Random Polymers and Algebraic Combinatorics

Date: 25 - 29 May 2015

Location: Mathematical Institute, University of Oxford

Random polymers models are the subject of intense research within probability theory and mathematical physics, with increasingly strong connections to algebraic combinatorics, representation theory and integrable systems.  Physically, the models seek to describe phenomena such as interface cracking, turbulence and pinning of magnetic flux lines.  Recast in terms of random walks in random potentials, they have also been applied to study stochastic optimizaton problems such as arise in queuing theory and bioinformatics.  The free energy of these models can be mapped onto problems of stochastic growth within the Kardar-Parisi-Zhang universality class.

Recently, there have been breakthroughs in this end as scaling exponents and limit theorems for quantities like the polymer free energy have been proved for a few exactly solvable models.  This enhanced level of solvability is due to connections to algebraic structures such a symmetric functions and combinatorial structures such as the Robinson-Schensted-Knuth correspondence.  These probabilistic advances have already sparked interesting new directions within the realm of algebraic combinatorics.  The purpose of this workshop is to bring together leading experts and new researchers in random polymers and algebraic combinatorics to help build further bridges between these areas.

Invited participants: Philippe Bougerol (Jussieu), Francis Comets (Paris Diderot), Sylvie Corteel (Paris Diderot), Philippe Di Francesco (Illinois), Vadim Gorin (MIT), Kurt Johansson (KTH Stockholm), Rinat Kedem (Illinois), Anatol Kirillov (Kyoto), Christian Korff (Glasgow), Thomas Lam (Michigan), James Martin (Oxford), Masatoshi Noumi (Kobe), Sergey Oblezin (Nottingham), Leonid Petrov (Virginia), Alexander Povolotsky (JINR Dubna), Dan Romik (UC Davis), Tomohiro Sasamoto (Tokyo Inst Tech), Timo Seppalainen (Wisconsin), Craig Tracy (UC Davis), Roger Tribe (Warwick), Jon Warren (Warwick), Oleg Zaboronski (Warwick)

Additional support provided by EPSRC grant EP/L012154/1.