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Large N Program Series: Joel Fine, Universite Libre de Bruxelles

Title: The second fundamental form of Kodaira embeddings, and quantization
Program Website: Large N limit problems in Kahler Geometry
Speaker: Joel Fine, Universite Libre de Bruxelles
Date: Tuesday, May 12, 2015
Time: 02:00pm – 03:00pm
Place: Seminar Room 313, Simons Center


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Abstract: I will discuss the second fundamental form of a complex submanifold of projective space and the role it plays in the quantization picture of Donaldson, relating constant scalar curvature Kahler metrics and balanced embeddings. In particular, the asymptotic behaviour of the second fundamental form is key to proving that the Hessian of Mabuchi energy (a 4th order operator similar to the square of the Laplacian) can be quantized by the Hessian of balancing energy (a finite dimensional operator acting on the spaces of Hermitian matrices and defined purely in terms of projective geometry). (Note to experts: this is relatively old work, so don’t expect to hear about any cutting edge results!)