Symplectic Geometry


Symplectic linear algebra. Symplectic manifolds. Symplectomorphisms. Lagrangian submanifolds. Theorems of Darboux and Weinstein (lagrangian neighborhood). Hamiltonian vector fields. Brief introduction to Poisson manifolds. Hamiltonian actions and moment map. Noether Theorem. Equivariance of the moment map and coadjoint orbits. Convexity Theorem. Symplectic reduction. Additional topics: Almost complex structures. Kähler manifolds. Contact manifolds. Lie algebroids and Poisson geometry. Toric symplectic manifolds.

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Defended Theses

  • Structure, algorithmics and dynamics of endomorphisms for certain classes of groups
      André da Cruz Carvalho (April 2023)
      Pedro V. Silva
  • A point-free study of z-embeddings, more general classes of localic maps, and uniform continuity
      Ana Belén Avilez García (April 2023)
      Jorge Picado
  • Analysis of equations of motion of inextensible strings and networks
      Ayk Telciyan (April 2023)
      Dmitry Vorotnikov
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