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MINI-COURSES

Tudor Ratiu (EPFL, Lausanne)
"Infinite dimensional Poisson geometry"
In this series of lectures I will present what little is known about infinite dimensional Poisson geometry with special emphasis on Lie-Poisson systems and their link to W* algebras. However, in spite of the dearth of hard theorems in this area, there are remarkable applications to concrete physical systems that can be dually formulated on the Hamiltonian (hence Poisson) side and the Lagrangian (hence variational) side. My intention is to spend at least half the time on such applications because, on one hand, they indicate the way how to proceed in the search of a general theory and, on the other hand, provide concrete applications that go as far as numerical implementations.
Tudor's course here.

Luca Vitagliano (U. Salerno)
"Characteristics, bicharacteristics, and geometric singularities of solutions of PDEs"
Many physical systems are described by partial differential equations (PDEs). Determinism then requires the Cauchy problem to be well-posed. Even when the Cauchy problem is well-posed for generic Cauchy surfaces, there may exist characteristic surfaces. Characteristics of PDEs play an important role both in Mathematics and in Physics. In this mini-course, I will review the theory of characteristics and bicharacteristics of PDEs, with a special emphasis on intrinsic aspects, i.e., those aspects which are invariant under general changes of coordinates. After a basically analytic introduction, I will pass to a modern, geometric point of view, presenting characteristics within the jet space approach to PDEs. In particular, I will discuss the relationship between characteristics and singularities of solutions and observe that: "wave-fronts are characteristic surfaces and propagate along bicharacteristics. This remark may be understood as a mathematical formulation of the wave-particle duality in quantum mechanics.
First lecture, Monday: here
Second lecture, Tuesday: here
Third lecture, Wednesday: here.


INVITED LECTURES

Roberto Emparan (ICREA, Barcelona)
"General Relativity in the limit of very many dimensions"
I will argue that it is natural, and useful, to investigate the properties of General Relativity and its black holes in the limit in which the number of spacetime dimensions grows to infinity. The theory simplifies dramatically: it reduces to a theory of non-interacting particles, of finite radius but vanishingly small cross sections, which do not emit nor absorb radiation of any finite frequency. This leads to efficient calculational approaches in an expansion around this limit, as well as to intriguing connections to low-dimensional string-theory black holes.

Andrea Loi (U. Cagliari)
"The Gromov width of Symmetric Spaces"
The Gromov width of a symplectic manifold is defined as the supremum of the square of a radius of an open ball which can be symplectically embedded into the given symplectic manifold. Gromov's width is an example of a symplectic capacity introduced by H. Hofer and E. Zehnder. The concept of symplectic capacity has been extended to that of pseudo symplectic capacity by G. Lu. This allows him (amongst other things) to compute the Gromov width of the complex Grassmannian. In this seminar, after recalling the basic definitions and concepts about symplectic capacities we will show how one can use Lu's techniques and Jordan triple systems tools to compute the Gromov width of all Hermitian symmetric spaces of compact and noncompact type.

Pawel Nurowski (U. Warsaw)
"Twistor space for rolling bodies"
On surfaces which when rolling on the plane have G_2 symmetry.

Vladimir Rubtsov (U. Angers)
"Parameter-dependent Poisson brackets: from usual to double"
We study meromorphic solutions of various Yang-Baxter relations and the corresponding Poisson algebras both usual and double in sense of Van den Bergh. This is a joint work with A. Odesskii and V. Sokolov.

Miguel Sánchez Caja (U. de Granada / IHES)
"Recent progress and links among Riemannian, Finslerian and Lorentzian Geometries"
A recent correspondence between a class of elements in Lorentzian geometry (the conformal structure of standard stationary spacetimes) and the geometry of a class of Finsler manifolds (Randers spaces), has revealed some links between Lorentzian and Finslerian geometries at some different levels. The progress in the latter includes also advances in Riemannian topics such as the existence of a Busemann boundary that generalizes Eberlein and O'Neill compactification for Hadamard manifolds, and is related to classical Gromov's compactification. Here, three stages of this interrelated progress will be explained: (1) Causal structure of spacetimes / properties of Finslerian distances (arxiv: 0903.3501). (2) Visibility and gravitational lensing in spacetimes / convexity of Finsler hypersurfaces (arxiv: 1112.3892, arxiv: 0911.0360). (3) Causal boundaries / Cauchy, Gromov, and Busemann boundaries in Riemannian and Finslerian settings (arXiv:1011.1154).


CONTRIBUTED TALKS

Ahmad Afuni (Freie Universität Berlin)
"On local monotonicity formulae for classical fields and their corresponding heat flows"

Jesse Alt (University of the Witwatersrand, Johannesburg, South Africa)
"Abnormal Cartan connections in parabolic geometry"

Margarida Camarinha (U. Coimbra)
"Optimal control of affine connection control systems from the point of view of Lie algebroids"

Beniamino Cappelletti-Montano (U. Cagliari)
"Constructions in cosymplectic geometry"

Nicola Ciccoli (U. Perugia)
"Multiplicative integrability of Poisson symmetric spaces"

Marek Elzanowski (Portland State U.)
"Homogeneous Spaces and Defective Elastic Crystals"

Maria Pilar García del Moral (U. Oviedo)
"Geometry of Gauging Processes"

Janus Grabowski (Polish Academy of Sciences)
"Modular classes of skew algebroid relations"

Thomas Leistner (U. Adelaide, Australia)
"Global aspects of Lorentzian manifolds with special holonomy"

Jeffrey Morton (U. Hamburg)
"2-Group Symmetries on Moduli Spaces of Higher Gauge Theory"

José Navarro (U. Badajoz)
"Characterization of variational equations on natural bundles"

Antonio de Nicola (U. Coimbra)
"Hard Lefschetz Theorem for Sasakian manifolds"

Esmeralda Sousa-Dias (U. Lisboa)
"Cluster-iteration maps and their symplectic reduction"

Miguel Teixidó Román (U. Politècnica de Catalunya)
"MGS form for cotangent lifted actions"

Abstracts of the contributed talks.


POSTERS (updated 31 July)

Abstracts of all posters.