Relative Calabi-Yau Structures for Legendrian Contact Homology

Legendrian Contact Homology (LCH) was among the first, and is still among the most important, non-classical invariants of Legendrian knots. In this talk, I will tell a story that builds up ever more sophisticated analogues of Poincare Duality in LCH. Despite the algebraic nature of the talk, I promise pictures and examples. This is joint work with Jason Ma (Duke) and, towards the end, work in progress in conversation with Zhenyi Chen (Northwestern).