Juan G. Escudero

Statement

"L´art est à l´opposé des idées générales, ne décrit que l´individuel, ne désire que l´unique. Il ne classe pas; il déclasse" (Art is opposite of general ideas; it describes only the individual, desires only what is unique. It does not classify; it declassifies) (Marcel Schwob, quoted by José Ángel Valente in "Diario anónimo") "Das Einzelne erweist sich immer wieder als unwichtig, aber die Möglichkeit jedes Einzelnen gibt uns einen Aufschluss über das Wesen der Welt" (Again and again the individual case turns out to be unimportant, but the possibility of each individual case discloses something about the essence of the world) (Ludwig Wittgenstein, Tractatus Logico-Philosophicus) "In theory there is no difference between theory and practice. In practice there is." (Berra, quoted by G.M. Greuel and G. Pfister in "A Singular Introduction to Commutative Algebra" )

Artworks

Folding polynomials of degree d with integer coefficients were used by S. Chmutov in 1991 to generate a family of complex algebraic surfaces with many nodes. For d=6,7,8,10 and 12, surfaces introduced by W. Barth, O. Labs, S. Endrass and A. Sarti, have a higher number of singularities. For d=3n, there is a family of surfaces S having also more singularities, which can be obtained by using certain bivariate polynomials Q with complex coefficients. As the folding polynomials, Q are related to the generalized cosine associated to the affine Weyl group of the root system A2. There are real variants of S with the same number of singularities which turn out to be real. (Hypersurfaces with many Aj-singularities: Explicit constructions. Journal of Computational and Applied Mathematics. http://dx.doi.org/10.1016/j.cam.2013.03.045).