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SUMMER@ICERM: 2014 Undergraduate Summer Research Program

Polygons and Polynomials (June 16 - August 8, 2014)

 

 

Faculty: Lead a S@I program!
2014 Organizing Committee:

Summer@ICERM 2014
Funding Includes*
  • $3,000 stipend
  • Travel support within U.S.
  • Dormitory housing
  • Meal plan
  • Fun activities
*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.

 

What to Expect

Frequently Asked Questions
Brown Students: UTRA Instructions
View Summer@ICERM 2012 and Summer@ICERM 2014


Summer@ICERM 2014 students and faculty leaders during a field trip
to the Providence headquarters of the American Mathematical Society.

 

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 2014 Summer@ICERM 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.

Research Project Topics for SUMMER@ICERM 2014
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.

2014 Research Project Topics:
Periods of Rational Polygons
Barker Sequences
Visualizing Harmonic Analysis

Participants will be expected to gain intuition into some of these problems via computer experimentation and visualization. The complete problem list for the 2014 program is available here: Problem list PDF. PDF


Applications for the 2014 Summer@ICERM are no longer being accepted. Please check our website and MathPrograms.org in the fall of 2014 for next year's program details.

Applicants must not yet have graduated with an undergraduate degree at the time of the program start. Funding is available for a limited number of students who are not US citizens or permanent residents.


“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

 

 

  • Tarik Aougab
    (Yale 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 *
    (Harvard University)
  • Alicia LaMarche
    (Shippensburg University)
  • Jiahui Liu
    (Columbia University)
  • Brooke Logan
    (Rowan University)
  • Tyrrell McAllister*
    (University of Wyoming)
  • Alexandru Mihai
    (Jacobs University)
  • Michael Mossinghoff
    (Davidson College)
  • Dat Nguyen
    (Stony Brook University)
  • Quang Nhat Le
    (Brown University)
  • Alexandra Pushkar
    (University of Maryland)
  • Sinai Robins
    (Nanyang Technological University)
  • Spencer Saunders
    (Regent University)
  • Melissa Sherman-Bennett
    (Bard College at Simons Rock)
  • Shashwat Silas
    (Brown University)
  • Sergei Tabachnikov *
    (Institute for Computational and Experimental Research in Mathematics (ICERM))
  • Tim Trudgian *
    (Australian National University)
  • Emmanuel Tsukerman
    (University of California, Berkeley)
  • Paxton Turner
    (Louisiana State University)
  • Yuhuai Wu
    (University of New Brunswick)
First Week Outline

Monday, June 16th: ICERM Orientation, Scavenger Hunt & Welcome Lunch from 10AM-2PM

Tuesday, June 17 – Friday, June 20: Research Topics Introductions 1:30PM – 2:30PM

Wednesday, June 18: IT Tutorial 3:00PM – 3:30PM

Students will be assigned to their Research Groups by end of the first week


Weekly Events Outline

Every Monday, Tuesday, Thursday & Friday
Meetings between research groups and supervisors (See Research Group Meeting Schedule)

Coffee & Tea Break at 2:30 – 3:00, Monday - Friday


Mini-Course Schedule

"Coefficients of Ehrhart quasi-polynomials" led by Tyrell McAllister, University of Wyoming
6/30, 7/1, 7/2, 7/3 (10:00 AM – 11:30 AM)

“Topics on Polynomials” led by Sergei Tabachnikov, ICERM
7/28, 7/29, 7/31, 8/1 (10:00 AM – 11:30 AM)


Special Events (with more to be scheduled)

6/23: “Adjacent primitive roots” Tim Trudgian, Australian National University (1:00 PM)

6/24 : ICERM BearCore/Professional Development (9AM – 11AM)

7/2: “Talk TBA” Speaker TBA (Time TBA)

7/9: “Talk TBA” Speaker TBA (Time TBA)

7/23: “Mating habits of polynomials”

Sarah Koch, University of Michigan (1:00 PM) - 10th Floor Classroom

7/30: “Talk TBA” Speaker TBA (Time TBA)

Writing Seminar: Date TBA

Group Talks on Research: Monday, August 4 – Thursday, August 7


Closing Reception: August 8th, Time TBA

Summer@ICERM will generally meet at ICERM Monday through Friday between 8:30AM and 5:00PM. Any after-hour activities at ICERM must occur with a faculty advisor, a TA, or an ICERM staff member present.

