6 problems

Let $G$ and $H$ be the groups occurring in the Local Langlands correspondence, let $\boldsymbol{Z}[[\sigma]$ be the group ring of…

Treumann–Venkatesh's linkage conjecture. Linkage is compatible with functorial transfer: if $\pi$ is linked to $\Pi$, then $\pi$ transfers to $\Pi$ under the Local Langlands corres…

Let $V$ be a self-dual integral form of the monster vertex algebra, let $g$ be a Fricke element, and suppose that $g^j$ is a Fricke element for every integer $j>0$. Weaker Borcherd…

Composite-order graded Brauer character conjecture. Each of these series is a linear combination of Hauptmoduls. This predicts a uniform Hauptmodul description for the graded Braue…

Let $V^\natural_{\mathbb{Z}}$ be a self-dual integral form of $V^\natural$ with Monster symmetry, and let $W_\infty M$ denote the big Witt vectors of a graded module $M$.…

Let $F\supset E$ be a degree $l$ extension of characteristic-zero non-archimedean local fields with residue characteristic $p$, where $p$ and $l$ are distinct primes. Let $\pi$ be…