منابع مشابه
Mirror-curve Codes for Knots and Links
Inspired by Lomonaco–Kauffman paper on quantum knots and knot mosaics we construct the more concise representation of knot mosaics and grid diagrams via mirror-curves. We introduce codes for mirror-curves treated as knot or link diagrams placed in rectangular square grid, suitable for software implementations and discuss possible applications of mirror-curves.
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 کاملTopological 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 کاملMirror Symmetry and Elliptic Curves
I review how recent results in quantum eld theory con-rm two general predictions of the mirror symmetry program in the special case of elliptic curves: (1) counting functions of holomorphic curves on a Calabi-Yau space (Gromov-Witten invariants) arèquasi-modular forms' for the mirror family; (2) they can be computed by a summation over trivalent Feynman graphs.
متن کاملLectures on Knot Homology and Quantum Curves
Besides offering a friendly introduction to knot homologies and quantum curves, the goal of these lectures is to review some of the concrete predictions that follow from the physical interpretation of knot homologies. In particular, it allows one to answer questions like Is there a direct relation between Khovanov homology and the A-polynomial of a knot? which would not have been asked otherwis...
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ژورنال
عنوان ژورنال: Computers & Mathematics with Applications
سال: 2012
ISSN: 0898-1221
DOI: 10.1016/j.camwa.2011.12.042