※ Zoom: ID 858 8649 9647 / PW 810093

    meeting information also available at https://researchseminars.org/seminar/ArithmeticMonday

I will begin by recalling the classical Cohen-Lenstra-Martinet heuristics on the statistical behaviour of class groups of number fields in families. I will then present joint work with Hendrik W. Lenstra Jr. in which we rephrase the heuristics in terms of Arakelov class groups of number fields, thereby explaining the otherwise somewhat mysterious looking probability weights in the original heuristics; but also disprove the heuristics in two different ways, and propose corrections.