MathOverflow

I am reading a paper about property (T) for groupoids: Topological property (T) for groupoids. In section 4.4 they discuss the HLS groupoids which I describe define here.
Let $\Gamma$ be a discrete group and $(N_k)_{k \in \mathbb N}$ a decreasing sequence of normal subgroups of finite index. Let $\Gamma_k := \Gamma/N_k$ and denote $q_k: \Gamma \rightarrow \Gamma_k$ the quotient homomorphism. If we let $\overline{\mathbb...

Let $S$ be a subset of $\{0,1\}^n$ with cardinality $k$.
Denote by $\Gamma_r(S)$ the union of all Hamming balls of radius $r$ centered at points of $S$.
Harper's theorem states that $|\Gamma_r(S)|$ is minimized when $S$ is a Hamming ball (see also this question)....

The ongoing SAIR Inverse Galois Problem challenge asks teams to find, for each pair $(G,r)$ consisting of a transitive subgroup $G$ of $S_{24}$ and a number $r$ such that $G$ contains an involution with $r$ fixed points, an irreducible polynomial over...

I have started to read about Geometric Langlands from Frenkel's book
https://arxiv.org/abs/hep-th/0512172.
As said in Theorem $3$ of the book, the Langlands correspondence is stated as follows