BIRS Workshop Lecture Videos
Gaussian measures no spaces of metrics Jakobson, Dmitry
The first part of the talk is joint work in progress with B. Clarke, N. Kamran, L. Silberman and J. Taylor. We define Gaussian measures on manifolds of metrics with the fixed volume form. We next compute the moment generating function for the L2 (Ebin) distance to the reference metric.\\r\\n\\r\\nThe second part of the talk is joint work with Linan Chen. We use the two-dimensional approach of Duplantier-Sheffield to define a 4- dimensional analogue of Gaussian Free Field, and use it to construct a canonical measure on a conformal class of metrics in R4. We derive a KPZ type relation for those measures.
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