Speaker
Jan Stienstra
Description
A Zhegalkin polynomial in n variables is a polynomial function on {F_2}^n; here F_2={0,1} is the field with 2
elements.
The zebra with frequency vector v is the F_2 - valued function Z on the plane R^2 defined by the formula
Z(x) = floor(2v\cdot x) mod 2.
By inserting an n-tuple of zebras into an n-variable Zhegalkin polynomial one obtains an F_2 - valued function F on
R^2, which we call a Zhegalkin zebra function. The graph of such a function gives a partion of the plane into black
(i.e. F=1) and white (i.e. F=0) areas. This easily produces many beautiful pictures.
We will focus on examples for which the picture is a doubly periodic tiling of the plane by black and white convex
polygons.
These tilings have a very rich geometric structure (including so-called brane tilings or dimer models, Poisson
structures, Calabi-Yau manifolds).
We focus in particular on examples which reproduce the quantum-periods of the DelPezzo surfaces, and may therefore
be considered as mirrors of DelPezzo surfaces.
