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.





    • 9:00 AM 9:10 AM
      Hello 10m

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

    • 9:15 AM 10:15 AM
      Cheryl Praeger: Big questions of finite permutation groups – some answered, others open 1h
    • 10:30 AM 11:00 AM
      Tea and coffee break 30m
    • 11:00 AM 11:15 AM
      Kamilla Rekvenyi: Orbital Diameter of Primitive Permutation Groups 15m
    • 11:25 AM 12:25 PM
      Getting to know each other 1h
    • 12:30 PM 3:00 PM
      Lunch break 2h 30m
    • 3:00 PM 4:00 PM
      Melissa Lee: Primitive permutation groups: more problems and open questions 1h
    • 4:00 PM 4:15 PM
      Hongyi Huang: Base-two primitive permutation groups 15m
    • 4:30 PM 5:00 PM
      Tea and coffee break 30m

      Cofee break

    • 5:00 PM 5:15 PM
      Emily Hall: Almost elusive groups 15m
    • 5:35 PM 5:50 PM
      Saul Freedman: The intersection graph of a finite simple group 15m
    • 6:20 PM 7:00 PM
      Rebecca Waldecker: Permutation groups acting under constraints 40m
    • 7:00 PM 8:00 PM
      Dinner break 1h
    • 9:00 AM 9:50 AM
      Donna Testerman: Linear groups seen from different angles 50m
    • 10:00 AM 10:40 AM
      Aluna Rizzoli 40m
    • 10:45 AM 11:15 AM
      Tea and coffee break 30m
    • 11:15 AM 12:05 PM
      Colva Roney-Dougal 50m
    • 12:15 PM 12:30 PM
      Eileen Pan: Finite groups of Lie type 15m
    • 12:30 PM 5:00 PM
      Lunch break 4h 30m

      ...and the early afternoon is off!

    • 5:00 PM 5:20 PM
      Meet for tea and coffee 20m
    • 5:30 PM 6:10 PM
      Veronica Kelsey: A survey of base size and other numerical invariants 40m
    • 6:20 PM 6:35 PM
      Luca di Gravina: Möbius function of finite classical groups 15m
    • 6:45 PM 7:00 PM
      David Szabo: Finite subgroups of transformation groups 15m

      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 8:30 PM
      Dinner break 1h
    • 9:00 AM 10:00 AM
      Inna Capdeboscq 1h
    • 10:10 AM 10:50 AM
      Gareth Tracey: The Goldschmidt-Sims conjecture 40m

      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 11:20 AM
      Tea and coffee break 20m
    • 11:20 AM 12:20 PM
      Mandi Schaeffer-Fry: Conjecture-Cracking with the Classification: Some Applications, New and Old, of the CFSG 1h
    • 12:30 PM 3:00 PM
      Lunch break 2h 30m
    • 3:00 PM 3:40 PM
      Noelia Rizo 40m
    • 3:50 PM 4:05 PM
      Virgilius-Aurelian Minuță: Group graded algebras over G-graded G-algebras 15m
    • 4:15 PM 4:45 PM
      Tea and coffee break 30m
    • 4:45 PM 5:00 PM
      Margherita Piccolo: Representation growth of semisimple profinite groups 15m
    • 5:10 PM 5:25 PM
      Sesuai "Yash" Madanha: Average number of zeros of characters of finite groups 15m
    • 7:00 PM 8:00 PM
      Dinner break 1h
    • 8:00 PM 8:15 PM
      SP Madireddi: The Foulkes module 15m
    • 8:25 PM 8:55 PM
      Teaser and poster, open end! 30m

      2 minutes teaser for a poster.

      Koushik Paul: Construction of Specht modules

    • 9:00 AM 10:00 AM
      Alice Niemeyer 1h
    • 10:10 AM 10:25 AM
      Daniel Rademacher: Constructive recognition of classical groups 15m
    • 10:30 AM 11:00 AM
      Tea and coffee break 30m
    • 11:00 AM 11:40 AM
      Rebecca Waldecker: Backtrack methods and canonical images 40m
    • 11:50 AM 12:05 PM
      Farzaneh Gholaminezhad: The G-graph of the Gyrogroups 15m
    • 12:15 PM 3:00 PM
      Lunch break 2h 45m
    • 3:00 PM 3:15 PM
      Friedrich Rober: Wreath Product Decompositions 15m
    • 3:25 PM 4:25 PM
      Mun See Chang: Overview 1h
    • 4:30 PM 5:00 PM
      Tea and coffee break 30m
    • 5:00 PM 5:20 PM
      Anna Sucker + Lucas Wollenhaupt: Computing the alternating and symmetric square representations of classical groups 20m
    • 5:30 PM 5:45 PM
      Laura Voggesberger: On algebraic groups, their Lie algebras, and nilpotent pieces 15m
    • 6:00 PM 6:15 PM
      John McHugh: On the image of the trivial source ring in the ring of virtual characters of a finite group 15m
    • 7:00 PM 8:00 PM
      Dinner 1h
    • 9:00 AM 9:45 AM
    • 9:55 AM 10:40 AM
      Scott Harper. The generating graph: spread and domination 45m

      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 11:10 AM
      Tea and coffee break 30m
    • 11:10 AM 12:00 PM
      Colva Roney-Dougal 50m
    • 12:15 PM 12:30 PM
      Short feedback round 15m

      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 1:30 PM
      Lunch break and departure 1h