Birational Geometry of Foliations.

In recent times there have been advancements in understanding the Birational Geometry of Foliations on Projective varieties, and how the geometry of Foliation interacts with that of the variety. Due to works of Dr. Calum Spicer and Dr. Paolo Cascini, we know the existence of minimal models for rank one and co-rank one foliations on three-fold. We are trying to provide sufficient conditions to gurantee existence of flops for foliations. We have been able to show that in general flops might not exist for rank one foliations. We have also been able to show that, for rank one foliations on three -olds, minimal models are unique ( which provide evidence for the fact that Birational Geometry of Foliations are much rigid than that of varietis. We are also trying to enquire if a rank one foliation with nice singularities admits separatrices, which will provide valuable insight about the dynamics induced by the foliation.