Mathematisches Kolloquium

Zusammenfassung: Statistical mechanics deals with systems with a very large number of elementary components. Some of the most studied models are discrete, in the sense that the positions of the elementary components are determined by the vertices of a regular lattice. A scaling limit is a procedure by which the mesh of the lattice is sent to zero in order to obtain a continuum model. Such a limit is very useful in the analysis of the large scale properties of discrete models, especially in the presence of a phase transition, when it gives rise to very interesting mathematical problems. In this lecture I will introduce two paradigm models in the theory of phase transitions (percolation and the Ising model) and present a new approach to scaling limits that has revolutionized the statistical mechanics of two-dimensional systems (and has lead to two Fields medals being awarded for work related to scaling limits at the last two International Congresses of Mathematicians). This new approach stems from an extremely fruitful combination of probability theory and complex analysis, and leads to the study of random fractal curves characterized by the way they transform under conformal maps.

Alle Interessierten sind hiermit herzlich eingeladen. Eine halbe Stunde vor dem Vortrag gibt es Kaffee und Tee im Sozialraum (Raum 448) im 4. Stock.

Treffpunkt zum Abendessen um 18.00 Uhr wird noch bekannt gegeben.