Abstract

Geometric Engineering is an important tool to construct a large class of non-Lagrangian theories in various dimensions. If a gauge algebra admits discrete automorphisms, there is the possibility to twist by them when performing a circle reduction. Since F-theory is related to M-theory by a circle reduction, and M-theory is sensitive to the full geometry, this begs the question which geometries capture such twisted gauge algebras. In this talk I will argue that so called genus-one fibrations are the key ingredient to engineer twisted algebras in five dimensions. I use the algebraic description of the threefold to compute multiplicities of BPS states, perform geometric transitions to untwisted algebras and outline further applications if time permits.