Speaker
Dr
Seul Bee Lee
(Seoul National University, South Korea)
Description
The extreme value theorem (EVT) is a theory concerning the distribution of the maximum of a sequence of random variables. For classical continued fractions, an EVT has been established, describing the limiting distribution of large partial quotients. Their significance is further explained by the correspondence with geodesic flow on the modular surface, where large partial quotients can be seen as excursions to the cusp. In this talk, we first establish an EVT for a modified version of the even continued fraction expansion. This result is then used to derive the EVT for the geodesic flow on the hyperbolic surface associated with the theta group, which has two cusps. This is joint work with Jaelin Kim and Seonhee Lim.