`A New Class of QFTs: from D-branes to Scattering Amplitudes'

Over the last decade, we have witnessed remarkable progress in our
understanding of Quantum Field Theories. New insights have emerged from a
multitude of fronts, ranging from the Gauge/Gravity Correspondence to
Integrability.  In this seminar I will discuss Bipartite Field Theories
(BFTs), a new class of QFTs embodying many of these new approaches. BFTs are
4d, N=1 quiver gauge theories with Lagrangians defined by bipartite graphs on
Riemann surfaces. Remarkably, they underlie a wide spectrum of interesting
physical systems, including: D-branes probing Calabi-Yau manifolds, their
mirror configurations, integrable systems in (0+1) dimensions and scattering
amplitudes in N=4 SYM. I will introduce new techniques for studying these
gauge theories. I will explain how their dynamics is captured graphically and
the interesting emergence of concepts such as Calabi-Yau manifolds, the
Grassmannian and cluster algebras in the classification of IR fixed points.
Finally, I will introduce a new framework for analyzing general systems of D3
and D7-branes over toric Calabi-Yau 3-folds.  These ideas can be exploited for
embedding BFTs in String Theory but have a much wider range of applicability.