Olivier Mila

activity

20182021

collaborators

4 papers

math.NT2021

Hyperbolic Heron Triangles and Elliptic Curves

Matilde Lalín, Olivier Mila

We define hyperbolic Heron triangles (hyperbolic triangles with "rational" side-lengths and area) and parametrize them in two ways as rational points of certain elliptic curves. We…

math.GT2020

Non-commensurable hyperbolic manifolds with the same trace ring

Olivier Mila

We prove that there are infinitely many pairwise non-commensurable hyperbolic $n$ -manifolds that have the same ambient group and trace ring, for any $n \geq 3$ . The manifolds can b…

math.GT2019

The trace field of hyperbolic gluings

Olivier Mila

We determine the adjoint trace field of gluings of general hyperbolic manifolds. This provides a new method to prove the nonarithmeticity of gluings, which can be applied to the cl…

math.GT2018

Hyperbolic manifolds and pseudo-arithmeticity

Vincent Emery, Olivier Mila

We introduce and motivate a notion of pseudo-arithmeticity, which possibly applies to all lattices in $PO (n, 1)$ with $n > 3$ . We further show that under an additional assump…