Objective The last few years have seen significant advances in the discovery and development of integrable models in probability, especially in the context of random polymers and the Kardar-Parisi-Zhang (KPZ) equation. Among these are the semi-discrete (O'Connell-Yor) and log-gamma (Seppalainen) random polymer models. Both of these models can be understood via a remarkable connection between the geometric RSK correspondence (a geometric lifting, or de-tropicalization, of the classical RSK correspondence) and the quantum Toda lattice, the eigenfunctions of which are known as Whittaker functions. This connection was discovered by the PI and further developed in collaboration with Corwin, Seppalainen and Zygouras. In particular, we have recently introduced a powerful combinatorial framework which underpins this connection. I have also explored this connection from an integrable systems point of view, revealing a very precise relation between classical, quantum and stochastic integrability in the context of the Toda lattice and some other integrable systems. The main objectives of this proposal are (1) to further develop the combinatorial framework in several directions which, in particular, will yield a wider family of integrable models, (2) to clarify and extend the relation between classical, quantum and stochastic integrability to a wider setting, and (3) to study thermodynamic and KPZ scaling limits of Whittaker functions (and associated measures) and their applications. The proposed research, which lies at the interface of probability, integrable systems, random matrices, statistical physics, automorphic forms, algebraic combinatorics and representation theory, will make novel contributions in all of these areas. Fields of science natural sciencesmathematicspure mathematicsmathematical analysisfunctional equationsnatural sciencesphysical sciencestheoretical physicsparticle physicsfermionsnatural sciencesmathematicsapplied mathematicsmathematical physicsnatural scienceschemical sciencespolymer sciencesnatural sciencesmathematicspure mathematicsdiscrete mathematicscombinatorics Programme(s) H2020-EU.1.1. - EXCELLENT SCIENCE - European Research Council (ERC) Main Programme Topic(s) ERC-ADG-2014 - ERC Advanced Grant Call for proposal ERC-2014-ADG See other projects for this call Funding Scheme ERC-ADG - Advanced Grant Host institution UNIVERSITY COLLEGE DUBLIN, NATIONAL UNIVERSITY OF IRELAND, DUBLIN Net EU contribution € 1 287 861,18 Address BELFIELD 4 Dublin Ireland See on map Region Ireland Eastern and Midland Dublin Activity type Higher or Secondary Education Establishments Links Contact the organisation Opens in new window Website Opens in new window Participation in EU R&I programmes Opens in new window HORIZON collaboration network Opens in new window Total cost € 1 287 861,18 Beneficiaries (3) Sort alphabetically Sort by Net EU contribution Expand all Collapse all UNIVERSITY COLLEGE DUBLIN, NATIONAL UNIVERSITY OF IRELAND, DUBLIN Ireland Net EU contribution € 1 287 861,18 Address BELFIELD 4 Dublin See on map Region Ireland Eastern and Midland Dublin Activity type Higher or Secondary Education Establishments Links Contact the organisation Opens in new window Website Opens in new window Participation in EU R&I programmes Opens in new window HORIZON collaboration network Opens in new window Total cost € 1 287 861,18 THE UNIVERSITY OF WARWICK Participation ended United Kingdom Net EU contribution € 116 376,51 Address Kirby Corner Road - University House CV4 8UW Coventry See on map Region West Midlands (England) West Midlands Coventry Activity type Higher or Secondary Education Establishments Links Contact the organisation Opens in new window Website Opens in new window Participation in EU R&I programmes Opens in new window HORIZON collaboration network Opens in new window Total cost € 116 376,51 UNIVERSITY OF BRISTOL Participation ended United Kingdom Net EU contribution € 175 061,06 Address BEACON HOUSE QUEENS ROAD BS8 1QU Bristol See on map Region South West (England) Gloucestershire, Wiltshire and Bristol/Bath area Bristol, City of Activity type Higher or Secondary Education Establishments Links Contact the organisation Opens in new window Website Opens in new window Participation in EU R&I programmes Opens in new window HORIZON collaboration network Opens in new window Total cost € 175 061,06
