Statistical physics, combinatorics and probability: from discrete to continuous models
Physique statistique, combinatoire et probabilités : approches du continu par le discret
7 September – 18 December 2009
A trimester at the Centre Émile Borel, Institut Henri Poincaré
Organizers: Mireille Bousquet-Mélou, Jérémie Bouttier, Grégory Miermont, Gilles Schaeffer
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This thematic term, held in the Institut Henri Poincaré in the heart of Paris, aims at bringing together mathematicians, physicists and computer scientists interested in problems at the interface between statistical mechanics, combinatorics and probability theory. Special emphasis is put on the interplay between discrete and continuous formalisms, which has recently been the subject of intense research, leading to a precise definition of universal objects such as the celebrated SLE but also CRT, ISE, GFF, etc. Participants will also become acquainted with the state-of-the-art techniques: analytic combinatorics, integrability, high-dimensional methods...
The program will revolve around series of lectures by experts:
- Extended courses: Philippe Di Francesco, Philippe Flajolet, Christian Krattenthaler, Grégory Miermont, Gordon Slade
- Mini-courses: Mihai Ciucu, Robert Cori, Bertrand Eynard, Emmanuel Guitter, Remco van der Hofstad, Des Johnston, Martin Loebl, Kirone Mallick
as well as seminars by participants, and several workshops:
- Introductory symposium (7-8 September 2009)
- Two-dimensional lattice models (5-10 October 2009), a workshop (8-10) coupled with les États de la Recherche SMF (5-7). Highlights: dimers, spins, loops, ASMs and plane partitions; relations with conformal invariance and integrability...
- Embedded random graphs (2-6 November 2009): enumerative and probabilistic aspects, limiting behaviors, connections with 2D quantum gravity and matrix models.
- Above the critical dimension (7-11 December 2009): lace expansion, renormalization, and high-dimensional-like settings, such as models on trees or complete graphs.
