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
longterm strategy for approaching the Four Colour Problem. Tutte's
approach was ultimately
sidestepped by the AppelHaken proof of 4CT,
but enumeration of maps remains a very active area of combinatorics,
with links to wideranging 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.