7. Elliptic Fibrations and FTheory

Problem 7.1.
Construct explicit examples of how gauge groups and representations appear from elliptic fibrations. 
Problem 7.2.
Is there an intrinsic characterisation of the gauge group arising from the singularities of an elliptic fibration that doesnâ€™t require passing through Dynkin diagrams?
Cite this as: AimPL: Singular geometry and Higgs bundles in string theory, available at http://aimpl.org/singularhiggs.