Index

• Speakers and organisers
• Registration
• Logistics
• Schedule
• Titles and abstracts
• About the AGGITatE series

Plenary speakers

• Dave Benson (Aberdeen)
• Karin Erdmann (Oxford)
• Eugenio Giannelli (Florence)
• John Greenlees (Warwick)
• Ellen Henke (TU Dresden)
• Radha Kessar (Manchester)
• Stacey Law (Birmingham)
• Markus Linckelmann (London City)
• Gunter Malle (RPTU Kaiserslautern)
• Lucas Ruhstorfer (Wuppertal)
• Jason Semeraro (Loughborough)
• Carolina Vallejo Rodriguez (Florence)

Contributed talks speakers

• Valentina Grazian (Padua)
• Adam Jones (Cambridge)
• Eoghan McDowell (Bristol)
• Marco Pradeiro Bova (TU Dresden)
• Jialin Wang (City St George’s, University of London)

Organisers

• Alastair Litterick (Essex)
• Jesus Martinez-Garcia (Essex)
• Harvey Sykes (Essex)
• Jay Taylor (Manchester)

Registration

Please, fill in the registration form if you want to attend. You must register by 30th June and if you want to be considered for funding you must register by 31st May.

There will be a registration fee of around £40 for all participants, to be paid after we confirm your attendance (to be paid later on in June).

Logistics

Arrival date is Sunday 3rd August. The Conference will start on Monday 4th August in the morning and finish at about 3.00pm on 7th August. We have 12 single ensuite rooms with shared kitchen facilities, booked for 4 nights (Arrival Sunday 3^rd, checking out Thursday 7^th August). These are prioritised for early-career UK-based participants due to funder’s conditions. If you want to be considered for accommodation, please clearly indicate it in the form.

Transportation: The University of Essex is based in Colchester. Find here a map of the university of Essex. Please, consult the university’s website on how to reach Colchester Campus. The closest railway station is Colchester Hythe, but Colchester North (AKA as Colchester, which is different from Colchester Town) is the one with the best connections. If you use buses, please be aware they can be unreliable, so leave extra time when using them. The closest airport is Stansted and it is best connected to Colchester by bus. Travelling from Gatwick or Stansted by train is not too long (2-3 hours). The cost of a taxi within Colchester is usually £10-15. There are a number of companies (google ‘Colchester taxi’ for a list) that operate independently from each other and the best way to arrange a taxi is to call them directly. It is very difficult to book a taxi at around school ‘rush hour’ or early in the morning, unless arranged in advance.

Wednesday afternoon: we will not have scheduled lectures. However, we have a couple of activities that you can take part on: a visit of Colchester (the oldest recorded town in the United Kingdom, founded by the Romans) or a Disc Golf game. The University of Essex is the home of the first Disc Golf course in England and the eighth oldest in the world. It has been recently redesigned.

Meals: We will have a conference dinner on Tuesday and probably a barbeque on Wednesday. We are also looking into providing lunch Monday-Thursday.

Rooms: We have booked rooms NTC 2.05 and NTC 2.06 for the conference.

Accommodation: If your accommodation is paid by the organisers, we will be in touch with details.
If you are self-funded, the following are good options for accommodation in Colchester. All are in the route of buses 62 and 62B which take you directly to Campus in about 20 minutes. You can also walk to campus in 40-60 minutes, depending on the hotel.

• Wivenhoe House Hotel. The university hotel on campus, which is 5 minutes from the main buildings on campus and 30 minutes by bus from the city centre.
• Best Western Rose and Crown Hotel in Colchester.
• St Nicholas Hotel
• Brook Red Lion
• North Hill Hotel
• Globe Hotel

Queries: Please contact essexaggitate AT gmail DOT com

Schedule

	Monday 4th	Tuesday 5th	Wednesday 6th	Thursday 7th
09:30	Welcome and registration	Main Speaker 3	Main Speaker 7	Main Speaker 10
10:00	Main Speaker 1
10:30		Tea break	Tea break	Tea break
11:00	Tea break	Main Speaker 4	Main Speaker 8	Main Speaker 11
11:30	Main Speaker 2
12:00		Lunch	Lunch	Lunch
12:30	Lunch
13:00
13:30		Main Speaker 5	Main Speaker 9	Main Speaker 12
14:00	Contributed Talk 1
14:30	Contributed Talk 2	Tea break	Activity (Disc Golf / Tour)
15:00	Tea break	Main Speaker 6
15:30	Contributed Talk 3
16:00	Contributed Talk 4	Contributed Talk 5
16:30		Contributed Talk 6
EVENING		Dinner (7pm)	Barbecue  (6:30pm)

Main talks details

• Eugenio Giannelli: “McKay bijections and character degrees”.
  Abstract: The McKay conjecture has been a central question in the representation theory of finite groups for over 60 years. A full proof was very recently achieved through thework of Cabanes and Spaeth. In this talk, I will explore new open problems that arise in connection with the conjecture and present recent results concerning the class of symmetric groups.
  
