Facts about Lie Groups and Algebras

In Spring 2016 I was taking 18.757 Representations of Lie Algebras. Since I knew next to nothing about either Lie groups or algebras, I was forced to quickly learn about their basic facts and properties. These are the notes that I wrote up accordingly. Proofs of most of these facts can be found in standard… Continue reading Facts about Lie Groups and Algebras

Uniqueness of Solutions for DiffEq’s

Let $latex {V}&fg=000000$ be a normed finite-dimensional real vector space and let $latex {U \subseteq V}&fg=000000$ be an open set. A vector field on $latex {U}&fg=000000$ is a function $latex {\xi : U \rightarrow V}&fg=000000$. (In the words of Gaitsgory: ``you should imagine a vector field as a domain, and at every point there is… Continue reading Uniqueness of Solutions for DiffEq’s