Pomeron Eigenvalue at Three Loops in N=4 Supersymmetric Yang-Mills Theory.

We obtain an analytical expression for the next-to-next-to-leading order of the Balitsky-Fadin-Kuraev-Lipatov (BFKL) Pomeron eigenvalue in planar N=4 SYM using quantum spectral curve (QSC) integrability-based method. The result is verified with more than 60-digit precision using the numerical method developed by us in a previous paper [N. Gromov, F.

Exact slope and interpolating functions in N=6 supersymmetric Chern-Simons theory.

Using the quantum spectral curve approach we compute, exactly, an observable (called slope function) in the planar Aharony-Bergman-Jafferis-Maldacena theory in terms of an unknown interpolating function h(λ) which plays the role of the coupling in any integrability based calculation in this theory. We verified our results with known weak coupling expansion in the gauge theory and with the results of semiclassical string calculations. Quite surprisingly at strong coupling the result is given by an explicit rational function of h(λ) to all orders.

Dynamics of inertial particles in a random flow with strong permanent shear.

We consider advection of small inertial particles by a random fluid flow with a strong steady shear component. It is known that inertial particles suspended in a random flow can exhibit clusterization even if the flow is incompressible. We study this phenomenon through statistical characteristics of a separation vector between two particles.