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 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.

Program Details

2015 Research Project Topics

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.

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 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.

Confirmed Speakers & Participants

  • Shuchi Agrawal
    Brown University
  • Tarik Aougab
    Brown University
  • Jeremy Ariche
    Morehouse College
  • Maxim Arnold
    UT Dallas
  • Daniel Barg
    Columbia University
  • Yuliy Baryshnikov
    University of Illinois at Urbana-Champaign (UIUC)
  • Emily Black
    Wesleyan University
  • Juan Claramunt
    University of Cantabria
  • Thomas Dauer
    Indiana University
  • Meg Doucette
    University of Chicago
  • Milana Golich
    Purdue University
  • Anna Grim
    Brown University
  • 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
  • Clarence Wayne
    Boston University
  • Shan Wolf
    University of Cambridge
  • Frank Yang
    Carleton College
  • Vadim Zharnitsky
    University of Illinois

Summer Schedule

Monday, June 15, 2015
TimeEventLocationMaterials
10:00 - 10:30Summer@ICERM 2015 Welcome/Meet Greet121 S. Main St.\, 11th Floor Collaborative Space 
10:00 - 10:30Summer@ICERM 2015 Welcome/Meet Greet121 S. Main St., 11th Floor Collaborative Space 
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 
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
TimeEventLocationMaterials
10:00 - 11:30Search Problem - Vadim Zharnitsky, University of Illinois at Urbana-Champaign11th Floor Lecture Hall 
11:45 - 1:00Break for lunch  
1:00 - 2:15Scavenger huntAround Providence 
1:00 - 2:15Scavenger huntAround Providence 
2:15 - 2:30Coffee/Tea Break11th Floor Collaborative Space 
2:15 - 2:30Coffee/Tea Break11th Floor Collaborative Space 
2:30 - 4:00Tangle Configuration Spaces - Yuliy Baryshnikov, University of Illinois at Urbana-Champaign11th Floor Lecture Hall 
Wednesday, June 17, 2015
TimeEventLocationMaterials
10:00 - 11:30Cyclic evasion problem - Maxim Arnold, University of Texas at Dallas11th Floor Lecture Hall 
11:45 - 1:00Break for lunch  
1:00 - 2:30non-smooth geodesics in sub-Riemannian geometry - Vadim Zharnitsky, University of Illinois at Urbana-Champaign11th Floor Lecture Hall 
2:30 - 3:00Coffee/Tea Break11th Floor Collaborative Space 
3:00 - 3:30IT Tutorial - Isani Cayetano, ICERM11th Floor Lecture Hall 
Thursday, June 18, 2015
TimeEventLocationMaterials
10:00 - 11:30Crowd Dynamics - Vadim 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  
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  
3:00 - 5:00Reading and Research: focus on problem selection  
5:00 - 5:00Submit Problem Preferences11th Floor Lecture Hall 
Friday, June 19, 2015
TimeEventLocationMaterials
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
TimeEventLocationMaterials
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
TimeEventLocationMaterials
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 problem - Supervisors:Stefan, Maxim, Vadim  
2:30 - 4:00Research Group Meeting: Configuration spaces of coverings. - Supervisors: Tarik, Yuliy  
Wednesday, June 24, 2015
TimeEventLocationMaterials
2:00 - 3:00The Navier-Stokes Equations - Gene Wayne, Boston University 10th Floor Classroom
3:00 - 4:00Coffee/Tea Break10th Floor Collaborative Space 
Thursday, June 25, 2015
TimeEventLocationMaterials
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
TimeEventLocationMaterials
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 problem - Supervisors:Stefan, Maxim, Vadim  
2:30 - 4:00Research Group Meeting: Configuration spaces of coverings. - Supervisors: Tarik, Yuliy  
Monday, June 29, 2015
TimeEventLocationMaterials
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
TimeEventLocationMaterials
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 problem - Supervisors:Stefan, Maxim, Vadim  
Wednesday, July 1, 2015
TimeEventLocationMaterials
2:00 - 3:00Coffee/Tea Break10th Floor Collaborative Space 
Thursday, July 2, 2015
TimeEventLocationMaterials
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
TimeEventLocationMaterials
8:30 - 5:00ICERM Closed for 4th of July  
Monday, July 6, 2015
TimeEventLocationMaterials
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 inference - Dmitry 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
TimeEventLocationMaterials
10:30 - 12:00Research Group Meeting: Mixing rates in robotic explorations. - Supervisors: Maxim, Yuliy  
1:00 - 2:30Geometric exponential random graphs and network geometry inference - Dmitry Krioukov, Northeastern University10th Floor Classroom 
2:30 - 4:00Research Group Meeting: Pinball dynamics and search problem - Supervisors: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
TimeEventLocationMaterials
3:00 - 4:00Coffee/Tea Break10th Floor Collaborative Space 
Thursday, July 9, 2015
TimeEventLocationMaterials
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 inference - Dmitry 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
TimeEventLocationMaterials
10:30 - 12:00Research Group Meeting: Mixing rates in robotic explorations. - Supervisors: Maxim, Yuliy  
