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 2017 Summer@ICERM program is designed for a select group of 16-20 undergraduate scholars. The program will give undergraduates an opportunity for exposure and research in the methods of “Applied Topology” in the study of complex data sets.

The program will offer mini-courses for students at the beginning of the program. The faculty advisors will then present several research projects that are highly interdisciplinary and represent areas where topological data analysis stands to have a deep and meaningful impact. Tackling these projects will require a combination of analytical and computational approaches, and students will be expected to gain intuition into some of these problems via analysis, computer experimentation, and visualization.

Throughout the eight-week program, students will work on their assigned projects in groups of two to four, supervised by faculty advisors and aided by teaching assistants. Students will meet daily, attend mini-courses, learn how to write reports in LaTeX, give weekly team talks about their findings, attend professional development seminars, and write up their research into a poster and/or paper by the end of the program.

ICERM provides an excellent research environment, and the students and their faculty and TA mentors will have access to shared offices and collaborative space throughout the institute. They also will have access to ICERM’s computer facilities and specialized software. ICERM staff will provide logistical support for students and will help build community through fun activities and events.

Hand image shows output of the Mapper algorithm, a topology based method for data visualization.
The Data Science Initiative, a hub at Brown University for research and education in the foundational methodologies, domain applications, and societal impacts of data science, is pleased to support this Summer@ICERM program through faculty and postdoctoral mentorship, and undergraduate support.

Program Details

2017 Research Project Topics
  • Shape Classification
  • Action Recognition
  • Feature Recognition from Persistent Diagrams
  • Local Persistence Diagrams
  • Configuration Spaces
  • Künneth Formula for Persistent Homology
  • Classification of Music Data Streams: Music Information Retrieval and
  • Analysis of Hippocampal Networks.
  • Downloadable PDF of Project Descriptions
Mini-Courses
Mini-Course 1: Theoretical Aspects of Computational Topology

Lecturer: Sara Kališnik Verovšek

Description: This course is devoted to theoretical foundations of computational topology. We will start with a short overview of the field and show some applications that students will learn more about by the end of the class. We will define simplicial complexes, homology groups, discuss triangulations of point clouds and learn the theory behind one of the most popular tools in applied topology, persistent homology.

More on Mini-Course 1

Mini-Course 2: Computational Topology

Lecturer: Henry Adams

Description: This course is an introduction to computational topology, and we motivate the course topics with recent applications of topology. The rst application is to data analysis: the shape of a dataset often re ects important patterns within. Two such datasets with interesting shapes are a space of 3x3 pixel patches from optical images, which can be well-modeled by a Klein bottle, and the conformation space of the cyclo-octane molecule, which is a Klein bottle glued to a 2-sphere along two circles of singularities. We introduce homology as a way to measure the number of holes in a topological space, and persistent homology as a way to measure the number of holes in a dataset.

More on Mini-Course 2

Mini-Course 3: Distances Between Metric Spaces and Applications

Lecturer: Facundo Mémoli

Description: This course is an introduction to Metric Geometry and applications. Of particular importance will be the definition and properties of the so called Gromov-Hausdorff distance between metric spaces and applications to shape and data analysis and matching. We'll also look into the setting of directed/asymmetric networks.

More on Mini-Course 3

Mini-Course 4: Topological Time Series Analysis

Lecturer: Jose Perea

Description: Time varying observations are ubiquitous in today's data rich world; examples include real- valued time series (like sounds and temperature measurements), video data (thought of as ordered sequences of image frames) and dynamic networks (again, ordered sequences of graphs).

More on Mini-Course 4

Funding Includes
  • $3,000 stipend
  • Dormitory housing
  • Meal plan
  • Travel support within U.S.
  • Fun events
  • Accepted Brown University students will receive Brown University's I-Team UTRA grant in lieu of the Summer@ICERM funding package.

