Organizing Committee
- Michael Mossinghoff
Davidson College - Sinai Robins
ICERM
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 2014 program is designed for a select group of 12-14 undergraduate scholars. Students work in groups of two or three, supervised by faculty advisors and aided by teaching assistants. The faculty advisors provide a number of interesting open problems in combinatorics, number theory, and discrete geometry concerning polygons and polynomials, each suitable for computation and experimentation. Students form research groups to work on the problems, give talks about their findings, and write up their research into a paper at the end of the program.
"The program exceeded my expectations by any standard I can think to apply -- the students were by and large strong and motivated, the ones I interacted with regularly were clearly learning quite a bit, the people
involved in organizing the program were a pleasure to work with, and the outcomes in terms of research have been impressive. It was both fun and rewarding to be involved in this program"
-- Summer@ICERM 2014 Participant
Program Details
- 2014 Research Project Topics
-
During the 2014 Summer@ICERM program the faculty organizers will describe a number of interesting, open-ended problems in combinatorics, discrete geometry, and number theory for study at the Summer@ICERM 2014 program. These problems arise in current research, are amenable to computation and experimentation, and may be approached from a number of different angles.
- Periods of Rational Polygons
- Barker Sequences
- Visualizing Harmonic Analysis Downloadable PDF of Project Descriptions
- Funding Includes
-
- $3,000 stipend
- Dormitory housing
- Meal plan
- Travel support within U.S.
- Fun events Brown University students must apply via MathPrograms.org AND also must apply for an UTRA grant with ICERM as sponsor in order to be eligible to receive the $3,000 stipend. The UTRA grant is provided in lieu of the Summer@ICERM funding package.
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
-
Zach Blumenstein
Brown University
-
Yiwang Chen
University of Illinois at Urbana-Champaign
-
Alexander Dunlap
University of Chicago
-
Nicholas Dunn
North Carolina State University
-
Molly Feldman
Swarthmore College
-
Lenny Fukshansky
Claremont McKenna College
-
Campbell Hewett
Brown University
-
Jason Hu
University of California, Berkeley
-
Robert Kenyon
McGill University
-
Sarah Koch
University of Michigan, Ann Arbor
-
Alicia LaMarche
Shippensburg University
-
Quang-Nhat Le
Brown University
-
Jiahui Liu
Columbia University
-
Tyrrell McAllister
University of Wyoming
-
Alexandru Mihai
Okinawa Institute of Science and Technology
-
Michael Mossinghoff
Davidson College
-
Dat Nguyen
Stanford University
-
Brooke Ogrodnik
Rowan University
-
James Propp
University of Massachusetts, Lowell
-
Alexandra Pushkar
University of Maryland
-
Sinai Robins
ICERM
-
Spencer Saunders
Regent University
-
Melissa Sherman-Bennett
Bard College at Simons Rock
-
Shashwat Silas
Brown University
-
Sergei Tabachnikov
ICERM and Penn State
-
Tim Trudgian
Australian National University
-
Emmanuel Tsukerman
University of California, Berkeley
-
Paxton Turner
Louisiana State University
-
