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18th - 22nd of July 2022
The representation theory of a reductive group G defined over a p-adic field is at the forefront of modern algebra and number theory. One of the largest open problems in this area is to classify all smooth, irreducible representations of G, which is fundamental to the p-adic local Langlands programme. Good techniques for exploring this problem have been developed in characteristic 0, and more generally in any characteristic not equal to p, so we are particularly interested in studying representations of G in characteristic p - natural characteristic.
The aim of this workshop is to bring together a small group, consisting of experts in the field together with interested and less experienced researchers, to discuss the most recent developments and results, to assess what are currently the most important questions, and to propose new ideas for where to direct research. We will focus on exploring the category of smooth mod-p representations of G=GL(n, Q_p), or an appropriate subcategory, and try to develop or build on methods of understanding its categorical or homological properties.
Organiser: Adam Jones
This meeting is supported by a focused research grant from the Heilbronn Institute for Mathematical Research.
Programme
Programme
Monday 18th:
9:00am - 9:15am : Welcome.
9:15am - 9:30am: Adam Jones : Introduction.
9:30am - 10:45am : Rachel Ollivier : The restricted centre of the Iwahori-Hecke algebra.
10:45am - 11:15am : Coffee.
11:15pm - 12:30pm : Konstantin Ardakov : The centre of Mod(G).
12:30pm - 1:50pm : Lunch.
1:50pm - 3:20pm : Peter Schneider : The injective spectrum of a locally Noetherian Grothendieck category (part 1).
3:20pm - 3:45pm : Coffee.
3:45pm - 5pm: Sabin Cautis : Some remarks on Coulomb branches.
Tuesday 19th:
9:30am - 10:55am : Peter Schneider : The injective spectrum of a locally Noetherian Grothendieck category (part 2).
10:55am - 11:15am : Coffee.
11:15am - 12:30pm : Rachel Ollivier : The structure of the Iwahori-Hecke Ext algebra.
12:30pm - 2pm : Lunch.
2pm - 3:15pm : Konstantin Ardakov : The quotient space of Mod(SL_2(Q_p)).
3:15pm - 3:45pm : Coffee.
3:45pm - 5pm : Nicolas Dupré : Model categories and pro-p Iwahori-Hecke modules (part 1).
Wednesday 20th:
9:30am - 10:45am : Nicolas Dupré: Model categories and pro-p Iwahori-Hecke modules (part 2).
10:45am - 11:15am : Coffee.
11:15am - 12:30pm : Discussion 1.
12:30pm - 2pm : Lunch.
Free afternoon.
Thursday 21st:
9:30am - 10:45am : Claudius Heyer : Parabolic induction via the parabolic pro-p Iwahori--Hecke algebra.
10:45am - 11:15am : Coffee.
11:15am - 12:30pm : Discussion 2.
12:30pm - 2pm : Lunch.
2pm - 3:15pm : Discussion 3.
3:15pm - 3:45pm : Coffee.
3:45pm - 5pm : Informal Discussions.
7pm: Dinner.
Friday 22nd:
9:30am - 10:45am : James Timmins : The augmented Iwasawa algebra.
10:45am - 11:15am : Coffee.
11:15 am - 12:30pm : Claudius Heyer: The left adjoint of derived parabolic induction.
12:30pm - 2pm : Lunch.
2pm - 3:15pm : Discussion 4.
3:15pm - 3:45pm : Coffee.
3:45pm - 5pm: Informal Discussions.
Participants
Participants
Konstantin Ardakov (University of Oxford).
Sabin Cautis, (University of British Columbia).
Nicolas Dupré (University of Duisberg-Essen).
Claudius Heyer (University of Münster).
Adam Jones (University of Manchester).
Rachel Ollivier (University of British Columbia).
Peter Schneider (University of Münster).
James Taylor (University of Oxford).
Further Information
Further Information
This event will take place in the Andrew Wiles Building at the University of Oxford, located on the map of below. All talks and discussions will take place in classroom C1 in the basement of the Mezzanine.
The dinner will take place on Thursday the 21st of July at 7pm at Pierre Victoria, on Little Clarendon Street.
Group Photo
Group Photo
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