MondayJune 16, 2014
TimeDescriptionSpeakerLocationAbstractsSlides
10:00 - 10:30Welcome/ Meet and Greet11th Floor Lecture Hall
10:30 - 11:45Scavenger hunt
12:00 - 1:30Welcome Lunch11th Floor Conference Room
1:30 - 2:30Periods of rational polygons: An introduction to discrete areas11th Floor Lecture Hall
2:30 - 3:00Coffee/Tea Break11th Floor Collaborative Space

TuesdayJune 17, 2014
TimeDescriptionSpeakerLocationAbstractsSlides
10:00 - 11:30Reinhardt PolygonsMichael Mossinghoff11th Floor Lecture Hall
PDF
1:00 - 2:30Dedekind sums: Their appearance in number theory, polytopes, and their computational aspects.11th Floor Lecture Hall
2:30 - 3:00Coffee/Tea Break11th Floor Collaborative Space

WednesdayJune 18, 2014
TimeDescriptionSpeakerLocationAbstractsSlides
10:00 - 11:30Come on down! An invitation to Barker polynomialsMichael Mossinghoff11th Floor Lecture Hall
PDF
1:00 - 2:30Visualizing harmonic analysis- roots of exponential polynomials.Sinai Robins11th Floor Lecture Hall
PDF
2:30 - 3:00Coffee/Tea Break11th Floor Collaborative Space
3:00 - 3:30IT TutorialIsani Cayetano, ICERM11th Floor Lecture Hall

ThursdayJune 19, 2014
TimeDescriptionSpeakerLocationAbstractsSlides
10:00 - 11:30Complex Pisot Numbers and Newman PolynomialsMichael Mossinghoff11th Floor Lecture Hall
PDF
1:00 - 1:30Reading and research; focus on problem selection
1:30 - 3:00Fourier MethodsSinai Robins11th Floor Lecture Hall
3:00 - 3:30Coffee/Tea Break11th Floor Collaborative Space
3:30 - 5:00Reading and research; focus on problem selection
5:00 - 5:15Submit Problem Preferences

FridayJune 20, 2014
TimeDescriptionSpeakerLocationAbstractsSlides
10:00 - 11:30Groups Formed; Begin working in groupsgroups
1:00 - 2:30Work in groupsgroups
2:30 - 3:00Coffee/Tea Break11th Floor Collaborative Space
3:00 - 4:00Work in groupsgroups

MondayJune 23, 2014
TimeDescriptionSpeakerLocationAbstractsSlides
11:00 - 12:00Research Group Meetings: EhrhartSupervisors: Sinai, Sanya and Tarik11th Floor Lecture Hall
11:00 - 12:00Research Group Meetings: BarkerSupervisors: Mike and Emmanuel10th Floor Classroom
1:30 - 2:30Adjacent primitive rootsTim Trudgian, Australian National University11th Floor Lecture Hall
PDF
2:30 - 3:00Coffee/Tea Break11th Floor Collaborative Space
3:00 - 4:00Research Group Meetings: ReinhardtSupervisors: Mike, Nhat and Tarik11th Floor Lecture Hall

TuesdayJune 24, 2014
TimeDescriptionSpeakerLocationAbstractsSlides
9:00 - 11:00ICERM BearCore/Professional Development 11th Floor Lecture Hall
1:30 - 2:30Research Group Meetings: PisotSupervisors: Mike, Sanya and Tarik10th Floor Classroom
1:30 - 2:30Research Group Meetings: DedekindSupervisors: Sinai, Emmanuel and Nhat11th Floor Lecture Hall
2:30 - 3:00Coffee/Tea Break11th Floor Collaborative Space
3:00 - 4:00Research Group Meetings: k-tilingsSupervisors: Sinai, Nhat and Sanya11th Floor Lecture Hall

WednesdayJune 25, 2014
TimeDescriptionSpeakerLocationAbstractsSlides
2:30 - 3:00Coffee/Tea Break10th Floor Collaborative Space

ThursdayJune 26, 2014
TimeDescriptionSpeakerLocationAbstractsSlides
1:30 - 2:30Research Group Meetings: EhrhartSupervisors: Sinai, Sanya and Tarik10th Floor Collaborative Space
1:30 - 2:30Research Group Meetings: BarkerSupervisors: Mike and Emmanuel10th Floor Classroom
2:30 - 3:00Coffee/Tea Break10th Floor Collaborative Space
3:00 - 4:00Research Group Meetings: ReinhardtSupervisors: Mike, Nhat and Tarik10th Floor Classroom

