Moment map flows and the Hecke correspondence for quivers

Morse Theory of the Moment Map for Representations of Quivers

The main results of this manuscript concern the Morse theory associated to the norm-square of a Kähler moment map f = ‖Φ − α‖2 on the space of representations Rep(Q,v) of a quiver; these are the first steps in a larger research program concerning the hyperkähler analogue of the well-known Kirwan surjectivity theorem in symplectic geometry. The first main result is that, although ‖Φ − α‖2 is not...

Non-commutative Integrability, Moment Map and Geodesic Flows

The purpose of this paper is to discuss the relationship between commutative and non-commutative integrability of Hamiltonian systems and to construct new examples of integrable geodesic flows on Riemannian manifolds. In particular, we prove that the geodesic flow of the biinvariant metric on any bi-quotient of a compact Lie group is integrable in the non-commutative sense by means of polynomia...

the search for the self in becketts theatre: waiting for godot and endgame

this thesis is based upon the works of samuel beckett. one of the greatest writers of contemporary literature. here, i have tried to focus on one of the main themes in becketts works: the search for the real "me" or the real self, which is not only a problem to be solved for beckett man but also for each of us. i have tried to show becketts techniques in approaching this unattainable goal, base...

The Moment Map Revisited

In this paper, we show that the notion of moment map for the Hamiltonian action of a Lie group on a symplectic manifold is a special case of a much more general notion. In particular, we show that one can associate a moment map to a family of Hamiltonian symplectomorphisms, and we prove that its image is characterized, as in the classical case, by a generalized “energy-period” relation.

The Moment Map