Yuhuai Wu
University of New Brunswick
Summer Schedule
Monday, June 16, 2014
Time | Event | Location | Materials |
---|---|---|---|
10:00 - 10:30am EDT | Welcome/ Meet and Greet | 11th Floor Lecture Hall | |
10:30 - 11:45am EDT | Scavenger hunt | ||
12:00 - 1:30pm EDT | Welcome Lunch | 11th Floor Conference Room | |
1:30 - 2:30pm EDT | Periods of rational polygons: An introduction to discrete areas | 11th Floor Lecture Hall | |
2:30 - 3:00pm EDT | Coffee/Tea Break | 11th Floor Collaborative Space |
Tuesday, June 17, 2014
Wednesday, June 18, 2014
Thursday, June 19, 2014
Friday, June 20, 2014
Time | Event | Location | Materials |
---|---|---|---|
10:00 - 11:30am EDT | Groups Formed; Begin working in groups | groups | |
1:00 - 2:30pm EDT | Work in groups | groups | |
2:30 - 3:00pm EDT | Coffee/Tea Break | 11th Floor Collaborative Space | |
3:00 - 4:00pm EDT | Work in groups | groups |
Monday, June 23, 2014
Tuesday, June 24, 2014
Time | Event | Location | Materials |
---|---|---|---|
9:00 - 11:00am EDT | ICERM BearCore/Professional Development | 11th Floor Lecture Hall | |
1:30 - 2:30pm EDT | Research Group Meetings: Pisot - Supervisors: Mike, Sanya and Tarik | 10th Floor Classroom | |
1:30 - 2:30pm EDT | Research Group Meetings: Dedekind - Supervisors: Sinai, Emmanuel and Nhat | 11th Floor Lecture Hall | |
2:30 - 3:00pm EDT | Coffee/Tea Break | 11th Floor Collaborative Space | |
3:00 - 4:00pm EDT | Research Group Meetings: k-tilings - Supervisors: Sinai, Nhat and Sanya | 11th Floor Lecture Hall |
Wednesday, June 25, 2014
Time | Event | Location | Materials |
---|---|---|---|
2:30 - 3:00pm EDT | Coffee/Tea Break | 10th Floor Collaborative Space |
Thursday, June 26, 2014
Time | Event | Location | Materials |
---|---|---|---|
1:30 - 2:30pm EDT | Research Group Meetings: Ehrhart - Supervisors: Sinai, Sanya and Tarik | 10th Floor Collaborative Space | |
1:30 - 2:30pm EDT | Research Group Meetings: Barker - Supervisors: Mike and Emmanuel | 10th Floor Classroom | |
2:30 - 3:00pm EDT | Coffee/Tea Break | 10th Floor Collaborative Space | |
3:00 - 4:00pm EDT | Research Group Meetings: Reinhardt - Supervisors: Mike, Nhat and Tarik | 10th Floor Classroom |
Friday, June 27, 2014
Monday, June 30, 2014
Time | Event | Location | Materials |
---|---|---|---|
10:00 - 11:30am EDT | Coefficients of Ehrhart quasi-polynomials - Tyrrell McAllister, University of Wyoming | 11th Floor Lecture Hall | |
1:30 - 2:30pm EDT | Research Group Meetings: Ehrhart - Supervisors - Sinai, Sanya and Tarik | 11th Floor Lecture Hall | |
1:30 - 2:30pm EDT | Research Group Meetings: Barker - Supervisors - Mike and Emmanuel | 10th Floor Classroom | |
2:30 - 3:00pm EDT | Coffee/Tea Break | 11th Floor Collaborative Space | |
3:00 - 4:00pm EDT | Research Group Meetings: Reinhardt - Supervisors - Mike, Nhat and Tarik | 11th Floor Lecture Hall |
Tuesday, July 1, 2014
Time | Event | Location | Materials |
---|---|---|---|
10:00 - 11:30am EDT | Coefficients of Ehrhart quasi-polynomials - Tyrrell McAllister, University of Wyoming | 11th Floor Lecture Hall | |
1:00 - 2:00pm EDT | The projective heat map - Richard Schwartz, Brown University | 11th Floor Lecture Hall | |
2:30 - 3:00pm EDT | Coffee/Tea Break | 11th Floor Collaborative Space | |
