b-lab Seminar by Konstantinos Kourliouros on May 3

On May 3 at 15:30h (google meet)  Konstantinos Kourliouros (ICMC-USP Säo Pao) will talk about

Title:    Impasse Singularities of Generalised Hamiltonian Systems

Abstract: By a Generalised (or Constrained) Hamiltonian System we mean a pair consisting of a function (the generalised Hamiltonian) and an arbitrary closed 2-form (i.e. not necessarily symplectic). Such systems, considered first by P. A. M. Dirac, appear in abundance when considering variational and optimal control problems with constraints, in quantisation problems, but also in hydrodynamics (general vortex theory) e.t.c. In this talk we give local classification results for typical singularities of such systems at impasse points, i.e. at points belonging on the singular locus of the 2-form, where its rank is smaller than the maximum possible. In particular we show how to obtain exact local normal forms with functional invariants for a wide class of impasse singularities, and we give a geometric description of them in terms of other invariant objects (discriminants and period mappings) naturally associated to the system.