Starting from the effective-action model for planckian scattering, I present a development of the eikonal representation of the S-matrix for 2->2 scattering which is able to describe particles' motion in 3-dimensions. The resulting particles' shock-waves undergo calculable position shifts and time delays during the scattering process, which turns out to be consistently described by both action and metric, up to order (R/b)^2 in the gravitational radius over impact parameter expansion

We present the complete NLO corrections for quark induced jets with a rapidity gap. We use Lipatov's QCD high energy effective action to determine the real part of the next-to-leading order corrections to the Mueller-Tang impact factor which is the only missing element for a complete NLO BFKL description of quark induced dijet events with a rapidity gap. We then combine our result with the already known virtual corrections and verify ultraviolet and collinear finiteness of our result.

We consider within QCD collinear factorization the process, where two forward jets are produced with a large separation in rapidity (Mueller-Navelet jets). In this case the (calculable) hard part of the reaction receives large higher-order corrections, which can be accounted for in the BFKL approach with next-to-leading logarithmic accuracy. We calculate several observables related with this process, using the next-to-leading order jet vertices, recently calculated in the approximation of small aperture of the jet cone in the pseudorapidity-azimuthal angle plane.

We review the approach to the high energy scattering in non-abelian gauge theories and gravity based on the effective field theory for reggeized gluons and gravitons. The corresponding Regge trajectories and various reggeon couplings can be obtained from the effective actions containing the interactions local in the particle rapidities. There are additional fields describing the production and annihilation of reggeons in the crossing channel. The action allows to construct the production amplitudes in quasi-multi-Regge kinematics of the final state particles. In N=4 SUSY the inelastic amplitudes in the planar approximation contain the Regge pole and Mandelstam cut contributions having the simple analytic properties including the dual Moebius invariance.

The high-energy factorization of gauge theory scattering amplitudes in terms of universal impact factors and a Reggeized exchange in the $t$-channel, corresponding to a Regge pole in the angular momentum plane, is know to conflict with the structure of soft anomalous dimensions starting at the two-loop level. I will review the arguments leading to the violation of this factorization at NNLL, and I will explore the implications of this for two- and three-loop QCD amplitudes.

We apply the recently proposed quantum spectral curve technique to the study of twist operators in planar N=4 SYM theory. Focusing on the small spin expansion of anomalous dimensions in the sl(2) sector we compute its first two orders exactly for any value of the `t Hooft coupling. At leading order in the spin S we reproduced Basso's slope function. The next term of order S^2 structurally resembles the Beisert-Eden-Staudacher dressing phase and takes into account wrapping contributions. This expansion contains rich information about the spectrum of local operators at strong coupling. In particular, we found a new coefficient in the strong coupling expansion of the Konishi operator dimension and confirmed several previously known terms. We also obtain several new orders of the strong coupling expansion of the BFKL pomeron intercept.

In this talk, I will present recent work on the calculation of scattering amplitudes in strongly coupled N=4 super Yang-Mills. To leading order, the calculation of scattering amplitudes in this theory corresponds to calculating specific minimal surfaces embedded into AdS5. The solution to this problem is given in terms of a set of non-linear integral equations, which do not have an analytic solution for general kinematics. Therefore, we specialise to the multi-Regge limit and find that the integral equations simplify and explicit results can be obtained. I will present a general algorithm for the calculation of scattering amplitudes in the multi-Regge regime and show results for the 6- and 7-point amplitude as specific examples.

The origins of multi-Regge theory, past and current successes, and the possible future deep significance will all be discussed.

Wilson line operators are a common tool for understanding infrared divergences in (non)-Abelian gauge theories. Similar operators for gravity have been considered only relatively recently. In this talk I will review the definition of gravitational Wilson lines, and discuss example applications. Particularly relevant for this meeting is the Regge limit, where the Wilson line language allows one to relate the behaviour of QCD and gravity in a particularly appealing way. I will also discuss how infrared singularities can be used to probe the recently proposed double copy between non-Abelian gauge and gravity theories.