Dedicated to the interaction between geometry and physics, this vertical explores the properties and applications of geometric structures. It seeks to deepen the understanding of the geometric aspects of energy functionals, special curvature and torsion regimes, and the topological properties of spaces.
Its main research areas include geometric flows and variational problems in geometry.
The goal is to uncover new insights into the geometric aspects of energy functionals, critical point theory, and the topological properties of manifolds.
Led by Claudio Gorodski (USP)
Analysis on manifolds, including isometric actions of groups and groupoids; submanifold theory; minimal and constant mean curvature (CMC) surfaces; calculus of variations and geometric variational problems; geometric theory of foliations; geometric flows and their self-similar solutions; spectral theory of geometric operators; the study of Finsler and pseudo-Finsler manifolds; and geometric measure theory in smooth and non-smooth metric spaces.
Structures arising from symmetries, related to gauge theory and symplectic geometry, playing a central role in the formulation of geometric functionals and in the description of moduli spaces of solutions. This includes the study of symplectic topology, mirror symmetry, Hamiltonian dynamics, and Riemannian manifolds with special holonomy.
Poisson geometry and related structures, including Lie groupoids and Lie algebroids; Dirac and Courant geometry; homogeneous manifolds, solvmanifolds, and nilmanifolds; geometric invariants; equivariant bifurcation; and symmetry breaking in geometric variational problems.