Organizing Committee
- Pat Hooper
City College of New York - Sergei Tabachnikov
ICERM and Penn State
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.


"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.
- Billiards and related systems
- Geometry
- Algebraic Geometry Downloadable PDF of Project Descriptions
- Funding Includes
-
- $3,000 stipend
- Dormitory housing
- Meal plan
- Travel support within U.S.
- Access to fun local events
Confirmed Speakers & Participants
Talks will be presented virtually or in-person as indicated in the schedule below.
- 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
Time | Event | Location | Materials |
---|---|---|---|
9:00 - 9:30am EDT | Summer@ICERM Non-Brown Student Meet & Greet | ||
9:30 - 10:00am EDT | Non-Brown Student Orientation | ||
10:00 - 11:30am EDT | All Summer@ICERM students orientation | ||
11:30 - 1:00pm EDT | ICERM Welcome Lunch | 11th Floor Collaborative Space | |
1:00 - 4:00pm EDT | Introductions | 11th Floor Lecture Hall |
Tuesday, June 19, 2012
Time | Event | Location | Materials |
---|---|---|---|
9:00 - 12:00pm EDT | Research Topic Introductions | 11th Floor Lecture Hall | |
12:00 - 1:30pm EDT | Break for Free Lunch | ||
1:30 - 3:00pm EDT | Research Topic Introductions | 11th Floor Lecture Hall | |
3:00 - 3:30pm EDT | Coffee/Tea Break | 11th Floor Collaborative Space |
Wednesday, June 20, 2012
Time | Event | Location | Materials |
---|---|---|---|
8:30 - 12:30pm EDT | BEARCORE Training | Medical Education Building - 222 Richmond Street, Providence RI | |
2:30 - 3:00pm EDT | IT Tutorial - Isani Cayetano, ICERM | 11th Floor Lecture Hall | |
3:00 - 3:30pm EDT | Coffee/Tea Break | 11th Floor Collaborative Space |
Thursday, June 21, 2012
Time | Event | Location | Materials |
---|---|---|---|
9:00 - 12:00pm EDT | Research Topic Introductions | 11th Floor Lecture Hall | |
1:30 - 3:00pm EDT | Problem Discussions | 11th Floor Lecture Hall | |
3:00 - 3:30pm EDT | Coffee/Tea Break | 11th Floor Collaborative Space |
Friday, June 22, 2012
Time | Event | Location | Materials |
---|---|---|---|
9:00 - 12:00pm EDT | Research Topic Introductions | 11th Floor Lecture Hall | |
1:30 - 3:00pm EDT | Form Research Groups | 11th Floor Lecture Hall | |
3:00 - 3:30pm EDT | Coffee/Tea Break | 11th Floor Collaborative Space |
Monday, June 25, 2012
Time | Event | Location | Materials |
---|---|---|---|
9:30 - 11:00am EDT | The JAVA programming language - Pat Hooper, City College of New York | 11th Floor Lecture Hall | |
3:00 - 3:30pm EDT | Coffee/Tea Break | 11th Floor Collaborative Space |
Tuesday, June 26, 2012
Time | Event | Location | Materials |
---|---|---|---|
9:30 - 11:00am EDT | Mathematical graphics - Pat Hooper, City College of New York | 11th Floor Lecture Hall | |
3:00 - 3:30pm EDT | Coffee/Tea Break | 11th Floor Collaborative Space |
Wednesday, June 27, 2012
Time | Event | Location | Materials |
---|---|---|---|
10:00 - 11:00am EDT | Working Seminar | 11th Floor Lecture Hall | |
11:00 - 12:30pm EDT | Square grids, double lattice PETS, and renormalization - Rich Schwartz, Brown University | 11th Floor Lecture Hall | |
3:00 - 3:30pm EDT | Coffee/Tea Break | 11th Floor Collaborative Space |
Thursday, June 28, 2012
Time | Event | Location | Materials |
---|---|---|---|
9:30 - 11:00am EDT | Creating interactive programs - Pat Hooper, City College of New York | 11th Floor Lecture Hall | |
3:00 - 3:30pm EDT | Coffee/Tea Break | 11th Floor Collaborative Space |
Friday, June 29, 2012
Time | Event | Location | Materials |
---|---|---|---|
9:30 - 11:00am EDT | Sharing programs with others - Pat Hooper, City College of New York | 11th Floor Lecture Hall | |
