| People
Teresa Monteiro Fernandes, Orlando Neto, Maria João Ferreira,
César Rodrigo, Susana Santos, Bruno Simões, Áurea Quintino, João Cabral,
António Araujo.
| Ongoing research
- Singularities:
Construction of a desingularization algorithm for conormals of
quasi-ordinary surfaces.
Existence of a canonical decomposition of the resolution graph of a plane
curve. Classification of the rigid local systems defined on the
complementary of a plane curve.
Existence of a semi-universal deformation of a Legendrian curve.
Classification of the Legendrian curves of low modality.
- Analytic spaces:
Applications of the D-module theory to twistor D-modules.
- Differential Geometry
Research interests:
Submanifold geometry; harmonic maps (they solve a variational problem
in Riemannian Geometry and include sigma models of heoretical
physics); integrable surface geometry (minimal surfaces, CMC surfaces,
Willmore surfaces and isothermic surfaces)
Objectives:
existence, stability, construction and geometric properties of
critical points of geometrically natural energy functionals, with
emphasis on the study of harmonic maps; geometric properties of
minimal and parallel mean curvature submanifolds; formal conservation
quantities; conserved quantities of Willmore surfaces and their
geometrical interpretations; constrained Willmore surfaces.
| Recent achievements
Characterization of the limits of tangents of quasi ordinary
singularities. Proof that the triviality of the limits of tangents is a
topological invariant of the quasi ordinary hypersurface.
Classification of the rigid local systems defined on the complementaray of
a quasi-homogeneous curve.
Construction of a desingularization algorithm for conormals of
quasi-ordinary surfaces .
Proof of: the solution and the De Rham complexes associated to a D-Module
underlying a twistor structure (in the sense of Simpson-Sabbah-Mochizuki)
are perverse for a natural t-structure. This is a by-product of the
general study of holonomic relative D-Modules and the relative
constructiblity of their solutions performed in this work.
Explicit construction of the extension of functors on categories of
modules on algebras of deformations
Geometric properties of immersions with parallel mean curvature into a
homogeneous space.
| Recent publications
Fernandes, Teresa Monteiro; Sabbah, C., On the de Rham complex of mixed twistor D-modules, International Mathematics Research Notices, published
online, 31/8/2012
D. BARLET AND T. MONTEIRO FERNANDES, Grauert’s theorem for
subanalytic open sets in real analytic manifolds, Studia Math., 204 (2011),
265-274 (IF: 0,567).
A.R.MARTINS AND T.MONTEIRO FERNANDES, Formal extension of the Whitney
functor and duality,
Rend. Sem. Mat. Univ. Padova, 126(2011),127–149,
(IF:0,271).
M. J. FERREIRA and B. A. SIMÕES, “Explicit construction of harmonic
two-spheres into the complex Grassmannian”, Math. Z. Online First 15
September 2011
| Papers to appear
Fernandes, Teresa Monteiro, Microsupport of tempered solutions of D-Modules
associated to smooth morphisms, to appear in Houston Journal of Mathematics
F. E. Burstall, J. F. Dorfmeister, K. Leschke, A. C. Quintino, Darboux transforms and simple factor dressing of constant mean curvature surfaces, manuscripta mathematica (2012); DOI: 10.1007/s00229-012-0537-2
A. Malheiro Casimiro, C. Rodrigo, First variation formula for discrete
variational problems in two independent variables, RACSAM Rev. R. Acad.
Cienc. Exactas Fis. Nat. Ser. A. Mat. 106(1) (2012), 111-135.
A. Fernández, P. L. García, C. Rodrigo, Variational integrators in
discrete vakonomic mechanics, RACSAM Rev. R. Acad. Cienc. Exactas Fis.
Nat. Ser. A. Mat. 106(1) (2012), 137-159
A. Malheiro Casimiro, C. Rodrigo, First variation formula and conservation laws in several independent discrete variables, Journal of Geometry and
Physics 62(1), 61-86 (2012).
F. E. Burstall, S. D. Santos, Special isothermic surfaces of type d,
Journal of the London Mathematical Society 2012; doi: 10.1112/jlms/jdr050 |