Gordon Craig's homepage

I am a graduate student in the math department at SUNY Stony Brook. My main interests are differential geometry and geometric analysis. I hail from the Eastern Townships of Quebec, and after Bachelor's and Master's degrees in math from McGill University in Montreal, I came down to Long Island, New York to pursue my studies.

My Curriculum Vitae in postscript or pdf format.)

Teaching

Right now, I'm teaching Math 130 at Stony Brook. This summer, I taught Math 261C at McGill University in Montreal, and Math 019 at the University of Western Ontario in London.

As well as teaching duties at McGill, Western and Stony Brook, I taught a statistics course at Champlain College in Saint-Lambert, Quebec.

The courses for which there are homepages are:

Math 130(Stony Brook, Spring 2003): Functions

Math 261C(McGill, Summer 2002): Ordinary Differential Equations

Math 017(Western, Summer 2002): Algebra and Geometry

Math 031(Western, Summer 2001): Probability and Linear Algebra

Research

My main interests are differential geometry and analysis, in particular using analytical methods to solve problems in Riemannian geometry. I'm working with Mike Anderson. My thesis problem involves attempting to cap off cusps on hyperbolic manifolds with finite volume. Thurston did this on hyperbolic three-manifolds by gluing on hyperbolic pieces. In higher dimensions, I'll be trying to glue on pieces to get an Einstein metric of negative curvature. One of the interesting features of this construction is that Einstein metrics are real analytic so the local structure on each piece determines the global structure. That means that the Einstein metric on the connected sum will probably be quite different from the original ones, even away from the neck. Kapouleas, Mazzeo, Pacard, Pollack, Schoen and Uhlenbeck, among others, have studied this type of connected sum construction in the cases of constant mean curvature hypersurfaces and complete positive scalar curvature metrics. I'll add more details as they develop.

I'm also trying to learn about the Ricci flow and complex differential geometry in my spare time.

My Master's thesis, under the direction of John Toth at McGill, was a survey of results relating the first eigenvalue of the Laplacian on a Riemannian manifold to isoperimetric inequalities.