FridayJune 27, 2014
TimeDescriptionSpeakerLocationAbstractsSlides
11:00 - 12:00Research Group Meetings: DedekindSupervisors: Sinai, Emmanuel and Nhat10th Floor Collaborative Space
11:00 - 12:00Research Group Meetings: PisotSupervisors: Mike, Sanya and Tarik10th Floor Collaborative Space
1:30 - 2:30FIFA Foe Fun!Michael Mossinghoff, Davidson College10th Floor Classroom
PDF
2:30 - 3:00Coffee/Tea Break10th Floor Collaborative Space
3:00 - 4:00Research Group Meetings: k-tilingsSupervisors: Sinai, Nhat and Sanya10th Floor Classroom

MondayJune 30, 2014
TimeDescriptionSpeakerLocationAbstractsSlides
10:00 - 11:30Coefficients of Ehrhart quasi-polynomialsTyrrell McAllister, University of Wyoming11th Floor Lecture Hall
1:30 - 2:30Research Group Meetings: EhrhartSupervisors - Sinai, Sanya and Tarik11th Floor Lecture Hall
1:30 - 2:30Research Group Meetings: BarkerSupervisors - Mike and Emmanuel10th Floor Classroom
2:30 - 3:00Coffee/Tea Break11th Floor Collaborative Space
3:00 - 4:00Research Group Meetings: ReinhardtSupervisors - Mike, Nhat and Tarik11th Floor Lecture Hall

TuesdayJuly 1, 2014
TimeDescriptionSpeakerLocationAbstractsSlides
10:00 - 11:30Coefficients of Ehrhart quasi-polynomialsTyrrell McAllister, University of Wyoming11th Floor Lecture Hall
1:00 - 2:00The projective heat mapRichard Schwartz, Brown University11th Floor Lecture Hall
2:30 - 3:00Coffee/Tea Break11th Floor Collaborative Space
3:00 - 4:00Research Group Meetings: k-tilingsSupervisors - Sinai, Nhat and Sanya11th Floor Lecture Hall

WednesdayJuly 2, 2014
TimeDescriptionSpeakerLocationAbstractsSlides
10:00 - 11:30Coefficients of Ehrhart quasi-polynomialsTyrrell McAllister, University of Wyoming11th Floor Lecture Hall
1:30 - 2:30Graduate School Roundtable11th Floor Lecture Hall
2:30 - 3:00Coffee/Tea Break11th Floor Collaborative Space
6:30 - 8:30Game Night!11th Floor Collaborative Space

ThursdayJuly 3, 2014
TimeDescriptionSpeakerLocationAbstractsSlides
10:00 - 11:30Coefficients of Ehrhart quasi-polynomialsTyrrell McAllister, University of Wyoming11th Floor Lecture Hall
1:30 - 2:30Research Group Meetings: BarkerSupervisors - Mike and Emmanuel11th Floor Lecture Hall
1:30 - 2:30Research Group Meetings: EhrhartSupervisors - Sinai, Sanya and Tarik10th Floor Classroom
2:30 - 3:00Coffee/Tea Break11th Floor Collaborative Space
3:00 - 4:00Research Group Meetings: ReinhardtSupervisors - Mike, Nhat and Tarik11th Floor Lecture Hall
4:00 - 5:00Research Group Meetings: PisotSupervisors: Mike, Sanya and Tarik11th Floor Lecture Hall

FridayJuly 4, 2014
TimeDescriptionSpeakerLocationAbstractsSlides
8:00 - 5:00ICERM Closed

MondayJuly 7, 2014
TimeDescriptionSpeakerLocationAbstractsSlides
11:00 - 12:00Research Group Meetings: BarkerSupervisors: Mike and Emmanuel10th Floor Classroom
11:00 - 12:00Research Group Meetings: EhrhartSupervisors: Sinai, Sanya and Tarik11th Floor Lecture Hall
2:30 - 3:00Coffee/Tea Break11th Floor Collaborative Space
3:00 - 4:00Research Group Meetings: ReinhardtSupervisors: Mike, Nhat and Tarik11th Floor Lecture Hall

