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.

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

  • Ian Alevy
    Brown University
  • Tarik Aougab
    Brown University
  • Tom Banchoff
    Brown University
  • Francisc Bozgan
    University of Chicago
  • Kevin Castro
    Brown University
  • HaiBin Chang
    Numerical Technologies
  • Feng Chen
    Brown University
  • Jeangoudoux Clothilde
    Laboratoire d'Informatique de Paris VI, Université de Paris VI (Pierre et Marie Curie)
  • Constantine Dafermos
    Brown University
  • Diana Davis
    Swarthmore College
  • Nadejda Drenska
    University of Minnesota
  • Katherine Engelman
    San Diego City College
  • Dmitri Gekhtman
    Harvard University
  • Vivian Healey
    Brown University
  • Patrick Hooper
    City College, CUNY
  • 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 Polytechnic Institute
  • Benjamin LeVeque
    Brown University
  • Caglayan Llyas
    Universite de Paris VI (Pierre et Marie Curie)
  • Cressot Loic
    École Nationale des Ponts et Chaussées
  • Yvon Maday
    University Pierre and Marie Curie
  • Elizabeth Makrides
    Brown University
  • Moreau Martin
    Universite de Paris VI (Pierre et Marie Curie)
  • Amy Nesky
    University of Michigan
  • Desislava Nikolov
    University of the Orange Free State
  • Ndiaye Pape
    Universite de Paris VI (Pierre et Marie Curie)
  • Loriot Paul
    Universite de Paris VI (Pierre et Marie Curie)
  • Chukiat Phonsom
    Brown University
  • Clara Redwood
    Reed College
  • Labady Rudy-Angele
    Universite de Paris VI (Pierre et Marie Curie)
  • Mohajeri Sarah
    Universite de Paris VI (Pierre et Marie Curie)
  • 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
    Universite de Paris VI (Pierre et Marie Curie)
  • France Thibaut
    Universite de Paris VI (Pierre et Marie Curie)
  • Emmanuel Tsukerman
    University of California, Berkeley
  • Martin Ulirsch
    Fields Institute for Research in Mathematical Sciences
  • Cedric Villani
    Universite de Lyon II
  • Mantchala Vincateish
    Universite de Paris VI (Pierre et Marie Curie)
  • Xu Wallon
    Universite de Paris VI (Pierre et Marie Curie)
  • Yilong Yang
    Brown University
  • Zuhal Yildirim
    Brown University

