Special Lagrangian fibrations, wall-crossing, and mirror symmetry [PDF]
arXiv, 2009 In this survey paper, we briefly review various aspects of the SYZ approach to mirror symmetry for non-Calabi-Yau varieties, focusing in particular on Lagrangian fibrations and wall-crossing phenomena in Floer homology. Various examples are presented, some of them new.
arxiv
Optimal geometry for a quartz multipurpose SPM sensor
Beilstein Journal of Nanotechnology, 2013 We propose a geometry for a piezoelectric SPM sensor that can be used for combined AFM/LFM/STM. The sensor utilises symmetry to provide a lateral mode without the need to excite torsional modes.
Julian Stirling
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Optimization of Conformal Mapping Functions used in Developing Closed-Form Solutions for Underground Structures with Conventional cross Sections [PDF]
International Journal of Mining and Geo-Engineering, 2015 Elastic solutions applicable to single underground openings usually suffer from geometry related simplification. Most tunnel shapes possess two axes of symmetry while a wide range of geometries used in tunneling practice involve only one symmetry axis. D-
Ali Nazem +3 more
doaj
Book Review: Mirror symmetry and algebraic geometry [PDF]
, 2000 Victor V. Batyrev
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The geometry of algebra: a twofold way for the rebirth of a symmetry [PDF]
, 2001 G. Bandelloni, S. Lazzarini
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On Symmetries of Finite Geometries
The isospectral set of the Dirac matrix D=d+d* consists of orthogonal Q for which Q* D Q is an equivalent Dirac matrix. It can serve as the symmetry of a finite geometry G. The symmetry is a subset of the orthogonal group or unitary group and isospectral Lax deformations produce commuting flows d/dt D=[B(g(D)),D] on this symmetry space.
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The three obdurate conjectures of differential geometry [PDF]
arXivWe explore the role of symmetry in three obdurate conjectures of differential geometry: the Carath\'eodory, the Willmore and the Lawson Conjectures.
arxiv
SPONTANEOUS SYMMETRY BROKEN CONDITION IN (DE)CONSTRUCTING DIMENSIONS FROM NONCOMMUTATIVE GEOMETRY [PDF]
, 2002 Jian S. Dai, Xing-Chang Song
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Non-Noether symmetries and their influence on phase space geometry [PDF]
, 2003 George Chavchanidze
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Homological mirror symmetry, deformation quantization and noncommutative geometry [PDF]
, 2004 Paul Bressler, Yan Soibelman
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