Programme:
Preseminar (for graduate students)
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10:00-11:00 |
H.W.Braden |
What is a root system? |
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11:00-11:30
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Coffee |
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11:30-12:30
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I.A.B. Strachan |
What is an integrable system? |
Location: Lecture Theatre C, James Clerk Maxwell Building
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3:00-4:00 |
Coincident root loci and Jack polynomials |
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4:00-5:00 |
Tea
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5:00-6:00 |
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
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9:30-10:30 |
Graded degenerate double affine Hecke algebras and completely integrable models with delta potential
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10:30-11:30 |
Coffee
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11:30-12:30 |
Prof. Berest |
Commutative Rings of Differential Operators on Curves
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Abstracts:
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.
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]