| Résume | Surreal numbers, as introduced by Conway, are abstract quantities constructed by taking Dedekind cuts in the set theoretic universe.
Regular growth rates are germs at infinity of sufficiently regular real-valued functions, e.g. functions definable in an o-minimal expansion of the real ordered field, or functions whose germ lies in a differential field closed under composition.
It turns out that surreal numbers can be represented as formal regular growth rates called "hyperseries", formaly built upon elementary blocks that behave like (possibly transfinite) iterators of the exponential function.
In my PhD thesis, I established this correspondence, but I left to future me the technically involved task of turning these formal growth rates into regular growth rates - i.e. defining a derivation and composition law on surreal numbers, with nice properties.
I will explain how to do this in the form of an interactive game. Winner / birthday person gets a free beer at Frog's. |
