250011 VO Enumerative Geometry (2020S)

Broadly speaking, enumerative geometry is about geometric questions the answer for which is a number. In practice, geometric questions are usually reduced to computations in intersection theory/K-theory. Proper treatment of the subject would be quite technical, instead we will attemt to develop a feeling of what a modern enumerative geometry is by working out some examples. Depending on the interests of participants, I will choose which examples to present.
Prerequisites: algebra, linear algebra, some familiarity with algebraic topology, manifolds, algebraic geometry will be helpful.
I will spend some time to explain the most important tools such as basics of algebraic geometry, K-theory, Chern classes, Riemann-Roch theorem.