Confirmed Speakers & Participants

Summer Schedule

Monday, June 19, 2017
TimeEventLocationMaterials
9:00 - 10:00Welcome / Meet and Greet121 South Main Street, 10th Floor 
10:00 - 11:45Scavenger HuntBrown Campus  
12:00 - 1:30Welcome Lunch10th Floor Collaborative Space 
1:30 - 3:00Project Orientation10th Floor Classroom 
3:00 - 3:30Coffee/Tea Break10th Floor Collaborative Space 
3:30 - 4:30Project Orientation10th Floor Classroom 
Tuesday, June 20, 2017
TimeEventLocationMaterials
9:00 - 10:30Theoretical Aspects of Computational Topology - Sara Kalisnik Verovsek, Brown University10th Floor Classroom 
10:30 - 11:00Coffee/ Tea Break  
11:00 - 12:30Theoretical Aspects of Computational Topology - Sara Kalisnik Verovsek, Brown University10th Floor Classroom 
2:00 - 3:00Mini-course on Computational Topology - Henry Adams, Colorado State University10th Floor Classroom 
3:00 - 3:30Coffee/ Tea Break  
3:30 - 5:00Mini-course on Computational Topology - Henry Adams, Colorado State University10th Floor Classroom 
Wednesday, June 21, 2017
TimeEventLocationMaterials
9:00 - 10:30Theoretical Aspects of Computational Topology - Sara Kalisnik Verovsek, Brown University10th Floor Classroom 
10:30 - 11:00Coffee/ Tea Break  
11:00 - 12:30Theoretical Aspects of Computational Topology - Sara Kalisnik Verovsek, Brown University10th Floor Classroom 
2:00 - 3:00Mini-course on Computational Topology - Henry Adams, Colorado State University10th Floor Classroom 
3:00 - 3:30Coffee/ Tea Break  
3:30 - 5:00Mini-course on Computational Topology - Henry Adams, Colorado State University10th Floor Classroom 
7:00 - 9:00Game Night10th Floor Collaborate Space 
Thursday, June 22, 2017
TimeEventLocationMaterials
9:00 - 10:30Theoretical Aspects of Computational Topology - Sara Kalisnik Verovsek, Brown University10th Floor Classroom 
10:30 - 11:00Coffee/ Tea Break  
11:00 - 12:30Theoretical Aspects of Computational Topology - Sara Kalisnik Verovsek, Brown University10th Floor Classroom 
2:00 - 3:00Mini-course on Computational Topology - Henry Adams, Colorado State University10th Floor Classroom 
3:00 - 3:30Coffee/ Tea Break  
3:30 - 5:00Mini-course on Computational Topology - Henry Adams, Colorado State University10th Floor Classroom 
5:00 - 7:00TA Meeting10th Floor Classroom 
Friday, June 23, 2017
TimeEventLocationMaterials
9:00 - 10:30Theoretical Aspects of Computational Topology - Sara Kalisnik Verovsek, Brown University10th Floor Classroom 
10:30 - 11:00Coffee/ Tea Break  
11:00 - 12:30Theoretical Aspects of Computational Topology - Sara Kalisnik Verovsek, Brown University10th Floor Classroom 
2:00 - 3:00Mini-course on Computational Topology - Henry Adams, Colorado State University10th Floor Classroom 
3:00 - 3:30Coffee/ Tea Break  
3:30 - 5:00Mini-course on Computational Topology - Henry Adams, Colorado State University10th Floor Classroom 
Monday, June 26, 2017
TimeEventLocationMaterials
9:00 - 10:30Distances Between Metric Spaces and Applications - Facundo Memoli10th Floor Classroom 
10:30 - 11:00Coffee/ Tea Break  
11:00 - 12:00Distances Between Metric Spaces and Applications - Facundo Memoli10th Floor Classroom 
2:00 - 3:00Distances between metric spaces and applications - Facundo Memoli, Ohio State University10th Floor Classroom 
3:00 - 3:30Coffee/ Tea Break  
3:30 - 5:00Distances between metric spaces and applications - Facundo Memoli, Ohio State University10th Floor Classroom 
Tuesday, June 27, 2017
