Globally Consistent Three-family Standard Models in F-theory

We present recent advances in constructions of globally consistent
F-theory compactifications with the exact chiral spectrum of the minimal
supersymmetric Standard Model. We highlight the first such example and
then turn to a subsequent systematic exploration of the landscape of
F-theory three-family Standard Models with a gauge coupling unification.
Employing algebraic geometry techniques, all global consistency
conditions of these models can be reduced to a single criterion on the
base of the underlying elliptically fibered Calabi-Yau fourfolds. For
toric bases, this criterion only depends on an associated polytope and
is satisfied for at least quadrillion bases, each of which defines a
distinct compactification. We conclude with pointing out important
outstanding issues.