8 problems

Let $(P,\lambda)$ be a hermitian, sesquilinear form on a free $\mathbb{Z}[\mathbb{Z}]$-module of rank $2g$, where $g\in\{1,2\}$. A form is surface hyperbolic if it is isometric to…

Let $q$ be the residue-field cardinality, and let $A_{\alpha\beta\gamma\delta}$ denote the relevant diagonal hermitian form with $\alpha>\beta\geq\gamma\geq\delta\geq0$. Let…

Let $E/F$ be the unramified quadratic extension, let ${\mathbb V}$ be the space of special homomorphisms with hermitian form $h$, and let $\lbrace x_1,\dots,x_{2n}\rbrace$ be a bas…

Hermitian forms graph classification conjecture. Let $q$ be a prime power. Let $f$ be a Boolean degree $1$ function on $H_q(\ell,k)$, where $k+\ell$ is sufficiently large depending…

Let $X=X({\mathcal O},{\mathcal L})$ be a standard module for the affine Hecke algebra with Hermitian Kazhdan–Lusztig polynomials…

Let $p$ be a prime with $p\geq 5$, let $\zeta$ be a primitive $2p$-th root of unity, and define … for odd $p$, and $A_p=\pm\exp\left(\frac{\pi i}{p}\right)$ for even $p$. Assume th…

Hodge–Riemann conjecture.

Let ${\cal I}$ index the vectors and transition-matrix columns $X_I$ arising from the Mellin–Barnes bases, let $H$ be a Hermitian matrix preserved by all monodromy matrices, and le…