10 problems

Let $\fg$ be the Lie algebra under consideration, with index set $I$, and let $\fF^\lambda_{\fg,\fb}$ be the corresponding fiber space with open stratum…

Let $G$ be a reductive group with Langlands dual $G^\vee$, let $C$ be the underlying curve, and let $D=\{c_i\}$ be the parabolic divisor. Let $(E,\varphi,Q)$ be a smooth fixed poin…

Jordan-type conjecture. There is an open set $\mathcal{N}\subseteq\mathfrak{n}_F\cap\mathfrak{n}_{F'}$ such that, for every $er\in\mathcal{N}$,

Let $\Fl_{\calG}$ be an affine flag variety, and let $\Fl_{\calG,\leq w}$ be its Schubert subvariety indexed by a double coset $w$ of the Iwahori--Weyl group. Its perfection is den…

Let $V_1$ and $V_2$ be $N$-dimensional vector spaces, let $\bI$ be an Iwahori subgroup, and let $\bFfl_i$ be the variety of complete flags in $V_i$. Define the dg-scheme with zero…

The local model conjecture. There exists a projective and flat scheme … over … which supports an action of ${\mathcal G}\otimes_{\mathbb Z_p}{\mathcal O}_E$ and is such that: (i) t…

Basic-class comparison conjecture. There exists $N_b\in\mathbb Z_{\ge 0}$ such that, for every $x\in\widetilde W$ with $\ell(x)\ge N_b$,

Reuman's conjecture. If $x$ lies in the shrunken Weyl chambers, then $X_x(b)\ne\emptyset$ if and only if

P-alcove conjecture. $X_x(b)\ne\emptyset$ if and only if, for every semistandard $P=MN$ for which $x\mathbf a$ is a $P$-alcove, $b$ is $\sigma$-conjugate to an element $b'\in M(L)$…

Let $\bD_{\mathrm{ren}}(\fD(\Fl^{\operatorname{aff}}_G)_\crit\operatorname{mod})$ carry the old and new t-structures, and let $J_\cla$ be the convolution objects indexed by…