Sergey Shadrin
Towards Lax formulation of integrable hierarchies of topological type.
Fri, 01/20/2012 - 15:01 — SomNambulAuthors: Sergey Shadrin, Guido Carlet, Johan van de Leur, Hessel Posthuma
Subjects: Mathematical Physics
AbstractTo each partition function of cohomological field theory one can associate an
Hamiltonian integrable hierarchy of topological type. The Givental group acts
on such partition functions and consequently on the associated integrable
hierarchies. We consider the Hirota and Lax formulations of the deformation of
the hierarchy of N copies of KdV obtained by an infinitesimal action of the
Givental group.Givental group action on Topological Field Theories and homotopy Batalin--Vilkovisky algebras.
Thu, 12/08/2011 - 15:01 — SomNambulAuthors: Sergey Shadrin, Vladimir Dotsenko, Bruno Vallette
Subjects: Quantum Algebra
AbstractIn this paper, we initiate the study of the Givental group action on
Cohomological Field Theories in terms of homotopical algebra. More precisely,
we show that the stabilisers of Topological Field Theories in genus 0
(respectively in genera 0 and 1) are in one-to-one correspondence with
commutative homotopy Batalin--Vilkovisky algebras (respectively wheeled
commutative homotopy BV-algebras).- 12 comments
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A group action on Losev-Manin cohomological field theories.
Mon, 09/07/2009 - 10:33 — SomNambulAuthors: Sergey Shadrin, Dimitri Zvonkine
Subjects: Algebraic Geometry
AbstractWe discuss an analog of the Givental group action for the space of solutions
of the commutativity equation. There are equivalent formulations in terms of
cohomology classes on the Losev-Manin compactifications of genus 0 moduli
spaces; in terms of linear algebra in the space of Laurent series; in terms of
differential operators acting on Gromov-Witten potentials; and in terms of
multi-component KP tau-functions. The last approach is equivalent to the
Losev-Polyubin classification that was obtained via dressing transformations
technique.
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