Summer Schedule

Monday, June 18, 2012
TimeEventLocationMaterials
9:00 - 9:30Summer@ICERM Non-Brown Student Meet & Greet  
9:30 - 10:00Non-Brown Student Orientation  
10:00 - 11:30All Summer@ICERM students orientation  
11:30 - 1:00ICERM Welcome Lunch11th Floor Collaborative Space 
1:00 - 4:00Introductions11th Floor Lecture Hall 
Tuesday, June 19, 2012
TimeEventLocationMaterials
9:00 - 12:00Research Topic Introductions11th Floor Lecture Hall 
12:00 - 1:30Break for Free Lunch  
1:30 - 3:00Research Topic Introductions11th Floor Lecture Hall 
3:00 - 3:30Coffee/Tea Break11th Floor Collaborative Space 
Wednesday, June 20, 2012
TimeEventLocationMaterials
8:30 - 12:30BEARCORE TrainingMedical Education Building - 222 Richmond Street, Providence RI 
2:30 - 3:00IT Tutorial - Isani Cayetano, ICERM11th Floor Lecture Hall 
3:00 - 3:30Coffee/Tea Break11th Floor Collaborative Space 
Thursday, June 21, 2012
TimeEventLocationMaterials
9:00 - 12:00Research Topic Introductions11th Floor Lecture Hall 
1:30 - 3:00Problem Discussions11th Floor Lecture Hall  
3:00 - 3:30Coffee/Tea Break11th Floor Collaborative Space 
Friday, June 22, 2012
TimeEventLocationMaterials
9:00 - 12:00Research Topic Introductions11th Floor Lecture Hall 
1:30 - 3:00Form Research Groups11th Floor Lecture Hall 
3:00 - 3:30Coffee/Tea Break11th Floor Collaborative Space 
Monday, June 25, 2012
TimeEventLocationMaterials
9:30 - 11:00The JAVA programming language - Pat Hooper, City College of New York11th Floor Lecture Hall 
3:00 - 3:30Coffee/Tea Break11th Floor Collaborative Space 
Tuesday, June 26, 2012
TimeEventLocationMaterials
9:30 - 11:00Mathematical graphics - Pat Hooper, City College of New York11th Floor Lecture Hall 
3:00 - 3:30Coffee/Tea Break11th Floor Collaborative Space 
Wednesday, June 27, 2012
TimeEventLocationMaterials
10:00 - 11:00Working Seminar11th Floor Lecture Hall 
11:00 - 12:30Square grids, double lattice PETS, and renormalization - Rich Schwartz, Brown University11th Floor Lecture Hall 
3:00 - 3:30Coffee/Tea Break11th Floor Collaborative Space 
Thursday, June 28, 2012
TimeEventLocationMaterials
9:30 - 11:00Creating interactive programs - Pat Hooper, City College of New York11th Floor Lecture Hall 
3:00 - 3:30Coffee/Tea Break11th Floor Collaborative Space 
Friday, June 29, 2012
TimeEventLocationMaterials
9:30 - 11:00Sharing programs with others - Pat Hooper, City College of New York11th Floor Lecture Hall 
3:00 - 3:30Coffee/Tea Break11th Floor Collaborative Space 
Monday, July 2, 2012
TimeEventLocationMaterials
10:00 - 11:00Introduction to Complex Dynamics - Sarah Koch, Harvard University11th Floor Lecture Hall 
3:00 - 3:30Coffee/Tea Break11th Floor Collaborative Space 
Tuesday, July 3, 2012
TimeEventLocationMaterials
10:00 - 11:00Introduction to Complex Dynamics - Sarah Koch, Harvard University11th Floor Lecture Hall 
3:00 - 3:30Coffee/Tea Break11th Floor Collaborative Space 
Thursday, July 5, 2012
TimeEventLocationMaterials
10:00 - 11:00Introduction to Complex Dynamics - Sarah Koch, Harvard University11th Floor Lecture Hall 
3:00 - 3:30Coffee/Tea Break11th Floor Collaborative Space 
Friday, July 6, 2012
TimeEventLocationMaterials
10:00 - 11:00Introduction to Complex Dynamics - Sarah Koch, Harvard University11th Floor Lecture Hall 
3:00 - 3:30Coffee/Tea Break11th Floor Collaborative Space 
Monday, July 9, 2012
TimeEventLocationMaterials
3:00 - 3:30Coffee/Tea Break11th Floor Collaborative Space 
Tuesday, July 10, 2012
TimeEventLocationMaterials
3:00 - 3:30Coffee/Tea Break11th Floor Collaborative Space 
Wednesday, July 11, 2012
TimeEventLocationMaterials
9:30 - 12:00Working Seminar11th Floor Lecture Hall 
2:00 - 3:00Building polyhedra by self-assembly - Govind Menon, Brown University11th Floor Lecture Hall 
3:00 - 3:30Coffee/Tea Break11th Floor Collaborative Space 
Thursday, July 12, 2012
TimeEventLocationMaterials
3:00 - 3:30Coffee/Tea Break11th Floor Collaborative Space 
Friday, July 13, 2012
TimeEventLocationMaterials
3:00 - 3:30Coffee/Tea Break11th Floor Collaborative Space 
Monday, July 16, 2012
TimeEventLocationMaterials
9:30 - 11:00Introduction to Hyperbolic Geometry - Jeff Brock, ICERM, Brown University11th Floor Lecture Hall 
3:00 - 3:30Coffee/Tea Break11th Floor Collaborative Space 
Tuesday, July 17, 2012
TimeEventLocationMaterials
9:30 - 11:00Introduction to Hyperbolic Geometry - Jeff Brock, ICERM, Brown University11th Floor Lecture Hall 
3:00 - 3:30Yellow Pig Day Celebration11th Floor Collaborative Space 
Wednesday, July 18, 2012
TimeEventLocationMaterials
2:00 - 3:00Geometric Discrepancy Theory - Jill Pipher, ICERM11th Floor Lecture Hall 
3:00 - 3:05Summer@ICERM Group Photo11th Floor Lecture Hall 
3:05 - 3:35Coffee/Tea Break11th Floor Collaborative Space 
Thursday, July 19, 2012
TimeEventLocationMaterials
9:30 - 11:00Introduction to Hyperbolic Geometry - Jeff Brock, ICERM, Brown University11th Floor Lecture Hall 
3:00 - 3:30Coffee/Tea Break11th Floor Collaborative Space 
Friday, July 20, 2012
TimeEventLocationMaterials
