Quantum field theories with identical local dynamics can admit different choices of global structure, leading to different partition functions and spectra of extended operators. Recent work has determined the structure of such choices via geometric methods for various classes of non-Lagrangian theories obtained from stringy geometric engineering techniques. In this talk I will discuss a purely field theoretical counterpart of this analysis, showing that global structures can be captured from a careful analysis of the infrared Coulomb-like phases. Our results confirm and extend the many results obtained within geometric engineering about the global structures of Argyres-Douglas theories, 5d SCFTs and 6d SCFTs.

Over the past decade we have witnessed the emergence of a plethora of correspondences between QFTs in various dimensions arising from higher dimensional SCFTs. In this talk I will overview another strategy to produce correspondences building upon geometric engineering techniques. As applications I will touch upon higher DT theory for Calabi-Yau 3-folds, the algebra of G(2) instantons, and generalizations of level/rank dualities.

The study of possible constraints on RG flows is an important question in our understanding of quantum field theory. In this talk I will discuss a constraint which arises by considering the spectrum of BPS excitations (an H-theorem). Examples are found in the context of four-dimensional supersymmetric quantum field theories with enough supersymmetry that the BPS spectrum is explicitly computable. Among others, we will discuss applications in the context of Maruyoshi-Song flows. [for zoom link please contact jung-wook(dot)kim(at)qmul(dot)ac(dot)uk]