Topic: In 2024, the research topic will be Topological Data Analysis (TDA). This program provides students with the opportunity to immerse themselves in active research projects in TDA, an important branch of applied topology, under the mentorship of senior and junior researchers in the field. During the final week of the program, students will showcase the results of their research through a written report and an oral presentation. During the project, students will also be asked to write code. The mentors will outline the expected outcomes at the beginning of the summer and will work closely with the students to ensure the successful completion of the final project. In addition to hands-on research, the REU will feature informative sessions run by the mentors and other researchers on career-development topics, such as how to do research in mathematics, career prospects in mathematics, preparing for graduate school, and writing graduate-school applications.

Applicants:

• The students must be US citizens or US permanent residents (green card holders). The program is being funded by an NSF grant and this is one of the grant requirements.
• The REU is designed to be local in nature, so the students must be living in the greater Los Angeles region and be able to commute to UCLA campus.
• The REU is only open to undergraduate students, so students should not have already received their Bachelors degree at the time of the REU.

Date and Location: In 2024, the program dates are 12 August through 20 September. The expected workload is 40hr/week for 6 weeks. The REU program will be conducted in a hybrid format, requiring participants to be physically present in Los Angeles and available during business hours (10 AM – 5 PM) to fully participate. Some weekdays will use a remote format with Zoom.

Funding: Each student will be provided a $5000 stipend for 6 weeks of REU at the end of the program. No additional funding is available for lodging or transportation. Because the students are supposed to be local, they are expected to commute to campus.

Mentors: In 2024, the REU mentors are Troy Kling (PhD student, UCSB), Sarah Tymochko (Hedrick Assistant Adjunct Professor, UCLA), and Sidhanth Raman (PhD student, UCI). The program will be overseen by Mason Porter (Professor, UCLA).

Schedule: The tentative schedule is as follows:

• Week 1-2: Introduction to algebraic topology, topological data analysis, and persistent homology (including use of TDA software with Python)
• Week 3-4: Analysis of a data set using persistent homology
• Week 5: Finalizing the analysis and conclusions
• Week 6: Present the results in both a written report and an oral presentation