Geometry Day/ Dia de Geometria (funded by FCT project PTDC/MAT/099880/2008)  Schedule (see below for the abstracts) 10:3011:30 Juan Carlos Marrero (Univ. de La Laguna), Further evidence that everything in Classical Mechanics is a Lagrangian submanifold. 11:3012:30 Mohammad Jawad Azimi (Univ. de Coimbra), Nijenhuis deformation of L_{\infty}algebras. 14:3015:30 Edith Padrón (Univ. de La Laguna), Reduction of Symplectic principal Rbundles. 15:3016:30 Ivan Yudin (Univ. de Coimbra), Hard Lefschetz theorem for Sasakian manifolds.  Juan Carlos Marrero (Universidad de La Laguna) Title: Further evidence that everything in Classical Mechanics is a Lagrangian submanifold. Abstract: In this talk, I will present a geometric description of Lagrange and Hamilton Poincaré equations as Lagrangian submanifolds of symplectic manifolds. The key point is to extend the construction of the socalled Tulczyjew's triple for Classical Mechanics.  Mohammad Jawad Azimi (CMUC/Universidade de Coimbra) Title: Nijenhuis deformation of L_{\infty}algebras. Abstract: We define Nijenhuis forms on L_{\infty} algebras and present some properties. The notion covers well known examples such as graded Lie algebras, Courant algebroids and Lie algebroids.  Edith Padrón (Universidad de La Laguna) Title: Reduction of Symplectic principal Rbundles. Abstract: In this talk, we will describe a reduction process for symplectic principal R bundles in the presence of a momentum map. These types of structures play an important role in the geometric formulation of nonautonomous Hamiltonian systems.  Ivan Yudin (CMUC/Universidade de Coimbra) Title: Hard Lefschetz theorem for Sasakian manifolds Abstract: It is well known that in the context of Kaehler geometry wedging with the suitable powers of the symplectic form gives isomorphisms between the de Rham cohomology groups of complementary degrees. This isomorphism is known as the Hard Lefschetz isomorphism. In my talk, I will present the recent joint work with B.Cappelletti Montano and A. De Nicola in which we show the existence of a similar isomorphism for compact Sasakian manifolds. Such isomorphism is proven to be independent of the choice of a Sasakian metric on a given contact manifold. As a consequence, a topological obstruction for a contact manifold to admit Sasakian structures is found. 
