Frank Calegari

collaborators

3 papers

math.NT2025

The adelic closure of triangle groups

Frank Calegari

Motivated by questions arising from billiard trajectories in the regular $n$ -gon, McMullen defined a pair of functions $I^º$ and $I^´$ on the cusps $c$ of the corresponding triangle…

math.GR2025

Finite groups whose real irreducible representations have unique dimensions

Thomas Breuer, Frank Calegari, Silvio Dolfi +2

We determine the finite groups whose real irreducible representations have different degrees.

math.GT2025

Fields of definition for triangle groups as Fuchsian groups

Frank Calegari, Qiankang Chen

The compact hyperbolic triangle group $I^ (p, q, r)$ admits a canonical representation to $PSL_{2} (R)$ with discrete image which is unique up to conjugation. The trace…