6 problems

Let $F$ be a non-Archimedean local field, let $G=\operatorname{GL}_{2n}(F)$, and let $P_{n,n}=MN$ be the standard parabolic subgroup with Levi factor…

Let $F$ be a split non-Archimedean local field with ring of integers $\mathfrak o$, and let $X$ be an affine spherical variety with a good model over $\mathfrak o$, satisfying the…

Exceptional-pole conjecture. The point $s_0$ is an exceptional pole of $L(\pi\times\sigma,s)$ if and only if it is a pole of

Novodvorsky compatibility conjecture. We have

Intersection-complex conjecture. The intersection complex of $\mathsf L^+X$, or rather of its finite-dimensional formal models, is conjectured to be related to special values of lo…

Braverman–Kazhdan–Ngo conjecture. The trace of Frobenius on the intersection complex of the formal arc space of $X$ is the generating series of the local unramified $L$-function as…