Next week seminars

[Emanuele Tuillier Illingworth]

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MATHEMATICAL PHYSICS COLLOQUIUM
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Monday 9 June, 14:30 SISSA Room D

Prof. Ramakrishnan Ramadas  (ICTP)

"A gauge-theoretic approach to the Hodge conjecture for certain abelian 
fourfolds"

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Geometry and Physics seminar

Tuesday 10 June, 14:30 SISSA Room C

Dr. Arthemy V. Kiselev (Utrecht)

"Operator-valued involutive distributions of evolutionary vector fields 
and  their affine geometry"

Abstract: Involutive distributions of evolutionary vector fields that 
belong to images of matrix operators in total derivatives are considered 
and some classifications of the operators are obtained. In particular, we 
describe endomorphisms of evolutionary derivations whose images are closed 
w.r.t. the commutation and which induce hierarchies of Lie algebra 
structures on the infinite jet spaces. Analysis of the deformation problem 
for the operators suggests to distinguish their homotopy compatibility as 
the analog of the Poisson pencils for Hamiltonian structures and the 
strong compatibility as the commutation closure of sums of images for 
N-tuples of the operators. This allows to endow the spaces of totally 
compatible operators, which may not be the endomorphism solutions of the 
classical Yang-Baxter equations, with a Lie algebra structure specified by 
bi-differential structural constants. We show that the operators with 
closed images determine flat non-Cartan connections on the module of 
evolutionary vector fields such that the structural constants of the Lie 
algebras are bi-differential Christoffel's symbols, and we conclude that 
completely integrable hierarchies are the geodesics. Also, differential 
complexes are constructed using the operators, which leads to a 
realization of Lie algebroids over jet spaces in terms of homological 
vector fields. A class of matrix operators, whose images are closed w.r.t. 
the commutation, and the Koszul brackets induced in their pre-images are 
assigned to integrable KdV-type hierarchies of symmetry flows on the 
hyperbolic Euler-Lagrange Liouville-type systems (e.g., on the open 2D 
Toda lattices associated with semi-simple Lie algebras). (following 
arXiv:math-ph/0703082 , joint with Johan W. van de Leur)

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Algebraic Geometry Seminar

Thursday 12 June, 14:30 SISSA Room C

Prof. Ugo Bruzzo (SISSA)

"Semistable principal Higgs bundles"

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Geometry and Physics seminar

Thursday 12 June, 16:00 SISSA Room D

Dr. Taras Skrypnyk (SISSA)

"Dual R-matrix integrability"

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Upcoming Colloquium:

Monday 30 June, 14:30 SISSA Room D

Prof.  A. Morozov  (ITEP Moscow)

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For further information:
http://www.sissa.it/fm/seminars.php