The Meta Home Paige

• 18.156: Differential Analysis II, taught by Prof. Larry Guth
• 18.099: Independent study on restriction theory and decoupling, with by Prof. Larry Guth

• 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

• 18.156: Differential Analysis II, taught by Prof. David Jerison
• Typing lecture notes for some lectures (to be uploaded here)
• Learning about Hardy spaces and BMO on my own using Elias Stein's "Harmonic Analysis".
• 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

• 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.

• 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

• 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

• 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

• 18.03: Differential Equations (ASE)

• 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.

• 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
• Math 26: Linear Algebra, taught by Matt Woods