Monodromy of $q$-difference equations of “geometric origin”

Study of the monodromy of differential and difference equations is a very classical subject that received a lot of input from many other branches of mathematics over its history (e.g. from the theory of quantum groups). Many, if not all, difference equations of “quantum-group”-theoretic and other algebraic origin may be viewed as special instances of equations associated to counting holomorphic curves (and similar geometric computations inspired by modern high-energy physics). In my talk, I will explain how to compute the monodromy of these equations, and the geometric meaning of the ingredients that enter the answer.