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Résumé |
It has only recently become possible to systematically study flux
compactifications in asymptotic regions of the field space without the necessity
to construct specific geometric examples. I will explain some key insights about
the structure of the complex structure moduli space, its boundaries and asymptotic
regions, that opened the door for this general approach. I will then argue that a
long conjectured and very non-trivial finiteness result about flux vacua has now
been proved. Motivated by these successes, I will suggest that requiring
finiteness properties on the coupling functions of any effective theory could be
key to generally uncover the structure of the string theory landscape. I will
briefly introduce a concrete framework, dealing with o-minimal structures and tame
topology, that automatically implements finiteness properties. |
