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 Courses:

This course is devoted to theoretical foundations of computational topology. We will start with a short overview of the eld and show some applications that students will learn more about by the end of the class. We will de ne 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.

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 3  3 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.

As a second application of topology, we will describe coverage problems in sensor networks. Suppose ball-shaped sensors wander in a bounded domain. A sensor doesn't know its location but does know when it overlaps a nearby sensor. We say that an evasion path exists in this sensor network if a moving intruder can avoid detection. Using zigzag persistent homology, one can compute a necessary condition for an evasion path to exist. However, no method with time-varying connectivity data (i.e. Cech complexes) as input can give necessary and sucient conditions for the existence of an evasion path. In the setting of planar sensors that also measure weak rotation information, we discuss necessary and sucient conditions for the existence of an evasion path, and pose an open question concerning Cech and alpha complexes. Course topics include simplicial complexes, Cech and nerve complexes, Vietoris-Rips com- plexes, persistent homology, and zigzag persistent homology.

The main ideas behind the construction and applications of the Gromov-Hausdor distance will be presented in a series of lectures.

Time series are ubiquitous in today's data rich world, so naturally their analysis is a fundamental object of study. In recent years, tools from the growing eld of topological data analysis have been adapted to the analysis of time series data. In short, time series can be transformed into high-dimensional point clouds (via delay-embeddings) and their shape can be probed via persistent homology to quantify characteristics such as periodicity, quasiperiodicity, existence of motifs, presence of dynamic chaos, etc [13, 14]. This mini-course we will cover some of the theory behind topological time series analysis, and will explore applications ranging from biology to music analysis.

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 - 10:30Basics of AATSara Kaliˇsnik Verovˇsek10th Floor Classroom
10:30 - 11:00Coffee/ Tea Break
11:00 - 12:30Basics of AATSara Kaliˇsnik Verovˇsek10th Floor Classroom
2:00 - 3:30TDA Concepts, JavaPlexHenry Adams10th Floor Classroom
3:30 - 4:00Coffee/ Tea Break
4:00 - 5:00TDA Concepts, JavaPlexHenry Adams10th Floor Classroom

Wednesday June 21, 2017
Time Description Speaker Location Abstracts Slides
9:00 - 10:30Basics of AATSara Kaliˇsnik Verovˇsek10th Floor Classroom
10:30 - 11:00Coffee/ Tea Break
11:00 - 12:30Basics of AATSara Kaliˇsnik Verovˇsek10th Floor Classroom
2:00 - 3:30TDA Concepts, JavaPlexHenry Adams10th Floor Classroom
3:30 - 4:00Coffee/ Tea Break
4:00 - 5:00TDA Concepts, JavaPlexHenry Adams10th Floor Classroom
7:00 - 9:00Game Night10th Floor Collaborate Space

Thursday June 22, 2017
Time Description Speaker Location Abstracts Slides
9:00 - 10:30Basics of AATSara Kaliˇsnik Verovˇsek10th Floor Classroom
10:30 - 11:00Coffee/ Tea Break
11:00 - 12:30Basics of AATSara Kaliˇsnik Verovˇsek10th Floor Classroom
2:00 - 3:30TDA Concepts, JavaPlexHenry Adams10th Floor Classroom
3:30 - 4:00Coffee/ Tea Break
4:00 - 5:00TDA Concepts, JavaPlexHenry Adams10th Floor Classroom
5:00 - 7:00TA Meeting10th Floor Classroom

Friday June 23, 2017
Time Description Speaker Location Abstracts Slides
9:00 - 10:30Basics of AATSara Kaliˇsnik Verovˇsek10th Floor Classroom
10:30 - 11:00Coffee/ Tea Break
11:00 - 12:30Basics of AATSara Kaliˇsnik Verovˇsek10th Floor Classroom
2:00 - 3:30TDA Concepts, JavaPlexHenry Adams10th Floor Classroom
3:30 - 4:00Coffee/ Tea Break
4:00 - 5:00TDA Concepts, JavaPlexHenry Adams10th 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 - 3:30Distance Between Metric Spaces and ApplicationsHands-on Session/ Discussion10th Floor Classroom
3:30 - 4:00Coffee/ Tea Break
4:00 - 5:00Distance Between Metric Spaces and ApplicationsHands-on Session/ Discussion10th 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 - 3:30Distance Between Metric Spaces and ApplicationsHands-on Session/ Discussion10th Floor Classroom
3:30 - 4:00Coffee/ Tea Break
4:00 - 5:00Distance Between Metric Spaces and ApplicationsHands-on Session/ Discussion10th 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 - 3:30Distance Between Metric Spaces and ApplicationsHands-on Session/ Discussion10th Floor Classroom
3:30 - 4:00Coffee/ Tea Break
4:00 - 5:00Distance Between Metric Spaces and ApplicationsHands-on Session/ Discussion10th 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 - 3:30Distance Between Metric Spaces and ApplicationsHands-on Session/ Discussion10th Floor Classroom
3:30 - 4:00Coffee/ Tea Break
4:00 - 5:00Distance Between Metric Spaces and ApplicationsHands-on Session/ Discussion10th Floor Classroom

