Summer@ICERM 2017: Topological Data Analysis

(June 19 - August 11, 2017)

 

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:

  • Persistent Homology from the Computational Viewpoint;
  • Distances Between Metric Spaces and Applications; and
  • Topological Time Series Analysis.

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:

  1. Shape Classification;
  2. Action Recognition;
  3. Feature Recognition from Persistent Diagrams;
  4. Local Persistence Diagrams;
  5. Configuration Spaces;
  6. Künneth Formula for Persistent Homology;
  7. Classification of Music Data Streams: Music Information Retrieval; and
  8. Analysis of Hippocampal Networks.
Downloadable PDF of Project Descriptions.

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.


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.

Applications are Closed for 2017

Organizing Committee

Summer@ICERM 2017
Funding include*

  • $3,000 stipend
  • Travel support within U.S.
  • Dormitory housing
  • Meal plan
  • Fun events
*Accepted Brown University students will receive Brown University's I-Team UTRA grant in lieu of the Summer@ICERM funding package.
What to Expect
View Summer@ICERM 2016 for sample schedule, completed projects, etc.
Hand image shows output of the Mapper algorithm, a topology based method for data visualization.

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 Méamoli

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

Monday June 19, 2017
Time Description Speaker Location Abstracts Slides
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
Time Description Speaker Location Abstracts Slides
9:00 - 10:30Theoretical Aspects of Computational TopologySara Kalisnik Verovsek, Brown University10th Floor Classroom
10:30 - 11:00Coffee/ Tea Break
11:00 - 12:30Theoretical Aspects of Computational TopologySara Kalisnik Verovsek, Brown University10th Floor Classroom
2:00 - 3:00Mini-course on Computational TopologyHenry Adams, Colorado State University10th Floor Classroom
3:00 - 3:30Coffee/ Tea Break
3:30 - 5:00Mini-course on Computational TopologyHenry Adams, Colorado State University10th Floor Classroom

Wednesday June 21, 2017
Time Description Speaker Location Abstracts Slides
9:00 - 10:30Theoretical Aspects of Computational TopologySara Kalisnik Verovsek, Brown University10th Floor Classroom
10:30 - 11:00Coffee/ Tea Break
11:00 - 12:30Theoretical Aspects of Computational TopologySara Kalisnik Verovsek, Brown University10th Floor Classroom
2:00 - 3:00Mini-course on Computational TopologyHenry Adams, Colorado State University10th Floor Classroom
3:00 - 3:30Coffee/ Tea Break
3:30 - 5:00Mini-course on Computational TopologyHenry Adams, Colorado State University10th Floor Classroom
7:00 - 9:00Game Night10th Floor Collaborate Space

Thursday June 22, 2017
Time Description Speaker Location Abstracts Slides
9:00 - 10:30Theoretical Aspects of Computational TopologySara Kalisnik Verovsek, Brown University10th Floor Classroom
10:30 - 11:00Coffee/ Tea Break
11:00 - 12:30Theoretical Aspects of Computational TopologySara Kalisnik Verovsek, Brown University10th Floor Classroom
2:00 - 3:00Mini-course on Computational TopologyHenry Adams, Colorado State University10th Floor Classroom
3:00 - 3:30Coffee/ Tea Break
3:30 - 5:00Mini-course on Computational TopologyHenry Adams, Colorado State University10th Floor Classroom
5:00 - 7:00TA Meeting10th Floor Classroom

Friday June 23, 2017
Time Description Speaker Location Abstracts Slides
9:00 - 10:30Theoretical Aspects of Computational TopologySara Kalisnik Verovsek, Brown University10th Floor Classroom
10:30 - 11:00Coffee/ Tea Break
11:00 - 12:30Theoretical Aspects of Computational TopologySara Kalisnik Verovsek, Brown University10th Floor Classroom
2:00 - 3:00Mini-course on Computational TopologyHenry Adams, Colorado State University10th Floor Classroom
3:00 - 3:30Coffee/ Tea Break
3:30 - 5:00Mini-course on Computational TopologyHenry Adams, Colorado State University10th Floor Classroom

