Venue: HIM lecture hall (Poppelsdorfer Allee 45, Bonn)
Organizers: Roland Bauerschmidt, Eveliina Peltola, Ellen Powell, Rémi Rhodes, Eero Saksman
Description:
Random geometry refers to the study of random geometric structures, such as curves and surfaces.
One of the most notable examples is the Schramm–Loewner Evolution (SLE), which has been shown to describe the scaling limits of interfaces in 2D critical models.
Significant progress has been made through its interplay with the Gaussian Free Field (GFF), deepening the understanding of the geometric properties of both SLE and the GFF.
The macroscopic features of lattice models are believed to be described by quantum field theories (QFTs).
Critical lattice models are expected to enjoy an additional conformal symmetry, and such QFTs are termed conformal field theories (CFTs).
For instance, the Ising model, a prototypical example with an order-disorder phase transition, has seen mathematical breakthroughs that have fully established its continuum description.
However, extending these results to other models, such as the Potts or random cluster models, remains a major challenge, e.g. due to the absence of similar powerful integrability techniques.
Another major theme in this workshop is Liouville quantum gravity (LQG),
a concept that can be approached through Liouville CFT, random planar maps, or the "mating-of-trees" framework.
These perspectives have recently seen significant advances and are increasingly interconnected, providing new insights into large-scale random geometry behavior.
This workshop will focus on these central themes and the challenges they pose, including:
- the construction of CFTs from lattice models
- probabilistic approaches to CFTs, such as the LQG, Liouville CFT, and its implications for 2D quantum gravity
- the development of new techniques for understanding scaling limits of
general lattice models
Trimester Program guests, who were invited and have confirmed to be at HIM during the period of this workshop, are eligible to attend this event.