Home /  MSRI-UP 2023: Topological Data Analysis


MSRI-UP 2023: Topological Data Analysis June 10, 2023 - July 23, 2023
Parent Program: --
Location: SLMath: Baker Board Room, Atrium
Organizers Federico Ardila (San Francisco State University), LEAD Maria Mercedes Franco (Queensborough Community College (CUNY)), Rebecca Garcia (Colorado College), Jose Perea (Northeastern University), Candice Price (Smith College), Robin Wilson (Loyola Marymount University)

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The MSRI Undergraduate Program (MSRI--UP) is an award-winning comprehensive summer program designed for undergraduate students who have completed two years of university-level mathematics courses and would like to conduct research in the mathematical sciences.

The main objective of the MSRI-UP is to identify talented students, especially those from underrepresented groups (including women and gender-expansive individuals), who are interested in mathematics and make available to them meaningful research opportunities, the necessary skills and knowledge to participate in successful collaborations, and a community of academic peers and mentors who can advise, encourage and support them through a successful graduate program.

Please help us to spread the word about this opportunity to your undergraduate contacts: 

Download MSRI-UP 2023 Program Flyer (PDF)

Research Theme

The theme of the 2023 MSRI-UP is “Topological Data Analysis" and the research leader is Dr. Jose Perea, Associate Professor in the Department of Mathematics and the Khoury College of Computer Sciences at Northeastern University. 

Topology is the branch of mathematics concerned with the study of abstract shapes. For most of its history it has been a purely theoretical discipline, but this has changed over the last couple of decades. Recently, topology has shown to be a powerful framework to tackle problems in data science, machine learning and engineering. The research program of the 2023 MSRI-UP on Topological Data Analysis will focus on how ideas from classic algebraic topology - like (co)homology and other descriptors - can be used in machine learning tasks such as dimensionality reduction, time series analysis and data alignment. Participants will contribute to research projects ranging from the needed mathematical foundations, to their algorithmic implementation, and subsequent application to specific scientific domains.

Students who have had a linear algebra course and a course in which they have had to write proofs are eligible to apply. 

Familiarity with Python/Jupyter Notebooks,  statistics or the topology of metric spaces will be helpful.

General Description

During the summer, each of the 18 student participants will:

  • participate in the mathematics research program under the direction of Dr. Jose Perea of Northeastern University, a post-doc and two graduate students;
  • complete a research project done in collaboration with other MSRI-UP students;
  • give a presentation and write a technical report on his/her research project;
  • attend a series of colloquium talks given by leading researches in their fields;
  • attend workshops aimed at developing skills and techniques needed for research careers in the mathematical sciences;
  • learn techniques that will maximize a student's likelihood of admissions to graduate programs as well as the likelihood of winning fellowships; and
  • receive a $3600 stipend, lodging, meals and round trip travel to Berkeley, CA.

After the summer, each student will:

  • have an opportunity to attend a national mathematics or science conference where students will present their research;
  • be part of a network of mentors that will provide continuous advice in the long term as the student makes progress in his/her studies; and
  • be contacted regarding future research opportunities.

How to Apply

Applications for MSRI-UP are hosted on the National Science Foundation's Education and Training Application site. 


Applications are now open for MSRI-UP 2023. See deadline info below.



Due to funding restrictions, only U.S. citizens and permanent residents are eligible to apply. Deferred Action for Childhood Arrivals (DACA) students are also eligible due to generous funding by the Alfred P. Sloan Foundation. The program cannot accept foreign students regardless of funding. In addition, students who have already graduated or will have graduated with a bachelor's degree by August 31, 2023 are not eligible to apply. 

Application Deadlines

Applications submitted by February 15, 2023 will receive full consideration. (Applications submitted after February 15, 2023 but by March 1, 2023 may still be considered in a second round of acceptances.) We expect to begin making offers for participation in late February or early March.

Applications are now open for MSRI-UP 2023. Visit the NSF ETAP website to apply.

Application Materials

A complete application consists of the following:

Common Application Requirements:

1. Personal Statement (5,000 characters) describing your academic and career goals and how the REU program will help you achieve these goals.  

2. Resume or CV

3. College transcript

4. Contact information for two referencesPlease designate two Faculty References; these should be someone from whom you have taken a class or with whom you have done independent mathematical or scientific work. The people you identify as the Faculty Reference on the website will be notified to fill out an on-line form . Although the person will be notified automatically by email, it is the student's responsibility to make sure the letter is uploaded on time. 

MSRI-UP Specific Application Requirements:

1. Additional Statement (limit 2,500 characters) sharing any further information that will help us get a complete picture of you as a potential participant in MSRI-UP. Please address the origins of your interest in mathematics and science, any experiences (school-related and otherwise) that have particularly stimulated you, any obstacles you have faced along the way, and your experience collaborating with and supporting your peers, particularly those from groups underrepresented in mathematics. Students from 2-Year Institutions: If you are currently attending a two-year institution, please describe your plans for transferring to a four-year institution.

2. Description of Previous Summer / Research Experiences.
Please list and give a brief description of all mathematics or science research or summer programs (high school or college), if any, in which you have participated. (Students who have not participated in any programs previously are encouraged to apply.)

3. List of Mathematics/Science Courses Taken with Grades.
Please list all mathematics and science courses taken, starting with the most recent.  State the Course Number, Course Title, Term Taken, Grade Received, and Institution where you took the course.
Example: MATH 201, Calculus 1, Spring 2015, B+, Carolina Community College 

For additional information, please contact the on-site director for the 2023 MSRI-UP, Dr. Mercedes Franco.

The directors of MSRI-UP are:

MSRI-UP Sponsors

Funding to support MSRI-UP is provided by the Alfred P. Sloan Foundation and the National Science Foundation (NSF).

View Previous Years:

Primary Mathematics Subject Classification No Primary AMS MSC
Secondary Mathematics Subject Classification No Secondary AMS MSC
Schedule, Notes/Handouts & Videos
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Jul 21, 2023
09:15 AM - 09:30 AM
  Opening Remarks
09:30 AM - 10:15 AM
  Using Persistent Cup Products for Dissonance Detection
Kimberly Herrera (University of California, Berkeley), Martin Martinez (University of Washington Bothell), Austin MBaye (Vassar College)
10:20 AM - 11:05 AM
  Circular Coordinates for Non-Uniform Distributions: Introducing Weights to Nonlinear Topological Dimensionality Reduction
Mathieu Chabaud (University of Washington), Sean Hadley (San Francisco State University ), Solís McClain (Reed College)
11:10 AM - 11:55 AM
  Topological Decoupling of Quasiperiodic Videos
Michael Eddy (Swarthmore College), Alpha Recio Valerio (University of Massachusetts Amherst), Juan Rosete (California State University of Channel Islands)
01:05 PM - 01:50 PM
  Manifold Modeling of Pentagon Spaces Using Laplacian Eigenfunctions
Quincy Alston (University of Pennsylvania), Elise Alvarez-Salazar (University of California, Santa Barbara), Kiyanna Porter (University of Utah)
01:55 PM - 02:40 PM
  Optimizing Gravitational Wave Detection Using Topological Data Analysis
Jillian Cervantes (University of Wisconsin-Milwaukee), Manny Lopez (University of Utah), Katherine Lovelace (Ohio State University)
02:45 PM - 03:30 PM
  Data Sets Resulting in Relatively Compact Sets of Persistence Diagrams
Daniel Gonzalez (University of Arizona), Tania Gonzalez (Sam Houston State University), Alberto Magana (Vanderbilt University)
03:30 PM - 03:45 PM
  Closing Remarks