Rational curves and noncommutative algebra


The geometry of contracting rational curves in three folds can be studied via noncommutative algebra, and I will recap how you can pass from the geometry to the algebra and back again via moduli space constructions. As an example of the advantages of the noncommutative algebra viewpoint I plan to discuss a noncommutative interpretation of the Gopakumar-Vafa invariants attached to the curve realised by Toda.