Wenyuan Li, USC

Abstract: Given a Lagrangian cobordism between Legendrian submanifolds in the contact boundary of a Weinstein domain, we construct a fully faithful Lagrangian cobordism functor between the categories of microlocal sheaves with singular support on the relative skeleton of the Weinstein domain with the Legendrian stops. When the Legendrians live in 1-jet bundles, we moreover prove that sheaves with singular support on the Legendrian lift of the Lagrangian cobordism is the fiber product of sheaves at the negative/concave end and local systems on the cobordism. This gives a sheaf theoretic description of the maps between Legendrian contact homologies with coefficients enhanced by chains of the based loop spaces. If time permits, we will explain related aspects in wrapped Fukaya categories and generating families.