294 research outputs found
Geometric transitions and SYZ mirror symmetry
We prove that the punctured generalized conifolds and punctured orbifolded
conifolds are mirror symmetric under the SYZ program with quantum corrections.
This mathematically confirms the gauge-theoretic prediction by
Aganagic-Karch-L\"ust-Miemiec, and also provides a supportive evidence to
Morrison's conjecture that geometric transitions are reversed under mirror
symmetry.Comment: v3: one compact example added. 25 pages, 12 figure
Local Calabi-Yau manifolds of type \tilde{A} via SYZ mirror symmetry
We carry out the SYZ program for the local Calabi--Yau manifolds of type
by developing an equivariant SYZ theory for the toric
Calabi--Yau manifolds of infinite-type. Mirror geometry is shown to be
expressed in terms of the Riemann theta functions and generating functions of
open Gromov--Witten invariants, whose modular properties are found and studied
in this article. Our work also provides a mathematical justification for a
mirror symmetry assertion of the physicists Hollowood--Iqbal--Vafa.Comment: v3: 43 pages, 12 figures, improved expositio
Mirror symmetry and rigid structures of generalized K3 surfaces
The present article is concerned with mirror symmetry for generalized K3
surfaces, with particular emphasis on complex and K\"ahler rigid structures.
Inspired by the works of Dolgachev, Aspinwall-Morrison and Huybrechts, we
introduce a formulation of mirror symmetry for generalized K3 surfaces. As an
application, we settle the long-standing problem of mirror symmetry for
singular K3 surfaces. Along the way, we investigate complex and K\"ahler rigid
structures of generalized K3 surfaces.Comment: restore some definitions, add some explanation
Analysis of the phenomenon of speculative trading in one of its basic manifestations: postage stamp bubbles
We document and analyze the empirical facts concerning one of the clearest
evidence of speculation in financial trading as observed in the postage
collection stamp market. We unravel some of the mechanisms of speculative
behavior which emphasize the role of fancy and collective behavior. In our
conclusion, we propose a classification of speculative markets based on two
parameters, namely the amplitude of the price peak and a second parameter that
measures its ``sharpness''. This study is offered to anchor modeling efforts to
realistic market constraints and observations.Comment: 9 pages, 5 figures and 2 tables, in press in Int. J. Mod. Phys.
What Orchestrates the Self-Assembly of Glycine Molecules on Cu(100)?
The structures of two competing phases and their interrelationship in the self-organization of glycine molecules on a Cu(100) surface were clarified. Despite their similar structural energies predicted using first-principles calculation, completely different mechanisms were found to stabilize the two phases. The balance and coordination of the two mechanisms that induce a variety of self-assembled structures in this attractive system were revealed. Furthermore, the importance of the microscopic arrangement of the molecules in designing the macroscopic electronic structures was directly demonstrated
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