SUMMER@ICERM: 2015 Undergraduate Summer Research Program
Computational Dynamics and Topology
(June 15 - August 7, 2015)

 

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*.



Summer@ICERM 2015 Participants

Summer@ICERM 2014 Participants: Back row, L to R: Tarik Aougab, Maxim Ar-nold, Vadim Zharnitsky, YM Baryshnikov, Derek Levinson, Milana Golich, Jeremy Ariche, Timothy Valicente, Daniel Barg, Juan Claramunt, Thomas Dauer, Shan Wolf; Front row, L to R: Emily Stark, Stefan Klajbor-Goderich, Anna Grim, Conrad Kosowsky, Chang He, Emily Black, Erin McCloskey, Shuchi Agrawal, Esther Hunt, Meg Doucette, Ben Lowe, Frank Yang, Laura Vargas-Hernandez



The 2015 Summer@ICERM program is designed for a select group of 14-16 undergraduate scholars. Students work in groups of two or three, supervised by faculty advisors and aided by teaching assistants. The faculty advisors present a number of interesting research topics that are centered around deep mathematical structures hidden in the everyday objects. The areas where the problems lie are dynamical systems and low-dimensional topology, but the origins of the problems themselves are mundane: how to find a gap in a fence? how complicated should be your finger movements to tie a knot? why standing waves develop in crowds? To crack the problems will require both ingenuity and computer experiments. 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.

Research Project Topics for SUMMER@ICERM 2015

During the 2015 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 2015 program. These problems arise in current research, are amenable to computation and experimentation, and may be approached from a number of different angles.

2015 Research Project Topics:
Applied Topology
Applied Computational Dynamics
PDE Models

Participants will be expected to gain intuition into some of these problems via computer experimentation and visualization. View the complete problem list for the 2015 program. PDF


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.

Applications for the 2015 Summer@ICERM program are closed.


“The program went above and beyond my expectations not only for academic material, but also for the quality of collaborative work with experts in the subject, the kindness and support from everyone at ICERM, the difficulty of the research topics, the numerous opportunities outside of work for leisure, and the help we received about pursuing graduate school. I learned more than I expected and am still benefiting from my experience” -- Summer@ICERM 2014 Participant

Organizing Committee

Summer@ICERM 2015
Funding include*

  • $3,000 stipend
  • Travel support within U.S.
  • Dormitory housing
  • Meal plan
  • Fun activities
*Brown University students must apply via MathPrograms.org AND contact info@icerm.brown.edu to discuss the special steps needed to apply for a Brown UTRA grant. The UTRA grant is awarded in lieu of the Summer@ICERM funding package.
(* = Speaker)
  • Shuchi Agrawal
    (Brown University)
  • Tarik Aougab
    (Yale University)
  • Jeremy Ariche
    (Morehouse College)
  • Maxim Arnold
    (University of Texas at Dallas)
  • Daniel Barg
    (Columbia University)
  • Yuliy Baryshnikov
    (University of Illinois at Urbana-Champaign)
  • Emily Black
    (Wesleyan University)
  • Juan Claramunt
    (University of Cantabria)
  • Thomas Dauer
    (Indiana University)
  • Meg Doucette
    (University of Chicago)
  • Milana Golich
    (Purdue University)
  • Anna Grim
    (University of St. Thomas)
  • Chang He
    (Centre College)
  • Esther Hunt
    (George Fox University)
  • Stefan Klajbor Goderich
    (University of Illinois at Urbana-Champaign)
  • Conrad Koskowsky
    (University of Pittsburgh)
  • Dmitri Krioukov *
    (Northeastern University)
  • Derek Levinson
    (Brown University)
  • Ben Lowe
    (University of Chicago)
  • Erin McCloskey
    (Brown University)
  • Emily Stark
    (Tufts University)
  • Jean-Luc Thiffeault *
    (University of Wisconsin)
  • Timothy Valicenti
    (Brown University)
  • Laura Vargas Hernandez
    (Instituto Tecnologico Autonomo de Mexico)
  • Gene Wayne *
    (Boston University)
  • Shan Wolf
    (University of Cambridge)
  • Frank Yang
    (Carleton College)
  • Vadim Zharnitsky
    (University of Illinois at Urbana-Champaign)
Monday June 15, 2015
Time Description Speaker Location Abstracts Slides
12:00 - 2:00Welcome Lunch11th Floor Conference Room
2:00 - 3:30Locking configurations of hard balls (disks) in box (square)Yuliy Baryshnikov, University of Illinois at Urbana-Champaign11th Floor Lecture Hall
3:30 - 4:00Coffee/Tea Break11th Floor Collaborative Space

