Given a graph with lines and 3-valent vertices, one can construct, via a simple dictionary, a Lagrangian with N=2 supersymmetry in 3+1 dimensions, generalizing the notion of quiver. The vacuum moduli space of such a theory gives moment map equations for a HyperKahler manifold. The Hilbert Series of these spaces can be computed and turns out to be a function of the number of external legs and loops in the graph but not of its detailed structure. The SCFT consequence of this property indicates a crucial universality of many Lagrangians, all of which have the same dynamics.

I will present a new way for evaluating modular integrals in String Theory that keeps all symmetries of the integrands manifest and induces a natural regularization of otherwise IR divergent integrals. It can be regarded as the equivalent of dimensional regularization in Field Theory. The procedure is particularly relevant for the quantum corrections to couplings in the low-energy effective action, since the resulting expressions are manifestly invariant under the duality group.

I will discuss classical gravitational bremsstrahlung in massive particle collisions at ultra-planckian energies, with emphasis on the fact that the radiation efficiency is considerably larger than in previous estimates. As a result, I will argue that gravitational bremsstrahlung may lead to extreme damping in ultra-planckian collisions of massive particles and that radiation reaction should be included in the analysis of black hole production.

I will discuss aspects of nonperturbative effects generated by Euclidean D3-branes (E3-branes) in F-theory compactifications. The standard approach considers E3-branes supporting vanishing world-volume flux and is based on the dual Euclidean M5-branes in M-theory compactifications on elliptically fibered Calabi-Yau four-folds. In contrast, I will propose an approach that is directly couched in type IIB. Not only will this open up an alternative perspective on known results, but it will also provide a framework to address problems which are more difficult to deal with in M-theory. In particular, I will focus on the introduction of non-vanishing world-volume fluxes on the E3-branes and on the associated lifting of non-universal fermionic zero-modes.

I will explain how to exploit systematically the structure of nilpotent orbits to obtain solvable equations describing extremal solutions of (super-)gravity theories, i.e. systems that can be solved in a linear way. I will concentrate on the STU model, as a truncation of N=8 supergravity, for which all extremal solutions with a flat three-dimensional base are fully described with the help of three different nilpotent orbits: the BPS, the almost-BPS and the composite non-BPS. The latter describes a new class of multi-center black hole solutions for which all centers are non-BPS. I will discuss these solutions in some detail and I will address the generalization to N=8 supergravity.

I will discuss a new method to find vacua of maximal gauged supergravity and its application to M-theory reductions. I will show how to produce interesting Minkowski vacua with partial SUSY breaking using locally geometric compactifications and I will discuss new non-supersymmetric Anti-de Sitter vacua and possible applications in the context of the gauge/gravity correspondence.