Lectures on K-theoretic computations in enumerative geometry

Understand

These are notes from my lectures on quantum K-theory of Nakajima quiver varieties and K-theoretic Donaldson-Thomas theory of threefolds given at Columbia and Park City Mathematics Institute.

• They contain an introduction to the subject and a number of new results.
• In particular, we prove the main conjecture of arXiv:hep-th/0412021 and the conjecture of arXiv:1404.2323 in the simplest case of reduced smooth curves.
• We also prove the the absence of quantum corrections to the capped vertex with descendents for sufficiently large framing (and polarization), which is a property we call large framing vanishing.