Tuesday June 16, 2015
Time Description Speaker Location Abstracts Slides
10:00 - 11:30Search ProblemVadim Zharnitsky, University of Illinois at Urbana-Champaign11th Floor Lecture Hall
11:45 - 1:00Break for lunch
1:00 - 2:15Scavenger huntAround Providence
2:15 - 2:30Coffee/Tea Break11th Floor Collaborative Space
2:30 - 4:00Tangle Configuration SpacesYuliy Baryshnikov, University of Illinois at Urbana-Champaign11th Floor Lecture Hall

Wednesday June 17, 2015
Time Description Speaker Location Abstracts Slides
10:00 - 11:30Cyclic evasion problemMaxim Arnold, University of Texas at Dallas11th Floor Lecture Hall
11:45 - 1:00Break for lunch
1:00 - 2:30non-smooth geodesics in sub-Riemannian geometryVadim Zharnitsky, University of Illinois at Urbana-Champaign11th Floor Lecture Hall
2:30 - 3:00Coffee/Tea Break11th Floor Collaborative Space
3:00 - 3:30IT TutorialIsani Cayetano, ICERM11th Floor Lecture Hall

Thursday June 18, 2015
Time Description Speaker Location Abstracts Slides
10:00 - 11:30Crowd DynamicsVadim Zharnitsky, University of Illinois at Urbana-Champaign11th Floor Lecture Hall
11:45 - 1:00Break for lunch
1:00 - 2:30Reading and Research: focus on problem selection
2:30 - 3:00Coffee/Tea Break11th Floor Collaborative Space
3:00 - 5:00Reading and Research: focus on problem selection
5:00 - 5:00Submit Problem Preferences11th Floor Lecture Hall

Friday June 19, 2015
Time Description Speaker Location Abstracts Slides
10:00 - 11:30Groups Formed: Begin working in groups11th Floor Lecture Hall
11:45 - 1:00Break for lunch
1:00 - 2:30Work in groups
2:30 - 3:00Coffee/Tea Break11th Floor Collaborative Space
3:00 - 4:00Work in groups

Monday June 22, 2015
Time Description Speaker Location Abstracts Slides
1:00 - 2:30Research Group Meeting: Configurations spaces of hard disks. Supervisors: Emily, Yuliy
1:00 - 2:30Research Group Meeting: Crowd dynamics.Supervisors: Stefan, Vadim
2:00 - 3:00Coffe/Tea Break11th Floor Collaborative Space
2:30 - 4:00Research Group Meeting: Cyclic pursuit/evasion systems.Supervisors:Emily, Maxim, Vadim
2:30 - 4:00Research Group Meeting: Configuration spaces of tangles.Supervisors:Tarik, Yuliy

Tuesday June 23, 2015
Time Description Speaker Location Abstracts Slides
9:00 - 11:00ICERM BearCore/Professional Development 11th Floor Lecture Hall
1:00 - 2:30Research Group Meeting: Mixing rates in robotic explorations.Supervisors: Maxim, Yuliy
2:00 - 3:00Coffee/Tea Break11th Floor Collaborative Space
2:30 - 4:00Research Group Meeting: Pinball dynamics and search problemSupervisors:Stefan, Maxim, Vadim
2:30 - 4:00Research Group Meeting: Configuration spaces of coverings. Supervisors: Tarik, Yuliy

Wednesday June 24, 2015
Time Description Speaker Location Abstracts Slides
2:00 - 3:00The Navier-Stokes EquationsGene Wayne, Boston University 10th Floor Classroom
PDF
3:00 - 4:00Coffee/Tea Break10th Floor Collaborative Space

