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Lectures on Holomorphic Curves in Symplectic and Contact Geometry
Holomorphic Curves Symplectic Contact Geometry
2010/11/12
This is a set of expository lecture notes created originally for a graduate course on holomorphic curves taught at ETH Zurich and the Humboldt University Berlin in 2009/2010. The notes are still incom...
Complementarity of Kinematics and Geometry in General Relativity Theory
Complementarity of Kinematics Geometry General Relativity Theory
2010/12/20
Relations between kinematics, geometry and law of reference frame motion are considered. We show, that kinematical tensors define geometry up to a space functiona arbitrariness when integrability cond...
Geometry of the Banach spaces C(beta mathbb N times K, l_p) for compact metric spaces K
Geometry of the Banach spaces C compact metric spaces K
2010/11/19
In this paper we provide the complete isomorphic classification of the spaces C(beta mathbb N times K, l_p) of all continuous l_p-valued functions, 1 <= p < infinity, defined on the topological produ...
Compact formulas for guiding-center orbits in axisymmetric tokamak geometry
Compact formulas guiding-center orbits axisymmetric tokamak geometry
2010/11/16
Compact formulas for trapped-particle and passing-particle guiding-center orbits in axisymmetric tokamak geometry are given in terms of the Jacobi elliptic functions and complete elliptic integrals. ...
Simulating Heliospheric and Solar Particle Diffusion using the Parker Spiral Geometry
Simulating Heliospheric Solar Particle Diffusion Parker Spiral Geometry
2010/11/16
Cosmic Ray transport in curved background magnetic fields is investigated using numerical Monte-Carlo simulation techniques. Special emphasis is laid on the So-lar system, where the curvature of the m...
Quaternionic Grassmannians and Pontryagin classes in algebraic geometry
Quaternionic Grassmannians Pontryagin classes algebraic geometry
2010/11/9
The quaternionic Grassmannian HGr(r,n) is the affine open subscheme of the ordinary Grassmannian parametrizing those 2r-dimensional subspaces of a 2n-dimensional symplectic vector space on which the ...
Gravitating magnetic monopole in Vaidya geometry
Gravitating magnetic monopole Vaidya geometry
2010/12/20
A magnetic-monopole solution of a non-Abelian gauge theory as proposed by ’t Hooft-Polyakov
is studied in the Vaidya space-time. We find that the solutions of Einstein equations generates a geometry ...
Short loop decompositions of surfaces and the geometry of Jacobians
Short loop decompositions the geometry of Jacobians
2010/11/19
Given a Riemannian surface, we consider a naturally embedded graph which captures part of the topology and geometry of the surface. By studying this graph, we obtain results in three different directi...
Modifications of Hodge bundles and enumerative geometry : the stable hyperelliptic locus. Part 1: semicompact type
Hodge bundles enumerative geometry stable hyperelliptic locus
2010/11/9
We compute, in terms of tautological classes, the fundamental class of the locus of stable hyperelliptic curves, i.e. the closure in the moduli space of stable curves of the locus of smooth hyperellip...
Five lectures on optimal transportation: Geometry, regularity and applications
optimal transportation Geometry regularity applications
2010/11/19
In this series of lectures we introduce the Monge-Kantorovich problem of optimally transporting one distribution of mass onto another, where optimality is measured against a cost function c(x,y). Con...
We reconsider the sub-leading quantum perturbative corrections to N=2 cubic special Kaehler geometries. Imposing the invariance under axion-shifts, all such corrections (but the imaginary constant one...
A projective Dirac operator on CP^2 within fuzzy geometry
projective Dirac operator fuzzy geometry
2010/12/22
We propose an ansatz for the commutative canonical spin_c Dirac operator on CP^2 in a global geometric approach using the right invariant (left action-) induced vector fields from SU(3). This ansatz ...
Holographic entanglement entropy: near horizon geometry and disconnected regions
Holographic entanglement entropy horizon geometry disconnected regions
2010/12/22
We study the finite term of the holographic entanglement entropy for the charged black hole in AdS(d+2) and other examples of black holes when the spatial region in the boundary theory is given by one...
On Explicit Holmes-Thompson Area Formula in Integral Geometry
Minkowski space Holmes-Thompson Volume symplectic structure
2010/12/13
In this article, we give an exposition on the Holmes-Thompson theory developed by Alvarez. The space of geodesics in Minkowski space has a symplectic structure which is induced by the projection from ...
Quantum correlation: Comparison of measures with geometry and mutual information
Quantum correlation Comparison measures geometry mutual information
2010/11/5
Two measures for quantum correlations were proposed recently from a geometric perspective [Phys. Rev. Lett. 104, 080501 (2010); e-print arXiv:1004.0190]. We prove the the equivalence of the two geomet...