Grupos de Lie e simetrias

Speaker: Maria Amelia Salazar, UFF.

Date: 08 dec 2020, 13h.

Place: Google Meet at https://meet.google.com/dvf-zbqt-vbk.

Abstract: Os grupos aparecem como espaços de simetrias de objetos e a definição formal de grupos reflete as propriedades naturais que tais simetrias possuem. Os grupos de Lie aparecem como simetrias contínuas deobjetos: por exemplo, as rotações de uma esfera no espaço Euclidiano. Nesta palestra vou dar uma introdução aos grupos de Lie e às ferramentas usadas para estudá-los.

Note: Esta palestra é parte do SemEAr 2020.

 

Espaço de moduli de polígonos: um passeio com vistas para a geometria simplética

Speaker: Alessia Mandini, UFF.

Date: 10 nov 2020, 13h.

Place: Google Meet at https://meet.google.com/dvf-zbqt-vbk.

Abstract: A geometria simplética é uma área da geometria que viveu uma vivaz expansão nos últimos 40 anos. Com raízes na física matemática, hoje essa vasta área de pesquisa tem relações com outras áreas da matemática também, como a geometria de Poisson, a geometria algébrica, a topologia, à análise entre outros.

Nessa palestra vamos seguir um roteiro que nos mostra algumas das características peculiares da geometria simplética por meio de uma família especial de variedades simpléticas, chamadas espaços de moduli de polígonos.

Note: Esta palestra é parte do SemEAr 2020.

 

 

Lifting Lagrangians from symplectic divisors

Speaker: Luís Diogo, UFF.

Date: 01 nov 2019, 11h.

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

Abstract: We prove that there are infinitely many non-symplectomorphic monotone Lagrangian tori in complex projective spaces, quadrics and cubics of complex dimension at least 3. This is a consequence of the following: if Y is a codimension 2 symplectic submanifold  of a closed symplectic manifold X, then we can explicitly relate the superpotential of a monotone Lagrangian L in Y with the superpotential of a monotone Lagrangian lift of L in X. This sometimes involves relative Gromov-Witten invariants of the pair (X,Y). We start by defining the superpotential, which is a count of pseudoholomorphic disks with boundary on a Lagrangian, and which plays an important role in Floer theory and mirror symmetry.

This is joint work with D. Tonkonog, R. Vianna and W. Wu.

 

Hamiltonian S1-spaces with large equivariant pseudo-index.

Speaker: Isabelle Charton, Universität zu Köln.

Date: 18 oct 2019, 11h. Cancelado! :(

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

Abstract: Let (M,\omega) be a compact symplectic manifold of dimension 2n endowed with a Hamiltonian circle action with only isolated fixed points. Whenever M admits a toric 1-skeleton S, which is a special collection of embedded 2-spheres in M, we define the notion of equivariant pseudo-index of S: this is the minimum of the evaluation of the first Chern class c1 on the spheres of S. This can be seen as the analog in this category of the notion of pseudo-index for complex Fano varieties. In this talk we discuss upper bounds for the equivariant pseudo-index. In particular, when the even Betti numbers of M are unimodal, we prove that it is at most n+1 . Moreover, when it is exactly n+1, M must be homotopically equivalent to CPn.

 

Leaf topology of minimal foliations on 3-manifolds

Speaker: Carlos Meniño, UFF.

Date: 11 oct 2019, 15h30m.

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

Abstract: We show that every oriented and noncompact surface is homeomorphic to a leaf of a minimal hyperbolic foliation of a closed 3-manifold. The example is a suspension of a suitable circle group action over the bitorus. Moreover, every prescribed countable family of noncompact oriented surfaces can be simultaneusly realized as leaves of the same minimal hyperbolic foliation. The interest of this example relies in the fact that there were no examples of minimal hyperbolic foliatons with leaves with leaves with finitely and infinitely generated groups coexisting in the same foliation (and in the first case, only foliations with leaves homeomorphic to planes and cylinders were described!). Our example cannot be smoothed to transverse regularity C2, this suggests possible obstructions on the leaf topology of minimal hyperbolic foliations in that regularity. This is a joint work with P. Gusmão (UFF).

 

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