TimeEventLocationMaterials
9:00 - 10:30Distances Between Metric Spaces and Applications - Facundo Memoli10th Floor Classroom 
10:30 - 11:00Coffee/ Tea Break  
11:00 - 12:00Distances Between Metric Spaces and Applications - Facundo Memoli10th Floor Classroom 
2:00 - 3:00Distances between metric spaces and applications - Facundo Memoli, Ohio State University10th Floor Classroom 
3:00 - 3:30Coffee/ Tea Break  
3:30 - 5:00Distances between metric spaces and applications - Facundo Memoli, Ohio State University10th Floor Classroom 
Wednesday, June 28, 2017
TimeEventLocationMaterials
9:00 - 10:30Distances Between Metric Spaces and Applications - Facundo Memoli10th Floor Classroom 
10:30 - 11:00Coffee/ Tea Break  
11:00 - 12:00Distances Between Metric Spaces and Applications - Facundo Memoli10th Floor Classroom 
2:00 - 3:00Distances between metric spaces and applications - Facundo Memoli, Ohio State University10th Floor Classroom 
3:00 - 3:30Coffee/ Tea Break  
3:30 - 5:00Distances between metric spaces and applications - Facundo Memoli, Ohio State University10th Floor Classroom 
Thursday, June 29, 2017
TimeEventLocationMaterials
9:00 - 10:30Distances Between Metric Spaces and Applications - Facundo Memoli10th Floor Classroom 
10:30 - 11:00Coffee/ Tea Break  
11:00 - 12:00Distances Between Metric Spaces and Applications - Facundo Memoli10th Floor Classroom 
2:00 - 3:00Distances between metric spaces and applications - Facundo Memoli, Ohio State University10th Floor Classroom 
3:00 - 3:30Coffee/ Tea Break  
3:30 - 5:00Distances between metric spaces and applications - Facundo Memoli, Ohio State University10th Floor Classroom 
5:30 - 6:30(REU)^2F Conversation11th Floor Lecture Hall 
Friday, June 30, 2017
TimeEventLocationMaterials
9:00 - 10:30Distances Between Metric Spaces and Applications - Facundo Memoli10th Floor Classroom 
10:30 - 11:00Coffee/ Tea Break  
11:00 - 12:00Distances Between Metric Spaces and Applications - Facundo Memoli10th Floor Classroom 
2:00 - 3:00Distances between metric spaces and applications - Facundo Memoli, Ohio State University10th Floor Classroom 
3:00 - 3:30Coffee/ Tea Break  
3:30 - 5:00Distances between metric spaces and applications - Facundo Memoli, Ohio State University10th Floor Classroom 
Monday, July 3, 2017
TimeEventLocationMaterials
3:00 - 3:30Coffee/ Tea Break  
Tuesday, July 4, 2017
TimeEventLocationMaterials
3:00 - 3:30Coffee/ Tea Break  
Wednesday, July 5, 2017
TimeEventLocationMaterials
9:00 - 11:00Comparing Songs: From math, statistics, and computer science to music and back again - Katherine Kinnaird, Brown University 11th Floor Lecture Hall 
2:00 - 3:00Summer@ICERM Ethics Training I  
3:00 - 3:30Coffee/ Tea Break  
7:00 - 9:00Movie Night11th Floor Lecture Hall 
Thursday, July 6, 2017
TimeEventLocationMaterials
9:00 - 11:00Large scale geometry of metric spaces - Jeff Brock, Brown University11th Floor Lecture Hall 
2:00 - 3:00Summer@ICERM Ethics Training II  
3:00 - 3:30Coffee/ Tea Break  
4:00 - 6:00TA Meeting10th Floor Classroom 
Friday, July 7, 2017
TimeEventLocationMaterials
9:00 - 12:00Linear Algebra Boot Camp - Isaac Solomon11th Floor Lecture Hall 
2:00 - 3:00Topology Boot Camp - Melissa McGuirl11th Floor Lecture Hall 
3:00 - 3:30Coffee/ Tea Break  
3:30 - 5:00Topology Boot Camp - Melissa McGuirl11th Floor Lecture Hall 
Monday, July 10, 2017
TimeEventLocationMaterials
9:00 - 10:00Mini-course on Topological Time Series Analysis - Jose Perea, Michigan State University10th Floor Classroom 
