Event Type:

Number Theory Seminar

Date/Time:

Tuesday, May 22, 2018 - 16:00 to 17:00

Location:

Bexell 207

Local Speaker:

Abstract:

We report on a preprint of G. Panti. Panti gives a direct proof using continued fraction-type maps which decrease heights (for appropriate sets of algebraic numbers) to reprove the result that any triangle group whose invariant trace field is a quadratic number field acts transitively on the elements of this field. Compare this result with the fact that the rational numbers form a single orbit of the action of PSL(2,Z). Earlier proofs have used a mixture of techniques, in particular results from the theory of translation surfaces. I will sketch the background and history of the problem, indicate some of Panti’s techniques and recall the main open question in the area.