Geometric analysis
Analytic methods for geometric questions, including curvature, variational problems, and geometric PDE.
Research
Geometry through analysis
My interests center on geometric analysis, differential geometry, and partial differential equations, with particular enthusiasm for manifolds, minimal surfaces, and ways to visualize geometric structure.
Differential geometry
Local and global geometry of manifolds, with emphasis on geometric intuition and computation.
Partial differential equations
Classical PDE techniques and their role in geometry, including elliptic and variational equations.
Publication
Published mathematical work.
f(x+y) + f(x−y) = 2f(x)f(y)
Published paper · September 2023
Defining Cosine Function with D’Alembert’s Functional Equation
This paper replaces a continuity assumption with more elementary conditions. It uses monotonicity, zeros, density, and Hamel-basis counterexamples to characterize the solution and give an elementary definition of the cosine function on the real line.
Research background
Selected projects and directed study.
Minimal surfaces
Surveyed recent developments in minimal surface theory, beginning with work on stable minimal hypersurfaces and related literature.
Directed Reading Program, UC Berkeley
Studied A Course in Minimal Surfaces by Colding and Minicozzi, with discussions in Riemannian geometry and PDE and a final presentation.
Partial differential equations
Worked through nonhomogeneous wave equations, Duhamel’s principle, Green functions for the Laplace equation, and a variational form of the p-Laplace equation.
Differential geometry
Studied geodesics on spheres and in the upper half-plane, supported by geometric visualizations.