Lorentz Center - Elliptic Integrable Systems and Hypergeometric Functions from 15 Jul 2013 through 19 Jul 2013
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    Elliptic Integrable Systems and Hypergeometric Functions
    from 15 Jul 2013 through 19 Jul 2013


The recent birth of elliptic hypergeometric function theory and of representation theory of elliptic algebras has led to exciting new developments at the intersection of mathematics and theoretical physics. A fundamental role in this context is provided by the theory of integrable systems. The relevant integrable systems are elliptic integrable systems, which are amongst the least accessible and most challenging ones.

The workshop aimed to increase our understanding of these developments. This is of great importance for the whole area and for its manifold applications to related subfields in mathematics and theoretical physics. The workshop capitalised on the underlying unifying trends, by enabling researchers from the various pertinent areas to meet, learn about ongoing projects, discuss open problems and novel directions, and begin new collaborations from different complementary and mutually beneficial perspectives.

Each workshop day focussed on a particular theme and started with a talk by a keynote speaker. The keynote speaker spent the first part of the talk on introducing the theme, placing it in a general perspective and relating it to the other themes. The themes and keynote speakers were:

Monday: "Elliptic hypergeometric functions and elliptic Painlevé equations", M. Noumi (Kobe, Japan).

Tuesday: "Integrable lattice equations/models", Frank Nijhoff (Leeds, UK).

Wednesday: "Integrable many body systems", Martin Hällnas (Loughborough, UK).

Thursday: "Representation theory", Giovanni Felder (Zürich, Switzerland).

Friday: "Applications in quantum field theory", Hugh Osborn (Cambridge, UK).

The workshop led to a successful exchange of ideas between researchers from the different fields. The participants appreciated the format of the workshop and explicitly noted that the workshop has led to new perspectives and potential collaborations for them. The special session of five short talks by young researchers, sponsored by Elsevier, was a successful addition to the program.

We thank the participants for the high quality talks and for the pleasant and stimulating atmosphere with lively discussions. We thank the Lorentz Center staff for the excellent support.

Erik Koelink (Nijmegen, The Netherlands)

Masatoshi Noumi (Kobe, Japan)

Eric Rains (Pasadena, USA)

Hjalmar Rosengren (Gothenburg, Sweden)

Simon Ruijsenaars (Leeds, UK)

Jasper Stokman (Amsterdam, The Netherlands)