Here are some of the miscellaneous mathematical documents that I have written. Feedback is always welcomed!
| File | Description
|
| GT Exam Organizational Guide
| A document to help students learn some of the less-commonly-taught-but-more-commonly-appearing content of
the geometry/topology qualifying exam. This guide lists some of the most useful theorems/lemmas for a few different topics and also lists previous problems that have appeared for each of
them. This will hopefully help make your studying more organized than mine was! |
| Symplectic Reduction Writeup | An organized exposition and proof the Marsden-Weinstein-Meyer theorem. Taking quotients of smooth manifolds is an already tricky problem, and doing so symplectically adds the extra challenge of managing your symplectic form and Hamiltonian action. Written as part of a Lie Groups class in Spring 2022.
|
| Mixed Proof of Poincaré Lemma
| A brief proof of the Poincaré lemma that incorporates both
geometric techniques and algebraic generality. When I was learning basic differential geometry, I had a hard time understanding this lemma, as the proofs provided in many sources missed either the algebraic or geometric perspective. The goal of the writeup is to retain both of these and preserve the intuition behind homotopy invariance.
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