TuesdayJuly 8, 2014
TimeDescriptionSpeakerLocationAbstractsSlides
1:30 - 2:30Research Group Meetings: DedekindSupervisors: Sinai, Emmanuel and Nhat11th Floor Lecture Hall
1:30 - 2:30Research Group Meetings: PisotSupervisors: Mike, Sanya and Tarik10th Floor Classroom
2:30 - 3:00Coffee/Tea Break11th Floor Collaborative Space
3:00 - 4:00Research Group Meetings: k-tilingsSupervisors: Sinai, Nhat and Sanya11th Floor Lecture Hall

WednesdayJuly 9, 2014
TimeDescriptionSpeakerLocationAbstractsSlides
1:00 - 2:30Negative Numbers in Combinatorics: Geometrical and Algebraic PerspectivesJames Propp, UMass Lowell11th Floor Lecture Hall
PDF
2:30 - 3:30IceCream@ICERM11th Floor Collaborative Space
6:30 - 8:30Game Night!11th Floor Collaborative Space

ThursdayJuly 10, 2014
TimeDescriptionSpeakerLocationAbstractsSlides
9:30 - 10:30Research Group Meetings: k-tilingsSupervisors: Sinai, Nhat and Sanya11th Floor Lecture Hall
10:30 - 11:30Research Group Meetings: EhrhartSupervisors: Sinai, Sanya and Tarik11th Floor Lecture Hall
11:00 - 12:00Research Group Meetings: BarkerSupervisors: Mike and Emmanuel10th Floor Classroom
1:00 - 2:30De-randomizing Randomness with Rotor-RoutersJames Propp, UMass Lowell11th Floor Lecture Hall
2:30 - 3:00Coffee/Tea Break11th Floor Collaborative Space
3:00 - 4:00Research Group Meetings: ReinhardtSupervisors: Mike, Nhat and Tarik11th Floor Lecture Hall
4:00 - 5:00Research Group Meetings: PisotSupervisors: Mike, Sanya and Tarik11th Floor Lecture Hall

FridayJuly 11, 2014
TimeDescriptionSpeakerLocationAbstractsSlides
6:40 - 10:40MoMath

MondayJuly 14, 2014
TimeDescriptionSpeakerLocationAbstractsSlides
1:30 - 2:30Research group meetings: BarkerSupervisors: Mike, EmmanuelOffice 1017
1:30 - 2:30Research group meetings: Ehrhart Supervisors: Sanya, Tarik10th Floor Classroom
2:30 - 3:00Coffee/Tea Break11th Floor Collaborative Space
3:00 - 4:00Research group meetings: Reinhardt Supervisors: Mike, Nhat, Tarik10th Floor Classroom

TuesdayJuly 15, 2014
TimeDescriptionSpeakerLocationAbstractsSlides
1:30 - 2:30Research group meetings: PisotSupervisors: Mike, Sanya, TarikOffice 1018
1:30 - 2:30Research group meetings: Dedekind Supervisors: Emmanuel, Nhat10th Floor Classroom
2:30 - 3:00Coffee/Tea Break
3:00 - 4:00Research group meetings: k-tilings Supervisors: Nhat, Tarik 10th Floor Classroom

WednesdayJuly 16, 2014
TimeDescriptionSpeakerLocationAbstractsSlides
1:30 - 2:30Discussion panel: Writing a paper10th Floor Classroom
2:30 - 3:00Coffee/Tea Break11th Floor Collaborative Space

ThursdayJuly 17, 2014
TimeDescriptionSpeakerLocationAbstractsSlides
1:30 - 2:301:30-2:30 Research group meetings: Ehrhart Supervisors: Sanya, Tarik 10th Floor Classroom
1:30 - 2:30Research group meetings: BarkerSupervisors: Mike, Emmanuel Office 1017
2:30 - 3:00Coffee/Tea Break11th Floor Collaborative Space
3:00 - 4:00Research group meetings: ReinhardtSupervisors: Mike, Nhat, Tarik10th Floor Classroom

FridayJuly 18, 2014
TimeDescriptionSpeakerLocationAbstractsSlides
1:30 - 2:30Research group meetings: Dedekind Supervisors: Emmanuel, Nhat 10th Floor Classroom
1:30 - 2:30Research group meetings: Pisot Supervisors: Mike, Sanya, Tarik Office 1018
2:30 - 3:00Coffee/Tea Break11th Floor Collaborative Space
3:00 - 4:00Research group meetings: k-tilings Supervisors: Nhat, Tarik 10th Floor Classroom

