Directed Reading Program
Below is a list of the directed reading program (DRP) projects I have mentored at UT Austin. The goal of the program is to expose advanced/talented undergraduate math majors
to more exotic and involved topics not typically covered in undergraduate coursework, under the tutelage of a graduate student mentor.
Each project ends with a symposium presentation, covering some component of the project; a secondary goal of the program is to coach the students on presenting technical math.
In addition to serving as a mentor on the projects below, I also served as a program organizer for 3 semesters (Spring 2025 - Spring 2026).
Projects Mentored
Dhruv Ajmera
Stochastic Calculus & Finance: The Heath-Jarrow-Morton Model (GitHub).
Anna Iskra
The Role of Architecture in the Convergence of Stochastic Gradient Descent
Krithi Prasad
Topology and Geometry of Surfaces
Arnav Lahoti
Mathematical Foundations of Machine Learning
Luke Hospenthal
The Birkhoff Ergodic Theorem
Sanay Salvi, William Hao, and Arnav Lahoti
Group project on recurrence and randomness in dynamical systems
Joseph Hummel
Geometry on Manifolds
Yanrong Yu
Bifurcation Theories and Chaos
Giancarlo Villatoro
Essence of Analytic and Probabilistic Number Theory
Allison Podanoffsky
Finite fields and Algebraic Number Theory
Ryan Charrette
Harmonic Analysis on Locally Compact Groups: p-Adics and Applications
Brandon Paez (UTEP)
Introduction to Riemannian Geometry and Ricci Flow
Ryan Charrette
$L$-functions and Modern Problems in Number Theory
Amanda Yin
Chaotic Dynamical Systems: Hyperbolic Toral Automorphisms
Thor Preimesberger
Benamou-Brenier and Metric Geometry
Amy Somers (UCSB)
An Introduction to Dynamical Systems
Abhinav Rachakonda
Complex Analysis and the Prime Number Theorem