3:00 - 4:00pm EDT | Research Group Meetings: k-tilings - Supervisors - Sinai, Nhat and Sanya | 11th Floor Lecture Hall |
Wednesday, July 2, 2014
Time | Event | Location | Materials |
---|---|---|---|
10:00 - 11:30am EDT | Coefficients of Ehrhart quasi-polynomials - Tyrrell McAllister, University of Wyoming | 11th Floor Lecture Hall | |
1:30 - 2:30pm EDT | Graduate School Roundtable | 11th Floor Lecture Hall | |
2:30 - 3:00pm EDT | Coffee/Tea Break | 11th Floor Collaborative Space | |
6:30 - 8:30pm EDT | Game Night! | 11th Floor Collaborative Space |
Thursday, July 3, 2014
Time | Event | Location | Materials |
---|---|---|---|
10:00 - 11:30am EDT | Coefficients of Ehrhart quasi-polynomials - Tyrrell McAllister, University of Wyoming | 11th Floor Lecture Hall | |
1:30 - 2:30pm EDT | Research Group Meetings: Barker - Supervisors - Mike and Emmanuel | 11th Floor Lecture Hall | |
1:30 - 2:30pm EDT | Research Group Meetings: Ehrhart - Supervisors - Sinai, Sanya and Tarik | 10th Floor Classroom | |
2:30 - 3:00pm EDT | Coffee/Tea Break | 11th Floor Collaborative Space | |
3:00 - 4:00pm EDT | Research Group Meetings: Reinhardt - Supervisors - Mike, Nhat and Tarik | 11th Floor Lecture Hall | |
4:00 - 5:00pm EDT | Research Group Meetings: Pisot - Supervisors: Mike, Sanya and Tarik | 11th Floor Lecture Hall |
Friday, July 4, 2014
Time | Event | Location | Materials |
---|---|---|---|
8:00 - 5:00pm EDT | ICERM Closed |
Monday, July 7, 2014
Time | Event | Location | Materials |
---|---|---|---|
11:00 - 12:00pm EDT | Research Group Meetings: Barker - Supervisors: Mike and Emmanuel | 10th Floor Classroom | |
11:00 - 12:00pm EDT | Research Group Meetings: Ehrhart - Supervisors: Sinai, Sanya and Tarik | 11th Floor Lecture Hall | |
2:30 - 3:00pm EDT | Coffee/Tea Break | 11th Floor Collaborative Space | |
3:00 - 4:00pm EDT | Research Group Meetings: Reinhardt - Supervisors: Mike, Nhat and Tarik | 11th Floor Lecture Hall |
Tuesday, July 8, 2014
Time | Event | Location | Materials |
---|---|---|---|
1:30 - 2:30pm EDT | Research Group Meetings: Dedekind - Supervisors: Sinai, Emmanuel and Nhat | 11th Floor Lecture Hall | |
1:30 - 2:30pm EDT | Research Group Meetings: Pisot - Supervisors: Mike, Sanya and Tarik | 10th Floor Classroom | |
2:30 - 3:00pm EDT | Coffee/Tea Break | 11th Floor Collaborative Space | |
3:00 - 4:00pm EDT | Research Group Meetings: k-tilings - Supervisors: Sinai, Nhat and Sanya | 11th Floor Lecture Hall |
Wednesday, July 9, 2014
Thursday, July 10, 2014
Time | Event | Location | Materials |
---|---|---|---|
9:30 - 10:30am EDT | Research Group Meetings: k-tilings - Supervisors: Sinai, Nhat and Sanya | 11th Floor Lecture Hall | |
10:30 - 11:30am EDT | Research Group Meetings: Ehrhart - Supervisors: Sinai, Sanya and Tarik | 11th Floor Lecture Hall | |
11:00 - 12:00pm EDT | Research Group Meetings: Barker - Supervisors: Mike and Emmanuel | 10th Floor Classroom | |
1:00 - 2:30pm EDT | De-randomizing Randomness with Rotor-Routers - James Propp, UMass Lowell | 11th Floor Lecture Hall | |
2:30 - 3:00pm EDT | Coffee/Tea Break | 11th Floor Collaborative Space | |
3:00 - 4:00pm EDT | Research Group Meetings: Reinhardt - Supervisors: Mike, Nhat and Tarik | 11th Floor Lecture Hall | |
