Organizing Committee
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 2016 Summer@ICERM program is designed for a select group of 14-16 undergraduate scholars. Students work in groups of two to four, supervised by faculty advisors and aided by teaching assistants. The faculty advisors present a number of research topics that are centered around modeling, dynamical systems, and stochastic systems.

Examples include stripe formation in zebrafish, the structure of roll patterns that arise in buckling and vegetation patterns, and the dynamics of planar spiral waves. Tackling these problems will require a combination of analytical and computational approaches. Students form research groups to work on these problems, give talks about their findings, and write up their research into a paper at the end of the program.

Image for "Summer@ICERM 2016: Dynamics and Stochastics"

Program Details

2016 Research Project Topics

During the 2016 Summer@ICERM program, the faculty organizers will describe a number of open-ended problems at the interface of applications, modeling, and deterministic and stochastic dynamical systems. These problems arise in current research, are amenable to analysis and computation, and may be approached from a number of different angles. Participants will be expected to gain intuition into some of these problems via analysis, computer experimentation, and visualization.

Funding Includes
  • $3,000 stipend
  • Dormitory housing
  • Meal plan
  • Travel support within U.S.
  • Fun events
  • Brown University students (only) should apply via the Brown I-TEAM UTRA for "Dimensions and Stochastics".

Confirmed Speakers & Participants

  • Speaker
  • Poster Presenter
  • Attendee
  • Virtual Attendee

Summer Schedule

Monday, June 20, 2016
TimeEventLocationMaterials
9:00 - 10:00am EDTWelcome / Meet & Greet121 South Main Street 11th Floor 
10:00 - 11:15am EDTScavenger HuntBrown Campus 
11:30 - 1:00pm EDTWelcome Lunch11th Floor Collaborative Space 
1:00 - 2:30pm EDTResearch Project Presentations11th Floor Lecture Hall 
2:30 - 3:00pm EDTCoffee/Tea Break11th Floor Collaborative Space 
3:00 - 4:30pm EDTResearch Project Presentations11th Floor Lecture Hall 
Tuesday, June 21, 2016
TimeEventLocationMaterials
9:00 - 10:00am EDTResearch Project Presentation11th Floor Lecture Hall 
10:00 - 10:30am EDTDiscussion11th Floor Lecture Hall 
10:30 - 11:30am EDTResearch Project Presentation11th Floor Lecture Hall 
11:30 - 1:00pm EDTLunch  
1:00 - 2:30pm EDTResearch Project Presentation11th Floor Lecture Hall 
2:30 - 3:00pm EDTCoffee/Tea Break11th Floor Collaborative Space 
3:00 - 5:00pm EDTDiscussion/Reading  
5:30 - 7:30pm EDTDinnerFlatbread Company, 161 Cushing St, Providence, RI 02906, USA 
Wednesday, June 22, 2016
TimeEventLocationMaterials
9:00 - 9:30am EDTIT Tutorial - Brian Lavall, ICERM11th Floor Lecture Hall 
7:00 - 9:00pm EDTGame Night170 Hope Street, Room 108 
Thursday, June 23, 2016
TimeEventLocationMaterials
9:00 - 11:00am EDTMini-course: Dynamical Systems11th Floor Lecture Hall 
12:00 - 1:00pm EDTLunch  
1:00 - 2:30pm EDTMini-course: Matlab11th Floor Lecture Hall 
2:30 - 3:00pm EDTBreak11th Floor Collaborative Space 
Friday, June 24, 2016
TimeEventLocationMaterials
9:00 - 11:00am EDTMini-course: Numerical Methods10th Floor Classroom 
12:00 - 1:00pm EDTLunch  
2:30 - 3:00pm EDTBreak11th Floor Collaborative Space 
Monday, June 27, 2016
TimeEventLocationMaterials
9:00 - 11:00am EDTMini-course: Modelling10th Floor Classroom 
12:00 - 1:00pm EDTLunch  
1:00 - 2:30pm EDTMini-course: Partial Differential Equations10th Floor Classroom 
2:30 - 3:00pm EDTBreak10th Floor Collaborative Space 
Tuesday, June 28, 2016
TimeEventLocationMaterials
9:00 - 11:00am EDTMini-course: Probability10th Floor Classroom 
12:00 - 1:00pm EDTLunch  
2:30 - 3:00pm EDTBreak10th Floor Collaborative Space 
Wednesday, June 29, 2016
TimeEventLocationMaterials
9:00 - 9:30am EDTHow to make illustrations170 Hope Street, Room 108 
9:30 - 10:00am EDTHow to use LaTeX170 Hope Street, Room 108 
Thursday, June 30, 2016
TimeEventLocationMaterials
9:00 - 10:00am EDTHow to give presentations170 Hope Street, Room 108 
Friday, July 1, 2016
TimeEventLocationMaterials
2:30 - 5:00pm EDTResearch team presentations (10 min per team; 3 slides max)170 Hope Street, Room 108 
Tuesday, July 5, 2016
TimeEventLocationMaterials
9:00 - 10:30am EDTEthics Training11th Floor Lecture Hall 
Wednesday, July 6, 2016
TimeEventLocationMaterials
9:00 - 10:00am EDTLorenz attractors in flows and maps - Ivan Ovsyannikov, Universität Bremen170 Hope St., room 108 
Monday, July 11, 2016
TimeEventLocationMaterials
2:30 - 3:00pm EDTCoffee/Tea Break11th Floor Collaborative Space 
Tuesday, July 12, 2016
TimeEventLocationMaterials
2:30 - 3:00pm EDTCoffee/Tea Break11th Floor Collaborative Space 
Wednesday, July 13, 2016
TimeEventLocationMaterials
9:00 - 10:00am EDTProofs (not) from the Book - Sergei Tabashnikov, Penn State University11th Floor Lecture Hall 
2:30 - 3:00pm EDTCoffee/Tea Break11th Floor Collaborative Space 
Thursday, July 14, 2016
TimeEventLocationMaterials
2:30 - 3:00pm EDTCoffee/Tea Break11th Floor Collaborative Space 
Friday, July 15, 2016
TimeEventLocationMaterials
12:00 - 1:00pm EDTTuring patterns without diffusion- how immobile pigment cells can color the skin of zebrafish - Domenico Bullara, University of the Balearic Islands - Palma11th Floor Lecture Hall 
2:00 - 2:30pm EDTCoffee/Tea Break11th Floor Collaborative Space 
2:30 - 5:00pm EDTResearch Team Presentations11th Floor Lecture Hall 
Monday, July 18, 2016
TimeEventLocationMaterials
2:30 - 3:00pm EDTBelated Yellow Pig Day Coffee/Tea Break  
Wednesday, July 20, 2016
TimeEventLocationMaterials
3:30 - 5:00pm EDTGraduate School Panel170 Hope Street, Room 108 
Tuesday, July 26, 2016
TimeEventLocationMaterials
4:15 - 5:30pm EDTFellowship Panel170 Hope Street, Room 108 
Wednesday, July 27, 2016
TimeEventLocationMaterials
5:15 - 7:30pm EDTMovie Night11th Floor Lecture Hall 
Thursday, July 28, 2016
TimeEventLocationMaterials
5:15 - 6:30pm EDTWomen in Math Social11th Floor Conference Room 
Tuesday, August 2, 2016
TimeEventLocationMaterials
1:00 - 2:00pm EDTSocial Factors and Underrepresentation in Mathematics - Margaret Beck, Boston University and Moon Duchin, Tufts University170 Hope Street, Room 108 
Friday, August 5, 2016
TimeEventLocationMaterials
11:00 - 1:00pm EDTSummer Research SymposiumSayles Hall, Providence, RI 02912, USA 
Wednesday, August 10, 2016
TimeEventLocationMaterials
4:30 - 5:15pm EDTGender Representation on Journal Editorial Boards in the Mathematical Sciences10th Floor Classroom 
Thursday, August 11, 2016
TimeEventLocationMaterials
2:00 - 2:30pm EDTCoffee/Tea Break and Cake!10th Floor Collaborative Space 

