Math 541: Harmonic Analysis 1, taught by Prof. Pablo Shmerkin
Typing lecture notes for some lectures (might be uploaded here with permission).
Presentation and Final Paper: The Restriction Conjecture and Tomas-Stein, joint work with Dylan Chaussoy.
Math 549: Thesis for Master's Degree, advised by Izabella Łaba, Pablo Shmerkin, and Josh Zahl
Math 590: Graduate Seminar (in Harmonic Analysis), run by Prof. Malabika Pramanik
Final Paper: An Introduction to the Furstenberg Set Problem
MIT Undergraduate Studies
Spring 2024
18.156: Differential Analysis II, taught by Prof. Larry Guth
18.099: Independent study on restriction theory and decoupling, with by Prof. Larry Guth
Fall 2023
18.225: Graph Theory and Additive Combinatorics, taught by Prof. Yufei Zhao
18.675: Theory of Probability, taught by Prof. Konstantinos Kavvadias
18.905: Algebraic Topology I, taught by Prof. Paul Seidel
Spring 2023
18.156: Differential Analysis II, taught by Prof. David Jerison
18.158: Fourier Analysis to Analytic Number Theory, taught by Prof. Larry Guth
18.821: Project Lab in Mathematics, taught by Prof. Lisa Piccirillo
Project 1: Exploring the relation between random walks and harmonic functions, solving the Discrete Dirichlet Problem using probabilty.
Project 2: Exploring Young Tableau with linear algebraic conditions, with relations to combinatorics.
18.966: Geometry of Manifolds II, taught by Prof. Tobias Colding
Fall 2022
18.112: Complex Analysis, taught by Prof. Roman Bezrukavnikov
Using this time to explore deRham theory on real and complex manifolds so I can better understand the algebraic topology/homology theory behind certain theorems in complex analysis. Reading Bott and Tu's book on this matter.
18.965: Geometry of Manifolds I, taught by Prof. Bill Minicozzi
18.994: Seminar in Geometry, taught by Prof. Qin Deng
On minimal surfaces, using the textbook developed by Bill Minicozzi and Tobias Colding.
Presented on Section 3.3 of do Carmo's text with Victor Luo, discussing the minimizing properties of Geodesics.
Presented on the first variation formula for minimal surfaces, defining minimal surfaces as being a critical point of the volume functional, and showing that this implies the mean curvature must be zero everywhere on the minimal surface (in fact this is an equivalent relationship).
Presented on Section 4.3-4.5.1 with Carlos on 1) Solving the Plateau problem and 2) harmonic maps.
Final project: Studying the relationship and the proofs of Sobolev inequalities and the Isoperimetric inequality on minimal surfaces. If time permits, trying to develop a proof of my own using techniques developed in my 2021 Summer UROP (see below). In particular, studying the equivalence of these inequalities.
Spring 2022
18.157: Microlocal Analysis, taught by Prof. Richard Melrose
18.099: Independent Study with Prof. Richard Melrose
To ask clarifying questions about Microlocal Analysis over the course of the semester.
18.118: Introduction to Chaotic Dynamics, taught by Prof. Semyon Dyatlov
18.952: Introduction to Differential Forms, taught by Prof. Victor Guillemin
Fall 2021
18.155: Differential Analysis, taught by Prof. Semyon Dyatlov
18.101: Analysis and Manifolds, taught by Prof. Richard Melrose
18.705: Commutative Algebra, taught by Prof. Wei Zhang
Spring 2021
18.702: Algebra II, taught by Prof. Michael Artin
18.102: Introduction to Functional Analysis, taught by Prof. Casey Rodriguez
18.901: Introduction to Topology, taught by Prof. George Lusztig
IAP 2021
18.03: Differential Equations (ASE)
Fall 2020
18.701: Algebra I, taught by Prof. Bjorn Poonen
18.100B: Real Analysis, taught by Prof. Tobias Colding
18.A06: What is a Number, taught by Prof. Haynes Miller
A first year seminar on the construction of numbers, with numerous philosophical conversations on what objects should or shouldn't be considered numbers.
Discussing Peano Axioms, Dedekind cuts, constructions of the real numbers, construction of the complex numbers, quarternions, surreal numbers, p-adic numbers, etc.
At Fresno City College
Math 5A: Mathematical Analysis I (Differential Calculus)
Math 5B: Mathematical Analysis II (Integral Calculus), taught by Travis McDonald
Math 6: Mathematical Analysis III (Multivariable Calculus), taught by Matt Woods
Math 7: Differential Equations, taught by Travis McDonald