Zurückliegende Veranstaltungen

Pentagramma Mirificum (the miraculous pentagram) is a beautiful geometric construction studied by Napier and Gauss. Its algebraic description yields the simplest instance of cluster transformations, a remarkable family of recurrences which arise in diverse mathematical contexts, from representation theory and enumerative combinatorics to theoretical physics and classical geometry (Euclidean, spherical, or hyperbolic).

Let X be an elliptic surface with a section defined over a number field. Specialization theorems by N\'eron and Silverman imply that the rank of the Mordell-Weil group of special fibers is at least equal to the MW rank of the generic fiber. We say that the rank jumps when the former is strictly large than the latter. In this talk, I will discuss rank jumps for elliptic surfaces fibred over the projective line. If the surface admits a conic bundle we show that the subset of the line for which the rank jumps is not thin in the sense of Serre. This is joint work with Dan Loughran. 

For every given integer m, Chebyshev's original interrogation is to investigate on the probability ("the bias") that given a random real number x, there are more prime numbers lower than x that are non-quadratic residues than that are quadratic residues modulo m.