| When |
Where |
Who |
Title (Click for abstract) |
| Thu 29 May 2008 9:30
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SISSA Room C
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Prof. J. Bellissard
(Georgia Institute of Technology)
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The Riemannian Geometry of the Atomic Surfaces
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| Abstract:
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| Thu 29 May 2008 14:30
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SISSA Room C
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Prof. B. Fantechi
(SISSA)
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Inertia Stack of \overline{M}_{g,n}
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| Abstract:
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| Thu 29 May 2008 11:00
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SISSA Room A
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L. Stefanini
(Zurich)
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Integration of quotient Poisson manifolds
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| Abstract:
After introducing the main facts about the integration of Poisson manifolds to symplectic groupoids, we shall discuss the integrability of quotients of Poisson manifolds under compatible Poisson grooupoid actions.
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| Fri 30 May 2008 14:30
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SISSA Room C
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Dr. V. Dragovic
(Belgrade)
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Poncelet porisms and beyond
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| Abstract:
We start from the set $T$ of lines in $\mathbf R^d$ simultaneously tangent to $d-1$ quadrics from a given confocal family. We analyse its structure and derive a fundamental property of $T$: any two lines from this set can be obtained from each other by at most $d-1$ billiard reflections at some quadrics from the confocal family. We introduce two hierarchies of notions: {\em $s$-skew lines} in $T$ and {\em $s$-weak Poncelet trajectories}, $s=-1,0,...,d-2$. The interrelations between billiard dynamics, linear subspaces of intersections of quadrics and hyperelliptic Jacobians developed in our joint paper with M. Radnovic (arXiv 0710.3656) enabled us to obtain higher-dimensional and higher-genera generalizations of several classical genus $1$ results.
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| Tue 3 June 2008 16:00
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SISSA Room C
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Prof. L. Ramero
(Lille I)
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Local systems on the punctured disc
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| Abstract:
We consider local systems of F-modules on the etale site of the p-adic punctured disc, where F is the algebraic closure of a finite field of characteristic different from p. We explain how such local systems admit a canonical decomposition which is fully analogous to the "break decomposition" for l-adic representations of a complete DVR of characteristic p.
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| Tue 3 June 2008 16:00
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SISSA Room B
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Prof. M. Correggi
(SNS Pisa)
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Vortices in Rotating Bose-Einstein Condensates
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| Abstract:
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| Wed 4 June 2008 14:30
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SISSA Room D
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A. Moro
(Loughbourough)
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Integrable regimes in nonlocal nonlinear optics
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| Abstract:
Nonlocal nonlinear optics (NNO) is one of the most important developments in modern optics. In the recent years it was shown that nonlocality plays a crucial role in the propagation of stable spatial "solitons" in three dimensions. The problem of the integrability of these kind of systems is still open, and, apart few (very interesting) cases the main theoretical results on the behaviour of solutions are obtained numerically. Most of the models in NNO are based on a nonlocal nonlinear Schrodinger (NNLS) type equation. The dispersionless limit of the NNLS equation is equivalent to the geometric optics limit. We analyze in detail singular phase solutions and introduce a class of integrable nonlocal perturbations. We also discuss the possibility to introduce wave(dispersive)-deformations for different nonlocal models.
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| Wed 4 June 2008 14:30
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SISSA Room C
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Prof. M. Manetti
(La Sapienza, Roma)
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Periods of generalized deformations
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| Abstract:
A generalized deformation of a complex manifold is defined algebraically as a solution, up to gauge, of the Maurer-Cartan equation in the algebra of polyvector fields. We show that in the Kaehler case, every generalized deformation gives canonically holomorphic maps into the Grassmannian of graded subspaces of the De Rham cohomology. For classical deformations the above maps reduces to Griffiths period maps.
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| Mon 9 June 2008 14:30
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SISSA Room D
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Prof. R. Ramadas
(ICTP)
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TBA
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| Abstract:
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| Tue 10 June 2008 14:30
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SISSA Room C
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Dr. A. V. Kiselev
(Utrecht)
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Operator-valued involutive distributions of evolutionary vector fields and their affine geometry
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| 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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| Thu 12 June 2008 14:30
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SISSA Room C
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Prof. U. Bruzzo
(SISSA)
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Semistable principal Higgs bundles
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| Abstract:
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| Mon 30 June 2008 14:30
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SISSA Room C
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Prof. A. Morozov
(ITEP Moscow)
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TBA
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| Abstract:
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| Wed 2 July 2008 14:30
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SISSA Room C
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Prof. M. Manas
(Madrid)
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TBA
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| Abstract:
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