| The Gaussian distribution is a central object in mathematics and it can be characterised as the unique probability on the real numbers that maximises entropy, for fixed mean and variance. It turns out that the same property can be used to define a discrete Gaussian distribution on the integers. Moreover, the discrete Gaussian is parametrised naturally by the Riemann theta function, and, as such, it has a natural connection to the theory of abelian varieties in algebraic geometry. The aim of the talk is to present this connection and to show how question in probability give rise to natural problems in algebraic geometry and viceversa. This is joint work with Carlos Amendola (TU Munich). |