, 2012
TimeEventLocationMaterials
1:00 - 2:00pm EDTPresentations11th Floor Lecture Hall 
3:00 - 3:30pm EDTCoffee/Tea Break11th Floor Collaborative Space 
Monday, July 30, 2012
TimeEventLocationMaterials
3:00 - 3:30pm EDTCoffee/Tea Break11th Floor Collaborative Space 
Tuesday, July 31, 2012
TimeEventLocationMaterials
2:00 - 2:20pm EDTConverse Desargues Theorem - Kevin Castro, Brown Univeristy and Desislava Nikolov, University of the Free State, South Africa11th Floor Lecture Hall 
2:20 - 2:40pm EDTSnaking under radical perturbations - Nadejda Drenska, Brown University11th Floor Lecture Hall 
2:40 - 3:00pm EDTBug dynamics on manifolds - Dmitri Gekhtman, Harvard University11th Floor Lecture Hall 
3:00 - 3:20pm EDTA model of chip firing - Alexander St. Laurent, Brown University11th Floor Lecture Hall 
3:20 - 3:40pm EDTOuter Billiards with Contraction - Francisc Bozgan, UCLA, Rumania, In-Jee Jeong, Brown University and Julienne LaChance, Rensselaer Polytechnic Institute11th Floor Lecture Hall 
3:40 - 4:00pm EDTFrom spots to target patterns in Swift-Hohenberg equation - Chukiat Phonsom, Brown University11th Floor Lecture Hall 
4:00 - 4:20pm EDTA warm little pond - Nash Rochman, Brown University11th Floor Lecture Hall 
4:20 - 4:40pm EDTBicycle Polygons, Solitons and the Darboux Transformation - Ian Alevy, University of Chicago and Emmanuel Tsukerman, Stanford University11th Floor Lecture Hall 
4:40 - 5:00pm EDTInstabilities of Euler flow - Zuhal Yildirim, Brown University11th Floor Lecture Hall 
5:00 - 5:30pm EDTCoffee & Dessert Reception11th Floor Collaborative Space 
Wednesday, August 1, 2012
TimeEventLocationMaterials
11:00 - 12:00pm EDTRandom Interfaces - Rick Kenyon, Brown University11th Floor Lecture Hall 
3:00 - 3:30pm EDTCoffee/Tea Break11th Floor Collaborative Space 
Thursday, August 2, 2012
TimeEventLocationMaterials
11:30 - 2:00pm EDT2012 UTRA SymposiumSayles Hall  
3:00 - 3:30pm EDTCoffee/Tea Break11th Floor Collaborative Space 
Friday, August 3, 2012
TimeEventLocationMaterials
3:00 - 3:30pm EDTCoffee/Tea Break11th Floor Collaborative Space 
Monday, August 6, 2012
TimeEventLocationMaterials
10:00 - 10:30am EDTCoffee/Tea Break11th Floor Collaborative Space 
10:30 - 11:30am EDTPresentations: Unicycle problem - Amy Nesky, Boston College and Clara Redwood, Reed College10th Floor Collaborative Space  
1:00 - 2:00pm EDTPresentations: Outer billiards with contraction (and, perhaps, without :) - Francisc Bozgan, UCLA, Rumania, In-Jee Jeong, Brown University and Julienne LaChance, Rensselaer Polytechnic Institute10th Floor Collaborative Space  
2:30 - 3:00pm EDTCoffee/Tea Break11th Floor Collaborative Space 
Tuesday, August 7, 2012
TimeEventLocationMaterials
10:00 - 10:30am EDTCoffee/Tea Break11th Floor Collaborative Space 
10:30 - 11:30am EDTPresentations: Billiards in near squares - Yilong Yang, Brown University and Hai Bin Chang, National University of Singapore10th Floor Collaborative Space  
1:00 - 2:00pm EDTPresentations: Bicycle curves and bicycle polygons - Ian Alevy, University of Chicago and Emmanuel Tsukerman, Stanford University10th Floor Collaborative Space  
2:30 - 2:45pm EDTCoffee/Tea Break11th Floor Collaborative Space 
Wednesday, August 8, 2012
TimeEventLocationMaterials
10:00 - 10:30am EDTCoffee/Tea Break11th Floor Collaborative Space 
10:30 - 11:30am EDTPresentations: Negative Snell propagation - Katherine Engelman, Bryn Mawr College and Andrew Kimball, Western Carolina University10th Floor Collaborative Space  
1:00 - 2:00pm EDTPresentations: Converse Desargues theorem - Desislava Nikolov, University of the Free State and Kevin Casto, Brown University10th Floor Collaborative Space  
2:30 - 3:00pm EDTCoffee/Tea Break11th Floor Collaborative Space 
Thursday, August 9, 2012
TimeEventLocationMaterials
10:00 - 10:30am EDTCoffee/Tea Break11th Floor Collaborative Space 
1:00 - 2:00pm EDTPresentations: Beetle problem - Dmitri Gekhtman, Harvard University10th Floor Collaborative Space  
2:30 - 3:00pm EDTCoffee/Tea Break11th Floor Collaborative Space 
Friday, August 10, 2012
TimeEventLocationMaterials
10:00 - 10:30am EDTCoffee/Tea Break11th Floor Collaborative Space 
1:00 - 1:30pm EDTClosing Remarks10th Floor Collaborative Space  
1:30 - 2:00pm EDTCoffee/Tea Break10th Floor Collaborative Space  

Final Projects

Final Student Presentations
Completed Student Projects

Other Summer@ICERM Events

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
Image for "Summer@ICERM 2016: Dynamics and Stochastics"
Summer@ICERM 2017: Topological Data Analysis
Image for "Summer@ICERM 2017: Topological Data Analysis"
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
Image for "Summer@ICERM 2021: Computational Polygonal Billiards"
Summer@ICERM 2022: Computational Combinatorics
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Summer@ICERM 2023: Mathematical Modeling of DNA Self-Assembly
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