Young Group theorists workshop: exploring new connections



Hotel Les Sources Chemin du Vernex 9 1865 Les Diablerets Switzerland
Donna Testerman (EPFL), Maroussia Schaffnerportillo (EPFL), Rebecca Waldecker (Martin-Luther-Universitat Halle-Wittenberg)

This workshop is aimed at early stage researchers and will focus on several aspects of modern group theory and group actions. Each day will be dedicated to a specific topic; the themes and main speakers for each day are:

  • Permutation groups: Cheryl Praeger (UWA Perth) and  Rebecca Waldecker (Halle)
  • Linear groups and maximal subgroups: Colva Roney-Dougal (St Andrews) and Donna Testerman (EPFL)
  • Computational methods in group theory: Alice Niemeyer (Aachen) and Rebecca Waldecker (Halle)
  • The Classification of the Finite Simple Groups and some applications: Inna Capdeboscq (Warwick) and Mandi Schaeffer-Fry (MSU Denver) 
  • Generation of finite groups: Eilidh McKemmie (Rutgers) and Colva Roney-Dougal (St Andrews)

The program will include further short talks by invited participants.

This is planned as an in-person workshop, and the deadline for applications to participate is 20th May.





    • 1

      We welcome you all, give some information for the week and thank our sponsors.

    • 2
      Cheryl Praeger: Big questions of finite permutation groups – some answered, others open
    • 10:30 AM
      Tea and coffee break
    • 3
      Kamilla Rekvenyi: Orbital Diameter of Primitive Permutation Groups
    • 4
      Getting to know each other
    • 12:30 PM
      Lunch break
    • 5
      Melissa Lee: Primitive permutation groups: more problems and open questions
    • 6
      Hongyi Huang: Base-two primitive permutation groups
    • 4:30 PM
      Tea and coffee break

      Cofee break

    • 7
      Emily Hall: Almost elusive groups
    • 8
      Saul Freedman: The intersection graph of a finite simple group
    • 9
      Rebecca Waldecker: Permutation groups acting under constraints
    • 7:00 PM
      Dinner break
    • 10
      Donna Testerman: Linear groups seen from different angles
    • 11
      Aluna Rizzoli
    • 10:45 AM
      Tea and coffee break
    • 12
      Colva Roney-Dougal
    • 13
      Eileen Pan: Finite groups of Lie type
    • 12:30 PM
      Lunch break

      ...and the early afternoon is off!

    • 5:00 PM
      Meet for tea and coffee
    • 14
      Veronica Kelsey: A survey of base size and other numerical invariants
    • 15
      Luca di Gravina: Möbius function of finite classical groups
    • 16
      David Szabo: Finite subgroups of transformation groups

      C. Jordan proved in 1877 that every finite subgroup of $\mathrm{GL}_n(\mathbb{C})$ has a normal abelian subgroup of index bounded by a function of $n$ -- in short, these finite subgroups are almost' abelian. It is natural to investigate whether an analogous statement holds for the finite subgroups of natural transformation groups like the birational automorphism group of an algebraic variety, or the diffeomorphism group of a compact manifold. Recent developments on the topic by A. Guld (2020) and Pyber--Csikós--E. Szabó (2022) gave a positive answer whenabelian' is replaced by nilpotent of class at most $2$', and bynilpotent' in the respective cases.
      We will briefly discuss why the nilpotency class has to be at least $2$ in both cases focusing on the common purely group theoretic ideas.

    • 7:30 PM
      Dinner break
    • 17
      Inna Capdeboscq
    • 18
      Gareth Tracey: The Goldschmidt-Sims conjecture

      The Classification of Finite Simple Groups has led to substantial progress on deriving sharp order bounds in various natural families of finite groups. One of the most well-known instances of this is Sims' conjecture, which states that the order of a point stabiliser in a primitive permutation group has order bounded in terms of its smallest non-trivial orbit length (this was proved by Cameron, Praeger, Saxl and Seitz using the CFSG in 1983). In the meantime, Goldschmidt observed that a generalised version of Sims' conjecture, which we now call the \emph{Goldschmidt--Sims conjecture}, would lead to important applications in graph theory. In this talk, we will describe the conjecture, and discuss some recent progress. Joint work with L. Pyber.

    • 11:00 AM
      Tea and coffee break
    • 19
      Mandi Schaeffer-Fry: Conjecture-Cracking with the Classification: Some Applications, New and Old, of the CFSG
    • 12:30 PM
      Lunch break
    • 20
      Noelia Rizo
    • 21
      Virgilius-Aurelian Minuță: Group graded algebras over G-graded G-algebras
    • 4:15 PM
      Tea and coffee break
    • 22
      Margherita Piccolo: Representation growth of semisimple profinite groups
    • 23
      Sesuai "Yash" Madanha: Average number of zeros of characters of finite groups
    • 7:00 PM
      Dinner break
    • 24
      SP Madireddi: The Foulkes module
    • 25
      Teaser and poster, open end!

      2 minutes teaser for a poster.

      Koushik Paul: Construction of Specht modules

    • 26
      Alice Niemeyer
    • 27
      Daniel Rademacher: Constructive recognition of classical groups
    • 10:30 AM
      Tea and coffee break
    • 28
      Rebecca Waldecker: Backtrack methods and canonical images
    • 29
      Farzaneh Gholaminezhad: The G-graph of the Gyrogroups
    • 12:15 PM
      Lunch break
    • 30
      Friedrich Rober: Wreath Product Decompositions
    • 31
      Mun See Chang: Overview
    • 4:30 PM
      Tea and coffee break
    • 32
      Anna Sucker + Lucas Wollenhaupt: Computing the alternating and symmetric square representations of classical groups
    • 33
      Laura Voggesberger: On algebraic groups, their Lie algebras, and nilpotent pieces
    • 34
      John McHugh: On the image of the trivial source ring in the ring of virtual characters of a finite group
    • 7:00 PM
    • 35
    • 36
      Scott Harper. The generating graph: spread and domination

      The generating graph of a group has as vertices the nontrivial elements of the group and two vertices are adjacent if the elements generate the group. I will discuss the recent classification of the finite groups whose generating graph is connected (joint with Burness and Guralnick) and related work on surprisingly small total dominating sets for generating graphs of simple groups (joint with Burness). Time permitting, I will discuss related ideas for infinite simple groups.

    • 10:40 AM
      Tea and coffee break
    • 37
      Colva Roney-Dougal
    • 38
      Short feedback round

      How was the workshop for you?
      What did you enjoy, what would you like more of in future workshops?
      What did you not like so much?

    • 12:30 PM
      Lunch break and departure