The Experts below are selected from a list of 816 Experts worldwide ranked by ideXlab platform
Logares Marina - One of the best experts on this subject based on the ideXlab platform.
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Torelli theorem for the Deligne--Hitchin moduli space
'Springer Science and Business Media LLC', 2009Co-Authors: Biswas Indranil, Gomez, Tomas L., Hoffmann Norbert, Logares MarinaAbstract:Fix integers g ≥ 3 and r ≥ 2, with r ≥ 3 if g = 3. Given a compact connected Riemann surface X of genus g, let MDH(X) denote the corresponding SL(r, C) Deligne-Hitchin moduli space. We prove that the complex analytic space MDH(X) determines (up to an isomorphism) the Unordered Pair {X, overline{X}} , where {overline{X}} is the Riemann surface defined by the opposite almost complex structure on X
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Torelli theorem for the Deligne--Hitchin moduli space
'Springer Science and Business Media LLC', 2008Co-Authors: Biswas Indranil, Gomez, Tomas L., Hoffmann Norbert, Logares MarinaAbstract:Fix integers $g\geq 3$ and $r\geq 2$, with $r\geq 3$ if $g=3$. Given a compact connected Riemann surface $X$ of genus $g$, let $\MDH(X)$ denote the corresponding $\text{SL}(r, {\mathbb C})$ Deligne--Hitchin moduli space. We prove that the complex analytic space $\MDH(X)$ determines (up to an isomorphism) the Unordered Pair $\{X, \overline{X}\}$, where $\overline{X}$ is the Riemann surface defined by the opposite almost complex structure on $X$.Comment: 14 page
Sridhar S. - One of the best experts on this subject based on the ideXlab platform.
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Light beams with general direction and polarization: Global description and geometric phase
Elsevier Inc., 2014Co-Authors: Nityananda R., Sridhar S.Abstract:Restricted Access. An open-access version is available at arXiv.org (one of the alternative locations)We construct the manifold describing the family of plane monochromatic light waves with all directions, polarizations, phases and intensities. A smooth description of polarization, valid over the entire sphere S2S2 of directions, is given through the construction of an orthogonal basis Pair of complex polarization vectors for each direction; any light beam is then uniquely and smoothly specified by giving its direction and two complex amplitudes. This implies that the space of all light beams is the six dimensional manifold View the MathML sourceS2×C2∖{0}, the (untwisted) Cartesian product of a sphere and a two dimensional complex vector space minus the origin. A Hopf map (i.e. mapping the two complex amplitudes to the Stokes parameters) then leads to the four dimensional manifold S2×S2S2×S2 which describes beams with all directions and polarization states. This product of two spheres can be viewed as an ordered Pair of two points on a single sphere, in contrast to earlier work in which the same system was represented using Majorana’s mapping of the states of a spin one quantum system to an Unordered Pair of points on a sphere. This is a different manifold, CP2CP2, two dimensional complex projective space, which does not faithfully represent the full space of all directions and polarizations. Following the now-standard framework, we exhibit the fibre bundle whose total space is the set of all light beams of non-zero intensity, and base space S2×S2S2×S2. We give the U(1)U(1) connection which determines the geometric phase as the line integral of a one-form along a closed curve in the total space. Bases are classified as globally smooth, global but singular, and local, with the last type of basis being defined only when the curve traversed by the system is given. Existing as well as new formulae for the geometric phase are presented in this overall framework
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Light beams with general direction and polarization: global description and geometric phase
2012Co-Authors: Nityananda R., Sridhar S.Abstract:We construct the manifold describing the family of plane monochromatic light waves with all directions, polarizations, phases and intensities. A smooth description of polarization, valid over the entire sphere S^2 of directions, is given through the construction of an orthogonal basis Pair of complex polarization vectors for each direction; any light beam is then uniquely and smoothly specified by giving its direction and two complex amplitudes. This implies that the space of all light beams is the six dimensional manifold S^2 X C^2, the Cartesian product of a sphere and a two dimensional complex vector space. A Hopf map (i.e mapping the two complex amplitudes to the Stokes parameters) then leads to the four dimensional manifold S^2 X S^2 which describes beams with all directions and polarization states. This product of two spheres can be viewed as an ordered Pair of two points on a single sphere, in contrast to earlier work in which the same system was represented using Majorana's mapping of the states of a spin one quantum system to an Unordered Pair of points on a sphere. This is a different manifold, CP^2, two dimensional complex projective space, which does not faithfully represent the full space of all directions and polarizations. Following the now-standard framework, we exhibit the fibre bundle whose total space is the set of all light beams of non-zero intensity, and base space S^2 X S^2. We give the U(1) connection which determines the geometric phase as the line integral of a one-form along a closed curve in the total space. Bases are classified as globally smooth, global but singular, and local, with the last type of basis being defined only when the curve traversed by the system is given. Existing as well as new formulae for the geometric phase are presented in this overall framework.Comment: 19 pages; submitted to Journal of Physics
Horsley Daniel - One of the best experts on this subject based on the ideXlab platform.
