Title:
Gaussian multiplicative Chaos and related topics
Abstract:
The mathematical theory of Gaussian multiplicative chaos was founded by J.
P. Kahane in 1985. This theory has numerous applications in mathematical
physics: 2d Liouville quantum gravity in the conformal gauge (boundary and
non boundary Liouville measure, KPZ equation), the Kolmogorov-Obukhov
model of energy dissipation in 3d turbulence, the maximum of
log-correlated fields, etc... In this talk, we will first review the
theory and discuss numerous extensions and related topics that have been
developed the past few years. We will then focus more specifically on
complex Gaussian multiplicative chaos, an extension of Gaussian
multiplicative chaos to the complex case.