MondayJuly 21, 2014
TimeDescriptionSpeakerLocationAbstractsSlides
1:30 - 2:30Research Group Meetings - EhrhartSupervisors: Sanya and Tarik10th Floor Classroom
2:30 - 3:00Coffee/Tea Break11th Floor Collaborative Space

TuesdayJuly 22, 2014
TimeDescriptionSpeakerLocationAbstractsSlides
9:00 - 10:00Research group meetings: BarkerSupervisors: Mike, EmmanuelOffice 1017
10:00 - 11:00Research group meetings: Reinhardt Supervisors: Mike, Nhat, TarikOffice 1021
11:00 - 12:00Research group meetings: PisotSupervisors: Mike, Sanya Office 1018
1:30 - 2:30Research group meetings: Dedekind Supervisors: Emmanuel, Nhat10th Floor Classroom
2:30 - 3:00Coffee/Tea Break11th Floor Collaborative Space
3:00 - 4:00Research group meetings: k-tilings Supervisors: Nhat, Tarik 10th Floor Classroom

WednesdayJuly 23, 2014
TimeDescriptionSpeakerLocationAbstractsSlides
9:00 - 10:00Mathbyte Filming10th Floor Classroom
1:00 - 2:00Mating habits of polynomialsSarah Koch, University of Michigan10th Floor Classroom
PDF
2:30 - 3:00Coffee/Tea Break11th Floor Collaborative Space

ThursdayJuly 24, 2014
TimeDescriptionSpeakerLocationAbstractsSlides
10:00 - 12:00American Mathematical Society201 Charles Street, Providence, RI
1:45 - 2:25Equality of Dedekind sums: experimental data, and theorySinai Robins, Nanyang Technological University and ICERM11th Floor Lecture Hall

FridayJuly 25, 2014
TimeDescriptionSpeakerLocationAbstractsSlides
2:30 - 3:00Coffee/Tea Break11th Floor Collaborative Space

MondayJuly 28, 2014
TimeDescriptionSpeakerLocationAbstractsSlides
10:00 - 11:30Topics on PolynomialsSergei Tabachnikov, ICERM11th Floor Lecture Hall
1:30 - 2:30TBALenny Fukshansky, Claremont McKenna College11th Floor Lecture Hall
2:30 - 3:00Coffee/Tea Break11th Floor Collaborative Space

TuesdayJuly 29, 2014
TimeDescriptionSpeakerLocationAbstractsSlides
10:00 - 11:30Topics on PolynomialsSergei Tabachnikov, ICERM11th Floor Lecture Hall
2:30 - 3:00Coffee/Tea Break11th Floor Collaborative Space

WednesdayJuly 30, 2014
TimeDescriptionSpeakerLocationAbstractsSlides
2:30 - 3:00Coffee/Tea Break11th Floor Collaborative Space

ThursdayJuly 31, 2014
TimeDescriptionSpeakerLocationAbstractsSlides
10:00 - 11:30Topics on PolynomialsSergei Tabachnikov, ICERM11th Floor Lecture Hall

FridayAugust 1, 2014
TimeDescriptionSpeakerLocationAbstractsSlides
10:00 - 11:30Topics on PolynomialsSergei Tabachnikov, ICERM11th Floor Lecture Hall

MondayAugust 4, 2014
TimeDescriptionSpeakerLocationAbstractsSlides
2:30 - 3:00Coffee/Tea Break11th Floor Collaborative Space

TuesdayAugust 5, 2014
TimeDescriptionSpeakerLocationAbstractsSlides
2:30 - 3:00Coffee/Tea Break11th Floor Collaborative Space

WednesdayAugust 6, 2014
TimeDescriptionSpeakerLocationAbstractsSlides
2:30 - 3:00Coffee/Tea Break11th Floor Collaborative Space

ThursdayAugust 7, 2014
TimeDescriptionSpeakerLocationAbstractsSlides
2:30 - 3:00Coffee/Tea Break11th Floor Collaborative Space

FridayAugust 8, 2014
TimeDescriptionSpeakerLocationAbstractsSlides
2:30 - 3:00Coffee/Tea Break11th Floor Collaborative Space