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Legendrian links are central objects of study in the intersection of low-dimensional topology and contact geometry. For Legendrian links in the 3-sphere, Ozsvath, Szabo, and Thurston defined combinatorial invariants that reside in grid homology, a combinatorial version of knot Floer homology. Known as the GRID invariants, they are effective in distinguishing some Legendrian knots that have the same classical invariants. In this talk, we describe how the GRID invariants also obstruct decomposable Lagrangian cobordisms, a result joint with John Baldwin and Tye Lidman. If time permits, we will also outline constructing decomposable Lagrangian cobordisms from any pair of Legendrian links to a common target Legendrian link, a result joint with Josh Sabloff and Shea Vela-Vick. No background in contact geometry or Floer homology will be assumed, and the talk will be self-contained.

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