Mathematics

The preimage of the unit circle under a rational map from the Riemann sphere to itself is called a lemniscate. Lemniscates appear in many branches of mathematics (from potential theory to algebraic geometry) and have been widely investigated. If we plot a "typical" lemniscate (for example sampling the coefficients of the polynomials defining the rational function from some Gaussian distribution) we see beautiful and mysterious pictures appearing (see for example http://people.sissa.it/~lerario/Antonio_Lerario/Random_curves.html).
In this talk I will discuss a probabilistic approach to the study of these curves, presenting also a soft introduction to the methods of random algebraic geometry.