Monday June 26, 2017
Time Description Speaker Location Abstracts Slides
9:00 - 10:30Distances Between Metric Spaces and ApplicationsFacundo Memoli10th Floor Classroom
10:30 - 11:00Coffee/ Tea Break
11:00 - 12:00Distances Between Metric Spaces and ApplicationsFacundo Memoli10th Floor Classroom
2:00 - 3:00Distances between metric spaces and applicationsFacundo Memoli, Ohio State University10th Floor Classroom
3:00 - 3:30Coffee/ Tea Break
3:30 - 5:00Distances between metric spaces and applicationsFacundo Memoli, Ohio State University10th Floor Classroom

Tuesday June 27, 2017
Time Description Speaker Location Abstracts Slides
9:00 - 10:30Distances Between Metric Spaces and ApplicationsFacundo Memoli10th Floor Classroom
10:30 - 11:00Coffee/ Tea Break
11:00 - 12:00Distances Between Metric Spaces and ApplicationsFacundo Memoli10th Floor Classroom
2:00 - 3:00Distances between metric spaces and applicationsFacundo Memoli, Ohio State University10th Floor Classroom
3:00 - 3:30Coffee/ Tea Break
3:30 - 5:00Distances between metric spaces and applicationsFacundo Memoli, Ohio State University10th Floor Classroom

Wednesday June 28, 2017
Time Description Speaker Location Abstracts Slides
9:00 - 10:30Distances Between Metric Spaces and ApplicationsFacundo Memoli10th Floor Classroom
10:30 - 11:00Coffee/ Tea Break
11:00 - 12:00Distances Between Metric Spaces and ApplicationsFacundo Memoli10th Floor Classroom
2:00 - 3:00Distances between metric spaces and applicationsFacundo Memoli, Ohio State University10th Floor Classroom
3:00 - 3:30Coffee/ Tea Break
3:30 - 5:00Distances between metric spaces and applicationsFacundo Memoli, Ohio State University10th Floor Classroom

Thursday June 29, 2017
Time Description Speaker Location Abstracts Slides
9:00 - 10:30Distances Between Metric Spaces and ApplicationsFacundo Memoli10th Floor Classroom
10:30 - 11:00Coffee/ Tea Break
11:00 - 12:00Distances Between Metric Spaces and ApplicationsFacundo Memoli10th Floor Classroom
2:00 - 3:00Distances between metric spaces and applicationsFacundo Memoli, Ohio State University10th Floor Classroom
3:00 - 3:30Coffee/ Tea Break
3:30 - 5:00Distances between metric spaces and applicationsFacundo Memoli, Ohio State University10th Floor Classroom
5:30 - 6:30(REU)^2F Conversation11th Floor Lecture Hall

Friday June 30, 2017
Time Description Speaker Location Abstracts Slides
9:00 - 10:30Distances Between Metric Spaces and ApplicationsFacundo Memoli10th Floor Classroom
10:30 - 11:00Coffee/ Tea Break
11:00 - 12:00Distances Between Metric Spaces and ApplicationsFacundo Memoli10th Floor Classroom
2:00 - 3:00Distances between metric spaces and applicationsFacundo Memoli, Ohio State University10th Floor Classroom
3:00 - 3:30Coffee/ Tea Break
3:30 - 5:00Distances between metric spaces and applicationsFacundo Memoli, Ohio State University10th Floor Classroom

Monday July 3, 2017
Time Description Speaker Location Abstracts Slides
3:00 - 3:30Coffee/ Tea Break

Tuesday July 4, 2017
Time Description Speaker Location Abstracts Slides
3:00 - 3:30Coffee/ Tea Break

Wednesday July 5, 2017
Time Description Speaker Location Abstracts Slides
9:00 - 11:00Comparing Songs: From math, statistics, and computer science to music and back againKatherine 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
Time Description Speaker Location Abstracts Slides
9:00 - 11:00Large scale geometry of metric spacesJeff 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
Time Description Speaker Location Abstracts Slides
9:00 - 12:00Linear Algebra Boot CampIsaac Solomon11th Floor Lecture Hall
2:00 - 3:00Topology Boot CampMelissa McGuirl11th Floor Lecture Hall
3:00 - 3:30Coffee/ Tea Break
3:30 - 5:00Topology Boot CampMelissa McGuirl11th Floor Lecture Hall

