Speaker: Paloma Bengoechea
Title: Cycle integrals of modular functions and continued fractions
Date: 26/11/2021 at 10:30

Abstract: 
Cycle integrals of a modular function are integrals along hyperbolic geodesics which endpoints are the two 
roots of an indefinite binary quadratic form with integer coefficients. They can be seen as hyperbolic 
periods or also as `values’ of the modular function at real quadratic irrationalities. Cycle integrals of 
Klein's $j$ modular function have recently gained importance because of their similarities with singular 
moduli discovered by Duke-Imamoglu-Toth. I will discuss a new approach in the study of these cycle integrals 
that relies on diophantine approximation. We can obtain a lot of information on their distribution from 
the continued fractions of the real quadratic irrationalities.