Speaker: Michael McAuley

Title: Smooth Gaussian fields and percolation


Abstract: The geometry of smooth Gaussian fields is significant in many areas of science including quantum chaos, medical imaging and cosmology. There is a longstanding heuristic from the physics literature, that the level sets of Gaussian fields should behave similarly to discrete percolation models, which are much simpler to analyse. In the last 15 years there has been significant progress in making this idea rigorous, and many of the classic results of percolation theory are now also known in the setting of Gaussian fields. The underlying reasons for this universality are not clear, but a possible explanation may be given by Schramm-Loewner Evolutions.


In this talk I will summarise the connections between Gaussian fields and discrete percolation models, describe recent work on one particular percolation-type quantity for Gaussian fields (the number of excursion/level set components) and consider some directions for future work in this topic (including connections with SLE). Part of this talk will be based on joint work with Dmitry Beliaev and Stephen Muirhead.