Organizing Committee
City College of New York
ICERM and Penn State
Abstract
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
Image: R. Schwartz
-- 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
Summer 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
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Summer Schedule
Monday, June 18, 2012
9:00 - 9:30 AM EDT
Summer@ICERM Non-Brown Student Meet & Greet
9:30 - 10:00 AM EDT
Non-Brown Student Orientation
10:00 - 11:30 AM EDT
All Summer@ICERM students orientation
11:30 AM - 1:00 PM EDT
ICERM Welcome Lunch
Location: 11th Floor Collaborative Space
1:00 - 4:00 PM EDT
Introductions
Location: 11th Floor Lecture Hall
Tuesday, June 19, 2012
9:00 AM - 12:00 PM EDT
Research Topic Introductions
Location: 11th Floor Lecture Hall
12:00 - 1:30 PM EDT
Break for Free Lunch
1:30 - 3:00 PM EDT
Research Topic Introductions
Location: 11th Floor Lecture Hall
3:00 - 3:30 PM EDT
Coffee/Tea Break
Location: 11th Floor Collaborative Space
Wednesday, June 20, 2012
8:30 AM - 12:30 PM EDT
BEARCORE Training
Location: Medical Education Building - 222 Richmond Street, Providence RI
2:30 - 3:00 PM EDT
IT Tutorial - Isani Cayetano, ICERM
Location: 11th Floor Lecture Hall
3:00 - 3:30 PM EDT
Coffee/Tea Break
Location: 11th 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.
