School of Mathematics & Physics, University of Lincoln
On 7th of February 2019 Dr Alex Bartel (University of Glasgow) visited the Charlotte Scott Centre for Algebra in Lincoln and gave a talk “What does a random finitely generated abelian group look like?”.
Abstract: “Often, in different branches of mathematics, if an algebraic object is somehow drawn “at random”, then the probability that it is isomorphic to a given object A is proportional to 1/#Aut(A). In this talk I will report on joint work with Hendrik Lenstra, in which we explain that this heuristic can even be made precise in a canonical way in certain situations in which #Aut(A) is infinite. Although the work is purely algebraic, the need for it arose in a number theoretic situation, namely in our attempt to shed more light on the Cohen-Lenstra heuristics concerning ideal class groups of number fields.”