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Organizing Committee
Davidson College
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.
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
Summer 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.
Gallery
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Lecture Videos
Tyrrell McAllister
University of Wyoming
June 30, 2014 • 12:00 AM
Tyrrell McAllister
University of Wyoming
July 1, 2014 • 12:00 AM
Tyrrell McAllister
University of Wyoming
July 2, 2014 • 12:00 AM
Tyrrell McAllister
University of Wyoming
July 3, 2014 • 12:00 AM
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.
