Results 11 to 20 of about 1,107 (66)

Complex solutions of Monge-Amp\`ere equations

, 2011
We describe a method to reduce partial differential equations of Monge-Amp\`ere type in 4 variables to complex partial differential equations in 2 variables. To illustrate this method, we construct explicit holomorphic solutions of the special lagrangian
Banos, Banos, Banos, Bertrand Banos, Bonan, Bryant, Bryant, Bryant, Doubrov, Harvey, Hitchin, Hitchin, Hitchin, Hong, Joyce, Joyce, Joyce, Joyce, Joyce, Lychagin, Lychagin, Strominger   +21 more
core   +2 more sources

Twistor construction of asymptotically hyperbolic Einstein--Weyl spaces

, 2013
Starting from a real analytic conformal Cartan connection on a real analytic surface $S$, we construct a complex surface $T$ containing a family of pairs of projective lines. Using the structure on $S$ we also construct a complex $3$-space $Z$, such that
Borówka, Aleksandra
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Deformations of calibrated D-branes in flux generalized complex manifolds [PDF]

, 2006
We study massless deformations of generalized calibrated cycles, which describe, in the language of generalized complex geometry, supersymmetric D-branes in N=1 supersymmetric compactifications with fluxes. We find that the deformations are classified by
A. Kapustin, A. Kapustin, A. Kapustin, A. Kapustin, C. Jeschek, C.M. Hull, D. Brecher, D. Brecher, D. Joyce, E. Sharpe, E. Witten, F. Gmeiner, F. Marchesano, G.R. Cavalcanti, J. De Boer, J. Gomis, J. Gutowski, L. Martucci, L. Martucci, L. Martucci, Luca Martucci, M. B. Green, M. Graña, M. Graña, M. Graña, M. Graña, M. Gualtieri, M. Gualtieri, M. Marino, M. Namba, M.R. Douglas, N. Hitchin, N.C. Leung, N.C. Leung, P. Grange, P. Griffiths, P. Koerber, P.S. Aspinwall, Paul Koerber, R. Minasian, R. Zucchini, R.C. McLean, R.P. Thomas, R.P. Thomas, S.H. Katz, V. Pestun, W.-Y. Chuang, Y. Li   +47 more
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Noncommutative polygonal cluster algebras

Journal of the London Mathematical Society, Volume 113, Issue 4, April 2026.
Abstract We define a new family of noncommutative generalizations of cluster algebras called polygonal cluster algebras. These algebras generalize the noncommutative surfaces of Berenstein–Retakh, and are inspired by the emerging theory of Θ$\Theta$‐positivity for the groups Spin(p,q)$\mathrm{Spin}(p,q)$.
Zachary Greenberg, Dani Kaufman, Merik Niemeyer, Anna Wienhard   +3 more
wiley   +1 more source

Gravitational duality, topologically massive gravity and holographic fluids

, 2014
Self-duality in Euclidean gravitational set ups is a tool for finding remarkable geometries in four dimensions. From a holographic perspective, self-duality sets an algebraic relationship between two a priori independent boundary data: the boundary ...
Petropoulos, P. Marios
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Graph potentials and topological quantum field theories

Proceedings of the London Mathematical Society, Volume 132, Issue 4, April 2026.
Abstract We introduce a new functional equation in birational geometry, whose solutions can be used to construct two‐dimensional topological quantum field theories (2d TQFTs), infinite‐dimensional in many interesting examples. The solutions of the equation give rise to a hierarchy of graph potentials, which, in the simplest setup, are Laurent ...
Pieter Belmans, Sergey Galkin, Swarnava Mukhopadhyay   +2 more
wiley   +1 more source