3:00 - 3:30pm EDT | Coffee/Tea Break | 11th Floor Collaborative Space |
Monday, July 2, 2012
Time | Event | Location | Materials |
---|---|---|---|
10:00 - 11:00am EDT | Introduction to Complex Dynamics - Sarah Koch, Harvard University | 11th Floor Lecture Hall | |
3:00 - 3:30pm EDT | Coffee/Tea Break | 11th Floor Collaborative Space |
Tuesday, July 3, 2012
Time | Event | Location | Materials |
---|---|---|---|
10:00 - 11:00am EDT | Introduction to Complex Dynamics - Sarah Koch, Harvard University | 11th Floor Lecture Hall | |
3:00 - 3:30pm EDT | Coffee/Tea Break | 11th Floor Collaborative Space |
Thursday, July 5, 2012
Time | Event | Location | Materials |
---|---|---|---|
10:00 - 11:00am EDT | Introduction to Complex Dynamics - Sarah Koch, Harvard University | 11th Floor Lecture Hall | |
3:00 - 3:30pm EDT | Coffee/Tea Break | 11th Floor Collaborative Space |
Friday, July 6, 2012
Time | Event | Location | Materials |
---|---|---|---|
10:00 - 11:00am EDT | Introduction to Complex Dynamics - Sarah Koch, Harvard University | 11th Floor Lecture Hall | |
3:00 - 3:30pm EDT | Coffee/Tea Break | 11th Floor Collaborative Space |
Monday, July 9, 2012
Time | Event | Location | Materials |
---|---|---|---|
3:00 - 3:30pm EDT | Coffee/Tea Break | 11th Floor Collaborative Space |
Tuesday, July 10, 2012
Time | Event | Location | Materials |
---|---|---|---|
3:00 - 3:30pm EDT | Coffee/Tea Break | 11th Floor Collaborative Space |
Wednesday, July 11, 2012
Time | Event | Location | Materials |
---|---|---|---|
9:30 - 12:00pm EDT | Working Seminar | 11th Floor Lecture Hall | |
2:00 - 3:00pm EDT | Building polyhedra by self-assembly - Govind Menon, Brown University | 11th Floor Lecture Hall | |
3:00 - 3:30pm EDT | Coffee/Tea Break | 11th Floor Collaborative Space |
Thursday, July 12, 2012
Time | Event | Location | Materials |
---|---|---|---|
3:00 - 3:30pm EDT | Coffee/Tea Break | 11th Floor Collaborative Space |
Friday, July 13, 2012
Time | Event | Location | Materials |
---|---|---|---|
3:00 - 3:30pm EDT | Coffee/Tea Break | 11th Floor Collaborative Space |
Monday, July 16, 2012
Time | Event | Location | Materials |
---|---|---|---|
9:30 - 11:00am EDT | Introduction to Hyperbolic Geometry - Jeff Brock, ICERM, Brown University | 11th Floor Lecture Hall | |
3:00 - 3:30pm EDT | Coffee/Tea Break | 11th Floor Collaborative Space |
Tuesday, July 17, 2012
Time | Event | Location | Materials |
---|---|---|---|
9:30 - 11:00am EDT | Introduction to Hyperbolic Geometry - Jeff Brock, ICERM, Brown University | 11th Floor Lecture Hall | |
3:00 - 3:30pm EDT | Yellow Pig Day Celebration | 11th Floor Collaborative Space |
Wednesday, July 18, 2012
Time | Event | Location | Materials |
---|---|---|---|
2:00 - 3:00pm EDT | Geometric Discrepancy Theory - Jill Pipher, ICERM | 11th Floor Lecture Hall | |
3:00 - 3:05pm EDT | Summer@ICERM Group Photo | 11th Floor Lecture Hall | |
3:05 - 3:35pm EDT | Coffee/Tea Break | 11th Floor Collaborative Space |
Thursday, July 19, 2012
Time | Event | Location | Materials |
---|---|---|---|
9:30 - 11:00am EDT | Introduction to Hyperbolic Geometry - Jeff Brock, ICERM, Brown University | 11th Floor Lecture Hall | |
3:00 - 3:30pm EDT | Coffee/Tea Break | 11th Floor Collaborative Space |
Friday, July 20, 2012
Time | Event | Location | Materials |
---|---|---|---|
10:00 - 11:00am EDT | Introduction to Hyperbolic Geometry - Jeff Brock, ICERM, Brown University | 11th Floor Lecture Hall | |
3:00 - 3:30pm EDT | Coffee/Tea Break | 11th Floor Collaborative Space |
Monday, July 23, 2012
Time | Event | Location | Materials |
---|---|---|---|
