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In the 1980s, IG Macdonald formulated a series of conjectures which predicted the constant terms of expressions that involve an important new class of symmetric functions called the Macdonald polynomials. Since their introduction, these conjectures and polynomials have been a central topic of study in Algebraic Combinatorics. Of particular note has been the variety of approaches used in efforts to solve the conjectures or to find an algebraic or geometric interpretation for the Macdonald polynomials themselves. Different approaches involve double affine Hecke algebras, homology of nilpotent Lie algebras, generalized traces of Lie algebra representations and diagonal actions of the symmetric group on polynomial rings in two sets of variables. In this programme we will attempt to unify these different approaches to the Macdonald polynomials and some of the outstanding conjectures that have resulted from this work. Links with other areas such as algebraic geometry, Lie algebras, non-commutative algebra, mathematical physics and mathematical statistics will be emphasised.
The EuroWorkshop: This EuroWorkshop will serve to launch the programme on Symmetric Functions and Macdonald Polynomials by providing an introduction to the subject. Specialists will give a series of lectures which cover the origins of the subject, the current state of knowledge and open problems & conjectures.
The EuroWorkshop is supported by the European Community and funding is available to support some young researchers. It is intended for nationals of EC Member States and of Iceland, Liechtenstein, Norway, Israel, Bulgaria, Cyprus, Czech Republic, Estonia, Hungary, Latvia, Lithuania, Poland, Romania, Slovakia, Slovenia and Switzerland, who must all be under 35 years of age. Self-supporting participants of any age and nationality are welcome to apply.
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