Event Type:

Number Theory Seminar

Date/Time:

Tuesday, January 24, 2017 - 16:00 to 17:00

Local Speaker:

Abstract:

With Calta and Kraaikamp, we define and study $\alpha$-type maps $T_{n,\alpha}$ for each of a countable number of (Fuchsian triangle) groups (thus playing the role of $\text{PSL}_2(\mathbb Z)$); these groups are defined over number fields (whose degree is unbounded). We show that the key property of orbit synchronization of the endpoints of the interval of definition holds for each $n$ on a set of $\alpha$ of full measure, and identify cross-sections for these $T_{n,\alpha}$.

In this second talk, we aim to sketch proofs of some of the main results.