About Me

I am currently a second year Ph.D. Student in Mathematics at UC Davis!

I graduated from High School in 2021 and Received a B.S. in Math from UC Davis in 2023.

I enjoy studying complex geometry, analysis, PDE's, and combinatorics applied to various theoretical physics problems!

Currently, I am interested in the interaction between the Riemann Zeta function and mirror symmetry of Fano Varieties and Calabi Yau Families! I'd like to understand the geometry of Zeta(3) and it's role in mirror symmetry between the Fano Variety V12 and the mirror Beukers-Peters Pencil of K3 Surfaces. 

In particular, I'd like to understand how to relate the asymptotic expansion at irregular singular points of a Quantum Curve associated to the K3-Pencil of surfaces and relate these asymptotics to the (g,n)-Gromov-Witten Invariants of a particular Fano 3 Manifold. Establishing a concrete statement of mirror symmetry in terms of an enumerative problem in Fano geometry is of interest for the mechanism of Topological Recursion and finding the appropriate cohomological field theory to complement this particular process would be significant.

I am also separately interested in representation theory and combinatorics. In particular, a generalization of the Kirilov Polynomial recursion for Polynomials of other simple Lie Algebra type. It is conjectured that these recursions would justify the affine springer correspondence for adjoint orbits associated to the natural action of simple Lie Groups on their Lie Algebras and their irreducible representations. This was done in the case of A_n by Fuchs and Kirilov and in the case of the exceptional Lie Algebra g_2 by Martin Luu, but recent progress seems to imply that a similar recursion to the A_n case should exist for the classical Lie Algebra D_n. This would be a result which contributes to the study of the orbit method in Physics pioneered by Kirilov.