Wendelin Werner

Thursday, 24th September, 4.15pm

Virtual Talk

Wendelin Werner, ETH Zürich

Basic geometric structures hidden in the free boson

The Gaussian Free field GFF has been a fundamental and very basic building block for numerous developments in theoretical physics since more than 50 years. More recently, in the special case of the GFF in two dimensions, the Schramm-Loewner Evolution and ideas based on gases of Brownian loops (a.k.a. the Brownian loop-soup) have shed some new mathematical light on this object, unveiling some natural random fractal structures within a GFF.

The goal of this talk will be to describe what can be said about such random geometric structures when the spatial dimension is greater than 2. While SLE-tools are not available anymore, ideas based on the loop-soups (some of which can be traced back to seminal work of Symanzik or Fröhlich and Spencer among others) turn out to be fruitful.