4:00 - 5:00pm EDT | Research Group Meetings: Pisot - Supervisors: Mike, Sanya and Tarik | 11th Floor Lecture Hall |
Friday, July 11, 2014
Time | Event | Location | Materials |
---|---|---|---|
6:40 - 10:40pm EDT | MoMath |
Monday, July 14, 2014
Time | Event | Location | Materials |
---|---|---|---|
1:30 - 2:30pm EDT | Research group meetings: Barker - Supervisors: Mike, Emmanuel | Office 1017 | |
1:30 - 2:30pm EDT | Research group meetings: Ehrhart - Supervisors: Sanya, Tarik | 10th Floor Classroom | |
2:30 - 3:00pm EDT | Coffee/Tea Break | 11th Floor Collaborative Space | |
3:00 - 4:00pm EDT | Research group meetings: Reinhardt - Supervisors: Mike, Nhat, Tarik | 10th Floor Classroom |
Tuesday, July 15, 2014
Time | Event | Location | Materials |
---|---|---|---|
1:30 - 2:30pm EDT | Research group meetings: Pisot - Supervisors: Mike, Sanya, Tarik | Office 1018 | |
1:30 - 2:30pm EDT | Research group meetings: Dedekind - Supervisors: Emmanuel, Nhat | 10th Floor Classroom | |
2:30 - 3:00pm EDT | Coffee/Tea Break | ||
3:00 - 4:00pm EDT | Research group meetings: k-tilings - Supervisors: Nhat, Tarik | 10th Floor Classroom |
Wednesday, July 16, 2014
Time | Event | Location | Materials |
---|---|---|---|
1:30 - 2:30pm EDT | Discussion panel: Writing a paper | 10th Floor Classroom | |
2:30 - 3:00pm EDT | Coffee/Tea Break | 11th Floor Collaborative Space |
Thursday, July 17, 2014
Time | Event | Location | Materials |
---|---|---|---|
1:30 - 2:30pm EDT | 1:30-2:30 Research group meetings: Ehrhart - Supervisors: Sanya, Tarik | 10th Floor Classroom | |
1:30 - 2:30pm EDT | Research group meetings: Barker - Supervisors: Mike, Emmanuel | Office 1017 | |
2:30 - 3:00pm EDT | Coffee/Tea Break | 11th Floor Collaborative Space | |
3:00 - 4:00pm EDT | Research group meetings: Reinhardt - Supervisors: Mike, Nhat, Tarik | 10th Floor Classroom |
Friday, July 18, 2014
Time | Event | Location | Materials |
---|---|---|---|
1:30 - 2:30pm EDT | Research group meetings: Dedekind - Supervisors: Emmanuel, Nhat | 10th Floor Classroom | |
1:30 - 2:30pm EDT | Research group meetings: Pisot - Supervisors: Mike, Sanya, Tarik | Office 1018 | |
2:30 - 3:00pm EDT | Coffee/Tea Break | 11th Floor Collaborative Space | |
3:00 - 4:00pm EDT | Research group meetings: k-tilings - Supervisors: Nhat, Tarik | 10th Floor Classroom |
Monday, July 21, 2014
Time | Event | Location | Materials |
---|---|---|---|
1:30 - 2:30pm EDT | Research Group Meetings - Ehrhart - Supervisors: Sanya and Tarik | 10th Floor Classroom | |
2:30 - 3:00pm EDT | Coffee/Tea Break | 11th Floor Collaborative Space |
Tuesday, July 22, 2014
Time | Event | Location | Materials |
---|---|---|---|
9:00 - 10:00am EDT | Research group meetings: Barker - Supervisors: Mike, Emmanuel | Office 1017 | |
10:00 - 11:00am EDT | Research group meetings: Reinhardt - Supervisors: Mike, Nhat, Tarik | Office 1021 | |
11:00 - 12:00pm EDT | Research group meetings: Pisot - Supervisors: Mike, Sanya | Office 1018 | |
1:30 - 2:30pm EDT | Research group meetings: Dedekind - Supervisors: Emmanuel, Nhat | 10th Floor Classroom | |
2:30 - 3:00pm EDT | Coffee/Tea Break | 11th Floor Collaborative Space | |
3:00 - 4:00pm EDT | Research group meetings: k-tilings - Supervisors: Nhat, Tarik | 10th Floor Classroom |