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 - 3:30Distance Between Metric Spaces and ApplicationsHands-on Session/ Discussion10th Floor Classroom
3:30 - 4:00Coffee/ Tea Break
4:00 - 5:00Distance Between Metric Spaces and ApplicationsHands-on Session/ Discussion10th Floor Classroom

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

Wednesday July 5, 2017
Time Description Speaker Location Abstracts Slides
2:00 - 3:00Summer@ICERM Ethics Training I
3:30 - 4:00Coffee/ Tea Break
7:00 - 9:00Movie Night11th Floor Lecture Hall

Thursday July 6, 2017
Time Description Speaker Location Abstracts Slides
2:00 - 3:00Summer@ICERM Ethics Training II
3:30 - 4:00Coffee/ Tea Break
4:00 - 6:00TA Meeting10th Floor Classroom

Friday July 7, 2017
Time Description Speaker Location Abstracts Slides
3:30 - 4:00Coffee/ Tea Break

Monday July 10, 2017
Time Description Speaker Location Abstracts Slides
9:00 - 10:00Summer@ICERM Mini-CourseJose Perea10th Floor Classroom
10:00 - 10:30Coffee/ Tea Break
10:30 - 12:00Summer@ICERM Mini-CourseJose Perea10th Floor Classroom
2:00 - 3:30TDA and Times Series DataHands-on Sessions/ Discussions10th Floor Classroom
3:30 - 4:00Coffee/ Tea Break
4:00 - 5:00TDA and Times Series DataHands-on Sessions/ Discussions10th Floor Classroom

Tuesday July 11, 2017
Time Description Speaker Location Abstracts Slides
9:00 - 10:00Summer@ICERM Mini-CourseJose Perea10th Floor Classroom
10:00 - 10:30Coffee/ Tea Break
10:30 - 12:00Summer@ICERM Mini-CourseJose Perea10th Floor Classroom
2:00 - 3:30TDA and Times Series DataHands-on Sessions/ Discussions10th Floor Classroom
3:30 - 4:00Coffee/ Tea Break
4:00 - 5:00TDA and Times Series DataHands-on Sessions/ Discussions10th Floor Classroom

Wednesday July 12, 2017
Time Description Speaker Location Abstracts Slides
9:00 - 10:00Summer@ICERM Mini-CourseJose Perea10th Floor Classroom
10:00 - 10:30Coffee/ Tea Break
10:30 - 12:00Summer@ICERM Mini-CourseJose Perea10th Floor Classroom
2:00 - 3:30TDA and Times Series DataHands-on Sessions/ Discussions10th Floor Classroom
3:30 - 4:00Coffee/ Tea Break
4:00 - 5:00TDA and Times Series DataHands-on Sessions/ Discussions10th Floor Classroom

Thursday July 13, 2017
Time Description Speaker Location Abstracts Slides
9:00 - 10:00Summer@ICERM Mini-CourseJose Perea10th Floor Classroom
10:00 - 10:30Coffee/ Tea Break
10:30 - 12:00Summer@ICERM Mini-CourseJose Perea10th Floor Classroom
2:00 - 3:30TDA and Times Series DataHands-on Sessions/ Discussions10th Floor Classroom
3:30 - 4:00Coffee/ Tea Break
4:00 - 5:00TDA and Times Series DataHands-on Sessions/ Discussions10th Floor Classroom

Friday July 14, 2017
Time Description Speaker Location Abstracts Slides
9:00 - 10:00Summer@ICERM Mini-CourseJose Perea10th Floor Classroom
10:00 - 10:30Coffee/ Tea Break
10:30 - 12:00Summer@ICERM Mini-CourseJose Perea10th Floor Classroom
2:00 - 3:30TDA and Times Series DataHands-on Sessions/ Discussions10th Floor Classroom
2:00 - 5:00Project - Presentations/ Assignments
3:30 - 4:00Coffee/ Tea Break
4:00 - 5:00TDA and Times Series DataHands-on Sessions/ Discussions10th Floor Classroom