Talk by Eva Kopfer
On April 3rd, 2024, Eva Kopfer (Universität Bonn) gave a talk about "Conformally Invariant Random Geometry on Manifolds of Even Dimension" as part of the research seminar Analysis of the FernUniversität in Hagen. This lecture is partially supported by the COST action Mathematical models for interacting dynamics on networks.
Abstract
Show Abstract
We present a concise introduction to conformally invariant, log-correlated Gaussian random fields on compact Riemannian manifolds of general even dimension uniquely defined through its covariance kernel given as inverse of the Graham-Jenne-Mason-Sparling (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, providing explicit conditions for its finiteness and computing the conformal anomaly.
