Michael Usher

I have moved to the University of Georgia, where I am an Assistant Professor in the Mathematics Department. My permanent e-mail address is [my surname] at alum dot mit dot edu.


Teaching

In Fall 2008, I will be teaching Math 4200 (Point Set Topology) at UGA.
Here is a fairly thorough set of lecture notes that I created for the Fall 2007 version of MAT 314 (Real Analysis; mostly metric spaces and measure theory) at Princeton.

Research

My research has generally dealt with symplectic topology, and more specifically with symplectic four-manifolds and symplectic Floer homology.

Research Papers

  • Floer homology in disc bundles and symplectically twisted geodesic flows.
  • Spectral numbers in Floer theories, to appear in Compositio Mathematica.
  • Kodaira dimension and symplectic sums, to appear in Commentarii Mathematici Helvetici.
  • Standard surfaces and nodal curves in symplectic 4-manifolds, Journal of Differential Geometry 77 (2007), no. 2, 237-290.
  • Minimality and symplectic sums, International Mathematics Research Notices 2006 (2006), article ID 49857.
  • Vortices and a TQFT for Lefschetz fibrations on 4-manifolds, Algebraic and Geometric Topology 6 (2006), 1677-1743.
  • Symplectic forms and surfaces of negative square, with Tian-Jun Li, Journal of Symplectic Geometry 4 (2006), no. 1, 71-91.
  • The Gromov invariant and the Donaldson-Smith standard surface count, Geometry and Topology 8 (2004), 565-610.

    • Surveys and talks

  • Slides from a talk about my proof of the spectrality axiom for Floer homology theories, given at various locations in Fall 2007.
  • Slides from a survey talk about symplectic four-manifolds, given at various locations in January 2007
  • A survey article, Lefschetz fibrations and pseudoholomorphic curves, written for the Proceedings of the 2004 McMaster Conference on the Geometry and Topology of Manifolds, summarizing the results of the G&T and JDG papers listed above.
  • Slides from a November 2004 talk at the MIT differential geometry seminar about Lefschetz fibrations and nodal curves.
  • Slides from a March 2004 talk at MSRI about the Gromov and Donaldson-Smith invariants.

    • The two most recent presentations above were created with the highly-recommended LaTeX Beamer class.