10:00 - 10:30Coffee/ Tea Break  
10:30 - 12:00Mini-course on Topological Time Series Analysis - Jose Perea, Michigan State University10th Floor Classroom 
2:00 - 3:00Mini-course on Topological Time Series Analysis - Jose Perea, Michigan Stae University10th Floor Classroom 
3:00 - 3:30Coffee/ Tea Break  
3:30 - 5:00Mini-course on Topological Time Series Analysis - Jose Perea, Michigan State University10th Floor Classroom 
Tuesday, July 11, 2017
TimeEventLocationMaterials
9:00 - 10:00Mini-course on Topological Time Series Analysis - Jose Perea, Michigan State University10th Floor Classroom 
10:00 - 10:30Coffee/ Tea Break  
10:30 - 12:00Mini-course on Topological Time Series Analysis - Jose Perea, Michigan State University10th Floor Classroom 
2:00 - 3:00Mini-course on Topological Time Series Analysis - Jose Perea, Michigan State University10th Floor Classroom 
3:00 - 3:30Coffee/ Tea Break  
3:30 - 5:00Mini-course on Topological Time Series Analysis - Jose Perea, Michigan State University10th Floor Classroom 
Wednesday, July 12, 2017
TimeEventLocationMaterials
9:00 - 10:00Mini-course on Topological Time Series Analysis - Jose Perea, Michigan State University10th Floor Classroom 
10:00 - 10:30Coffee/ Tea Break  
10:30 - 12:00Mini-course on Topological Time Series Analysis - Jose Perea, Michigan State University10th Floor Classroom 
2:00 - 3:00Mini-course on Topological Time Series Analysis - Jose Perea, Michigan State University10th Floor Classroom 
3:00 - 3:30Coffee/ Tea Break  
3:30 - 5:00Mini-course on Topological Time Series Analysis - Jose Perea, Michigan State University10th Floor Classroom 
Thursday, July 13, 2017
TimeEventLocationMaterials
9:00 - 10:00Mini-course on Topological Time Series Analysis - Jose Perea, Michigan State University10th Floor Classroom 
10:00 - 10:30Coffee/ Tea Break  
10:30 - 12:00Mini-course on Topological Time Series Analysis - Jose Perea, Michigan State University10th Floor Classroom 
2:00 - 3:00Mini-course on Topological Time Series Analysis - Jose Perea, Michigan State University10th Floor Classroom 
3:00 - 3:30Coffee/ Tea Break  
3:30 - 5:00Mini-course on Topological Time Series Analysis - Jose Perea, Michigan State University10th Floor Classroom 
Friday, July 14, 2017
TimeEventLocationMaterials
9:00 - 10:00Mini-course on Topological Time Series Analysis - Jose Perea, Michigan State University10th Floor Classroom 
10:00 - 10:30Coffee/ Tea Break  
10:30 - 12:00Mini-course on Topological Time Series Analysis - Jose Perea, Michigan State University10th Floor Classroom 
2:00 - 3:00Mini-course on Topological Time Series Analysis - Jose Perea, Michigan State University10th Floor Classroom 
3:00 - 3:30Coffee/ Tea Break  
3:30 - 5:00Mini-course on Topological Time Series Analysis - Jose Perea, Michigan State University10th Floor Classroom 
Monday, July 17, 2017
TimeEventLocationMaterials
10:00 - 10:30Coffee/ Tea Break  
3:00 - 3:30Coffee/ Tea Break  
Tuesday, July 18, 2017
TimeEventLocationMaterials
10:00 - 10:30Coffee/ Tea Break  
3:00 - 3:30Coffee/ Tea Break  
Wednesday, July 19, 2017
TimeEventLocationMaterials
10:00 - 10:30Coffee/ Tea Break  
3:00 - 3:30Coffee/ Tea Break  
Thursday, July 20, 2017
TimeEventLocationMaterials
10:00 - 10:30Coffee/ Tea Break  
3:00 - 3:30Coffee/ Tea Break  
4:00 - 5:00EIRENE demo - Greg Henselman, University of Pennsylvania10th Floor Classroom 
