DRP Projects

Below is a list of the directed reading program (DRP) projects I have mentored at UT Austin. The participants in this program are typically advanced or talented undergraduate math majors. The goal of the program is to expose these students to more exotic or involved math 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's work; a secondary goal of the program is to coach undergraduates 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).

• Summer 2026 (UT Groups and Dynamics REU)

  • Dhruv Ajmera

• Spring 2026

  • Anna Iskra - The Role of Architecture in the Convergence of Stochastic Gradient Descent

• Fall 2025

  • Krithi Prasad - Topology and Geometry of Surfaces

• Summer 2025 (UT Groups and Dynamics REU)

  • Arnav Lahoti - Mathematical Foundations of Machine Learning

• Spring 2025

  • Luke Hospenthal - The Birkhoff Ergodic Theorem

  • Group project (3 students) on recurrence and randomness in dynamical systems:

    • Sanay Salvi - Dynamical Systems and the Recurrence Theorem

    • William Hao - Benford’s Law: From Logarithms to Dynamical Systems

    • Arnav Lahoti - Measure Theory

• Fall 2024

  • Joseph Hummel - Geometry on Manifolds

  • Yanrong Yu - Bifurcation Theories and Chaos

• Summer 2024 (UT Groups and Dynamics REU)

  • Giancarlo Villatoro - Essence of Analytic and Probabilistic Number Theory

• Spring 2024

  • Allison Podanoffsky - Finite fields and Algebraic Number Theory

• Fall 2023

  • Ryan Charrette - Harmonic Analysis on Locally Compact Groups: p-Adics/Applications

• Summer 2023 (UT Groups and Dynamics REU)

  • Brandon Paez (UTEP) - Introduction to Riemannian Geometry and Ricci Flow

• Spring 2023

  • Ryan Charrette - L-functions and Modern Problems in Number Theory

  • Amanda Yin - Chaotic Dynamical Systems: Hyperbolic Toral Automorphisms

• Fall 2022

  • Thor Preimesberger - Benamou-Brenier and Metric Geometry

• Summer 2022 (UT Groups and Dynamics REU)

  • Amy Somers (UCSB) - An Introduction to Dynamical Systems

• Spring 2022

  • Abhinav Rachakonda - Complex Analysis and the Prime Number Theorem