Isaac Newton Institute for Mathematical Sciences

Symmetric Functions and Macdonald Polynomials

8 Jan - 6 Jul 2001

Organisers: Professor P Hanlon (Michigan), Professor IG Macdonald (QMW), Professor AO Morris (Aberystwyth)

Isaac Newton Institute for Mathematical Sciences, Cambridge, UK

EuroWorkshop

CONJECTURES, RECENT RESULTS AND OPEN PROBLEMS RELATED TO THE MACDONALD POLYNOMIALS

Programme

Participants

Organisers: Professor P Hanlon, Professor IG Macdonald and Professor AO Morris.

The overall programme: 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.

Speakers: Adriano Garsia (University of California at San Diego); Phil Hanlon (University of Michigan); Ian Macdonald (Queen Mary College); Eric Opdam (University of Amsterdam); John Stembridge (University of Michigan).

Location and Cost: The EuroWorkshop will take place at the Newton Institute and accommodation for participants will be provided in single study bedrooms at Wolfson Court, a hall of residence adjacent to the Institute. The workshop package costs 300, which includes registration fee, accommodation, breakfast and dinner from dinner on Sunday 7 January until breakfast on Saturday 13 January, and lunches and refreshments on the days that lectures take place

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.

Closing date for receipt of applications and abstracts is 20 October 2000

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