Introduction to hyperrings and hyperfields.

We introduce hyperrings and hyperfields. These are algebraic structures which generalize the classical commutative rings and fields. In this talk, we aim to introduce these rather exotic structures and illustrate several examples. We also discuss how hyperrings and hyperfields show up and fit into the classical theory, in particular, algebraic geometry and combinatorics. If time permits, we discuss how hyperfields can be used to reformulate some basic definitions of Berkovich’s theory of analytic spaces.