## Furstenberg’s Proof of Szemerédi’s Theorem

Here are lecture slides for a 15 minute presentation on Furstenberg’s 1977 proof of Szemerédi’s theorem. The presentation was given during Dr. Bowen’s dynamical systems class in Fall, 2020.

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# Author: Joseph K. Miller

## Furstenberg’s Proof of Szemerédi’s Theorem

## Fall 2020, Jr. Analysis Presenation

## Real Analysis Prelim Camp

## Expressibility of Single Layer Neural Networks

## Partial Fourier Sums and Some Probability

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I am a first year Ph.D. student working in PDE/Analysis at the University of Texas - Austin.

Here are lecture slides for a 15 minute presentation on Furstenberg’s 1977 proof of Szemerédi’s theorem. The presentation was given during Dr. Bowen’s dynamical systems class in Fall, 2020.

Here’s the slides from the talk I gave at Jr. Analysis at UT – Austin on the mathematics of Bose-Einstein condensates. I mostly used this paper by Lewin as reference: https://arxiv.org/abs/1510.04407

Here is where I will upload notes, problems, and solutions for the real analysis prelim camp in Summer, 2020. All the problems come from past UT prelim exams. Measure Theory – Problems Measure Theory – Solutions Integration and Limits – Problems Integration and Limits – Solutions For problem 11, there is actually an alternative way … Continue reading Real Analysis Prelim Camp

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