Craig van Coevering

C.L.E. Moore Instructor

Address:
Department of Mathematics 2-380
M.I.T.
Cambridge, MA 02139

Phone: (617) 253-6544
Email: craig(at)math.mit.edu


Teaching


Research

Differential geometry, algebraic geometry

I am currently working on non-compact Calabi-Yau manifolds. These include resolutions and deformations of certain singularities. The project includes proving that many examples have Ricci-flat Kähler metrics with good asymptotic properties.

A particularly interesting case is to start with an affine toric singularity. In many cases, such as dimension 3, it can easily be resolved to a smooth Calabi-Yau manifold. And in some cases it can also be deformed to a smooth affine Calabi-Yau variety. This generalizes the familiar case of the quadric hypersurface {XY-UV=0:(X,Y,U,V)∈C3} which can both be resolved and deformed to smooth non-compact Calabi-Yau manifolds. When this occurs both the resolution and the deformation admit special Lagrangian fibrations, so this should be of interest in mirror symmetry.

My interests also include physics, in particular dualities in string theory such as AdS/CFT.

Here is a summary of some recent work.

A list of Papers.

From November 19 to February 19 I am going to be at the Tokyo Institute of Technology.

Conferences:

Sugadaira, Japan, October 2007. Here are some pictures.

Kähler and Sasakian Geometry in Rome, 2009, June 16-19.

Geometry of Einstein Metrics, Nantes France, June 24 to July 3, 2009.

I'm giving a talk at the Harvard Differential Geometry Seminar Tuesday 11/17

Some math related links

Seminars: M.I.T, Harvard.
Preprints: arXiv and the front for the mathematics arXiv.
Mathematical reviews: MathSciNet
M.I.T. Libraries
Springer Online Encyclopedia of Mathematics
A string theory wiki

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