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.
me


Research

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.  


Teaching

Next semester, I will be teaching MATH 2310H (Honors Integral Calculus) and MATH 8210 (Topology of Manifolds).

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.