Chebyshev Varieties

Chebyshev varieties are algebraic varieties parametrized by Chebyshev polynomials. They arise naturally when solving polynomial equations expressed in the Chebyshev basis. More precisely, when passing from monomials to Chebyshev polynomials, Chebyshev varieties replace toric varieties. I will introduce these objects, discuss their defining equations and present key properties. Via examples, I will motivate their use in practical computations. This is joint work with Zaïneb Bel-Afia and Chiara Meroni.