Colloquium abstracts

Subhajit Goswami
March 18, 2021

Level-sets of correlated Gaussian processes: connectivity and local geometry:  In this talk we will review some recent developments in the study of percolation of Gaussian free field level-sets on the hypercubic lattice in three and more dimensions. As a canonical percolation model with slow algebraic decay of correlations, the new methodologies that emerged in the course of these developments form a robust toolkit for answering some classical questions in percolation theory in non-classical contexts. We will spend considerable time discussing the motivation behind this model, in particular its interplay with other very natural questions in Probability theory as well the rich interplay with the potential theory of random walks which is its another appealing feature. The main focus of the talk will be a recent result on equality of several natural critical parameters associated with this model --- relevant for understanding the local geometry of level-set components. No prior knowledge of percolation theory is necessary. Based on joint work with H. Duminil-Copin