Probabilistic methods in group theoryLecture

by Dr Alp Muyesser

Tuesday Nov 11, 2025, 11:30 AM → 12:15 PM Europe/Berlin

Endenicher Allee 60/1-016 - Lipschitzsaal (Mathezentrum)

Motivated by Euler's work on mutually orthogonal Latin squares, the Hall–Paige conjecture from 1955 asserts that a finite group admits a bijection φ: G → G such that the map g ↦ gφ(g) is bijective if and only if the product of all group elements is trivial in the abelianization. This conjecture was confirmed in a series of papers by Wilcox, Evans, and Bray in 2009, using the classification of finite simple groups. We present a strengthening of the Hall–Paige conjecture for large and generic subsets of groups. The resulting statement is quite flexible and can be used to settle several long-standing problems in combinatorial group theory. Our proof uses a mixture of probabilistic and algebraic methods and has spurred further developments. In this talk, we will give a broad overview of the area.