7 problems

Let $g_t$ and $u_A$ be the diagonal flow and unipotent matrix associated with an $m\times1$ real matrix $A$, and let $\lambda_i$ denote the successive minima of the corresponding l…

Let $\mathfrak{T}$ be a tower type. Let $\mathcal{S}(\mathfrak{T})$ be the associated family of orders, let $\operatorname{Spectrum}(\mathcal{S}(\mathfrak{T}))$ be its spectrum of…

Fix a tower type $\mathfrak{T}=(n_1,\dots,n_t)$, let $n$ be its degree, and choose integers $0\leq i,j\leq i+j<n$. For an order $\mathcal{O}$ in the family…

Linear upper-bound conjecture. The upper bound $n!$ should be improvable to $Kn$ for some universal constant $K>0$. This is an attempted sharpening of the classical transference bo…

Let $q$ be a Minkowski-reduced positive definite quadratic form with associated positive definite symmetric matrix $Q$, and let $\lambda_i(Q)$ denote its $i$th successive minimum.…

Let $n\geq1$, and consider the successive minima associated with the simultaneous approximation problem for a vector $\boldsymbol{\zeta}$ whose entries, together with $1$, are line…

Let $K\in\mathcal{K}^n_0$ be a $0$-symmetric convex body and let $\Lambda\in\mathcal{L}^n$ be an $n$-dimensional lattice. The lattice point enumerator is…