I gave a presentation Fall, 2019 for the Junior Analysis seminar at UT – Austin on the expressibility of single layer neural networks. It follows the general outline for the first part of the paper by Grant M. Rotskoff and Eric Vanden-Eijnden in May, 2018. Here are the notes I made for this presentation.
These are the lecture notes for a harmonic analysis reading group talk I gave October 14th, 2019 at UT Austin. They are based off of the book Classical and Multilinear Harmonic Analysis Vol. 1 by Muscalu and Schlag Throughout the following notes, we will be working on . Our Fourier transform will be defined to … Continue reading Partial Fourier Sums and Some Probability
This topic first came up while attending a talk by Daniel Restrepo at the UT Austin harmonic analysis learning seminar last Friday. Daniel gave a basic overview of singular integral operators, and in the process proved and used the classical Calderon-Zygmund decomposition: Theorem 1 (Calderón-Zygmund Decomposition) Given and there exists a collection of almost disjoint … Continue reading Calderon-Zygmund Decomposition Via Martingales
Here are the notes I used to prepare for my Junior Analysis seminar at UT – Austin. Heisenberg’s inequality and the Malgrange-Ehrenpreis Theorem
Here are the notes for my short presentation on the higher dimensional analog of integration by parts. Packet Packet Solutions Here is the handout for my second presentation and my teaching philosophy. Packet II Teaching Philosophy
Here are my solutions to the exercises assigned for the course Topics in Complex Analysis (Math246C) during the Spring 2018 quarter at UCLA. The original course notes and exercises can be found at Dr. Tao’s Blog. Math246C, Spring 2018 – Homework 1 Math246C, Spring 2018 – Homework 2 Math246C, Spring 2018 – Homework 3 … Continue reading Topics in Complex Analysis (Solutions)