Davis, Diana Bastien, Fanny

Mathematicians have long understood periodic trajectories on the square billiard table. In the present work, we describe periodic trajectories on the regular pentagon – their geometry, symbolic dynamics, and group structure. Some of the periodic trajectories exhibit a surprising "dense but not equidistributed" behavior. I will show pictures of peri...

Girard, Yohan Santharoubane, Ramanujan

I will show how we can produce exotic representations of surface groups from the Witten-Reshetikhin-Turaev TQFT. These representations have infinite images and give points on character varieties that are fixed by the action of the mapping. Moreover we can approximate these representations by representations into finite groups in order to build exot...

Gadre, Vaibhav Bastien, Fanny

Effective convergence of ergodic averages and cusp excursions of geodesics on moduli spaces We survey some applications of effective convergence of ergodic averages to the analysis of cusp ex-cursions of typical geodesics on moduli spaces. This will cover Teichmuller geodesics, Weil-Petersson geodesics and geodesics typical for harmonic measures ar...

Girard, Yohan Wright, Alex

Multicurves have played a fundamental role in the study of mapping class groups of surfaces since the work of Dehn. A beautiful method of describing such systems on the n-punctured disk is given by the Dynnikov coordinate system. In this talk we describe polynomial time algorithms for calculating the number of connected components of a multi curve,...

Davis, Diana Bastien, Fanny

Mathematicians have long understood periodic trajectories on the square billiard table. In the present work, we describe periodic trajectories on the regular pentagon – their geometry, symbolic dynamics, and group structure. Some of the periodic trajectories exhibit a surprising "dense but not equidistributed" behavior. I will show pictures of peri...

Girard, Yohan Wright, Alex

Multicurves have played a fundamental role in the study of mapping class groups of surfaces since the work of Dehn. A beautiful method of describing such systems on the n-punctured disk is given by the Dynnikov coordinate system. In this talk we describe polynomial time algorithms for calculating the number of connected components of a multi curve,...

Gadre, Vaibhav Bastien, Fanny

Effective convergence of ergodic averages and cusp excursions of geodesics on moduli spaces We survey some applications of effective convergence of ergodic averages to the analysis of cusp ex-cursions of typical geodesics on moduli spaces. This will cover Teichmuller geodesics, Weil-Petersson geodesics and geodesics typical for harmonic measures ar...

Girard, Yohan Santharoubane, Ramanujan

I will show how we can produce exotic representations of surface groups from the Witten-Reshetikhin-Turaev TQFT. These representations have infinite images and give points on character varieties that are fixed by the action of the mapping. Moreover we can approximate these representations by representations into finite groups in order to build exot...

Davis, Diana Bastien, Fanny

Mathematicians have long understood periodic trajectories on the square billiard table. In the present work, we describe periodic trajectories on the regular pentagon – their geometry, symbolic dynamics, and group structure. Some of the periodic trajectories exhibit a surprising "dense but not equidistributed" behavior. I will show pictures of peri...

Girard, Yohan Wright, Alex

Multicurves have played a fundamental role in the study of mapping class groups of surfaces since the work of Dehn. A beautiful method of describing such systems on the n-punctured disk is given by the Dynnikov coordinate system. In this talk we describe polynomial time algorithms for calculating the number of connected components of a multi curve,...