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Orals Weekly Readings (09/02-09/23)

3 minute read

Published: September 26, 2026

Over the past few weeks, I have been reading about various results from the theory of functional analysis, harmonic analysis, and (non)linear wave equations (as mentioned in the first blog post). I figured that it would be a valuable exercise to summarize what I have read each week in a blog post. This post is the first in such a series. Since the gap between my first two meetings with my advisor was three weeks apart, this blog post covers three weeks of readings, rather than the usual one.

Notes on Hyperbolic Partial Differential Equations

less than 1 minute read

Published: July 18, 2026

As part of my orals exam for PhD candidacy in the math department at Stony Brook, I’m currently reading a compilation of lecture notes and texts on nonlinear wave equations, harmonic analysis, geometry, and fluids (the first three forming the bulk of my major topic, and the latter forming my minor topic). The following notes I’ve written are based on my latest understanding of these topics. The content itself is not unique, having been based strongly upon my readings (which include lecture notes on nonlinear wave equations by Profs. Gustav Holzegel, Andrew Lawrie, and Jonathan Luk), but perhaps the organization is. Over this semester and the next, I will gradually be adding more material to these notes, and revising already existent notes.

Download notes

Orals Weekly Readings (09/02-09/23)

3 minute read

Published: September 26, 2026

Over the past few weeks, I have been reading about various results from the theory of functional analysis, harmonic analysis, and (non)linear wave equations (as mentioned in the first blog post). I figured that it would be a valuable exercise to summarize what I have read each week in a blog post. This post is the first in such a series. Since the gap between my first two meetings with my advisor was three weeks apart, this blog post covers three weeks of readings, rather than the usual one.

Notes on Hyperbolic Partial Differential Equations

less than 1 minute read

Published: July 18, 2026

As part of my orals exam for PhD candidacy in the math department at Stony Brook, I’m currently reading a compilation of lecture notes and texts on nonlinear wave equations, harmonic analysis, geometry, and fluids (the first three forming the bulk of my major topic, and the latter forming my minor topic). The following notes I’ve written are based on my latest understanding of these topics. The content itself is not unique, having been based strongly upon my readings (which include lecture notes on nonlinear wave equations by Profs. Gustav Holzegel, Andrew Lawrie, and Jonathan Luk), but perhaps the organization is. Over this semester and the next, I will gradually be adding more material to these notes, and revising already existent notes.

Download notes