Mathematisches Kolloquium

Zusammenfassung: I will address the recent progress in our mathematical understanding of the scaling limits of critical O(n) models in two dimensions, through the Fields Medal work of Wendelin Werner and his co-authors. The presentation is aimed at a non-specialized audience. In particular, no special knowledge of O(n) models, scaling limits or Schramm-Loewner Evolution (SLE) is assumed. The main aim is to explain that there exists just a one-parameter family of possible scaling limits for the models considered, namely the so-called Conformal Loop Ensembles (CLEs). To explain this, I will focus on the critical Ising model, and use physics arguments to conclude that its scaling limit, if it exists, should be a CLE. Then, I will present an independent construction of CLEs through the Brownian loop soup introduced by Lawler and Werner. Finally, we will conclude that the scaling limit of the critical Ising model, and indeed of other critical O(n) models, can only be one of these CLEs.

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.