The REU was a six-week summer program offered by the Geometry and Topology group at
UCLA and was funded by a NSF Research and Training Grant (RTG).
Topic
The research topic was Knot Theory. This program provided students
with the opportunity to immerse themselves in active research projects in Knot
Theory, an important branch of Low-Dimensional topology, under the supervision of
senior and junior faculty in the field. During the final week of the program,
students showcased the results of their research through a written report and
an oral presentation. During the project, students also wrote
software. The faculty mentors clearly outlined the expected outcomes at the
beginning of the summer and worked closely with students to ensure the successful
completion of the final project. In addition to hands-on research, the REU
featured informative sessions run by faculty members on topics such as research
methodology, career prospects in mathematics, and preparing for graduate school.
Outcome
Date and Location
The program dates were 2023-06-26 to 2023-08-04. The workload was 40hr/week
for 6 weeks. The REU program was conducted in a hybrid format, requiring
participants to be physically present in Los Angeles and available during business
hours (09:00 to 16:00) to fully participate. On Mondays, Wednesdays, and Fridays,
participants met in-person on the UCLA campus. On Tuesdays and Thursdays,
they met remotely via Zoom.
Funding
Each student was provided a $5000 stipend for 6 weeks of REU at the
end of the program. No additional funding was available for lodging or
transportation. Since the students were supposed to be local, they were expected to
commute to campus.
Mentors
The REU mentors were Hyunki Min (Hedrick Assistant Adjunct
Professor at UCLA), Sumeyra Sakalli (Visiting Assistant Professor at University of Arkansas), and Konstantinos
Varvarezos (Assistant
Adjunct Professor at
UCLA); the program will be overseen by Sucharit Sarkar (Professor at UCLA).
Schedule
The schedule was as follows:
- Week 1: Introduction to knot theory
- Week 2: Computing knot invariants (Alexander, Jones polynomial)
- Week 3: Learning about special families of knots (2-bridge)
- Week 4: Dehn surgery and the cosmetic surgery conjecture
- Week 5: Write a python program to verify the conjecture
- Week 6: Present the results in both a written report and an oral presentation