Michael Usher

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

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.

Papers on Hamiltonian dynamics and Morse theory
Papers on symplectic four-manifolds and Lefschetz fibrations
Slides from research talks given over the years.

Teaching

This semester, I am teaching Multivariable Calculus (MATH 2500; syllabus) and Introduction to Higher Mathematics (MATH 3200; 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 (part 1, part 2) for some of the Topology of Manifolds course that I taught in Fall 2011 (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 coveredin detail in the book).
Here are lecture notes for a course on vector bundles and cohomology from Fall 2012.