1,561 research outputs found
Geometric Aspects of Mirror Symmetry (with SYZ for Rigid CY manifolds)
In this article we discuss the geometry of moduli spaces of (1) flat bundles
over special Lagrangian submanifolds and (2) deformed Hermitian-Yang-Mills
bundles over complex submanifolds in Calabi-Yau manifolds.
These moduli spaces reflect the geometry of the Calabi-Yau itself like a
mirror. Strominger, Yau and Zaslow conjecture that the mirror Calabi-Yau
manifold is such a moduli space and they argue that the mirror symmetry duality
is a Fourier-Mukai transformation. We review various aspects of the mirror
symmetry conjecture and discuss a geometric approach in proving it.
The existence of rigid Calabi-Yau manifolds poses a serious challenge to the
conjecture. The proposed mirror partners for them are higher dimensional
generalized Calabi-Yau manifolds. For example, the mirror partner for a certain
K3 surface is a cubic fourfold and its Fano variety of lines is birational to
the Hilbert scheme of two points on the K3. This hyperkahler manifold can be
interpreted as the SYZ mirror of the K3 by considering singular special
Lagrangian tori.
We also compare the geometries between a CY and its associated generalized
CY. In particular we present a new construction of Lagrangian submanifolds.Comment: To appear in the proceedings of International Congress of Chinese
Mathematicians 2001, 47 page
Efficient Generation of Stable Planar Cages for Chemistry
In this paper we describe an algorithm which generates all colored planar
maps with a good minimum sparsity from simple motifs and rules to connect them.
An implementation of this algorithm is available and is used by chemists who
want to quickly generate all sound molecules they can obtain by mixing some
basic components.Comment: 17 pages, 7 figures. Accepted at the 14th International Symposium on
Experimental Algorithms (SEA 2015
The Crescent Student Newspaper, February 24, 1995
Student newspaper of George Fox College (later George Fox University). 8 pages, black and white.https://digitalcommons.georgefox.edu/the_crescent/2130/thumbnail.jp
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