Organizing Committee
Brown University
Brown University
The Ohio State University
Michigan State University
Abstract
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.
Summer 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.
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.
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.
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).
- 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.
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Summer Schedule
Monday, June 19, 2017
9:00 - 10:00 AM EDT
Welcome / Meet and Greet
Location: 121 South Main Street, 10th Floor
10:00 - 11:45 AM EDT
Scavenger Hunt
Location: Brown Campus
12:00 - 1:30 PM EDT
Welcome Lunch
Location: 10th Floor Collaborative Space
1:30 - 3:00 PM EDT
Project Orientation
Location: 10th Floor Classroom
3:00 - 3:30 PM EDT
Coffee/Tea Break
Location: 10th Floor Collaborative Space
3:30 - 4:30 PM EDT
Project Orientation
Location: 10th Floor Classroom
Tuesday, June 20, 2017
9:00 - 10:30 AM EDT
Theoretical Aspects of Computational Topology - Sara Kalisnik Verovsek, Brown University
Location: 10th Floor Classroom
10:30 - 11:00 AM EDT
Coffee/ Tea Break
11:00 AM - 12:30 PM EDT
Theoretical Aspects of Computational Topology - Sara Kalisnik Verovsek, Brown University
Location: 10th Floor Classroom
2:00 - 3:00 PM EDT
Mini-course on Computational Topology - Henry Adams, Colorado State University
Location: 10th Floor Classroom
3:00 - 3:30 PM EDT
Coffee/ Tea Break
3:30 - 5:00 PM EDT
Mini-course on Computational Topology - Henry Adams, Colorado State University
Location: 10th Floor Classroom
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)
- Conference Presentation
- "SuPP & MaPP: Adaptable Structure-based Representations for MIR Tasks." C. Savard, E.H. Bugbee, M.R. McGuirl, K.M. Kinnaird. Presented at the 21st International Society for Music Information Retrieval (ISMIR), 2020. Abstract, Paper, Poster, and Video presentation
Recipient of the MAA "Outstanding Poster Award" at JMM 2018
*Recipient of a poster prize at LatinX conference at IPAM 2018
