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Universidade de São Paulo (USP). Instituto de Matemática e Estatística (IME) (Institutional affiliation from the last research proposal) Birthplace: Chile
Cristián Andrés Ortiz González in research grants and scholarships supported by FAPESP.
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In this project we are concerned with an extension of the Localization Theorem of Atiyah-Bott and Berline-Vergne for the equivariant cohomology of a Lie 2-group acting on a stack/Lie groupoid. We also study Hamiltonian actions of 2-groups on both 0-shifted and 1-shifted symplectic stacks with the aim of describing their equivariant cohomology. Also, in the 1-shifted case we plan to descri…
In this project we study symplectic Lefschetz fibrations on certain classes of symplectic manifolds, namely, symplectic leaves of semi-simple Poisson Lie groups and nilpotent adjoint orbits. We also study the Fukaya-Seidel category of symplectic leaves of Poisson Lie groups and their homogeneous Poisson spaces, by studying the Fukaya-Seidel category of the corresponding symplectic groupoi…
(Only some records are available in English at this moment)
In this doctoral research project, we study infinitesimal symmetries of 2-bundle gerbes, extending recent results by Krepski and Vaughan on infinitesimal symmetries of bundle gerbes. We also study the relation between symmetries of 2-bundle gerbes, n-plectic manifolds and higher Courant algebroids. As an application, we plan to describe the symmetries of the Chern-Simons 2-gerbe which enc…
In this project we are concerned with symmetries of multiplicative Courant algebroids, also known as CA-groupoids. Motivated by recent results of Ortiz-Waldron on the category of multiplicative sections of both VB-groupoids and LA-groupoids, we study the underlying algebraic structure on the category of multiplicative sections of a CA-groupoid and its Morita invariance. We also investigat…
In this postdoctoral project we study Lefschetz fibrations over a special class of symplectic manifolds given by symplectic leaves of Poisson Lie groups. Our main goal consists on the construction of new examples of Lefschetz fibrations over symplectic manifolds, relying on techniques which combine Lie Theory and Poisson Geometry. On the other hand, as a continuation of previous works, we…
In this project we study the geometry of S^1-gerbes with connection to describe a geometric pre-quantization of quasi-symplectic groupoids and their Hamiltonian spaces. As an application, we describe a pre-quantization of quasi-Hamiltonian spaces in the sense of Alekseev-Malkin-Meinrenken.
This master project studies the necessary geometric concepts to understand a theorem by Arnold on the geodesic formulation of Euler equations describing an incompressible fluid. The main goal of the project consists on studying recent results by Izosimov and Khesin in which Arnolds strategy is generalized to the setting of Lie groupoids equipped with an invariant Riemannian metric. Such a…
In this project we study equivariant cohomology of Lie 2-groups acting on Lie groupoids. We investigate how the models of equivariant cohomology studied by Barbosa and Neumann (arXiv:1912.00316) extend to this setting. Our main goal is the study of equivariant cohomology of differentiable stacks with symmetries, hence we investigate the corresponding Morita invariance of the equivariant c…
(Only some records are available in English at this moment)
In this project we propose to start the study of the problem concerning the existence of closed geodesics on a Riemannian stack. For that purpose we plan to study the properties of the energy functional defined over stacky curves as well as a proper notion of Jacobi field along stacky geodesics on the Riemannian stack. This proposal is framed in the Fapesp project "Morse theory on Lie gro…
| 5 / 5 | Completed research grants |
| 3 / 3 | Ongoing scholarships in Brazil |
| 6 / 6 | Completed scholarships in Brazil |
| 1 / 1 | Completed scholarships abroad |
| 15 / 15 | All research grants and scholarships |
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