Below are various notes and talks for classes or seminars and expository papers (these also appear on the publications page).

Book about low-dimensional contact geometry:

Bülent Tosun and I are writing a book on low-dimensional contact geometry. The plan is to cover all the details about convex surface theory and how to use it to classify contact structures, Legendrian knots, and related topics. We welcome input from readers on all the drafts. Please let us know of anything you would like to see included in the book, any parts of the book whose exposition could be improved, and, of course, any typos that you find. Thanks.        

• You may download Version 0.1 of the book from this link
  

  Version 0.1 for Low-dimensional contact geometry

  This version contains most of Part I of the book. There are still a few sections that need to be completed and a few proofs provided, but it is mostly complete.

Reviews, history, public engagement, and general advice articles:

1. Eliashberg's work concerining Tight and overtwisted contact structures. This was part of Eliashberg's Celebratio Mathematica provile, which is highly recommended!
2. What’s the shape of the universe? This is an article published at The Conversation that tries to give some flavor of topology to a general audience.
3. AMS notices Early Career Section: The Art of Writing Introductions.
4. AMS notices Early Career Section: Applying for Grants: Why and How?
5. Review of Surgery on contact 3-manifolds and Stein surfaces, by Burak Ozbagci and András I. Stipsicz for the Bulletin of the AMS.

Notes:

1. Lectures on Morse theory and handlebodies given at the 2019 PCMI Undergraduate Faculty Program.
2. Lectures from an introduction to algebraic topology for undergraduates with an emphasis on knot theory.
3. Survey talk on open books decompositions at MSRI, May 2009. There is only a pdf version of these notes.
4. Lecture notes from the 2006 PCMI. These notes are on "Conatact geometry and low-dimensional topology" and focus on the techniques used to apply contact geometry to questions in low-dimensional topology. In particular, they cover perturbations of foliations into contact structures, symplectic handle attachment and symplectic caps. These note were written by Shea Vick. There is only a pdf version of these notes.
5. Notes on convex surfaces from a contact geomety class. Last revised July 2004 (very rough form!) pdf and ps.gz Do not use these notes! The book above expands on the material here significantly. These notes have many typos and use old-fashioned notation that can be confusing (especially when reading more recent papers). I am only leaving the notes here for historical purposes, as many people have cited these notes.
6. Very basic notes on sheaves and divisors. These were from a series of seminars I gave as a graduate student some time in the early 90's. These should definitely be used at your own risk! pdf and ps.gz

Expository Articles:

1.  Legendrian contact homology in $\mathbb{R}^3$
   joint work with Lenhard Ng, Preprint 2018.
2. Lectures on contact geometry in low-dimensional topology
   Preprint 2006.
3. Lectures on open book decompositions and contact structures
   Preprint 2004.
4. Legendrian and Transversal Knots
   Preprint 2003.
5. Introductory Lectures on Contact Geometry
   Proc. Sympos. Pure Math. 71 (2003), 81-107.
6. Problems in Low Dimensional Contact Topology
   joint work with Lenhard Ng, Proc. Sympos. Pure Math. 71 (2003), 337-357.
7. Symplectic convexity in low-dimensional topology
   Topol. and its Appl. 88 (1998), 3-25.