Wednesday, July 23, 2014
Thursday, July 24, 2014
Time | Event | Location | Materials |
---|---|---|---|
10:00 - 12:00pm EDT | American Mathematical Society | 201 Charles Street, Providence, RI | |
1:45 - 2:25pm EDT | Equality of Dedekind sums: experimental data, and theory - Sinai Robins, Nanyang Technological University and ICERM | 11th Floor Lecture Hall | |
2:30 - 3:00pm EDT | Coffee/Tea Break | 11th Floor Collaborative Space | |
2:35 - 3:15pm EDT | Polynomials, number theory, and experimental mathematics - Michael Mossinghoff, Davidson College and ICERM | 11th Floor Lecture Hall |
Friday, July 25, 2014
Time | Event | Location | Materials |
---|---|---|---|
9:00 - 10:00am EDT | Research group meetings: Ehrhart - Supervisors: Sanya, Tarik | 10th Floor Classroom | |
9:00 - 10:00am EDT | Research group meetings: Barker - Supervisors: Mike, Emmanuel | Office 1017 | |
10:00 - 11:00am EDT | Research group meetings: Reinhardt - Supervisors: Mike, Nhat, Tarik | 10th Floor Classroom | |
11:00 - 12:00pm EDT | Research group meetings: Pisot - Supervisors: Mike, Sanya, Tarik | Office 1018 | |
1:30 - 2:30pm EDT | Research group meetings: Dedekind - Supervisors: Emmanuel, Nhat | 10th Floor Classroom | |
2:30 - 3:00pm EDT | Coffee/Tea Break | 11th Floor Collaborative Space | |
3:00 - 4:00pm EDT | Research group meetings: k-tilings - Supervisors: Nhat, Tarik | 10th Floor Classroom |
Monday, July 28, 2014
Tuesday, July 29, 2014
Time | Event | Location | Materials |
---|---|---|---|
10:00 - 11:30am EDT | Topics on Polynomials - Sergei Tabachnikov, ICERM | 11th Floor Lecture Hall | |
1:30 - 2:30pm EDT | Research group meetings: Dedekind - Supervisors: Sinai, Emmanuel and Nhat | 11th Floor Lecture Hall | |
1:30 - 2:30pm EDT | Research group meetings: Pisot - Supervisors: Mike, Sanya, Tarik | 10th Floor Classroom | |
2:30 - 3:00pm EDT | Coffee/Tea Break | 11th Floor Collaborative Space | |
3:00 - 4:00pm EDT | Research group meetings: k-tilings - Supervisors: Sinai, Nhat and Tarik | 11th Floor Lecture Hall |
Wednesday, July 30, 2014
Time | Event | Location | Materials |
---|---|---|---|
2:30 - 3:00pm EDT | Coffee/Tea Break | 11th Floor Collaborative Space | |
7:00 - 9:00pm EDT | Summer@ICERM Movie Night | 11th Floor Lecture Hall |
Thursday, July 31, 2014
Time | Event | Location | Materials |
---|---|---|---|
10:00 - 11:30am EDT | Topics on Polynomials - Sergei Tabachnikov, ICERM | 11th Floor Lecture Hall | |
1:30 - 2:30pm EDT | Research group meetings: Barker - Supervisors: Mike, Emmanuel | 11th Floor Lecture Hall | |
1:30 - 2:30pm EDT | Research group meetings: Ehrhart - Supervisors: Sinai, Sanya and Tarik | 10th Floor Classroom | |
2:30 - 3:00pm EDT | Coffee/Tea Break | 11th Floor Collaborative Space | |
3:00 - 4:00pm EDT | Research group meetings: Reinhardt - Supervisors: Mike, Nhat, Tarik | 11th Floor Lecture Hall |
Friday, August 1, 2014
Time | Event | Location | Materials |
---|---|---|---|
10:00 - 11:30am EDT | Topics on Polynomials - Sergei Tabachnikov, ICERM | 11th Floor Lecture Hall | |
1:30 - 2:30pm EDT | Research group meetings: Dedekind - Supervisors: Sinai, Emmanuel and Nhat | 11th Floor Lecture Hall | |
1:30 - 2:30pm EDT | Research group meetings: Pisot - Supervisors: Mike, Sanya | 10th Floor Classroom | |