Thursday June 25, 2015
Time Description Speaker Location Abstracts Slides
1:00 - 2:30Research Group Meeting: Configurations spaces of hard disks.Supervisors: Emily, Yuliy
1:00 - 2:30Research Group Meeting: Crowd dynamics.Supervisors: Stefan, Vadim
2:00 - 3:00Coffee/Tea Break10th Floor Collaborative Space
2:30 - 4:00Research Group Meeting: Cyclic pursuit/evasion systems.Supervisors:Emily, Maxim, Vadim
2:30 - 4:00Research Group Meeting: Configuration spaces of tangles.Supervisors:Tarik, Yuliy

Friday June 26, 2015
Time Description Speaker Location Abstracts Slides
1:00 - 2:30Research Group Meeting: Mixing rates in robotic explorations.Supervisors: Maxim, Yuliy
2:00 - 3:00Coffee/Tea Break10th Floor Collaborative Space
2:30 - 4:00Research Group Meeting: Pinball dynamics and search problemSupervisors:Stefan, Maxim, Vadim
2:30 - 4:00Research Group Meeting: Configuration spaces of coverings. Supervisors: Tarik, Yuliy

Monday June 29, 2015
Time Description Speaker Location Abstracts Slides
1:00 - 2:30Research Group Meeting: Configurations spaces of hard disks. Supervisors: Emily, Yuliy
1:00 - 2:30Research Group Meeting: Crowd dynamics.Supervisors: Stefan, Vadim
2:00 - 3:00Coffe/Tea Break10th Floor Collaborative Space
2:30 - 4:00Research Group Meeting: Configuration spaces of tangles.Supervisors:Tarik, Yuliy
2:30 - 4:00Research Group Meeting: Cyclic pursuit/evasion systems.Supervisors:Emily, Maxim, Vadim

Tuesday June 30, 2015
Time Description Speaker Location Abstracts Slides
1:00 - 2:30Research Group Meeting: Mixing rates in robotic explorations.Supervisors: Maxim, Yuliy
2:00 - 3:00Coffee/Tea Break10th Floor Collaborative Space
2:30 - 4:00Research Group Meeting: Configuration spaces of coverings. Supervisors: Tarik, Yuliy
2:30 - 4:00Research Group Meeting: Pinball dynamics and search problemSupervisors:Stefan, Maxim, Vadim

Wednesday July 1, 2015
Time Description Speaker Location Abstracts Slides
2:00 - 3:00Coffee/Tea Break10th Floor Collaborative Space

Thursday July 2, 2015
Time Description Speaker Location Abstracts Slides
1:00 - 2:30Research Group Meeting: Crowd dynamics.Supervisors: Stefan, Vadim
1:00 - 2:30Research Group Meeting: Configurations spaces of hard disks.Supervisors: Emily, Yuliy
2:00 - 3:00Coffee/Tea Break10th Floor Collaborative Space
2:30 - 4:00Research Group Meeting: Cyclic pursuit/evasion systems.Supervisors:Emily, Maxim, Vadim
2:30 - 4:00Research Group Meeting: Configuration spaces of tangles.Supervisors:Tarik, Yuliy

Friday July 3, 2015
Time Description Speaker Location Abstracts Slides
8:30 - 5:00ICERM Closed for 4th of July

Monday July 6, 2015
Time Description Speaker Location Abstracts Slides
10:30 - 12:00Research Group Meeting: Crowd dynamics.Supervisors: Stefan, Vadim
10:30 - 12:00Research Group Meeting: Configurations spaces of hard disks. Supervisors: Emily, Yuliy
1:00 - 2:30Geometric exponential random graphs and network geometry inferenceDmitry Krioukov, Northeastern University10th Floor Classroom
2:30 - 4:00Research Group Meeting: Cyclic pursuit/evasion systems.Supervisors:Emily, Maxim, Vadim
2:30 - 3:30Coffee/Tea Break10th Floor Collaborative Space
2:30 - 4:00Research Group Meeting: Configuration spaces of tangles.Supervisors:Tarik, Yuliy

