# Lambda calculus and the Four Colour Theorem

- 14:00 22nd June 2018 ( Trinity Term 2018 )Lecture Theatre B

The enumerative study of graphs on surfaces (or "maps") began in the

1960s with the pioneering work of Bill Tutte, who figured out how to

count various families of planar maps as the initial steps of a

long-term strategy for approaching the Four Colour Problem. Tutte's

approach was ultimately side-stepped by the Appel-Haken proof of 4CT,

but enumeration of maps remains a very active area of combinatorics,

with links to wide-ranging domains such as algebraic geometry, knot

theory, mathematical physics... and apparently lambda calculus! In

this talk I will survey some of the surprisingly tight connections

that have been found over recent years between the combinatorics of

(rooted) maps and the combinatorics of (linear) lambda terms, and

place them within the context of older ties between logic and geometry

such as string diagrams for monoidal categories, and proof nets for

linear logic. I hope to convey how these newly discovered links

suggest some fascinating questions for research in both directions,

including a tight connection between typing of lambda terms and

coloring of maps. Only a basic background in lambda calculus will be

assumed.