10:00 - 11:00Introduction to Hyperbolic Geometry - Jeff Brock, ICERM, Brown University11th Floor Lecture Hall 
3:00 - 3:30Coffee/Tea Break11th Floor Collaborative Space 
Monday, July 23, 2012
TimeEventLocationMaterials
10:00 - 11:30Presentations11th Floor Lecture Hall 
3:00 - 3:30Coffee/Tea Break11th Floor Collaborative Space 
Tuesday, July 24, 2012
TimeEventLocationMaterials
10:00 - 11:30Presentations11th Floor Lecture Hall 
3:00 - 3:30Coffee/Tea Break11th Floor Collaborative Space 
Wednesday, July 25, 2012
TimeEventLocationMaterials
2:00 - 3:00Snakes and ladders - Bjorn Sandstede, Brown University, ICERM11th Floor Lecture Hall 
3:00 - 3:30Coffee/Tea Break11th Floor Collaborative Space 
Thursday, July 26, 2012
TimeEventLocationMaterials
10:00 - 11:30Presentations11th Floor Lecture Hall 
3:00 - 3:30Coffee/Tea Break11th Floor Collaborative Space 
Friday, July 27, 2012
TimeEventLocationMaterials
1:00 - 2:00Presentations11th Floor Lecture Hall 
3:00 - 3:30Coffee/Tea Break11th Floor Collaborative Space 
Monday, July 30, 2012
TimeEventLocationMaterials
3:00 - 3:30Coffee/Tea Break11th Floor Collaborative Space 
Tuesday, July 31, 2012
TimeEventLocationMaterials
2:00 - 2:20Converse Desargues Theorem - Kevin Castro, Brown Univeristy and Desislava Nikolov, University of the Free State, South Africa11th Floor Lecture Hall 
2:20 - 2:40Snaking under radical perturbations - Nadejda Drenska, Brown University11th Floor Lecture Hall 
2:40 - 3:00Bug dynamics on manifolds - Dmitri Gekhtman, Harvard University11th Floor Lecture Hall 
3:00 - 3:20A model of chip firing - Alexander St. Laurent, Brown University11th Floor Lecture Hall 
3:20 - 3:40Outer Billiards with Contraction - Francisc Bozgan, UCLA, Rumania, In-Jee Jeong, Brown University and Julienne LaChance, Rensselaer Polytechnic Institute11th Floor Lecture Hall 
3:40 - 4:00From spots to target patterns in Swift-Hohenberg equation - Chukiat Phonsom, Brown University11th Floor Lecture Hall 
4:00 - 4:20A warm little pond - Nash Rochman, Brown University11th Floor Lecture Hall 
4:20 - 4:40Bicycle Polygons, Solitons and the Darboux Transformation - Ian Alevy, University of Chicago and Emmanuel Tsukerman, Stanford University11th Floor Lecture Hall 
4:40 - 5:00Instabilities of Euler flow - Zuhal Yildirim, Brown University11th Floor Lecture Hall 
5:00 - 5:30Coffee & Dessert Reception11th Floor Collaborative Space 
Wednesday, August 1, 2012
TimeEventLocationMaterials
11:00 - 12:00Random Interfaces - Rick Kenyon, Brown University11th Floor Lecture Hall 
3:00 - 3:30Coffee/Tea Break11th Floor Collaborative Space 
Thursday, August 2, 2012
TimeEventLocationMaterials
11:30 - 2:002012 UTRA SymposiumSayles Hall  
3:00 - 3:30Coffee/Tea Break11th Floor Collaborative Space 
Friday, August 3, 2012
TimeEventLocationMaterials
3:00 - 3:30Coffee/Tea Break11th Floor Collaborative Space 
Monday, August 6, 2012
TimeEventLocationMaterials
10:00 - 10:30Coffee/Tea Break11th Floor Collaborative Space 
10:30 - 11:30Presentations: Unicycle problem - Amy Nesky, Boston College and Clara Redwood, Reed College10th Floor Collaborative Space  
1:00 - 2:00Presentations: 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 - 3:00Coffee/Tea Break11th Floor Collaborative Space 
Tuesday, August 7, 2012
TimeEventLocationMaterials
10:00 - 10:30Coffee/Tea Break11th Floor Collaborative Space 
10:30 - 11:30Presentations: Billiards in near squares - Yilong Yang, Brown University and Hai Bin Chang, National University of Singapore10th Floor Collaborative Space  
1:00 - 2:00Presentations: Bicycle curves and bicycle polygons - Ian Alevy, University of Chicago and Emmanuel Tsukerman, Stanford University10th Floor Collaborative Space  
2:30 - 2:45Coffee/Tea Break11th Floor Collaborative Space 
Wednesday, August 8, 2012
TimeEventLocationMaterials
10:00 - 10:30Coffee/Tea Break11th Floor Collaborative Space 
10:30 - 11:30Presentations: Negative Snell propagation - Katherine Engelman, Bryn Mawr College and Andrew Kimball, Western Carolina University10th Floor Collaborative Space  
1:00 - 2:00Presentations: Converse Desargues theorem - Desislava Nikolov, University of the Free State and Kevin Casto, Brown University10th Floor Collaborative Space  
2:30 - 3:00Coffee/Tea Break11th Floor Collaborative Space 
Thursday, August 9, 2012
TimeEventLocationMaterials
10:00 - 10:30Coffee/Tea Break11th Floor Collaborative Space 
1:00 - 2:00Presentations: Beetle problem - Dmitri Gekhtman, Harvard University10th Floor Collaborative Space  
2:30 - 3:00Coffee/Tea Break11th Floor Collaborative Space 
Friday, August 10, 2012
TimeEventLocationMaterials
10:00 - 10:30Coffee/Tea Break11th Floor Collaborative Space 
1:00 - 1:30Closing Remarks10th Floor Collaborative Space  
1:30 - 2:00Coffee/Tea Break10th Floor Collaborative Space  

Final Projects

Final Student Presentations
Completed Student Projects

Other Summer@ICERM Events

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 2018: Low Dimensional Topology and Geometry