Some notes from undergrad

I made all of these for my own personal use while learning a topic in the past, so I should warn that they are far from being polished. However, I have found them useful and maybe someone else will too.

• Optimization on Smooth Manifolds Crash Course
  A short monograph I made while learning about optimization on smooth manifolds myself. I use the Burer-Monteiro problem as a running example (see my publications for some original work I did on this problem). The notes are heavily based on Nicolas Boumal’s excellent and very new textbook.

• Introduction to Topology and Manifolds
  Based on the first five of a series of lectures by Frederic Schuller.

• Notes on Measure Theory
  Some older notes on measure theory from when I learned some of it individually. Since then I have taken a full class on it and plan to update these notes when I have the time.

• Real Analysis Cheat Sheet
  A list of important definitions and theorems from Chapters 2–5 of Baby Rudin.

• Talk: The Burer-Monteiro Method Can Fail Above the Barvinok-Pataki Bound
  An older mini talk I gave as part of the Northwestern January 2022 Undergraduate Research Showcase. (Note that the audience is mainly undergraduates, so it is not very technical.) A more recent (and frankly better) mini talk can be found on my publications page.