Event

String/M-Theory provides various approaches for constructing 5d Superconformal Field Theories, most notably geometric engineering via M-theory on toric Calabi-Yau 3-folds and webs of (p,q) 5-branes in Type IIB String Theory. These two approaches are related by dualities. Generalized Toric Polygons (GTPs) extend the notion of toric geometry to 5-brane webs suspended from 7-branes. In the first part this talk, we will discuss a new type of quivers, denoted Twin Quivers, which offer a useful perspective on GTPs and their corresponding 5d theories. Twin quivers capture the symmetries of the underlying theories, the generalized s-rule and Hanany-Witten transitions in the webs. They can also be regarded as a first step towards the generalization of brane tilings to GTPs. In the second part of the seminar, we will delve into the geometry of GTPs and the connection between polytope mutations and Hanany-Witten moves. This geometric understanding leads to a new set of mutation invariants that resolves existing puzzles in the classification of 5d theories.