Conley-Zehnder Banana
The SL(2,R) "banana" helps us to compute Conley-Zehnder indices in three dimensions.

My research investigates two intertwined themes. What can we learn about two-dimensional dynamics and four-dimensional symplectic embeddings via three-dimensional contact geometry (specifically, from the invariants of embedded contact homology)? And how can we leverage low-dimensional topology to compute these contact invariants? Key tools I use are open book decompositions, torus and circle actions on three- and four-manifolds, and symplectic fillings/cobordisms.

In Preparation