A classic result of general relativity is that the topology of 4-dimensional black holes is spherical. In higher dimensions, this is not the case. I shall review the state of the art of the problem using as paradigm the black holes of heterotic supergravity. I shall provide evidence that there exist black holes with exotic topology.

During the last decade it has become clear that the phase structure of higher-dimensional black hole spacetimes is far more complex and vast than what was a priori thought. I will discuss a new method that has been recently developed to to understand the landscape of higher dimensional black holes. This is an effective world-volume approach to the construction of black holes, called the blackfold approach, obtained by curving black branes into a submanifold of a background spacetime. I will discuss the essentials of this formalism, which regards the black hole as an effective fluid living on a dynamical worldvolume. A number of illustrative applications to new families of stationary black holes, including charged cases and black holes in anti-de Sitter backgrounds will be discussed. I will also comment on relations to extremal black holes in string theory and the DBI action. Finally, I will exhibit how the fluid-dynamical aspects of the blackfold approach can be used to address stability of black holes.

We compute the tensorial perturbations to a general spherically symmetric metric in d dimensions with string-theoretical Gauss-Bonnet corrections. We use this result to derive their respective potential, which may be used to study the stability of such solutions. We then obtain a general formula for the absorption cross section of low-frequency tensor type gravitational waves for every black hole of this kind. After obtaining the general solution to the dilaton in this kind of background, we derive a new black hole solution with dilatonic charge in heterotic string theory, to which we apply our formula. We compare the results for the absorption cross section with the black hole entropy, obtained through Wald's formula.

All-loop asymptotic Bethe equations for a 3-parameter deformation of AdS5/CFT4 have been proposed by Beisert and Roiban. We propose a Drinfeld-Reshetikhin twist of the AdS5/CFT4 S-matrix, together with c-number diagonal twists of the boundary conditions, from which we derive these Bethe equations. On the other hand, certain twists of the S-matrix elements describe the ?-deformation of $N = 4$ supersymmetric Yang-Mills theory. We computed the perturbative four-loop anomalous dimension of one-impurity states and the Konishi operator of the deformed gauge theory from the Luescher formula based on these twisted S-matrix elements. The result agrees exactly with the perturbative gauge theory computations.

We examine the process of Deep Inelastic Scattering (DIS) in the Regge limit, where Pomeron exchange dominates. Using the AdS/CFT correspondence, we study Pomeron exchange in the dual string theory in AdS space, which allows us to study DIS at strong coupling. Two possibilites are examined, a purely conformal model, and a model with a hard-wall cutoff introduced to take into account effects of confinement. Comparing our calculations with HERA DIS data, we find a very good agreement not only at large $Q^{2}$ dominated by conformal symmetry, but due to our strong coupling approach which allows us to go beyond traditional pQCD methods, at small $Q^{2}$ as well, taking into account all available HERA small x data.

Lovelock gravities are the most general higher dimensional second order theories free of ghosts when expanding about flat space. They admit a family of AdS vacua for generic values of the couplings. Most of them support black hole solutions displaying novel interesting features. I will present some aspects of AdS/CFT applied to this framework, including non-trivial checks of the conjectured duality.

Conformal field theories are good friends for both physicists (since they have many applications to critical phenomena, condensed matter, and high energy physics) and mathematicians (they are mathematically well-defined). In two dimensions, conformal field theories have been studied to near-exhaustion. In three and four dimensions, much less is known, and the field is wide open. I will discuss the 'bootstrap' system of equations which, in a sense, defines conformal field theories, and recent results following from the numerical exploration of this system. I will argue that many more results lie ahead ready to be discovered by the same methods. The whole story is crying out for an analytical understanding.

I shall discuss the construction of Hermitian Yang-Mills instantons over Calabi-Yau cones, as well as over their resolutions. In particular, in d complex dimensions, I shall present an infinite family of $SU(d)$ instantons, parametrised by an integer $k$ and a continuous modulus. A detailed study of their properties, including the computation of the instanton numbers is provided. Then, I shall also explain how they can be used in the construction of heterotic non-Kahler solutions, including heterotic string duals of 4d $N=1$ SYM theories.

