Geometry and topology of homogeneous spaces

• Grant number: 14/17337-0
• Support Opportunities: Regular Research Grants
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Lino Anderson da Silva Grama
• Grantee: Lino Anderson da Silva Grama
• Host Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil

Abstract

The proposed project consists of applying Lie theory, in particular semissimple Lie theory, to the study of geometry and topology of homogeneous spaces.One of the proposed problems is the study of Lefschetz fibrations on adjoint orbits of semissimple Lie algebras, in order to describe explicitly certain geometric objects such as vanishing cycles, Lefschetz (Lagrangian) thimbles and Fukaya-Seidel categories.Other proposed problems are the study of geometric formality on generalized flag manifolds, and the study of variational aspects of certain class of geodesics on flag manifolds. (AU)

Scientific publications

(5)

(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)

GRAMA, LINO; NEGREIROS, CAIO J. C.; OLIVEIRA, AILTON R.. Invariant almost complex geometry on flag manifolds: geometric formality and Chern numbers. Annali di Matematica Pura ed Applicata, v. 196, n. 1, p. 165-200, FEB 2017. (14/17337-0, 12/18780-0)

GRAMA, LINO; MARTINS, RICARDO MIRANDA. A brief survey on the Ricci flow in homogeneous manifolds. SAO PAULO JOURNAL OF MATHEMATICAL SCIENCES, v. 9, n. 1, p. 37-52, JUN 2015. (14/17337-0, 12/06879-1)

GASPARIM, ELIZABETH; GRAMA, LINO; SAN MARTIN, LUIZ A. B.. ADJOINT ORBITS OF SEMI-SIMPLE LIE GROUPS AND LAGRANGIAN SUBMANIFOLDS. PROCEEDINGS OF THE EDINBURGH MATHEMATICAL SOCIETY, v. 60, n. 2, p. 361-385, MAY 2017. (14/17337-0, 12/18780-0)

BALLICO, E.; GASPARIM, E.; GRAMA, L.; MARTIN, L. A. B. SAN. Some Landau-Ginzburg models viewed as rational maps. INDAGATIONES MATHEMATICAE-NEW SERIES, v. 28, n. 3, p. 615-628, JUN 2017. (14/17337-0)

GASPARIM, ELIZABETH; GRAMA, LINO; MARTIN, LUIZ A. B. SAN. Symplectic Lefschetz fibrations on adjoint orbits. FORUM MATHEMATICUM, v. 28, n. 5, p. 967-979, SEP 2016. (14/17337-0, 12/10179-5, 12/18780-0)