Tuesday July 7, 2015
Time Description Speaker Location Abstracts Slides
10:30 - 12:00Research Group Meeting: Mixing rates in robotic explorations.Supervisors: Maxim, Yuliy
1:00 - 2:30Geometric exponential random graphs and network geometry inferenceDmitry Krioukov, Northeastern University10th Floor Classroom
2:30 - 4:00Research Group Meeting: Pinball dynamics and search problemSupervisors:Stefan, Maxim, Vadim
2:30 - 4:00Research Group Meeting: Configuration spaces of coverings. Supervisors: Tarik, Yuliy
2:30 - 3:30Coffee/Tea Break10th Floor Collaborative Space

Wednesday July 8, 2015
Time Description Speaker Location Abstracts Slides
3:00 - 4:00Coffee/Tea Break10th Floor Collaborative Space

Thursday July 9, 2015
Time Description Speaker Location Abstracts Slides
10:30 - 12:00Research Group Meeting: Crowd dynamics.Supervisors: Stefan, Vadim
10:30 - 12:00Research Group Meeting: Configurations spaces of hard disks.Supervisors: Emily, Yuliy
1:00 - 2:30Geometric exponential random graphs and network geometry inferenceDmitry Krioukov, Northeastern University10th Floor Classroom
2:30 - 3:30Coffee/Tea Break10th Floor Collaborative Space
2:30 - 4:00Research Group Meeting: Configuration spaces of tangles.Supervisors:Tarik, Yuliy
2:30 - 4:00Research Group Meeting: Cyclic pursuit/evasion systems.Supervisors:Emily, Maxim, Vadim

Friday July 10, 2015
Time Description Speaker Location Abstracts Slides
10:30 - 12:00Research Group Meeting: Mixing rates in robotic explorations.Supervisors: Maxim, Yuliy
1:00 - 2:30Geometric exponential random graphs and network geometry inferenceDmitry Krioukov, Northeastern University10th Floor Classroom
2:30 - 4:00Research Group Meeting: Pinball dynamics and search problemSupervisors:Stefan, Maxim, Vadim
2:30 - 3:30Coffee/Tea Break10th Floor Collaborative Space
2:30 - 4:00Research Group Meeting: Configuration spaces of coverings. Supervisors: Tarik, Yuliy

Monday July 13, 2015
Time Description Speaker Location Abstracts Slides
1:00 - 2:30Research Group Meeting: Crowd dynamics.Supervisors: Stefan, Vadim
1:00 - 2:30Research Group Meeting: Configurations spaces of hard disks. Supervisors: Emily, Yuliy
2:00 - 3:00Coffee/Tea Break
2:30 - 4:00Research Group Meeting: Cyclic pursuit/evasion systems.Supervisors:Emily, Maxim, Vadim
2:30 - 4:00Research Group Meeting: Configuration spaces of tangles.Supervisors:Tarik, Yuliy

Tuesday July 14, 2015
Time Description Speaker Location Abstracts Slides
10:00 - 11:30Research Group Meeting: Mixing rates in robotic explorations.Supervisors: Maxim, Yuliy
1:30 - 3:00Summer@ICERM Mini-CourseJean-Luc Thiffeault, University of Wisconsin-Madison10th Floor Classroom
3:00 - 4:00Coffee/Tea Break
3:30 - 5:00Research Group Meeting: Pinball dynamics and search problemSupervisors:Stefan, Maxim, Vadim
3:30 - 5:00Research Group Meeting: Configuration spaces of coverings. Supervisors: Tarik, Yuliy

Wednesday July 15, 2015
Time Description Speaker Location Abstracts Slides
10:00 - 11:30Summer@ICERM Mini-CourseJean-Luc Thiffeault, University of Wisconsin-Madison10th Floor Classroom
2:00 - 3:00Coffee/Tea Break10th Floor Collaborative Space
6:30 - 8:00Game Night!11th Floor Collaborative Space

