These notes are subject to change without notice. Please email me with any comments, questions, or mistakes.


Surface bundles over S^1, the Thurston norm, and the Whitehead link. In this note I first review the basic theory of the Thurston norm, and then present an explicit visualization of two distinct fibrations of the Whitehead link complement. August 16, 2014.

Morse homology. Notes for a talk I gave in a graduate student symplectic geometry seminar at Yale, Spring 2014.

Seifert surfaces and genera of knots. Notes for an undergraduate colloquium at SUMRY, Summer 2014.


TikZ examples. Some examples of commutative diagrams, graphs, and other pictures.

Dictating in TeX. How I typeset mathematics using dictation software.