• Carolina Vallejo Rodriguez: “On the properties of conductors of characters of degree prime to p”.
  Abstract: For an irreducible character of a finite group, the conductor is the smallest positive integer such that all of its values lie in the corresponding cyclotomic field. In this talk, I will discuss some interesting features of the p-part of character conductors, specifically for characters whose degree is prime to p.
  
  This talk is based on joint work with G. Malle and J. M. Martínez

Contributed talks details

• Valentina Grazian: “The ongoing quest for exotic fusion systems”
  Abstract: Saturated fusion systems are structures that encode the properties of conjugation between p-subgroups of a group, for p any prime number. For example, it is always possible to define the saturated fusion system realized by a finite group G on one of its Sylow p-subgroups S: this is the category where the objects are the subgroups of S and the morphisms are the restrictions of conjugation maps induced by the elements of G. An active research direction in the theory of fusion systems consists in the understanding of the ones that are not realized by a finite group, called exotic, especially for odd primes (this question was suggested by Oliver in [1]). Many of the known examples of exotic fusion systems are now captured by two key theorems: The classification of fusion systems on p-groups having a maximal subgroup that is abelian ([2],[5],[6]) and the classification of fusion systems on p-groups of maximal nilpotency class ([3]). The next step consists in generalizing these two theorems in order to frame more exotic fusion systems into unified contexts. In this talk we will present recent results in this direction and a new family of exotic fusion systems (described in the preprint [4]). This is a joint work with J. Lynd, B. Oliver, C. Parker, J. Semeraro and M. van Beek.
  
  References:
  [1] M. Aschbacher; R. Kessar; B. Oliver, Fusion systems in algebra and topology, London Math. Soc. Lecture Note Ser., 391 Cambridge University Press, Cambridge (2011). vi+320 pp.
  [2] D. Craven; B. Oliver; J. Semeraro, Reduced fusion systems over p-groups with abelian subgroup of index p: II, Adv. Math. 322 (2017), 201–268.
  [3] V. Grazian; C. Parker, Saturated Fusion Systems on p-Groups of Maximal Class, Mem. Amer. Math. Soc. 307 (2025), no. 1549, v+115 pp.
  [4] V. Grazian; C. Parker; J. Semeraro; M. van Beek, Fusion systems related to polynomial representations of SL₂(q), arXiv preprint: 2502.20873 (2025).
  [5] B. Oliver, Simple fusion systems over p-groups with abelian subgroup of index p: I, J. Algebra 398 (2014), 527–541.
  [6] B. Oliver; A. Ruiz, Reduced fusion systems over p-groups with abelian subgroup of index p: III, Proc. Roy. Soc. Edinburgh Sect. A 150 (2020), no. 3, 1187–1239.
  
• Marco Praderio Bova: “Fusion systems and homotopy theory”
  Abstract: During this talk we will start by briefly review the concepts of fusion systems and localities. We will then use the latter to provide a connection between fusion systems and homotopy theory, we will then use this relation tointroduce what is known as the “sharpness conjecture for fusion sysytems”. After reviewing what is known regarding this conjecture we will conclude by presenting the results developed in collaboration with G. Carrión Castillo and wich will allow us to prove the conjecture for a variety of different exotic fusion systems related to sporadic simple groups.
  
• Jialin Wang: “On the solvability of the Lie algebra HH^1(B) for blocks of finite groups.”
  Abstract: We give some criteria for the Lie algebra of first degree Hochschild cohomology of the twisted group algebra, i.e. HH^1(k_\alpha(P ⋊ E)), to be solvable, where P is a finite abelian p-group, E is an abelian p′-subgroup of Aut(P) and α ∈ Z^2(E; k^×) inflated to P ⋊ E via the canonical surjection P ⋊ E → E. As a special case, this gives the criterion to the solvability of the Lie algebra HH^1(B) where B is a p-block of a finite group algebra with abelian defect P and inertial quotient E.
  

About the AGGITatE series

The first AGGITatE conference was to take place in 2020 but was delayed to 2022 due to the CoViD panemic and, back then it stood for “Algebraic Groups and Geometric Invariant Theory at Essex” as a way to bring together researchers working in algebraic groups and algebraic geometry. The second AGGITatE took place in 2023, focused in algebraic groups and the Cremona group. The third AGGITatE (2024) was focused on moduli theory of varieties. The fifth edition of AGGITatE (2026) will be part of a one-month INI Satellite Programme.