ARTIN/Classical and Quantum Integrability Workshop,

27th / 28th   Oct. 2006

Location: School of Mathematics Edinburgh University

Directions to the School of Mathematics

Participants should congregate in the coffee room in the department.

Programme:

 

Preseminar (for graduate students)

 

Friday morning
Location Room: 6203 James Clerk Maxwell Building

 

10:00-11:00

H.W.Braden

What is a root system?

11:00-11:30

 

 

Coffee

11:30-12:30

 

I.A.B. Strachan

What is an integrable system?

 

Workshop

 

Friday afternoon

Location: Lecture Theatre C, James Clerk Maxwell Building

 

 

3:00-4:00

Prof Veselov

Coincident root loci and Jack polynomials

4:00-5:00

Tea

 

 

5:00-6:00

Prof. Chalykh

KZ twist and Cherednik algebras

 

 

Friday evening:

 

There will be an early dinner. Please contact the organisers if you wish to attend.

 

There is a maths ceilidh  on Friday evening. The place is St. Peter's Church Hall, on Lutton Place (between South Clerk Street and St Leonards Street.

Time: Friday 27th Oct from 7:00pm to 11:00pm. Everyone is invited!! The map has the location marked by an arrow.

 

 

Saturday Morning

Location: Lecture Theatre C, James Clerk Maxwell Building

 

 

9:30-10:30

Prof. Opdam

Graded degenerate double affine Hecke algebras and completely integrable models with delta potential

 

10:30-11:30

Coffee

 

 

11:30-12:30

Prof. Berest

Commutative Rings of Differential Operators on Curves

 

 

 

 

 

Abstracts:

 

Prof. Veselov: Coincident root loci and Jack polynomials

 

Abstract:  In 1857 Arthur Cayley addressed the question (which he prescribed
to Sylvester) of how to determine when a polynomial has a multiple root
of a given multiplicity or, more generally, several roots with prescribed
multiplicities. The corresponding varieties are known as coincident root
loci and the question is what are the algebraic equations defining them.

Recently some interesting relations of this problem with the theory of
quantum Calogero-Moser systems and related theory of Jack polynomials
have been discovered.  

 

 

 

Prof. Chalykh:  KZ twist and Cherednik algebras

       

 

Prof. Opdam: Graded degenerate double affine Hecke algebras and

completely integrable models with delta potential
 
Abstract: The graded degenerate double affine Hecke algebra
has a large center. We discuss certain integrable models
related to this fact, and various open problems.
 

This talk is based on joint work (in progress) with
Stokman and Emsiz.

 

Prof. Berest: Commutative Rings of Differential Operators on Curves

Abstract: We shall discuss the structure of maximal commutative
subalgebras of differential operators on algebraic curves,
which act ad-nilpotently on the whole ring of (global) differential
operators. The problem turns out to be non-trivial only for a special
class of rational curves, in which case a complete description of both
the individual subalgebras and of the space of all such is now available.
The proofs involve a curious mixture of standard algebraic arguments
and analytic considerations familiar from the theory of integrable
systems. In particular, the Burchnall-Chaundy theory of commuting
differential operators plays a crucial role.
[The talk is based on joint work with George Wilson]

 


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