Georgia Institute of Technology College of Sciences

Two knots are said to be concordant if they jointly form the boundary of a cylinder in four-dimensional Euclidean space. In the symplectic setting, we say they are Lagrangian concordant if the knots are Legendrian and the cylinder is Lagrangian. Interestingly, Lagrangian concordance is, unlike smooth concordance, not a symmetric relation. In this talk, I'll discuss various strategies that can be used to obstruct Lagrangian concordance, from basic invariants of Legendrian knots, to the Chekanov-Eliashberg DGA, to building new obstructions from Weinstein cobordisms.