Michael Usher

I am an Associate Professor in the Mathematics Department at the University of Georgia.
My email address is [my surname]@math.uga.edu.


My research generally deals with symplectic topology, the study of global questions relating to spaces equipped with the geometric structures that lie at the root of classical mechanics.  


This semester, I am teaching Multivariable Mathematics II (MATH 3510(H); syllabus).

Here are links to webpages for older courses (for more recent courses I have generally used ELC instead of a webpage).

Lecture Notes
  • I created these notes on metric spaces and measure theory (78 pp.) for an analysis course that I taught as a postdoc in Fall 2007.
  • Here are some brief notes on symplectic cutting and blow-ups (6 pp.) that I wrote while teaching symplectic geometry in Fall 2009.
  • Here are the notes for the majority of my course on pseudoholomorphic curves (74 pp.) from Spring 2010; these are designed to give an accessible account of the basic analytic foundations of the theory. 
  • Here are lecture notes for some of the Topology of Manifolds course that I taught in Fall 2011 (54 pp. For most of the course we followed the start of Bott and Tu's Differential Forms in Algebraic Topology; these notes concern background material not covered in detail in the book).
  • Here are lecture notes for a course on vector bundles and cohomology (99 pp.) from Fall 2012.
  • Here are lecture notes for the start of my Spring 2014 algebraic topology course (30 pp. We used Hatcher's book for the rest of the course).
  • Here are lecture notes (50 pp.) for the first half of my Spring 2015 topics course, which used the theory of area-preserving maps as an entry point to symplectic geometry. (We used Cannas' Lectures on Symplectic Geometry for the second half of the course.)
  • Here are lecture notes for a topics course on elliptic PDE's on manifolds (111 pp.) that I taught in Fall 2016. They give a through treatment of Sobolev spaces and the de Rham and Dolbeault versions of the Hodge theorem, and a brief introduction to pseudoholomorphic curves.