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More nonexistence results for symmetric Pair coverings
'Elsevier BV', 2015Co-Authors: Francetic Nevena, Herke Sarada, Horsley DanielAbstract:A (v,k,λ)-covering is a Pair (V,B), where V is a v-set of points and B is a collection of k-subsets of V (called blocks), such that every Unordered Pair of points in V is contained in at least λ blocks in B. The excess of such a covering is the multigraph on vertex set V in which the edge between vertices x and y has multiplicity rxy - λ, where rxy is the number of blocks which contain the Pair {x,y}. A covering is symmetric if it has the same number of blocks as points. Bryant et al. [4] adapted the determinant related arguments used in the proof of the Bruck-Ryser-Chowla Theorem to establish the nonexistence of certain symmetric coverings with 2-regular excesses. Here, we adapt the arguments related to rational congruence of matrices and show that they imply the nonexistence of some cyclic symmetric coverings and of various symmetric coverings with specified excesses
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More nonexistence results for symmetric Pair coverings
2015Co-Authors: Francetic Nevena, Herke Sarada, Horsley DanielAbstract:A $(v,k,\lambda)$-covering is a Pair $(V, \mathcal{B})$, where $V$ is a $v$-set of points and $\mathcal{B}$ is a collection of $k$-subsets of $V$ (called blocks), such that every Unordered Pair of points in $V$ is contained in at least $\lambda$ blocks in $\mathcal{B}$. The excess of such a covering is the multigraph on vertex set $V$ in which the edge between vertices $x$ and $y$ has multiplicity $r_{xy}-\lambda$, where $r_{xy}$ is the number of blocks which contain the Pair $\{x,y\}$. A covering is symmetric if it has the same number of blocks as points. Bryant et al.(2011) adapted the determinant related arguments used in the proof of the Bruck-Ryser-Chowla theorem to establish the nonexistence of certain symmetric coverings with $2$-regular excesses. Here, we adapt the arguments related to rational congruence of matrices and show that they imply the nonexistence of some cyclic symmetric coverings and of various symmetric coverings with specified excesses.Comment: Submitted on May 22, 2015 to the Journal of Linear Algebra and its Application
Biswas Indranil - One of the best experts on this subject based on the ideXlab platform.
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Torelli theorem for the Deligne--Hitchin moduli space
'Springer Science and Business Media LLC', 2009Co-Authors: Biswas Indranil, Gomez, Tomas L., Hoffmann Norbert, Logares MarinaAbstract:Fix integers g ≥ 3 and r ≥ 2, with r ≥ 3 if g = 3. Given a compact connected Riemann surface X of genus g, let MDH(X) denote the corresponding SL(r, C) Deligne-Hitchin moduli space. We prove that the complex analytic space MDH(X) determines (up to an isomorphism) the Unordered Pair {X, overline{X}} , where {overline{X}} is the Riemann surface defined by the opposite almost complex structure on X
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Torelli theorem for the Deligne--Hitchin moduli space
'Springer Science and Business Media LLC', 2008Co-Authors: Biswas Indranil, Gomez, Tomas L., Hoffmann Norbert, Logares MarinaAbstract:Fix integers $g\geq 3$ and $r\geq 2$, with $r\geq 3$ if $g=3$. Given a compact connected Riemann surface $X$ of genus $g$, let $\MDH(X)$ denote the corresponding $\text{SL}(r, {\mathbb C})$ Deligne--Hitchin moduli space. We prove that the complex analytic space $\MDH(X)$ determines (up to an isomorphism) the Unordered Pair $\{X, \overline{X}\}$, where $\overline{X}$ is the Riemann surface defined by the opposite almost complex structure on $X$.Comment: 14 page
Nityananda R. - One of the best experts on this subject based on the ideXlab platform.
