James Montaldi

Postgraduate Opportunities

I am interested in many questions about Dynamical Systems with symmetry - especially Hamiltonian systems,  momentum maps, and symplectic and Poisson geometry.

Research Group(s)

• Analysis and Dynamical Systems
• Geometry Topology and Mathematical Physics

I am a reader in the School of Mathematics, and have been here since 2001. Prior to that I was a Professor at the University of Nice in France. I have a BSc in Mathematical Physics from the University of Sussex and a PhD in Mathematics from the University of Liverpool.

My research is a mixture of Pure and Applied Mathematics. 

My principal interest is in the dynamics and bifurcations of symmetric Hamiltonian systems, making the use of symmetry systematic rather than ad hoc.  This involves a general understanding of (symplectic) group actions, and the geometry of the resulting momentum map.

Current projects:

Bifurcations at zero momentum:  Zero momentum is special for geometric reasons (related to coadjoint actions) and this influences the types of bifurcation one would expect to see at such points.

Transition of Momentum Polytopes: The momentum map is determined by the symplectic form, and I am interested in how the image of the momentum map can vary as the symplectic form is changed.