We review our recent work on solitons in the Higgs phase. We use U (NC) gauge theory with
NF Higgs scalar fields in the fundamental representation, which can be extended to possess …

During the last 20 years,``localization''has been one of the dominant themes in the area of
equivariant differential geometry. Typical results are the Duistermaat-Heckman theory, the …

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We prove the Arnold-Givental conjecture for a class of Lagrangian submanifolds in Marsden-
Weinstein quotients which are fixed point sets of an antisymplectic involution. For these …

In this paper we define invariants of Hamiltonian group actions for central regular values of
the moment map. The key hypotheses are that the moment map is proper and that the …

Rabinowitz Floer homology is the semi-infinite dimensional Morse homology associated to
the Rabinowitz action functional used in the pioneering work of Rabinowitz. Gradient flow …

We define a gauged non-linear sigma model for a 2-sphere valued field and a $ SU (2) $
connection on an arbitrary Riemann surface whose energy functional reduces to that for …

We study pseudoholomorphic curves in symplectic quotients as adiabatic limits of solutions
to the symplectic vortex equations. Our main theorem asserts that the genus zero invariants …

Given a J-holomorphic Morse function on a symplectic manifold, a new construction of the
Fukaya-Seidel category is outlined. Applying this construction in an infinite dimensional …

1.2. Coupled equations. Among the various generalisations of the set-up of the previous
subsection, one of the most useful is to the study of connections combined with additional …