6:30 - 7:30WiSDM Panel for Summer@ICERM11th Floor Lecture Hall 
Friday, July 21, 2017
TimeEventLocationMaterials
10:00 - 10:30Coffee/ Tea Break  
2:30 - 3:00Coffee/ Tea Break11th Floor Collaborative Space 
3:00 - 4:00TDA Persistence Explorer - Rachel Levanger, Rutgers University10th Floor Classroom 
4:00 - 5:00A linear Algebra primer (from a combinatorial point of view) - Greg Henselman, University of Pennsylvania10th Floor Classroom 
Monday, July 24, 2017
TimeEventLocationMaterials
3:00 - 4:00Lesson 1: The LU decomposition - Greg Henselman, University of Pennsylvania10th Floor Classroom 
Tuesday, July 25, 2017
TimeEventLocationMaterials
3:00 - 4:00Lesson 3: Jordan Canonical Form - Greg Henselman, University of Pennsylvania10th Floor Classroom 
Wednesday, July 26, 2017
TimeEventLocationMaterials
2:30 - 3:00Coffee/ Tea Break  
3:00 - 4:00Lesson 2: Gauss, Jordan, and Gabriel - Greg Henselman, University of Pennsylvania10th Floor Classroom 
Thursday, July 27, 2017
TimeEventLocationMaterials
2:30 - 3:00Coffee/ Tea Break  
3:00 - 4:00Lesson 4: Gauss-Jordan Elimination - Greg Henselman, University of Pennsylvania10th Floor Classroom 
6:30 - 8:00HUG Panel11th Floor Lecture Hall 
Friday, July 28, 2017
TimeEventLocationMaterials
2:30 - 3:00Coffee/ Tea Break  
3:00 - 3:30Lesson 5a: Möbius Inversion - Greg Henselman, University of Pennsylvania10th Floor Classroom 
3:30 - 4:00Lesson 5b: Synthesis - Greg Henselman, University of Pennsylvania10th Floor Classroom 
Monday, July 31, 2017
TimeEventLocationMaterials
2:30 - 3:00Coffee/ Tea Break  
Tuesday, August 1, 2017
TimeEventLocationMaterials
2:30 - 3:00Coffee/ Tea Break  
Wednesday, August 2, 2017
TimeEventLocationMaterials
2:30 - 3:00Coffee/ Tea Break  
Thursday, August 3, 2017
TimeEventLocationMaterials
2:30 - 3:00Coffee/ Tea Break  
6:30 - 8:00Grad Student Panel - Isaac Solomon, Brown University10th Floor Classroom  
Friday, August 4, 2017
TimeEventLocationMaterials
2:30 - 3:00Coffee/ Tea Break  
Monday, August 7, 2017
TimeEventLocationMaterials
2:30 - 3:00Coffee/ Tea Break  
Tuesday, August 8, 2017
TimeEventLocationMaterials
2:30 - 3:00Coffee/ Tea Break  
Wednesday, August 9, 2017
TimeEventLocationMaterials
2:30 - 3:00Coffee/ Tea Break  
Thursday, August 10, 2017
TimeEventLocationMaterials
9:00 - 9:45Comparing Songs Without Listening - Erin Bugbee, Claire Savard, & Jonathan Weisskoff10th Floor Classroom 
10:00 - 10:45Vietoris-Rips Complexes of Regular Polygons - Adam Jaffe & Bongi Sibanda10th Floor Classroom 
11:00 - 11:20Coffee/ Tea Break  
11:20 - 12:05Number Theory, Dynamics and Sliding Windows - Tequania Lake & Yixuan (Monica) Zhang10th Floor Classroom 
12:15 - 2:00Lunch Break/ Free Time  
2:00 - 2:45Recurrence in Dynamic Networks - Biraj Pandey, Timothy Sudijono, & Vivienne Xu10th Floor Classroom 
3:00 - 3:45Recovering Surfaces from Real Valued Functions - Alice Antia, Michael Lin, & Boyan Xu10th Floor Classroom 
3:45 - 4:15Coffee/ Tea Break  
Friday, August 11, 2017
TimeEventLocationMaterials
10:00 - 10:45Curvature Sets - Peter Eastwood & Anna Ellison10th Floor Classroom 
11:00 - 11:20Coffee/ Tea Break  
11:20 - 12:05Shape Matching: The case of zeolites - Gabrielle Ferra & Danny Lopez10th Floor Classroom 
12:15 - 2:00Lunch/ Free Time  
2:00 - 2:45Other Filtrations and Local Persistence Diagrams - Nate Clause, Jose Angel Sanchez, & Zoe Wellner10th Floor Classroom 
3:00 - 3:10Group Picture10th Floor Classroom 
3:10 - 3:40Final Coffee Break  