We will discuss the basic first order formalism that captures the flow of moduli and the dynamics of the metric in the presence of a black attractor- with a brief review of black hole systems in flat space to introduce the formalism, we will then go on to exploit the full machinery of this formalism to study black branes in the presence of fluxes in an $N=2$ SUSY setup. (Based on work with S. Barisch, G. Cardoso, M. Haack and N. Obers)

Stokes phenomena are quite general behaviors in non-perturbative regime and essential information beyond perturbative analysis of physical systems. In this talk, we discuss the Stokes phenomena in non-critical string/M theory within the corresponding multi-cut two-matrix models and their isomonodromy formulation. The explicit solutions to the Stokes multipliers are shown in general k-cut multi-critical points of the systems. We also would like to suggest a new integrable structure of Stokes phenomena which becomes manifest in higher-cut critical points.

We compute the coefficient of the massless tree-level, one, two-loop four-point amplitude from first principles. Contrasting with the mathematical difficulties in the RNS formalism where unknown normalizations of chiral determinant formula force the two-loop coefficient to be determined only indirectly through factorization, the computation in the pure spinor formalism can be smoothly carried out.

Perturbative expansions of physical quantities such as free energies can give us some insight into the weakly coupled regime of the theory we started from. But such expansions are often divergent and defined only as asymptotic series. In fact, this divergence is connected to the existence of nonperturbative contributions, i.e. instanton effects that cannot be captured by a perturbative analysis. The theory of resurgence is a mathematical tool which allows us to effectively study this connection and its consequences. This will be the main subject of this talk, specifically how one can construct a full nonperturbative solution from pertubative data, and how this relates to the existence of background independence in matrix models.

I explain how the representation theory of symmetric groups
provides elegant solutions to problems related to local operators
in \(N=4\) super-Yang Mills. Gauge-invariant local operators in
this theory are constructed from matrices transforming in the
adjoint of the U(N) gauge group. Permutations can be used to
organise the operators. Characters and Clebsch-Gordan coefficients
associated with representations as well as certain universal
elements in the symmetric group algebras play a role in these
applications. Schur-Weyl duality is also a recurrent theme.

In this talk, closed bosonic strings propagating in a flat background with constant H-flux as well as in its T-dual configurations are studied. For that purpose, a conformal field theory capturing linear effects in the flux will be defined and scattering amplitudes of tachyon vertex operators will be computed. In the resulting expressions, the Rogers dilogarithm plays a prominent role. Furthermore, indications for a nonassociative structure are found, which can be described in terms of a deformed tri-product. Finally, it is argued that the non-geometric R-flux background flows to an asymmetric CFT.

I will discuss massless open and closed string scattering amplitudes in flat space at high energies. Similarly to the case of AdS space I will demonstrate that, under the $T$-duality map, the open string amplitudes are given by the exponential of minus minimal surface areas whose boundaries are cusped closed loops formed by lightlike momentum vectors. I will then explain how the Douglas boundary functional can be used to study various relations between amplitudes at strong coupling.

After a brief review of several contexts where (BPS) invariants change as function of the external moduli, I will discuss how the use of Maxwell-Boltzmann statistics (as opposed to Bose-Fermi statistics) simplifies the problem of determining the change of the BPS spectrum. I will continue with explaining how the BPS invariant corresponding to a multi-center black hole can be determined using localization. Based on work with B. Pioline and A. Sen.

Supersymmetric string configurations with D-branes have been successfully used to provide a microscopic explanation for the entropy of extremal black-holes, the prototipical example being the 3-charge black-hole in type IIB string theory compactified on $S^1\times T^4$. I will discuss how mixed open/closed string amplitudes can be used to study each microstate when the string coupling $g_s$ is switched on and one moves from the free string/D-brane regime to the black hole regime. As an example, I will focus on a particular class of 3-charge vacua and derive from string theory their corresponding geometric description.