Speaker
Peiyi Cui
(Morningside Center of Mathematics)
Description
Reduction to depth zero is a promising approach for understanding $\ell$-modular blocks of $p$-adic groups when $\ell$ differs from $p$. In this talk, I will introduce $\ell$-modular blocks of $\mathrm{SL}_n$ from this perspective. We will explore the technical challenges in associating an $\ell$-modular block with a depth-zero block and consider a natural candidate for this potential connection. Toward the end, I will also discuss related topics on both the automorphic and Galois sides.