10:00 - 11:30am EDT | Presentations | 11th Floor Lecture Hall | |
3:00 - 3:30pm EDT | Coffee/Tea Break | 11th Floor Collaborative Space |
Tuesday, July 24, 2012
Time | Event | Location | Materials |
---|---|---|---|
10:00 - 11:30am EDT | Presentations | 11th Floor Lecture Hall | |
3:00 - 3:30pm EDT | Coffee/Tea Break | 11th Floor Collaborative Space |
Wednesday, July 25, 2012
Time | Event | Location | Materials |
---|---|---|---|
2:00 - 3:00pm EDT | Snakes and ladders - Bjorn Sandstede, Brown University, ICERM | 11th Floor Lecture Hall | |
3:00 - 3:30pm EDT | Coffee/Tea Break | 11th Floor Collaborative Space |
Thursday, July 26, 2012
Time | Event | Location | Materials |
---|---|---|---|
10:00 - 11:30am EDT | Presentations | 11th Floor Lecture Hall | |
3:00 - 3:30pm EDT | Coffee/Tea Break | 11th Floor Collaborative Space |
Friday, July 27, 2012
Time | Event | Location | Materials |
---|---|---|---|
1:00 - 2:00pm EDT | Presentations | 11th Floor Lecture Hall | |
3:00 - 3:30pm EDT | Coffee/Tea Break | 11th Floor Collaborative Space |
Monday, July 30, 2012
Time | Event | Location | Materials |
---|---|---|---|
3:00 - 3:30pm EDT | Coffee/Tea Break | 11th Floor Collaborative Space |
Tuesday, July 31, 2012
Time | Event | Location | Materials |
---|---|---|---|
2:00 - 2:20pm EDT | Converse Desargues Theorem - Kevin Castro, Brown Univeristy and Desislava Nikolov, University of the Free State, South Africa | 11th Floor Lecture Hall | |
2:20 - 2:40pm EDT | Snaking under radical perturbations - Nadejda Drenska, Brown University | 11th Floor Lecture Hall | |
2:40 - 3:00pm EDT | Bug dynamics on manifolds - Dmitri Gekhtman, Harvard University | 11th Floor Lecture Hall | |
3:00 - 3:20pm EDT | A model of chip firing - Alexander St. Laurent, Brown University | 11th Floor Lecture Hall | |
3:20 - 3:40pm EDT | Outer Billiards with Contraction - Francisc Bozgan, UCLA, Rumania, In-Jee Jeong, Brown University and Julienne LaChance, Rensselaer Polytechnic Institute | 11th Floor Lecture Hall | |
3:40 - 4:00pm EDT | From spots to target patterns in Swift-Hohenberg equation - Chukiat Phonsom, Brown University | 11th Floor Lecture Hall | |
4:00 - 4:20pm EDT | A warm little pond - Nash Rochman, Brown University | 11th Floor Lecture Hall | |
4:20 - 4:40pm EDT | Bicycle Polygons, Solitons and the Darboux Transformation - Ian Alevy, University of Chicago and Emmanuel Tsukerman, Stanford University | 11th Floor Lecture Hall | |
4:40 - 5:00pm EDT | Instabilities of Euler flow - Zuhal Yildirim, Brown University | 11th Floor Lecture Hall | |
5:00 - 5:30pm EDT | Coffee & Dessert Reception | 11th Floor Collaborative Space |
Wednesday, August 1, 2012
Time | Event | Location | Materials |
---|---|---|---|
11:00 - 12:00pm EDT | Random Interfaces - Rick Kenyon, Brown University | 11th Floor Lecture Hall | |
3:00 - 3:30pm EDT | Coffee/Tea Break | 11th Floor Collaborative Space |
Thursday, August 2, 2012
Time | Event | Location | Materials |
---|---|---|---|
11:30 - 2:00pm EDT | 2012 UTRA Symposium | Sayles Hall | |
3:00 - 3:30pm EDT | Coffee/Tea Break | 11th Floor Collaborative Space |
Friday, August 3, 2012
Time | Event | Location | Materials |
---|---|---|---|
3:00 - 3:30pm EDT | Coffee/Tea Break | 11th Floor Collaborative Space |
Monday, August 6, 2012
Time | Event | Location | Materials |
---|---|---|---|
10:00 - 10:30am EDT | Coffee/Tea Break | 11th Floor Collaborative Space | |
10:30 - 11:30am EDT | Presentations: Unicycle problem - Amy Nesky, Boston College and Clara Redwood, Reed College | 10th Floor Collaborative Space | |
