Workshop
Conformally Invariant Random Geometry on Riemannian Manifolds of Even Dimension
- Karl-Theodor Sturm (University of Bonn, Bonn, Germany)
Abstract
We construct and analyze conformally invariant, log-correlated Gaussian random fields on compact Riemannian manifolds of general even dimension defined through its covariance kernel given as inverse of the Graham-Jenne-Mason-Sparkling (GJMS) operator. The corresponding Gaussian multiplicative chaos is a generalization to the n-dimensional case of the celebrated Liouville quantum gravity measure in dimension two. Finally, we study the Polyakov-Liouville measure on the space of distributions on M induced by the copolyharmonic Gaussian field, provide explicit conditions for its finiteness and compute the conformal anomaly.
