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Counting conjectures and beyond


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18th May 2020 to 22nd May 2020
Britta Späth
Gabriel Navarro
Carolina Vallejo


**The activities of the GRA programme were disrupted by the global spread of coronavirus (COVID-19).  Further information about its resumption will be made available in due course. See this page for further details**


Workshop theme:

The fascinating survey on the representation theory of finite groups written by R. Brauer in 1963 starts in the following way: "It has been said by E. T. Bell that “wherever groups disclosed themselves or could be introduced, simplicity crystallized out of comparative chaos.” This may often be true, but, strangely enough, it does not apply to group theory itself, not even when we restrict ourselves to groups of finite order.” Much has been achieved since the publication of this survey, for example, the Classification of Finite Simple Groups was completed, but still we do not know, for instance, if the number of irreducible characters in a Brauer p-block is bounded by the size of its defect group. Stated as Problem 20 in Brauer’s survey, this is now known as the k(B)-conjecture. Also, we still do not know if a block with only height zero characters has an abelian defect group (that is, one implication of the height zero conjecture, Problem 23 in Brauer’s list, is still open).

The announcement of the McKay conjecture in 1971 is the origin of a different kind of counting conjectures of finite groups. These include several refinements of the McKay conjecture, the Alperin weight conjecture and the Dade-Robinson conjectures. In a few words, they assert that important information of a finite group, as the number of irreducible complex characters of degree not divisible by a given prime p, can be calculated locally, namely in a much smaller group with restricted normal structure. It is believed that an explanation for all these phenomena might involve derived categories (as in Broué’s conjecture), methods in algebraic topology and working over the field of p-adic numbers. In the meantime, all these conjectures (but not the k(B)-conjecture) have been reduced to questions on simple groups, in the hope that a better understanding of the representation theory of (quasi-)simple groups can provide proofs for them ultimately using the Classification of Finite Simple Groups. This has happened with the McKay conjecture for the prime p = 2. The purpose of this meeting is to gather relevant mathematicians working on counting conjectures and related global-local problems in  order to discuss the state of the art and the new developments in the area. In particular, this workshop will celebrate the great influence of Gunter Malle on those developments



  • Michel Broué
  • David Craven
  • Olivier Dudas
  • Charles Eaton
  • Niamh Farrell
  • Meinolf Geck
  • Eugenio Giannelli
  • Bob Guralnick
  • Gerhard Hiß
  • Radha Kessar
  • Alexander Kleshchev
  • Stacey Law
  • Michael Livesey
  • George Lusztig 
  • Noelia Rizo
  • Geoff Robinson
  • Raphaël Rouquier
  • Lucas Ruhstorfer
  • Benjamin Sambale
  • Mandi Schaeffer-Fry
  • Jay Taylor
  • Donna Testerman
  • Ulrich Thiel
  • Pham Huu Tiep


Deadline for applications: 16th February 2020

GRA programme participants DO NOT need to apply, programme participants with visit dates during GRAW04 will automatically be added to the attendee list.

Please note members of Cambridge University are welcome to turn up and sign in as a non-registered attendee on the day(s) during the workshop and attend the lecture(s). Please note that we cannot provide you with any support including name badge, meals or accommodation.

In addition to visiting the INI, there are multiple ways in which you can participate remotely.

Apply now


Registration Only    
  • Registration Package: £200
  • Student Registration Package: £150

The Registration Package includes admission to all seminars, lunches and refreshments on the days that lectures take place (Monday - Friday), wine reception and formal dinner, but does not include other meals or accommodation.

Formal Dinner Only
  • Formal Dinner: £50

Participants on the Accommodation Package or Registration Package, including organisers and speakers, are automatically included in this event. For all remaining participants who would like to attend, such as programme participants, the above charge will apply.


Unfortunately we do not have any accommodation to offer so all successful applicants will need to source their own accommodation.  Please see the Hotels Combined website for a list of local hotels and guesthouses.



Lunch timings and location will be confirmed with timetable.

Evening Meal

Participants are free to make their own arrangements for dinner.

Formal Dinner

The Formal Dinner location and date is to be confirmed. Participants on the Accommodation Package or Registration Package, including organisers and speakers, are automatically included in this event.

University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons