- I work with Abby Thompson in
Geometric Topology within the context of
3-manifolds and
knot theory. My current project with her and Patrick Weed
focuses on handle decompositions of knot complements in the three-sphere.
- I am also interested in the applications of both
Morse Theory,
Cerf Theory,
Singularity Theory (a la Thom and Mather), and
Topological Data Analysis.
- To a lesser extent, I also work with Javier Arsuaga
in Applied Topology. My project with him (along with Kai Ishihara and Koya Shimokawa) focuses on the recognition of knot conformations
within Hi-C data extracted from DNA. Our hope is to see this work applied to the study of certain types of cancer whose development is
predicted by finding particular knotting patterns within the strands of DNA.
- My undegraduate thesis with Vincent Bonini at Cal Poly
entailed the study of
Weierstrass-Enneper parametrizations of minimal surfaces and correlated the parametrizations' algebraic features with their
corresponding surfaces' topologies and geometries.
- I worked on an REU at Cal Poly with Mark Stankus and Anna Kopcrak researching the factorizations of noncommutative algebraic expressions.

- UC Davis COSMOS Program (Summer 2015, 2016, 2017)
- I participated in UC Davis's COSMOS program as a teaching assistant. The UC-wide program is designed as a sort of summer camp for high school students to learn more extra-curricular math and science. The 2015 program for the math cluster consisted of Combinatorics, Group Theory, Knot Theory and Topology, and Hyperbolic Geometry (led by Lawrence Marx, Monica Vazirani, Abby Thompson, and Anastasiia Tsvietkova, respectively). The 2016 program replaced the Topology and Geometry sections with a short course in Graph Theory led by Brad Ballinger. My role as a TA for this program was to mentor and help students learn the material as well as help teach a few classes labeled as "Math and Art".

- Math Improvement Program (Winter/Spring 2016)
- I worked with Becca Thomases, Tim Lewis, and Sam Walcott on a project for UC Davis's MAT 17 series, the biosciences Calculus classes. The aim of this project was to refocus the curriculum to be more modeling- and application-based. My role as a TA for this project was to help design and then lead a flipped-classroom discussion section (with the help of undergraduate learning assistants) with this curriculum goal in mind.

- Student-Run Geometry/Topology Seminar (2015-2017)
- Along with Nate Gallup, Dale Koenig, and John Murray, I co-organized the Student-run Geometry/Topology Seminar for the 2015-2016 and 2016-2017 schoolyears. This seminar is open to all students and serves to be a forum for students to both present and learn about interesting topics found in Geometry and Topology.