Coordination: Nathanael Berestycki, University of Vienna
Research network: TU Wien (Michael Drmota, Marcin Lis, Benedikt Stufler, Fabio Toninelli), University of Vienna (Ilse Fischer, Christian Krattenthaler), Graz University of Technology (Mihyun Kang)
Funding volume: €4.3 million / four-year term
This research network focuses on random discrete structures, which are ubiquitous in many areas of modern mathematics, but are also essential for the description of various phenomena in mathematical physics. For example, they play a key role in understanding phase transitions that physical systems undergo during abrupt changes – such as water transitioning from a liquid to a solid state when the temperature falls below freezing. The researchers in this Special Research Area will be investigating various two-dimensional models, such as the famous dimer model and planar graphs. They will be combining probabilistic and combinatorial perspectives to answer fundamental questions about these models. How can they be counted, either exactly or approximately? How can their random geometry be understood under suitable scaling? How can we explain the fascinating observation that the same structures and laws occur over and over again in completely different contexts? These and similar questions are deeply rooted in mathematical physics, from topological phase transitions to Liouville quantum gravity, which are part of the consortium’s research.