Positive Legendrian isotopy via h-principle

In this talk, I will explain the following theorem : a Legendrian submanifold has a positive loop of legendrian isotopy when it is loose. Using h-principle technique, it means the existence problem here is a flexible phenomenon in contact topology. The main idea is to allow good singularities (wrinkles), then resolve them. First, I will give motivation and background, then I will discuss a test example: the case of sphere. Finally I will show the general case by h-principle.