4 problems

Geometric realization conjecture. For every $\pi^\mu w,\pi^\nu v\in W_{\mathcal{T}}$, there exists an affine algebraic variety defined over $\Bbbk$, with a contracting…

Let $G^+$ be the semigroup of a $p$-adic loop group on which the Cartan decomposition holds, let $I$ be an Iwahori subgroup, and let $\mathcal{H}(G^+,I)$ be the algebra of complex-…

Let $G$ be the affine Kac–Moody group in the global setting, let $f$ be a function on the relevant moduli space, and let $\mathcal{P}$ and $\mathcal{Q}$ be opposite parahoric subgr…

Let $G$ be a reductive group, let $k$ be a positive integer, and consider the varieties closely related to $\operatorname{Bun}_G(\mathbb{A}^2/\Gamma_k)$ constructed in the affine g…