1:00 - 2:00pm EDT | Presentations: Outer billiards with contraction (and, perhaps, without :) - Francisc Bozgan, UCLA, Rumania, In-Jee Jeong, Brown University and Julienne LaChance, Rensselaer Polytechnic Institute | 10th Floor Collaborative Space | |
2:30 - 3:00pm EDT | Coffee/Tea Break | 11th Floor Collaborative Space |
Tuesday, August 7, 2012
Time | Event | Location | Materials |
---|---|---|---|
10:00 - 10:30am EDT | Coffee/Tea Break | 11th Floor Collaborative Space | |
10:30 - 11:30am EDT | Presentations: Billiards in near squares - Yilong Yang, Brown University and Hai Bin Chang, National University of Singapore | 10th Floor Collaborative Space | |
1:00 - 2:00pm EDT | Presentations: Bicycle curves and bicycle polygons - Ian Alevy, University of Chicago and Emmanuel Tsukerman, Stanford University | 10th Floor Collaborative Space | |
2:30 - 2:45pm EDT | Coffee/Tea Break | 11th Floor Collaborative Space |
Wednesday, August 8, 2012
Time | Event | Location | Materials |
---|---|---|---|
10:00 - 10:30am EDT | Coffee/Tea Break | 11th Floor Collaborative Space | |
10:30 - 11:30am EDT | Presentations: Negative Snell propagation - Katherine Engelman, Bryn Mawr College and Andrew Kimball, Western Carolina University | 10th Floor Collaborative Space | |
1:00 - 2:00pm EDT | Presentations: Converse Desargues theorem - Desislava Nikolov, University of the Free State and Kevin Casto, Brown University | 10th Floor Collaborative Space | |
2:30 - 3:00pm EDT | Coffee/Tea Break | 11th Floor Collaborative Space |
Thursday, August 9, 2012
Time | Event | Location | Materials |
---|---|---|---|
10:00 - 10:30am EDT | Coffee/Tea Break | 11th Floor Collaborative Space | |
1:00 - 2:00pm EDT | Presentations: Beetle problem - Dmitri Gekhtman, Harvard University | 10th Floor Collaborative Space | |
2:30 - 3:00pm EDT | Coffee/Tea Break | 11th Floor Collaborative Space |
Friday, August 10, 2012
Time | Event | Location | Materials |
---|---|---|---|
10:00 - 10:30am EDT | Coffee/Tea Break | 11th Floor Collaborative Space | |
1:00 - 1:30pm EDT | Closing Remarks | 10th Floor Collaborative Space | |
1:30 - 2:00pm EDT | Coffee/Tea Break | 10th Floor Collaborative Space |
Final Projects
- Final Student Presentations
-
- "Bicycle Polygons, Solitons, and the Darboux Transform" by E. Tsukerman and I. Alevy
- "Billiards in Near Rectangle" by Y. Yilong and C. Hai Bin
- "Outer Billiards with Contraction" by I. Jeong, F. Bozgan, and J. LaChance
- "Converse Desargues' Theorem" by K. Casto and D. Nikolov
- "A Cute Little Rhombus" by Y. Yilong and C. Hai Bin
- "Negative Snell Propagation" by K. Engelman and A. Kimball
- "Bicycle "Unicycle" Path" by A. Nesky and C. Redwood
- "Bugs" by D. Gekhtman
- Completed Student Projects
-
- H. Chang, Y. Yang. Billiards in near rectangles. arXiv:1610.09579.
- I. Alevy, E. Tsukerman. Polygonal bicycle paths and the Darboux transformation. Involve 9 (2016), 57–66.
- D. Gekhtman. Cyclic Pursuit on Compact Manifolds, published Pacific J. Math. 289 (2017), 153–168..
- I.-J. Jeong. Outer billiards with contraction: attracting Cantor sets. Exp. Math. 24 (2015), 53–64.
- A.Nesky, C. Redwood. On bicycle uni-track path efficiency: bicycle "unicycle" paths. The College Mathematics Journal, Vol. 47, No. 3, pp. 180-189.
- S. Tabachnikov, E. Tsukerman. On the discrete bicycle transformation. Publ. Math. Uruguay (proc. Montevideo Dynamical Systems Congress 2012), 14 (2013), 190-199.
- S. Tabachnikov, E. Tsukerman. Circumcenter of Mass and generalized Euler line. Discr. Comp. Geom., 51 (2014), 815-836.
- A simple visualizer for outer billiards with contraction: visualizer developed by Julienne LaChance, for use in her S@I research project with Francisc Bozgan and In-Jee Jeong.