Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 14 (2018), 110, 29 pages      arXiv:1805.09627      https://doi.org/10.3842/SIGMA.2018.110
Contribution to the Special Issue on Modular Forms and String Theory in honor of Noriko Yui

Zhegalkin Zebra Motives Digital Recordings of Mirror Symmetry

Jan Stienstra
Department of Mathematics, Utrecht University, P.O. Box 80010, 3508 TA Utrecht, The Netherlands

Received May 10, 2018, in final form October 02, 2018; Published online October 13, 2018

Abstract
Zhegalkin zebra motives are tilings of the plane by black and white polygons representing certain ${\mathbb F}_2$-valued functions on ${\mathbb R}^2$. They exhibit a rich geometric structure and provide easy to draw insightful visualizations of many topics in the physics and mathematics literature. The present paper gives some pieces of a general theory and a few explicit examples. Many more examples will be shown in the forthcoming article ''Zhegalkin zebra motives: algebra and geometry in black and white''.

Key words: Zhegalkin polynomials; motives; dimer models; mirror symmetry.

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