Speaker: Ipsita Datta
Date: January 12, 2026
Affiliation: ETH Zurich

Abstract: Lagrangians are widely studied and important objects in Symplectic geometry. We present a novel Floer theory associated with a pair of Lagrangians with boundary (viewed as Lagrangian cobordisms between smooth knots) in $4$-manifolds of the type surface times the complex plane. This Floer theory is a ``manifold with boundary” analogue of Lagrangian intersection Floer homology. It is constructed by counting holomorphic curves with boundary on Lagrangian tangles which are immersed Lagrangians with boundary that generalize Arnol’d’s Lagrangian cobordisms between Lagrangians and Lagrangian cobordisms between Legendrians. This Floer theory is filtered and can be seen as persistence modules, thereby giving geometric information about Lagrangian tangles. This is joint work with Joshua Sabloff (Haverford College).