Lefschetz fibrations, Lie groupoids and noncommutative geometry

• 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

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)

Scientific publications

(4)

(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)

GASPARIM, ELIZABETH; SUZUKI, BRUNO. Curvature grafted by instantons. INDIAN JOURNAL OF PHYSICS, JUN 2021. (19/13204-0)

BALLICO, EDOARDO; GASPARIM, ELIZABETH; KOEPPE, THOMAS; SUZUKI, BRUNO. POISSON STRUCTURES ON THE CONIFOLD AND LOCAL CALABI-YAU THREEFOLDS. REPORTS ON MATHEMATICAL PHYSICS, v. 90, n. 3, p. 26-pg., 2022-12-01. (19/13204-0)

GASPARIM, ELIZABETH; SUZUKI, BRUNO. Curvature grafted by instantons. INDIAN JOURNAL OF PHYSICS, v. 95, n. 8, SI, p. 1631-1638, AUG 2021. (19/13204-0)

BALLICO, E.; GASPARIM, E.; RUBILAR, F.; SUZUKI, B.. The Kuranishi map for vector bundles on certain products of curves. Topology and its Applications, v. 312, p. 12-pg., 2022-05-01. (19/13204-0)