Final Projects

Final Student Presentations
  • "Plurality and Stability in Continuous Time Opinion Formation on Weighted Directed Graphs" by J. Bujalski, G. Dwyer, H. Malvai, and J. Rosenthal-Kay
  • "Propagation of Lead in Mammals" by M. Morrissey and J. Collignon
  • "Diffusion Maps in Equation-Free Modeling" by T. Chin, J. Ruth, and R. Santorella
  • "Summary of Koopman Theory Results" by C. Chain, M. Pedrick, and R. Utke
  • "Nonorientable Bundles" by S. Desai, M. Stadt, and A. Wheeler
  • "Snaking in the Swift-Hohenberg Equation in Dimensions 1 Versus 1+" D. Altschuler, C. Avery and T. Sangsawang
  • "Stability of Agent-based Models: Overview" by C. Cole, P. Doldo, Q. Fan
  • "Modelling Stripe Formation on Zebrafish Fins" by M. Abbott, D. Catey, N. Chandra, F. Lim, and B. Dubois
  • Read more about each project
Completed Student Projects
Posters presented at JMM 2017 in Atlanta Georgia
  • Snaking in the Swift-Hohenberg Equation in Dimensions 1 vs 1 + ε (C. Avery)
  • Spectral Theory of Koopman Operators (M. Pedrick, R. Utke, C. Chain)
  • Stability of Agent-based Models (C. Cole, P. Doldo, Q. Fan)**
  • **This poster received the MAA’s “Outstanding Poster” during the Student Poster Session at JMM 2017
Posters presented during the Nebraska Conference for Undergraduate Women in Mathematics in winter 2017
  • Snaking in Systems with Non-Orientable Manifolds (S. Desai)
  • Continuous Time Opinion Formation on Directed Weighted Graphs (J. Malvai)

T. Kapitula gave talks at the AMS SE Sectional meeting in Charleston, SC, and at a seminar at Michigan State U.

Other Summer@ICERM Events

Summer@ICERM 2012: Geometry and Dynamics
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Summer@ICERM 2013: Geometry and Dynamics
Image for "Summer@ICERM 2013: Geometry and Dynamics"
Summer@ICERM 2014: Polygons and Polynomials
Image for "Summer@ICERM 2014: Polygons and Polynomials"
Summer@ICERM 2015: Computational Dynamics and Topology
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Summer@ICERM 2017: Topological Data Analysis
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Summer@ICERM 2018: Low Dimensional Topology and Geometry
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Summer@ICERM 2019: Computational Arithmetic Dynamics
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Summer@ICERM 2021: Computational Polygonal Billiards
Image for "Summer@ICERM 2021: Computational Polygonal Billiards"