Georgios Dimitroglou Rizell

Talks

Here you can find slides and videos from selected talks.

Slides:
  • The classification of monotone Lagrangian tori in a four-dimensional symplectic vectorspace.
    AMS-EMS-SPM International Meeting 2015.
    Porto, 12 June 2015.
    Abstract: We prove that there are exactly two monotone Lagrangian tori in a four-dimensional symplectic vectorspace up to Hamiltonian isotopy and rescaling: the Clifford and the Chekanov torus. This is shown by, first, Hamiltonian isotoping the torus to a homotopically non-trivial torus inside C*×C* and, second, applying a classification result for homotopically non-trivial Lagrangian tori inside T*T2. The latter result follows using methods due to Ivrii.
  • Lagrangian unknottedness in the cotangent bundle of a torus and applications.
    IX Workshop on Symplectic Geometry, Contact Geometry, and Interactions.
    ENS Lyon, 31 January 2015.
    Abstract: The homotopically non-trivial Lagrangian tori in the cotangent bundle of a two-torus are classified up to Hamiltonian isotopy. This is done by following ideas and techniques due to Ivrii, who treated the case when the torus is homologous to the zero-section. We apply this result to obtain answers concerning the classification of monotone Lagrangian tori in a symplectic vector space. Both questions are studied by considering the behaviour of pseudo-holomorphic foliations when stretching the neck around the Lagrangian submanifold.
  • The effect of ambient Legendrian surgery on the Chekanov-Eliashberg DGA.
    Workshop on Legendrian submanifolds, holomorphic curves and generating families.
    Brussels, 30 August 2014.
Videos:
  • Classification results for two-dimensional Lagrangian tori.
    Princeton/IAS Symplectic Geometry Seminar.
    Princeton, USA, 7 April 2016.
    Abstract: We present several classification results for Lagrangian tori, all proven using the splitting construction from symplectic field theory. Notably, we classify Lagrangian tori in the symplectic vector space up to Hamiltonian isotopy; they are either product tori or rescalings of the Chekanov torus. The proof uses the following results established in a recent joint work with E. Goodman and A. Ivrii. First, there is a unique torus up to Lagrangian isotopy inside the symplectic vector space, the projective plane, as well as the monotone S2×S2. Second, the nearby Lagrangian conjecture holds for the cotangent bundle of the torus.
  • Classification results for two-dimensional Lagrangian tori.
    IBS-CGP, Postech.
    Pohang, Korea, 3 March 2016.
    Abstract: We discuss recent classification results for two-dimensional Lagrangian tori in certain symplectic manifolds, all proven using the splitting construction from symplectic field theory. Notably, these techniques are used to give a complete classification result for Lagrangian tori in the symplectic vector space up to Hamiltonian isotopy. In addition, in joint work with E. Goodman and A. Ivrii, we also show that there is a unique torus up to Lagrangian isotopy inside the symplectic vector space, the projective plane, and the monotone S2×S2. Finally, the nearby Lagrangian conjecture for the cotangent bundle of the torus is established.
  • Floer homology for Lagrangian cobordisms.
    IBS-CGP, Postech.
    Pohang, Korea, 8 March 2016.
    Abstract: Legendrian contact homology (LCH) is a Legendrian isotopy invariant. We introduce a version of wrapped Floer homology for pairs of Lagrangian cobordisms having Legendrian ends that admit augmentations. This theory is used to establish long exact sequences involving the singular homology of a Lagrangian cobordism and the linearised LCH of its Legendrian ends. As an application we show that an exact Lagrangian cobordism from a Legendrian sphere to itself necessarily is a concordance in high dimensions. This is joint work with B. Chantraine, P. Ghiggini and R. Golovko.