My talk is about geodesics on the infinite dimensional symmetric space of kahler metrics in a fixed kahler class on a compact kahler
manifold. The question is the extent to which the exponential map is well defined, i.e. can one solve the initial value problem for
geodesics. Although this is very natural in geometry, the equation for geodesics is a homogeneous Monge Ampere equation on D x
M where D is the unit disc, and the Cauchy problem is badly behaved. We will recall a formal method of solution by Donaldson,
and propose a rigorous method using kahler quantization and complex Fourier integrals. It is closely related to work of Phong-
Sturm on the boundary problem. Joint work with Yanir Rubinstein, building on earlier joint work with Jian Song.

Lecture #12971

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