Society

Sam Qunell

Office 6146 Math Sciences Building
Office Hours Thursdays, Fridays 2-3
E-Mail sdqunell at math .ucla .edu

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.