I am a fifth-year graduate student at UCLA advised by Inwon Kim. My research focus is in free boundary problems. More broadly, I am interested in elliptic and parabolic partial differential equations, geometric measure theory, and optimal transport. I completed my undergraduate degree at the University of Chicago.
Preprints and Publications
- C. Collins, W. Feldman. Rate independent capillary motion on a narrow Wilhelmy plate (2025). Preprint.
- C. Collins, W. Feldman. Minimizing movements solutions for a monotone model of droplet motion (2024). Submitted.
- C. Collins, M. Jacobs, I. Kim. Regularity and Nondegeneracy for Tumor Growth with Nutrients. Arch. Ration. Mech. Anal. vol. 249 no. 11 (2025). Also available on Arxiv.
Teaching
Here are the courses I’ve TAed at UCLA:
- PIC 10A: Introduction to Programming (Spring 2025)
- Math 266B: Applied Partial Differential Equations (Graduate Course; Winter 2025, Winter 2023)
- Math 177: Theory of Interest and Applications (Fall 2024)
- Math 135: Ordinary Differential Equations (Fall 2024, Fall 2023, Winter 2022)
- Math 136: Partial Differential Equations (Spring 2024)
- Math 134: Linear and Nonlinear Systems of Differential Equations (Spring 2024)
- Math 171: Stochastic Processes (Winter 2024)
- Math 179: Advanced Topics in Financial Mathematics (Fall 2023)
- Math Graduate Summer Bootcamp (Summer 2023)
- Math 174E: Mathematics of Finance for Mathematics/Economics Students (Spring 2023)
- Math 266A: Applied Ordinary Differential Equations (Fall 2022)
- Math 132H: Honors Complex Analysis (Spring 2022)
- Math 131A: Analysis (Winter 2022)
- Math 32B: Calculus of Several Variables (Fall 2021)