**Speaker:** Gonçalo Oliveira, UFF.

**Date:** 27 sep 2019, 11h. **CANCELADO (Palestrante vai receber o Prêmio Jovem Cientista do Nosso Estado. Parabéns!)**

**Place: ** Room 407, Bloco H, Campus Gragoatá, UFF.

**Abstract: **A conjecture of Richard Thomas gives a stability condition supposed to control the existence of a special Lagrangian sphere in a Hamiltonian isotopy class. In this talk, I will describe joint work with Jason Lotay where we prove a version of this conjecture for real 4-dimensional examples arising from the Gibbons-Hawking ansatz. In these same examples, I will also give a description of Seidel's symplectically knotted Lagrangian spheres and, if time permits, I will give a thorough study of minimal submanifolds of this class of examples.

**Speaker:** Cornelia Vizman, West University of Timisoara.

**Date:** 20 sep 2019, 11h.

**Place: ** Room 407, Bloco H, Campus Gragoatá, UFF.

**Abstract: **(Joint work with Stefan Haller from the University of Vienna) Generalizing the canonical symplectization of contact manifolds, we construct an infinite dimensional manifold of weighted embeddings into a contact manifold. This space carries a symplectic structure such that the contact group and the group of reparametrizations act in a Hamiltonian fashion with equivariant moment maps, respectively, giving rise to a dual pair, called the EPContact dual pair. Via symplectic reduction, it provides a conceptual identification of nonlinear Grassmannians of weighted isotropic submanifolds of the contact manifold with certain coadjoint orbits of the contact group. For the projectivized cotangent bundle, the EPContact dual pair is closely related to the EPDiff dual pair due to Holm and Marsden, and leads to a geometric description of some coadjoint orbits of the full diffeomorphism group.

**Speaker:** Camilo Angulo, UFF.

**Date:** 06 sep 2019, 11h.

**Place: ** Room 407, Bloco H, Campus Gragoatá, UFF.

**Abstract: **A Lie 2-algebra is a groupoid object in the category of Lie algebras. These can naturally be seen as an infinitesimal version of Lie 2-groups which are groupoids in the category of Lie groups. Lie 2-algebras are known to be integrable in this sense. To understand this integration process from a cohomological point of view, we present appropriate notions of representations for both Lie 2-groups and Lie 2-algebras and the corresponding complexes whose cohomologies classify extensions. Finally, we discuss a van Est type theorem.

**Speaker:** Grace Mwakyoma, IST Lisboa - IMPA.

**Date:** 16 aug 2019, 11h.

**Place: ** Room 407, Bloco H, Campus Gragoatá, UFF.

**Abstract: **Circle actions have attracted much recent attention in geometry and topology. In the terminology of dynamical systems, they are regarded as periodic flows and their fixed points correspond to equilibrium points.

A complete classification of Hamiltonian circle actions on compact manifolds of dimension four was obtained by Y. Karshon, following the work of M. Audin and K. Ahara and A. Hattori. In particular, it was shown that all these spaces are Kahler, that every example can be obtained from a simple model by a sequence of symplectic blowups and, if the fixed points are isolated, the circle actions extend to toric actions. In higher dimensions much less is known. There are however some partial classification results.

The present research aims at completely classifying Hamiltonian circle actions on compact orbifolds of dimension 4 when the fixed points are isolated. These spaces appear, for example, as reduced spaces of Hamiltonian torus actions at regular level sets of the moment map where the action is not free. L. Godinho shows in her classification of semifree Hamiltonian circle actions on compact 4-orbifolds that the situation is much different from the manifold case. For example, these actions can have any number of fixed points while, in the manifold case, they have exactly four fixed points.

**Speaker:** Hossein Movasati, IMPA.

**Date:** 05 jul 2019, 15h30.

**Place: ** Room 407, Bloco H, Campus Gragoatá, UFF.

**Abstract: **Is it possible to classify all homological cycles of a given symplectic manifold supported in Lagrangian spheres? The question in this generality might be ambiguous and too difficult. However, for complex projective varieties endowed with the Fubini-Study metric, Lefschetz vanishing cycles turn out to be supported in Lagrangian spheres and the monodromy action on them gives us a big class of such homological cycles. In this talk, I will report on a partial result in this direction for a family of Calabi-Yau threefolds called mirror quintic. The talk is partially based on my book 'A course in Hodge Theory: With Emphasis on multiple integrals' and Daniel Lopes Ph.D. thesis.