8 Jan - 6 Jul 2001

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

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