7 problems

Let a Teichmüller curve be a curve generated by the omega^0 differential in a stratum with more than one zero, and let its trace field be the field generated by the traces of the c…

Consider a reasonable model of a random hyperbolic $3$-manifold, and let its trace field be the number field generated by the traces of a holonomy representation. Real trace-field…

Let $M$ be a $k$-cusped hyperbolic $3$-manifold. A Dehn filling point is a point corresponding to a Dehn filling of $M$, and its height is the height used in the associated Dehn fi…

Let $S=S(g,p)$ be an orientable, connected surface of genus $g$ with $p$ punctures, and let $M$ be a hyperbolic surface bundle over $S^1$ with fiber of type $(-\chi,p)$, where…

Let $q>9$, let $\lambda_q=2\cos(\pi/q)$, let $\mathbb Q(\lambda_q)$ be the field generated by $\lambda_q$, and let $G_q$ be the corresponding Hecke group acting on the real project…

Let $M={\mathbb H}^3/\Gamma$ be a hyperbolic $3$-manifold, and let $\mathbb{Q}({\rm tr}\,\Gamma)$ denote the trace field, namely the smallest extension of $\mathbb{Q}$ containing…

Let $n$ be an odd, negative integer, and let the trace field of a hyperbolic knot complement mean its invariant trace field. Trace-field symmetry conjecture. The $(-2,3,n)$ and…