We are happy to present Quentin Guilmant’s talk titled “Surreal Numbers”.

Surreal numbers form a class of number very singular in which we can embed every ordered field. In particular, transseries, studied for instance in Asymptotic Theory. Surreal numbers are in fact an even larger field which contains numbers that represent hyper exponential functions or half exponential functions (whose composition by themselves is the exponential function). It is also possible to get the derivative and the anti-derivative of surreal numbers.

Polynomial differential equations can form an analog model of computation, which has been introduced by Shanon in 1941, the general purpose analog computer (GPAC). It had been developed by Lipschitz, Pour El and more recently by Graça and Cost in 2003 to define a notion of computability on it. It has also been proven that this model is equivalent to Turing Computability in the sense of computable analysis.

In this talk, Quentin will introduce you to the wonderful world of surreal numbers and show you his work to solve polynomial differential equations whose solutions are surreal numbers. This may lead to a better understanding of asymptotics of the GPACs, and then, of GPAC-computable functions.

Quentin recently finished his PhD at the LIX (Palaiseau, France). He works on surreal number and their suspected link with computability theory. Before that he studied in the ENS Lyon where he got his Master in fundamental computer science.

15 Dec 2022