Geometry

Principal Investigator

Maria Teresa de Lemos Monteiro Fernandes<mtfernandes@fc.ul.pt>

List of PhD Integrated Members

António Manuel Bandeira Barata Alves de Araújo<ant.arj@gmail.com>

Áurea Quintino<amquintino@fc.ul.pt>

César Rodrigo Fernandez<crodrigo@geomat-pt.com>

M. Teresa Monteiro Fernandes<mtfernandes@fc.ul.pt>

Orlando Neto<omneto@fc.ul.pt>

Susana Duarte Santos<sdsantos@fc.ul.pt>

PhD Students

Marco Mendes<msmendes@fc.ul.pt>

Other PhD Researchers

Azizeh Nozad <anozad@ciencias.ulisboa.pt>

Carlos Florentino<carlos.florentino@tecnico.ulisboa.pt>

Daniel Ramos<dramos@ciencias.ulisboa.pt>

João Cabral<joao.cabral.70@gmail.com>

Pedro Cristiano Silva<pcsilva@isa.ulisboa.pt>

Description of the Research Group

Thematically, the group existed in 2008-12, but not under the name "Geometry", as its members were included in two groups of the former center CMAF.

There are two main direction of research within the group, with reciprocal interaction:

 

1) Differential and Riemanian Geometry:

Geometric formulation of the calculus of variations, and of equations obtained from the application of a variational principle in mechanics, control or field theories,with recent results on the reduction of variational principles when the Lagrangian density is invariant with respect to a Lie group action.

The study of the existence of conserved quantities of constrained Willmore surfaces, both polynomial and of formal series type, and their geometrical interpretation.

Baecklund and Darboux transformations of contrained Willmore surfaces.

 

2) Singularity theory and D-Module theory:

Deformations of germs of Legendrian curves on a 3-dimensional contact manifold and its generalization to higher dimensions. Relation with D-Module theory, álgebras of deformation-quantization, perverse sheaves, holomorphic families of perverse sheaves, subanalytic geometry.