Lovelock theory is the natural extension of general relativity to higher dimensions. It can be also thought of as a toy model for ghost-free higher curvature gravity. It admits a family of AdS vacua, most (but not all) of them supporting black holes, that display interesting features such as a generalized variant of the Hawking-Page phase transition. This provides an appealing arena to explore different holographic aspects in the context of the AdS/CFT correspondence which I will discuss in this talk.

Abstract: Recently the existence of a new quantity which decreases along RG-flows of 4d supersymmetric QFT's with R-symmetry has been conjectured. I will analyze this conjecture from a dual supergravity perspective: using some general properties of domain-wall solutions dual to R-symmetric RG flows, I will define a function interpolating between the correct values at the UV and IR fixed points. I will finally test its monotonicity properties in a class of examples.

I'll explain a new way of looking at 4d supergravity --- as a theory of holomorphic maps into Penrose's twistor space. Allowing twistor space to have N fermionic directions, the theory is anomaly free when N=8. Via the Penrose transform, the vertex operators correspond to an N=8 Einstein supergravity multiplet. Conformal symmetry is explicitly broken by the presence of the infinity twistor in the BRST operator. I will show how to compute the complete classical S-matrix from worldsheet correlation functions, and interpret these amplitudes geometrically.

How many H2O molecules are needed to form water? While the precise answer is not known, it is clear that the answer should be a finite number rather than infinity. We revisit with care the ideal Bose gas confined in a cubic box which is discussed in most statistical physics textbooks. We show that the isobar of the ideal gas zigzags on the temperature-volume plane featuring a `boiling-like' discrete phase transition, provided the number of particles is equal to or greater than a particular value: 7616. This demonstrates for the first time how a finite system can feature a mathematical singularity and realize the notion of `Emergence', without resorting to the thermodynamic limit. ref: arXiv:1310.5580

Abstract: There has been much progress in understanding the four-point correlator of Stress Energy multiplets in N=4 SYM recently. I will discuss recent progress in evaluating high loop Feynman integrals using leading singularities, asymptotics and the symbol. This is used to evaluate the three-loop four-point correlation function from its integrand. Then I will show how the full (parity even and odd) 5-point amplitude can be found from the same four-point correlator integrand.

I'll review some progress over the past 18 months in computing Ohm's law using holography.

I will discuss the mathematical structure of tree level amplitudes among massless superstring states. String corrections to these amplitudes take a compact and elegant form once the contributions from different classes of multiple zeta values (MZVs) are disentangled. The idea is to lift MZVs to their motivic versions endowed with a Hopf algebra structure: It induces an isomorphism which casts the amplitudes into a very symmetric form and represents the generalization of the symbol of a transcendental function. I will also comment on generalizations to loop amplitudes.

Three dimensional quantum field theories provide a nice testing grounds for exploring quantum field theory phenomena. Very simple UV theories can have highly nontrivial, and rich IR dynamics. These lectures will give a pedagogical review of various aspects of quantum field theory, including instantons, monopoles, the conformal window, vortices, skyrmions, Chern-Simons terms, etc., in the context of 3d quantum field theories. In the context of susy theories, we will review older work on exact results, mirror symmetry and duality, and also mention some more recent results.