**Abstract:** In linear algebra we often solve a linear equation $\sum_{i=1}^n a_ix_i$ by giving a parametrization, for example $x_n = -\sum_{i=1}^{n-1}\frac{a_i}{a_n}x_i$ if $a_n \not=0$. Similarly one would like to solve algebraic equations, for example $x^3+y^3+z^3+xyz = 0$ by giving a parametrization of the form$z = polynomial(x,y)$. Unfortunately this is often impossible. A more modest question would be to ask wether a parametrization ispossible for a given equation and if so find one. Even this question is a surprisingly difficult problem leading to a lot of nice geometry. In this talk I will present classical and modern results as well as open questions on this topic.

Jan 20, 2014 | 04:15 PM

SR 119, Arnimallee 3