GGI 2026: Week 4 (20th July-24th July)

Workshop 3: AGGITatE 2026

The second GGI workshop, “AGGITatE 2026”, will run 22nd-24th July. Please, check the workshop’s website.

Seminars

Because of the workshop, we will only run the daily seminars on Monday and Tuesday.
Seminars take place in EBS.2.66 from 11am. Tea and cakes will be served in the same room from 10.30am.

Monday 20th July

Speaker: Bernhard Mühlherr (Justus Liebig University Giessen)
Title: Generalized Root Systems
Abstract: Generalized root systems (GRS) were introduced by Dimitrov and Fioresi in 2024. In their paper they observed that many results for classical root systems (CRS) can proved for GRS by essentially the same arguments. They managed to classify all irreducible GRS of rank 2 up to equivalence and they observe that any GRS of rank 2 is equivalent to a quotient of a CRS. Based on this observation they conjectured that each irreducible GRS of rank at least 2 is equivalent to a quotient of a GRS.
In joint work with Cuntz we confirmed this conjecture. Our proof is based on the classification of Weyl groupoids due to Cuntz and Heckenberger. In my talk I will outline the basic theory of GRS and the main ideas of our proof of this conjecture.

Tuesday 21st July

Speaker: Joel Summerfield (University of Birmingham)
Title: Lusztig–Spaltenstein Induction of Non-Nilpotent Orbits
Abstract: The Lusztig–Spaltenstein induction of nilpotent orbits is already well-studied for connected reductive algebraic groups (over algebraically closed fields). However, Spaltenstein demonstrated that we need not be limited to considering only nilpotent orbits. In this talk, we will expand upon Spaltenstein’s work and establish that many of the known properties of nilpotent Lusztig–Spaltenstein induction still hold for arbitrary adjoint orbits in all characteristics. In particular, using an outline provided by Spaltenstein, we prove that the induced orbit is independent of the choice of parabolic used in its construction.

Social activities

Tea and cakes will be served from 3pm on Monday and Tuesday in 4SW.6.18.
On Wednesday afternoon, we will have a tour of Colchester Castle, a Norman castle who was built under orders of William the Conqueror over the ruins of a Roman Temple.

Participants

  • Michael Bate
  • Dominic Bunnett
  • Elena Denisova
  • Shuo Feng
  • Joshua Jackson
  • Kanwal Khalid
  • Lufeng Li
  • Alastair Litterick
  • Runqi Liu
  • Benjamin Martin
  • Jesus Martinez-Garcia
  • Bernhard Muehlherr
  • Eileen Pan
  • Rachel Pengelly
  • David Penman
  • Cheryl Praeger
  • Aluna Rizzoli
  • Gerhard Roehrle
  • Charlotte Satchwell
  • Harvey Sykes
  • Adam Thomas
  • Gerald Williams
  • Billy Woods