Lectures on Generalized Complex Geometry for Physicists

, 2010
In these lectures we review Generalized Complex Geometry and discuss two main applications to string theory: the description of supersymmetric flux compactifications and the supersymmetric embedding of D-branes. We start by reviewing G-structures, and in
Aganagic, Aganagic, Aharony, Ahn, Andriot, Andriot, Apostolov, Atiyah, Becker, Becker, Behrndt, Behrndt, Ben-Bassat, Benmachiche, Bergshoeff, Bergshoeff, Berkovits, Blumenhagen, Bovy, Boyer, Bursztyn, Butruille, Butti, Bär, Candelas, Cassani, Cassani, Cassani, Castellani, Castellani, Caviezel, Caviezel, Caviezel, Cederwall, Cederwall, Chiantese, Corrado, Corrigan, Cámara, D'Auria, Dall'Agata, Danckaert, Danielsson, Danielsson, de Wit, Denef, Donaldson, Douglas, Duff, Eels, Ellwood, Evslin, Fidanza, Flauger, Font, Gabella, Gaiotto, Gaiotto, Gates, Gauntlett, Gauntlett, Gauntlett, Gauntlett, Gibbons, Giddings, Grange, Graña, Graña, Graña, Graña, Graña, Graña, Graña, Green, Grey, Grimm, Grimm, Grisaru, Gukov, Gukov, Gurrieri, Gutowski, Gutowski, Gutowski, Haack, Halmagyi, Halmagyi, Haque, Harvey, Held, Hellerman, Hikida, Hitchin, Hitchin, Hitchin, Hitchin, Hitchin, Hohenegger, House, Howe, Hull, Hull, Hull, Hull, Jafferis, Kachru, Kapustin, Kapustin, Kapustin, Kashani-Poor, Kashani-Poor, Koerber, Koerber, Koerber, Koerber, Koerber, Koerber, Koerber, Koerber, Koerber, Koerber, Koerber, Kosmann-Schwarzbach, Larfors, Lindström, Lindström, Lindström, Lindström, Lopes Cardoso, Louis, Louis, Lüst, Lüst, Lüst, Lüst, Lüst, Maldacena, Martelli, Martelli, Martelli, Martucci, Martucci, Martucci, Martucci, McLean, Michelsohn, Micu, Minasian, Myers, Nilsson, Ooguri, Pacheco, Pestun, Petrini, Romans, Roček, Samtleben, Schwarz, Schwarz, Sevrin, Sevrin, Shelton, Shelton, Taylor, Tian, Tomasiello, Tomasiello, Tomasiello, Triendl, Uhlenbeck, Warner, Zabzine, Zabzine, Zucchini   +173 more
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Connected components of the space of flags of SO0(p,q)$\operatorname{SO}_0(p,q)$ transverse to a fixed pair and restrictions on Anosov subgroups

Journal of the London Mathematical Society, Volume 113, Issue 3, March 2026.
Abstract We count and give a parametrization of connected components in the space of flags transverse to a given transverse pair in every flag varieties of SO0(p,q)$\operatorname{SO}_0(p,q)$. We compute the effect the involution of the unipotent radical has on those components and, using methods of Dey–Greenberg–Riestenberg, we show that for certain ...
Clarence Kineider, Roméo Troubat
wiley   +1 more source

Supersymmetric D-branes on flux backgrounds

, 2007
Several aspects concerning the physics of D-branes in Type II flux compactifications preserving minimal N=1 supersymmetry in four dimensions are considered. It is shown how these vacua are completely characterized in terms of properly defined generalized
Aspinwall, Becker, Benmachiche, Gmeiner, Graña, Graña, Graña, Gualtieri, Gutowski, Gutowski, Harvey, Hitchin, Kapustin, Kapustin, Koerber, Koerber, Martucci, Martucci, Minasian   +18 more
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Entropy rigidity for cusped Hitchin representations

Journal of Topology, Volume 19, Issue 1, March 2026.
Abstract We establish an entropy rigidity theorem for Hitchin representations of geometrically finite Fuchsian groups which generalizes a theorem of Potrie and Sambarino for Hitchin representations of closed surface groups. In the process, we introduce the class of (1,1,2)‐hypertransverse groups and show for such a group that the Hausdorff dimension of
Richard Canary, Tengren Zhang, Andrew Zimmer   +2 more
wiley   +1 more source