Program

17-21 April 2023

The mini-course will take place at building S8, campus Sterre. 

Rooms: 

• coffee breaks, lunch and reception: Vergaderzaal 3.1

• classroom Monday: Leslokaal 3.2

• classroom Tuesday, Wednesday and Thursday: Leslokaal 1.4 

• classroom Friday: Leslokaal 3.1

Special events

• Small reception Monday

• City excursion and visit to Vooruit Thursday

Tuesday April 18

Stefan Dawydiak 

Towards a coherent categorification of the based ring of the lowest two-sided cell

In the 1980s, Kazhdan-Lusztig and independently Ginzburg showed that the affine Hecke algebra H can be realized as the Grothendieck group of the category of coherent sheaves on the Steinberg variety. The correct coherent Hecke category was however found only later, by Bezrukavnikov. A crucial ingredient in this coherent categorification of H is viewing the Steinberg variety as a derived scheme. 

On the other hand, Lusztig's asymptotic Hecke algebra J is a certain based ring receiving a map from H via which its representation theory is closely related to that of H In the 1990s, Xi showed that the best-understood direct summand J₀ of J can be realized as the Grothendieck group of coherent sheaves on the square of the flag variety, and Ginzburg gave a K-theoretic definition of the map from H to J₀. In this talk we will explain how to upgrade this realization to a monoidal category receiving a natural monoidal functor from the coherent Hecke category. A crucial ingredient is again to consider a derived enhancement, this time of the flag variety.

(40 min)

Wednesday April 19

Marcelo De Martino

Coxeter complexes and Morse contractions

To compute the Ext groups in homological algebra, a fundamental tool is to construct projective resolutions of objects in some module category. In this short talk, I will present a contraction of the affine Coxeter complex that can be used to compute Ext groups for the affine Hecke algebra and for p-adic groups (via its building). This circle of ideas started with the works Solleveld-Opdam and of Bestvina-Savin. 

(20 min)

Thursday April 20

Gert Vercleyen

On Low Rank Fusion Rings

We present a method to generate all fusion rings of a specific rank and multiplicity. This method was used to generate exhaustive lists of fusion rings up to order 9 for several multiplicities. A website containing data on fusion rings is introduced and an introduction to a Wolfram Language package for working with these rings is given. 

(20 min)

Plus poster presentation