Organisers: Prof. Dr. Gunter Malle, Jun.-Prof. Dr. Caroline Lassueur, Dr. Edoardo Salati

Room: 48-436

• Thursday the 11^th of December, 2025
  • 17:00-17:50:  Juan Martínez Madrid [Universitat de València]
  • Title: The picky and subnormalizer conjectures
  • Abstract

• Thursday the 22^nd of January, 2026
  • 17:00-17:50:  Eoghan McDowell [University of Bristol]
  • Title: Zeros of characters of symmetric and alternating groups
  • Abstract: I will discuss some results on zeros of characters of symmetric and alternating groups. Interest in zeros of characters stretches back to Burnside's classical result that every non-linear character has a zero, and persists to this day in open problems such as Moretó--Rizo's proposed generalisation of the McKay conjecture. Zeros of characters of the symmetric group are connected to the hook structure of partitions via the Murnaghan--Nakayama rule; a result of Belonogov shows that a character of the symmetric group is uniquely determined (up to multiplication by sign) by its zero values. I will present joint work with Giannelli and Law in which we prove that the zero values on just the Sylow subgroups suffices to determine the degree of a character of the symmetric group (and a best possible analogue for the alternating group).

• Thursday the 29^th of January, 2026
  • 15:00-16:00:  Jason Semeraro [Loughborough University]
  • Title: Classifying fusion systems and applications
  • Abstract: The occurrence of anomalous objects in group theory and topology, such as sporadic simple groups or exotic loop spaces is often best understood by analysing associated fusion systems at a prime p. A fusion system is a particular category of subgroups of a finite p-group whose morphisms satisfy some weak axioms motivated by Sylow's theorem. Classifying all simple fusion systems on a p-group thus places limitations on the exotic behavior that can occur. This can be done by hand for infinite families of p-groups or else automatically for small groups using programs I wrote jointly with Chris Parker. I will discuss the methods used, present some results and conclude with some applications to block theory.