1:00 - 2:30Geometric exponential random graphs and network geometry inference - Dmitry Krioukov, Northeastern University10th Floor Classroom 
2:30 - 4:00Research Group Meeting: Pinball dynamics and search problem - Supervisors: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
TimeEventLocationMaterials
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
TimeEventLocationMaterials
10:00 - 11:30Research Group Meeting: Mixing rates in robotic explorations. - Supervisors: Maxim, Yuliy  
1:30 - 3:00Summer@ICERM Mini-Course - Jean-Luc Thiffeault, University of Wisconsin-Madison10th Floor Classroom 
3:00 - 4:00Coffee/Tea Break  
3:30 - 5:00Research Group Meeting: Pinball dynamics and search problem - Supervisors:Stefan, Maxim, Vadim  
3:30 - 5:00Research Group Meeting: Configuration spaces of coverings. - Supervisors: Tarik, Yuliy  
Wednesday, July 15, 2015
TimeEventLocationMaterials
10:00 - 11:30Summer@ICERM Mini-Course - Jean-Luc Thiffeault, University of Wisconsin-Madison10th Floor Classroom 
10:00 - 11:30Summer@ICERM Mini-Course - Jean-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 
6:30 - 8:00Game Night!11th Floor Collaborative Space 
Thursday, July 16, 2015
TimeEventLocationMaterials
10:00 - 11:30Summer@ICERM Mini-Course - Jean-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
TimeEventLocationMaterials
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 problem - Supervisors:Stefan, Maxim, Vadim  
2:30 - 4:00Research Group Meeting: Configuration spaces of coverings. - Supervisors: Tarik, Yuliy  
Monday, July 20, 2015
TimeEventLocationMaterials
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
TimeEventLocationMaterials
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 problem - Supervisors:Stefan, Maxim, Vadim  
2:30 - 4:00Research Group Meeting: Configuration spaces of coverings. - Supervisors: Tarik, Yuliy  
Wednesday, July 22, 2015
TimeEventLocationMaterials
2:00 - 3:00Coffee/Tea Break10th Floor Collaborative Space 
Thursday, July 23, 2015
TimeEventLocationMaterials
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
TimeEventLocationMaterials
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 problem - Supervisors:Stefan, Maxim, Vadim  
2:30 - 4:00Research Group Meeting: Configuration spaces of coverings - Supervisors: Tarik, Yuliy  
Monday, July 27, 2015
TimeEventLocationMaterials
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  
Tuesday, July 28, 2015
TimeEventLocationMaterials
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 problem - Supervisors:Stefan, Maxim, Vadim  
Wednesday, July 29, 2015
TimeEventLocationMaterials
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
TimeEventLocationMaterials
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 31, 2015
TimeEventLocationMaterials
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 problem - Supervisors:Stefan, Maxim, Vadim  
2:30 - 4:00Research Group Meeting: Configuration spaces of coverings - Supervisors: Tarik, Yuliy  
Monday, August 3, 2015
TimeEventLocationMaterials
12:00 - 1:00Grad School Q&A11th Floor 
2:00 - 3:00Coffee/Tea Break10th Floor Collaborative Space 
Tuesday, August 4, 2015
TimeEventLocationMaterials
2:00 - 3:00Coffee/Tea Break10th Floor Collaborative Space 
Wednesday, August 5, 2015
TimeEventLocationMaterials
2:00 - 3:00Coffee/Tea Break10th Floor Collaborative Space 
3:00 - 4:00Group Presentation- Crowd Dynamics - Jeremy Ariche, Timothy Valicenti, Juan ClaramuntTBA 
Thursday, August 6, 2015
TimeEventLocationMaterials
1:30 - 2:30Group Presentations- Cyclic pursuit/evasion systems - Anna Grim, Milana Golich, Laura Vargas Hernandez11th Floor Lecture Hall 
2:30 - 3:00Coffee/Tea Break11th Floor Collaborative Space 
3:00 - 4:00Group Presentation- Pinball dynamics - Meg Doucette, Thomas Dauer, Shan Wolf11th floor lecture halll
Friday, August 7, 2015
TimeEventLocationMaterials
10:00 - 11:00Group Presentation- Mixing rates in robotic exploration - Frank Yang, Chang He11th Floor Lecture hall
11:15 - 12:15Group Presentation- Configuration spaces of tangles - Conrad Koskowsky, Ben Lowe11th Floor Lecture Hall
1:30 - 2:30Group Presentations- Configuration spaces of hard disks - Emily Black, Esther Hunt11th Floor Lecture Hall
2:30 - 3:00Coffee/Tea Break11th Floor Collaborative Space 
3:00 - 4:00Group Presentation- Configuration spaces of coverings - Daniel Barg, Shuchi Agrawal, Derek Levinson11th Floor Lecture Hall 
3:00 - 4:00Group Presentation- Configuration spaces of coverings - Daniel Barg\, Shuchi Agrawal\, Derek Levinson11th Floor Lecture Hall 

Final Projects

Final Student Presentations
Completed Student Projects
  • "On a Very Steep Version of the Standard Map" by M. Arnold, T. Dauer, M. Doucette & S.-C. Wolf; published online in Experimental Mathematics, pages: 1-7 | DOI: 10.1080/10586458.2016.1226993: 10.1080/10586458.2016.1226993
  • MAA 2016 Outstanding Poster for their "Mixing Time in Robotic Explorations" research, C. He and S. Yang.

Other Summer@ICERM Events

Summer@ICERM 2012: Geometry and Dynamics
Summer@ICERM 2013: Geometry and Dynamics
Summer@ICERM 2014: Polygons and Polynomials
Summer@ICERM 2016: Dynamics and Stochastics
Summer@ICERM 2017: Topological Data Analysis
Summer@ICERM 2018: Low Dimensional Topology and Geometry