27/03/2012, 10:30 — 11:30 — Room P4.35, Mathematics Building
Daniele Sepe, CAMGSD/IST
Lecture V - Non-degenerate singularities
Having established several structural results for Lagrangian
fibrations which are submersions in the first four sessions, this
lecture aims to study a more general class of fibrations which
allows for topologically well-behaved (i.e. Morse-Bott in some
sense) singularities. These naturally arise in the theory of
completely integrable Hamiltonian systems (e.g. if the phase space
is compact, they must exist) and in mirror symmetry. The notion of
non-degenerate singularities is introduced and illustrated with
several examples. Time permitting, the Eliasson-Miranda
linearization theorem for non-degenerate singularities is going to
be studied in some detail (but probably without proof).
See also
https://www.math.tecnico.ulisboa.pt/~jmourao/inves/D_Sepe_Lagrangian_Fibrations.pdf