Diptaishik Choudhury

Hyperbolic geometry, especially in low dimensions, has been a classical subject of study and is noted due to its interactions with different areas of mathematics and physics. In this talk, our main interest mainly will be on closed hyperbolic surfaces and a certain class of hyperbolic 3 manifolds called quasi-Fuchsian manifolds which as topological spaces are homeomorphic to a closed hyperbolic surface times the real line. Although different aspects of these manifolds have been studied before, in this talk we will focus primarily on the conformal boundary at infinity, which is homeomorphic to two copies of the surface. We will see how certain objects called measured foliations can appear naturally on the boundary at infinity and finish with a few questions and partial results in this direction.