A Talk on Combinatorial Growth of Reciprocal Geodesics in Hecke Groups by Debadattam Das

About the Talk:
A geodesic in a hyperbolic orbifold is said to be ‘reciprocal’ if it passes through at least one even ordered cone point. These geodesics correspond to conjugacy classes of reciprocal elements. First, we classify the reciprocal geodesics in the Hecke groups; then, we study the growth of the reciprocal geodesics in terms of word lengths on the hyperbolic orbifolds associated with Hecke groups. In particular, we have completed the results of Marmolejo for the even cases of Hecke groups. Furthermore, we generalise the relation between the low-lying words and geodesics with an excursion of the modular group to Hecke groups. This is joint work with Dr Krishnendu Gondopadhyay.

About the Speaker:
Debattam Das is currently a PhD student at IISER Mohali. His research interest lies in the broad area of Geometry and Topology, particularly in Fuchsian Groups, Mapping Class Groups, Teichmüller Space, and Hyperbolic 3-Space.