Applications of Lie theory in the symplectic and hermitian geometry of homogeneous...
Lagrangian submanifolds: open Gromov-Witten theory and Mirror Symmetry
| Grant number: | 19/13204-0 |
| Support Opportunities: | Regular Research Grants |
| Start date: | March 01, 2020 |
| End date: | February 28, 2022 |
| Field of knowledge: | Physical Sciences and Mathematics - Mathematics - Geometry and Topology |
| Agreement: | Comisión Nacional de Investigación Científica y Tecnológica (CONICYT) |
| Principal Investigator: | Cristián Andrés Ortiz González |
| Grantee: | Cristián Andrés Ortiz González |
| Principal researcher abroad: | Elizabeth Terezinha Gasparim |
| Institution abroad: | Universidad Católica del Norte, Antofagasta , Chile |
| Host Institution: | Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil |
| City of the host institution: | São Paulo |
Abstract
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 groupoids integrating a Poisson Lie group and their homogeneous spaces, respectively. Other topics such as: deformations of Calabi-Yau threefolds, characteristic classes of stacks, deformations of complex manifolds and homological Mirror Symmetry, are presented as Ph.D. projects related to this research proposal. (AU)
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