منابع مشابه
Topological recursion and mirror curves
We study the constant contributions to the free energies obtained through the topological recursion applied to the complex curves mirror to toric Calabi-Yau threefolds. We show that the recursion reproduces precisely the corresponding Gromov-Witten invariants, which can be encoded in powers of the MacMahon function. As a result, we extend the scope of the “remodeling conjecture” to the full fre...
متن کاملQuantum Curves and Topological Recursion
This is a survey article describing the relationship between quantum curves and topological recursion. A quantum curve is a Schrödinger operator-like noncommutative analogue of a plane curve which encodes (quantum) enumerative invariants in a new and interesting way. The Schrödinger operator annihilates a wave function which can be constructed using the WKB method, and conjecturally constructed...
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We study topological recursion on the irregular spectral curve xy2 − xy + 1 = 0, which produces a weighted count of dessins d’enfant. This analysis is then applied to topological recursion on the spectral curve xy2 = 1, which takes the place of the Airy curve x = y2 to describe asymptotic behaviour of enumerative problems associated to irregular spectral curves. In particular, we calculate all ...
متن کاملMirror Curves
BRIDGES Mathematical Connections in Art, Music, and Science Mirror curves are present in ethnical art, as Tamil threshold designs or Tchokwe sand drawings. Historically, they are to be found in the art of most peoples surrounding the Mediterranean, the Black and Caspian Seas, in the art of Egyptians, Greeks, Romans, Byzantines, Moors, Persians, Turks, Arabs, Syrians, Hebrews and African tribes....
متن کاملLectures on the Topological Recursion for Higgs Bundles and Quantum Curves
The paper aims at giving an introduction to the notion of quantum curves. The main purpose is to describe the new discovery of the relation between the following two disparate subjects: one is the topological recursion, that has its origin in random matrix theory and has been effectively applied to many enumerative geometry problems; and the other is the quantization of Hitchin spectral curves ...
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ژورنال
عنوان ژورنال: Advances in Theoretical and Mathematical Physics
سال: 2012
ISSN: 1095-0761,1095-0753
DOI: 10.4310/atmp.2012.v16.n5.a3