[Turkmath:7152] Bogazici Matematik Seminerleri - ilan ekte

[ferit.ozturk at boun.edu.tr]

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http://www.math.boun.edu.tr/index.php?option=com_content&task=section&id=49&Itemid=405
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Integrable maps and Poisson algebras derived from cluster algebras

Allan P. Fordy
University of Leeds

Bogazici Mathematics Colloquium

Date	  : Tuesday, August 3, 2010
Time	  : 15:00
Place     : TB 250, Boðaziçi Üniversitesi


Abstract: We consider a class of map, recently derived in the context of
cluster
mutation [1].  Not all of these are integrable, but we specialise to some
particular families which are.  We discuss invariant Poisson brackets, along
with the Poisson algebra of special families of functions associated with some
of these maps. For one particular family, a bi-Hamiltonian structure is derived
and used to construct a sequence of Poisson commuting functions and hence show
complete integrability [2]. One of the most important open questions regards
the identification and classification of the integrable cases of maps obtained
through the construction of [1].  This classification is the main theme of
[3].

[1] A.P. Fordy and R.J. Marsh, Cluster mutation-periodic quivers and associated
laurent sequences (2009). Preprint arXiv:0904.0200v2 [math.CO].

[2] A.P. Fordy, Mutation-periodic quivers, integrable maps and associated
Poisson algebras (2010). Preprint arXiv:1003.3952v1 [nlin.SI].

[3] A.P. Fordy and A.N.W. Hone, Integrable maps and Poisson algebras derived
from cluster algebras (2010). In preparation.


Tea and coffee will be served at 16:00
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