Thursday July 16, 2015
Time Description Speaker Location Abstracts Slides
10:00 - 11:30Summer@ICERM Mini-CourseJean-Luc Thiffeault, University of Wisconsin-Madison10th Floor Classroom
1:00 - 2:30Research Group Meeting: Configurations spaces of hard disks.Supervisors: Emily, Yuliy
1:00 - 2:30Research Group Meeting: Crowd dynamics.Supervisors: Stefan, Vadim
2:00 - 3:00Coffee/Tea Break10th Floor Collaborative Space
2:30 - 4:00Research Group Meeting: Cyclic pursuit/evasion systems.Supervisors:Emily, Maxim, Vadim
2:30 - 4:00Research Group Meeting: Configuration spaces of tangles.Supervisors:Tarik, Yuliy

Friday July 17, 2015
Time Description Speaker Location Abstracts Slides
1:00 - 2:30Research Group Meeting: Mixing rates in robotic explorations.Supervisors: Maxim, Yuliy
2:00 - 3:00Coffee/Tea Break10th Floor Collaborative Space
2:30 - 4:00Research Group Meeting: Pinball dynamics and search problemSupervisors:Stefan, Maxim, Vadim
2:30 - 4:00Research Group Meeting: Configuration spaces of coverings. Supervisors: Tarik, Yuliy

Monday July 20, 2015
Time Description Speaker Location Abstracts Slides
1:00 - 2:30Research Group Meeting: Crowd dynamics.Supervisors: Stefan, Vadim
1:00 - 2:30Research Group Meeting: Configurations spaces of hard disks. Supervisors: Emily, Yuliy
2:00 - 3:00Coffee/Tea Break10th Floor Collaborative Space
2:30 - 4:00Research Group Meeting: Configuration spaces of tangles.Supervisors:Tarik, Yuliy
2:30 - 4:00Research Group Meeting: Cyclic pursuit/evasion systems.Supervisors:Emily, Maxim, Vadim

Tuesday July 21, 2015
Time Description Speaker Location Abstracts Slides
1:00 - 2:30Research Group Meeting: Mixing rates in robotic explorations.Supervisors: Maxim, Yuliy
2:00 - 3:00Coffee/Tea Break10th Floor Collaborative Space
2:30 - 4:00Research Group Meeting: Pinball dynamics and search problemSupervisors:Stefan, Maxim, Vadim
2:30 - 4:00Research Group Meeting: Configuration spaces of coverings. Supervisors: Tarik, Yuliy

Wednesday July 22, 2015
Time Description Speaker Location Abstracts Slides
2:00 - 3:00Coffee/Tea Break10th Floor Collaborative Space

Thursday July 23, 2015
Time Description Speaker Location Abstracts Slides
1:00 - 2:30Research Group Meeting: Crowd dynamics.Supervisors: Stefan, Vadim
1:00 - 2:30Research Group Meeting: Configurations spaces of hard disks.Supervisors: Emily, Yuliy
2:00 - 3:00Coffee/Tea Break10th Floor Collaborative Space
2:30 - 4:00Research Group Meeting: Configuration spaces of tangles.Supervisors:Tarik, Yuliy
2:30 - 4:00Research Group Meeting: Cyclic pursuit/evasion systems.Supervisors:Emily, Maxim, Vadim

Friday July 24, 2015
Time Description Speaker Location Abstracts Slides
1:00 - 2:30Research Group Meeting: Mixing rates in robotic explorationsSupervisors: Maxim, Yuliy
2:00 - 3:00Coffee/Tea Break10th Floor Collaborative Space
2:30 - 4:00Research Group Meeting: Pinball dynamics and search problemSupervisors:Stefan, Maxim, Vadim
2:30 - 4:00Research Group Meeting: Configuration spaces of coveringsSupervisors: Tarik, Yuliy

Monday July 27, 2015
Time Description Speaker Location Abstracts Slides
1:00 - 2:30Research Group Meeting: Crowd dynamicsSupervisors: Stefan, Vadim
1:00 - 2:30Research Group Meeting: Configurations spaces of hard disksSupervisors: Emily, Yuliy
2:00 - 3:00Coffee/Tea Break10th Floor Collaborative Space
2:30 - 4:00Research Group Meeting: Cyclic pursuit/evasion systemsSupervisors:Emily, Maxim, Vadim
2:30 - 4:00Research Group Meeting: Configuration spaces of tanglesSupervisors:Tarik, Yuliy