2:30 - 3:00pm EDT | Coffee/Tea Break | 11th Floor Collaborative Space | |
3:00 - 4:00pm EDT | Research group meetings: k-tilings - Supervisors: Sinai, Nhat and Tarik | 11th Floor Lecture Hall |
Monday, August 4, 2014
Time | Event | Location | Materials |
---|---|---|---|
1:30 - 2:30pm EDT | Research group meetings: Ehrhart - Supervisors: Sinai, Sanya, Tarik | ||
1:30 - 2:30pm EDT | Research group meetings: Barker - Supervisors: Mike, Emmanuel | ||
2:30 - 3:00pm EDT | Coffee/Tea Break | 11th Floor Collaborative Space | |
3:00 - 4:00pm EDT | Research group meetings: Reinhardt - Supervisors: Mike, Nhat, Tarik | ||
6:30 - 8:30pm EDT | Summer@ICERM Game Night |
Tuesday, August 5, 2014
Time | Event | Location | Materials |
---|---|---|---|
1:30 - 2:30pm EDT | Research group meetings: Dedekind - Supervisors: Sinai, Emmanuel, Nhat | ||
1:30 - 2:30pm EDT | Research group meetings: Pisot - Supervisors: Mike, Sanya | ||
2:30 - 3:00pm EDT | Coffee/Tea Break | 10th Floor Collaborative Space | |
3:00 - 4:00pm EDT | Research group meetings: K-tilings - Supervisors: Sinai, Nhat, Tarik |
Wednesday, August 6, 2014
Thursday, August 7, 2014
Friday, August 8, 2014
Final Projects
- Final Student Presentations
-
- "Equality of Dedekind sums" by Y. Chen, N. Dunn, C. Hewett, and S. Silas
- "Computation and analysis on Reinhardt polygons with multiple distinct prime divisors" by M.Feldman, R.Kenyon and J.Liu
- "Equidecomposability and period collapse" by P.Turner and Y.Wu
- "Will it k-tile? Structural aspects of polytopes and lattices in multiple tiling" by A.Dunlap, A.Mihai, D.Nguyen and M.Sherman-Bennett
- "Complex Pisot numbers and Newman multiples" by Z.Blumenstein, A.Lamarche and S.Saunders
- "Advances in possible orders of circulant Hadamard matrices and sequences with large merit factor" by J.Hu and B. Logan
- Talks were also given by Alicia Lamarche and Zach Blumenstein:
"Covering Systems of the Integers" by A.Lamarche
"The Incompleteness of Arithmetic and Systems that Contain It" by Z.Blumenstein
- "Equality of Dedekind sums" by Y. Chen, N. Dunn, C. Hewett, and S. Silas
- Completed Student Projects
-
- P.Turner, Y.Wu. Conditions for Discrete Equidecomposabilty of Polygons. arXiv:1412.0191
- P.Turner, Y.Wu. Discrete Equidecomposabilty and Ehrhart Theory of Polygons. arXiv:1412.0196.
- B. Logan and M. J. Mossinghoff, Double Wieferich pairs and circulant Hadamard matrices: published J. Combin. Math. Combin. Comput. 101 (2017), 145–156.
- Y. Chen, N. Dunn, C. Hewett, S. Silas, Dedekind sums s(a, b) and inversions modulo b, International Journal of Number Theory, Vol. 11, No. 08, pp. 2325-2339 (2015).
-
There are three preprints from the k-tiling group:
- A. Dunlap, A. Mihai, D. Nguyen, S. Robins, and M. Sherman-Bennett, A constructive description of convex multi-tiling polygons, 2015.
- A. Dunlap, A. Mihai, D. Nguyen, and M. Sherman-Bennett, A classification of multi-tiling polytopes in three dimensions, 2015.
- A. Dunlap, A. Mihai, D. Nguyen, S. Robins, and M. Sherman-Bennett, On the structure of translation sets in multiple tiling of zonotopes, 2015.
There is also an applet constructed by A. Mihai, which offers a computational tool and he published it as a Wolfram applet for Mathematica.