Final Projects

Final Student Presentations
  • "Comparing Songs Without Listening" by Erin Bugbee, Claire Savard, and Jonathan Weisskoff
  • "Vietoris-Rips Complexes of Regular Polygons" by Adam Jaffe and Bongi Sibanda
  • "Number Theory, Dynamics and Sliding Windows" by Tequania Lake and Yixuan (Monica) Zhang
  • "Recurrence in Dynamic Networks" by Biraj Pandey, Timothy Sudijono, and Vivienne Xu
  • "Recovering Surfaces from Real Valued Functions" by Alice Antia, Michael Lin, and Boyan Xu
  • "Curvature Sets" by Peter Eastwood and Anna Ellison
  • "Shape Matching: The case of zeolites" by Gabrielle Ferra and Danny Lopez
  • "Other Filtrations and Local Persistence Diagrams" by Nate Clause, Jose Angel Sanchez, and Zoe Wellner
Posters Presented at JMM 2018 in San Diego, CA
  • Comparing Songs Using Matrix Pattern Preservation" (Erin Bugbee and Claire Savard)
  • A First Approach to a General Theory of Filtration Functions" (Nathaniel Clause and Jose Angel Sanchez Gomez)
  • Vietoris-Rips Complexes of Regular Polygons" (Adam Jaffee)*
  • Shape-Matching: The Case of Zeolites" (Daniel Lopez, Gabrielle Ferra)
  • Delay embeddings and topological time series analysis" (Boyan Xu)
  • Geometry and Topology of the Curvature Sets of S 1" (Anna Ellison, Peter Eastwood)

Recipient of the MAA "Outstanding Poster Award" at JMM 2018
*Recipient of a poster prize at LatinX conference at IPAM 2018

Papers

Other Summer@ICERM Events

Summer@ICERM 2012: Geometry and Dynamics
Summer@ICERM 2013: Geometry and Dynamics
Summer@ICERM 2014: Polygons and Polynomials
Summer@ICERM 2015: Computational Dynamics and Topology
Summer@ICERM 2016: Dynamics and Stochastics
Summer@ICERM 2018: Low Dimensional Topology and Geometry
Summer@ICERM 2019: Computational Arithmetic Dynamics