Related papers: Vortices, Painlev\'e integrability and projective …
A few years ago Selivanova gave an existence proof for some integrable models, in fact geodesic flows on two dimensional manifolds, with a cubic first integral. However the explicit form of these models hinged on the solution of a nonlinear…
Using two innovations, smooth, but distinctly different, scaling laws for the numerical reconnection of pairs of initially orthogonal and anti-parallel quantum vortices are obtained using the three-dimensional Gross-Pitaevskii equations,…
Motivated by generalized geometry (\`a la Hitchin), we discuss the integrability conditions for four natural almost complex structures on the product bundle ${\mathcal Z}\times {\mathcal Z}\to M$, where ${\mathcal Z}$ is the twistor space…
The abelian Higgs model on a compact Riemann surface \Sigma supports vortex solutions for any positive vortex number d \in \ZZ. Moreover, the vortex moduli space for fixed d has long been known to be the symmetrized d-th power of \Sigma, in…
We introduce a notion of Gieseker stability for a filtered holomorphic vector bundle $F$ over a projective manifold. We relate it to an analytic condition in terms of hermitian metrics on $F$ coming from a construction of the Geometric…
We derive general expressions for the Kaehler form of the L^2-metric in terms of standard 2-forms on vortex moduli spaces. In the case of abelian vortices in gauged linear sigma-models, this allows us to compute explicitly the Kaehler class…
A class of harmonic solutions to the steady Euler equations for incompressible fluids is presented in two dimensions in circular, elliptic and bipolar coordinates. Since the velocity field is solenoidal in this case, it can be written as…
We demonstrate the common bihamiltonian nature of several integrable systems. The first one is an elliptic rotator that is an integrable Euler-Arnold top on the complex group GL(N) for any $N$, whose inertia ellipsiod is related to a choice…
Some new Hamiltonian systems of quasi-Painlev\'e type are presented and the analogue of Okamoto's space of initial conditions computed. Using the geometric approach that was introduced originally for the identification problem of Painlev\'e…
We study topological vortex solutions in a generalized Abelian Higgs model with non-polynomial dielectric and potential functions. These quantities are chosen by requiring integrability of the self-dual limit of the theory for all values of…
The primary aim of this thesis is to investigate metrics which are induced by a differential form and arise as a critical point of Hitchin's variational principle. Firstly, we investigate metrics associated with the structure group PSU(3)…
Let L --> X be a complex line bundle over a compact connected Riemann surface. We consider the abelian vortex equations on L when the metric on the surface has finitely many point degeneracies or conical singularities and the line bundle…
The paper concerns discrete versions of the three well-known results of projective differential geometry: the four vertex theorem, the six affine vertex theorem and the Ghys theorem on four zeroes of the Schwarzian derivative. We study…
Conformal geometry is studied using the unfolded formulation \`a la Vasiliev. Analyzing the first-order consistency of the unfolded equations, we identify the content of zero-forms as the spin-two off-shell Fradkin-Tseytlin module of…
In this paper we first formulate a dually gauged harmonic map model, suggested from a product Abelian Higgs field theory arising in impurity-inspired field theories, and obtain a new BPS system of equations governing coexisting vortices and…
Remarkable parallelism between the theory of integrable systems of first-order quasilinear PDE and some old results in projective and affine differential geometry of conjugate nets, Laplace equations, their Bianchi-Baecklund transformations…
Integrable Hamiltonian systems on symplectic manifolds have been well-studied. However, an intrinsic property of these kind of systems is that they can only live on even dimensional manifolds. To introduce a similar notion of integrability…
Weighted degrees of quasihomogeneous Hamiltonian functions of the Painlev\'{e} equations are investigated. A tuple of positive integers, called a regular weight, satisfying certain conditions related to singularity theory is classified.…
We comment on an analysis by Contopoulos et al. which demonstrates that the governing six-dimensional Einstein equations for the mixmaster space-time metric pass the ARS or reduced Painlev\'{e} test. We note that this is the case…
We report on a breakdown of both monopole dominance and positivity in abelian-projected lattice Yang-Mills theory. The breakdown is associated with observables involving two units of the abelian charge. We find that the projected lattice…