Monday July 10, 2017
Time Description Speaker Location Abstracts Slides
9:00 - 10:00Mini-course on Topological Time Series AnalysisJose Perea, Michigan State University10th Floor Classroom
10:00 - 10:30Coffee/ Tea Break
10:30 - 12:00Mini-course on Topological Time Series AnalysisJose Perea, Michigan State University10th Floor Classroom
2:00 - 3:00Mini-course on Topological Time Series AnalysisJose Perea, Michigan Stae University10th Floor Classroom
3:00 - 3:30Coffee/ Tea Break
3:30 - 5:00Mini-course on Topological Time Series AnalysisJose Perea, Michigan State University10th Floor Classroom

Tuesday July 11, 2017
Time Description Speaker Location Abstracts Slides
9:00 - 10:00Mini-course on Topological Time Series AnalysisJose Perea, Michigan State University10th Floor Classroom
10:00 - 10:30Coffee/ Tea Break
10:30 - 12:00Mini-course on Topological Time Series AnalysisJose Perea, Michigan State University10th Floor Classroom
2:00 - 3:00Mini-course on Topological Time Series AnalysisJose Perea, Michigan State University10th Floor Classroom
3:00 - 3:30Coffee/ Tea Break
3:30 - 5:00Mini-course on Topological Time Series AnalysisJose Perea, Michigan State University10th Floor Classroom

Wednesday July 12, 2017
Time Description Speaker Location Abstracts Slides
9:00 - 10:00Mini-course on Topological Time Series AnalysisJose Perea, Michigan State University10th Floor Classroom
10:00 - 10:30Coffee/ Tea Break
10:30 - 12:00Mini-course on Topological Time Series AnalysisJose Perea, Michigan State University10th Floor Classroom
2:00 - 3:00Mini-course on Topological Time Series AnalysisJose Perea, Michigan State University10th Floor Classroom
3:00 - 3:30Coffee/ Tea Break
3:30 - 5:00Mini-course on Topological Time Series AnalysisJose Perea, Michigan State University10th Floor Classroom

Thursday July 13, 2017
Time Description Speaker Location Abstracts Slides
9:00 - 10:00Mini-course on Topological Time Series AnalysisJose Perea, Michigan State University10th Floor Classroom
10:00 - 10:30Coffee/ Tea Break
10:30 - 12:00Mini-course on Topological Time Series AnalysisJose Perea, Michigan State University10th Floor Classroom
2:00 - 3:00Mini-course on Topological Time Series AnalysisJose Perea, Michigan State University10th Floor Classroom
3:00 - 3:30Coffee/ Tea Break
3:30 - 5:00Mini-course on Topological Time Series AnalysisJose Perea, Michigan State University10th Floor Classroom

Friday July 14, 2017
Time Description Speaker Location Abstracts Slides
9:00 - 10:00Mini-course on Topological Time Series AnalysisJose Perea, Michigan State University10th Floor Classroom
10:00 - 10:30Coffee/ Tea Break
10:30 - 12:00Mini-course on Topological Time Series AnalysisJose Perea, Michigan State University10th Floor Classroom
2:00 - 3:00Mini-course on Topological Time Series AnalysisJose Perea, Michigan State University10th Floor Classroom
3:00 - 3:30Coffee/ Tea Break
3:30 - 5:00Mini-course on Topological Time Series AnalysisJose Perea, Michigan State University10th Floor Classroom

Monday July 17, 2017
Time Description Speaker Location Abstracts Slides
10:00 - 10:30Coffee/ Tea Break
3:00 - 3:30Coffee/ Tea Break

Tuesday July 18, 2017
Time Description Speaker Location Abstracts Slides
10:00 - 10:30Coffee/ Tea Break
3:00 - 3:30Coffee/ Tea Break

Wednesday July 19, 2017
Time Description Speaker Location Abstracts Slides
10:00 - 10:30Coffee/ Tea Break
3:00 - 3:30Coffee/ Tea Break

Thursday July 20, 2017
Time Description Speaker Location Abstracts Slides
10:00 - 10:30Coffee/ Tea Break
3:00 - 3:30Coffee/ Tea Break
6:30 - 7:30WiSDM Panel for Summer@ICERM11th Floor Lecture Hall

Friday July 21, 2017
Time Description Speaker Location Abstracts Slides
10:00 - 10:30Coffee/ Tea Break
3:00 - 3:30Coffee/ Tea Break