2 problems

Bhargava–H. Piper equidistribution conjecture. The shapes of $S_n$ number fields of degree $n$ are equidistributed for every $n\geq 6$.

Let $Q(v_1,v_2,v_3):=2v_1v_3-v_2^2$ be a quadratic form of signature $(2,1)$, and let … Write $V_Q^1(\mathbb{Z}):=V_Q^1\cap\mathbb{Z}^3$. For a rank-2 discrete subgroup…