  In this thesis we discuss various classical problems in enumerative geometry.
We are focused on ideas and methods which can be used explicitly for practical
computations. Our approach is based on studying the limits of elliptic stable
envelopes with shifted equivariant or Kahler variables from elliptic cohomology
to K-theory.
  We prove that for a variety X we can obtain K-theoretic stable envelopes for
the variety X^G of the G-fixed points of X, where G is a cyclic group acting on
X preserving the symplectic form.
  We formalize the notion of symplectic duality, also known as 3-dimensional
mirror symmetry. We obtain a factorization theorem about the limit of elliptic
stable envelopes to a wall, which generalizes the result of M.Aganagic and
A.Okounkov. This approach allows us to extend the action of quantum groups,
quantum Weyl groups, R-matrices etc., to actions on the K-theory of the
symplectic dual variety. In the case of the Hilbert scheme of points in plane,
our results imply the conjectures of E.Gorsky and A.Negut.
  We propose a new approach to K-theoretic quantum difference equations.