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Light beams with general direction and polarization: Global description and geometric phase
Elsevier Inc., 2014Co-Authors: Nityananda R., Sridhar S.Abstract:Restricted Access. An open-access version is available at arXiv.org (one of the alternative locations)We construct the manifold describing the family of plane monochromatic light waves with all directions, polarizations, phases and intensities. A smooth description of polarization, valid over the entire sphere S2S2 of directions, is given through the construction of an orthogonal basis Pair of complex polarization vectors for each direction; any light beam is then uniquely and smoothly specified by giving its direction and two complex amplitudes. This implies that the space of all light beams is the six dimensional manifold View the MathML sourceS2×C2∖{0}, the (untwisted) Cartesian product of a sphere and a two dimensional complex vector space minus the origin. A Hopf map (i.e. mapping the two complex amplitudes to the Stokes parameters) then leads to the four dimensional manifold S2×S2S2×S2 which describes beams with all directions and polarization states. This product of two spheres can be viewed as an ordered Pair of two points on a single sphere, in contrast to earlier work in which the same system was represented using Majorana’s mapping of the states of a spin one quantum system to an Unordered Pair of points on a sphere. This is a different manifold, CP2CP2, two dimensional complex projective space, which does not faithfully represent the full space of all directions and polarizations. Following the now-standard framework, we exhibit the fibre bundle whose total space is the set of all light beams of non-zero intensity, and base space S2×S2S2×S2. We give the U(1)U(1) connection which determines the geometric phase as the line integral of a one-form along a closed curve in the total space. Bases are classified as globally smooth, global but singular, and local, with the last type of basis being defined only when the curve traversed by the system is given. Existing as well as new formulae for the geometric phase are presented in this overall framework
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Light beams with general direction and polarization: global description and geometric phase
2012Co-Authors: Nityananda R., Sridhar S.Abstract:We construct the manifold describing the family of plane monochromatic light waves with all directions, polarizations, phases and intensities. A smooth description of polarization, valid over the entire sphere S^2 of directions, is given through the construction of an orthogonal basis Pair of complex polarization vectors for each direction; any light beam is then uniquely and smoothly specified by giving its direction and two complex amplitudes. This implies that the space of all light beams is the six dimensional manifold S^2 X C^2, the Cartesian product of a sphere and a two dimensional complex vector space. A Hopf map (i.e mapping the two complex amplitudes to the Stokes parameters) then leads to the four dimensional manifold S^2 X S^2 which describes beams with all directions and polarization states. This product of two spheres can be viewed as an ordered Pair of two points on a single sphere, in contrast to earlier work in which the same system was represented using Majorana's mapping of the states of a spin one quantum system to an Unordered Pair of points on a sphere. This is a different manifold, CP^2, two dimensional complex projective space, which does not faithfully represent the full space of all directions and polarizations. Following the now-standard framework, we exhibit the fibre bundle whose total space is the set of all light beams of non-zero intensity, and base space S^2 X S^2. We give the U(1) connection which determines the geometric phase as the line integral of a one-form along a closed curve in the total space. Bases are classified as globally smooth, global but singular, and local, with the last type of basis being defined only when the curve traversed by the system is given. Existing as well as new formulae for the geometric phase are presented in this overall framework.Comment: 19 pages; submitted to Journal of Physics