Tuesday July 28, 2015
Time Description Speaker Location Abstracts Slides
1:00 - 2:30Research Group Meeting: Mixing rates in robotic explorationsSupervisors: Maxim, Yuliy
2:00 - 3:00Coffee/Tea Break10th Floor Collaborative Space
2:30 - 4:00Research Group Meeting: Configuration spaces of coveringsSupervisors: Tarik, Yuliy
2:30 - 4:00Research Group Meeting: Pinball dynamics and search problemSupervisors:Stefan, Maxim, Vadim

Wednesday July 29, 2015
Time Description Speaker Location Abstracts Slides
2:00 - 3:00Coffee/Tea Break10th Floor Collaborative Space
4:00 - 5:00What if it's too Complex? Parameterized Algorithms in Scientific Data Analysis Blair Sullivan, North Carolina State University10th Floor Classroom

Thursday July 30, 2015
Time Description Speaker Location Abstracts Slides
1:00 - 2:30Research Group Meeting: Configurations spaces of hard disksSupervisors: Emily, Yuliy
1:00 - 2:30Research Group Meeting: Crowd dynamicsSupervisors: Stefan, Vadim
2:00 - 3:00Coffee/Tea Break10th Floor Collaborative Space
2:30 - 4:00Research Group Meeting: Cyclic pursuit/evasion systemsSupervisors:Emily, Maxim, Vadim
2:30 - 4:00Research Group Meeting: Configuration spaces of tanglesSupervisors:Tarik, Yuliy

Friday July 31, 2015
Time Description Speaker Location Abstracts Slides
1:00 - 2:30Research Group Meeting: Mixing rates in robotic explorationsSupervisors: Maxim, Yuliy
2:00 - 3:00Coffee/Tea Break10th Floor Collaborative Space
2:30 - 4:00Research Group Meeting: Pinball dynamics and search problemSupervisors:Stefan, Maxim, Vadim
2:30 - 4:00Research Group Meeting: Configuration spaces of coveringsSupervisors: Tarik, Yuliy

Monday August 3, 2015
Time Description Speaker Location Abstracts Slides
12:00 - 1:00Grad School Q&A11th Floor
2:00 - 3:00Coffee/Tea Break10th Floor Collaborative Space

Tuesday August 4, 2015
Time Description Speaker Location Abstracts Slides
2:00 - 3:00Coffee/Tea Break10th Floor Collaborative Space

Wednesday August 5, 2015
Time Description Speaker Location Abstracts Slides
2:00 - 3:00Coffee/Tea Break10th Floor Collaborative Space
3:00 - 4:00Group Presentation- Crowd DynamicsJeremy Ariche, Timothy Valicenti, Juan ClaramuntTBA

Thursday August 6, 2015
Time Description Speaker Location Abstracts Slides
1:30 - 2:30Group Presentations- Cyclic pursuit/evasion systemsAnna Grim, Milana Golich, Laura Vargas Hernandez11th Floor Lecture Hall
2:30 - 3:00Coffee/Tea Break11th Floor Collaborative Space
3:00 - 4:00Group Presentation- Pinball dynamicsMeg Doucette, Thomas Dauer, Shan Wolf11th floor lecture halll
PDF

Friday August 7, 2015
Time Description Speaker Location Abstracts Slides
10:00 - 11:00Group Presentation- Mixing rates in robotic explorationFrank Yang, Chang He11th Floor Lecture hall
PDF
11:15 - 12:15Group Presentation- Configuration spaces of tanglesConrad Koskowsky, Ben Lowe11th Floor Lecture Hall
PDF
1:30 - 2:30Group Presentations- Configuration spaces of hard disksEmily Black, Esther Hunt11th Floor Lecture Hall
PDF
2:30 - 3:00Coffee/Tea Break11th Floor Collaborative Space
3:00 - 4:00Group Presentation- Configuration spaces of coveringsDaniel Barg, Shuchi Agrawal, Derek Levinson11th Floor Lecture Hall

  • "On a very steep version of a standard map" by by M. Arnold, T. Dauer, M. Doucette, and S. Conrad-Wolf (Experimental Mathematics) to appear

  • MAA 2016 Outstanding Poster for their "Mixing Time in Robotic Explorations" research, C. He and S. Yang.