I will review the intermediate long wave equation which interpolates between the celebrated Korteweg-de Vries and Benjamin-Ono equations, describing the one-dimensional waves in a shallow and deep water, respectively. The quantum version of this equation is of some interest to the theory of quantum wires and other quasi-one dimensional condensed matter systems. I will explain the unexpected connection of this equation to the dynamics of gauge theories in two, four, and six dimensions. This connection is one of the applications of the BPS/CFT correspondence. Based on the work in progress with Andrei Okounkov

I will discuss recent developments in the duality between gauge-fields and Strings.

**Polygon Seminar** Over the past several years, it has become increasingly apparent that many interesting and tractable superconformal field theories (SCFTs) can be realized without resorting to a UV Lagrangian description. Although many of these theories have N=2 supersymmetry, these is an even larger class of N=1 theories that can be studied, certain aspects of which remain calculable despite the reduced amount of supersymmetry. In this talk, I will give an introduction to these N=1 theories, how they can be realized via M-theory and F-theory, and which tools we can use to explore them.

Computation of conformal dimensions in planar N=4 SYM using integrability techniques was a hot topic during the last decade, with more than thousand publications devoted to it. I will tell you about our new results in this domain: Instead of the Y-system used previously, we are now able to encode the conformal dimensions, at any value of the 't Hooft coupling, in much simpler way: through a Riemann-Hilbert problem. This appears to be not only a very beautiful mathematical setup, but also the most efficient approach to explicitly compute the dimensions. For instance, we've analytically computed the so called Konishi anomalous dimension up to 8 loops in perturbation theory. The talk will include a pedagogical overview of the subject, no special knowledge in this domain is required.

We study a holographic model dual to a CFT in 2+1 dimensions at finite temperature and chemical potential with a global U(2) symmetry. At large enough chemical potential spontaneous symmetry breaking occurs and breaks the symmetry to U(1). The non-abelian nature of the symmetry and the explicit Lorentz breaking by the chemical potential imply the presence of an ungapped mode with quadratic dispersion relation in the broken phase. Such modes are called Type II Goldstone bosons and have several distinguished features that we study within the framework of this holographic model.

In this talk I will explain a new method to numerically construct stationary black holes with non-Killing horizons. As an example, we will use AdS/CFT to describe a time-independent CFT plasma flowing through a static spacetime which asymptotes to Minkowski in the flow's past and future, with a varying spatial geometry in-between. When the boundary geometry varies slowly, the holographic stress tensor is well-described by viscous hydrodynamics. For fast variations it is not, and the solutions are stationary analogs of dynamical quenches, with the plasma being suddenly driven out of equilibrium. We find evidence that these flows become unstable for sufficiently strong quenches and speculate that the instability may be turbulent. The gravitational dual of these flows are the first examples of stationary black holes with non-Killing horizons.

I will present the quantized function algebras associated with various examples of generalized sine-Gordon models. These are quadratic algebras of the general Freidel-Maillet type, the classical limits of which reproduce the lattice Poisson algebra recently obtained for these models formulated as gauged Wess-Zumino-Witten models plus an integrable potential. More specifically, I will argue based on these examples that the natural framework for constructing quantum lattice integrable versions of generalized sine-Gordon models is that of affine quantum braided groups.

Quivers are directed graphs which encode information about the gauge groups and matter content of a large class of gauge theories, many of which have AdS/CFT duals. The counting of local gauge invariant operators and the computation of their correlators (in the free field limit) can be done by simple diagrammatic manipulations of the quiver, with the help of permutation group theory data. This data includes Young diagrams, Littlewood-Richardson numbers and branching coefficients of permutation groups. Riemann surfaces obtained by thickening the quivers are intimately related to these computations.

Tom Kibble was a pioneer of the symmetry breaking paradigm in fundamental physics. His view of physics is exceptionally broad, and Tom also led efforts to see how to test ideas of grand unification through exploring their consequences for the very early universe. Over time, this led to new paradigms for cosmology, like cosmic inflation, with a plethora of observational tests. In this talk, I shall review some of Tom's cosmological innovations and also look forward to new and even more fundamental paradigms capable of tackling the big bang singularity. [Symmetry and Fundamental Physics - Tom Kibble at 80]

In a seminal 1976 paper Tom Kibble pointed out that, in cosmological phase transitions, causality precludes coordination between local choices of broken symmetry, and, as a result, formation of topological defects is all but inevitable. I shall discuss consequences of this Kibble mechanism for condensed matter physics, where its experimentally testable extrapolation is being studied. [Symmetry and Fundamental Physics - Tom Kibble at 80]

In July 2012 ATLAS and CMS experiments reported the discovery of a Higgs-like boson, most likely confirming the mechanism for generation of mass of fundamental particles put forward by Higgs, Kibble and others in the 1960’s. An outline of the challenges faced during the construction of both the LHC and the experiments will be presented as well as an overview of the current operation and performance. Selected physics results and future aims, in particular those relating to the discovery of the Higgs-like boson, will be discussed. [Symmetry and Fundamental Physics - Tom Kibble at 80]

The talk will describe my first interaction with Tom Kibble, when I visited Imperial College in 1961-2; Tom's ground-breaking work on broken symmetry and the Higgs boson; and how a 1967 paper by Tom laid the foundation for understanding the photon. [Symmetry and Fundamental Physics - Tom Kibble at 80]

We will explain the notion of T-duality in supergravity backgrounds with non-Abelian isometries and non-vanishing RR fluxes. We will then focus on type-II backgrounds on which the duality action preserves supersymmetry. For the case of D3-branes at the tip of the conifold dualising along an SU(2) isometry provides a type-IIA background with M-theory lift is of the type describing duals to certain N=1 SCFT quivers produced by M5-branes wrapping a Riemann surface. In the non-conformal cases we find smooth duals in massive IIA supergravity with a Romans mass naturally quantised. We initiate the interpretation of these geometries in the context of the AdS/CFT correspondence and discuss the fate of various charges under dualisation. The backgrounds suggest a form of Seiberg duality in the dual field theories which also exhibit domain walls and confinement in the infrared.

I will present the exact computation of the two-dimensional supersymmetric theories on two-sphere using the localization techniques. I will then apply these new results to study type II string compactifications (with emphasis on the exact Kaehler potential of quantum Kaehler moduli of Calabi-Yau geometry and mirror symmetry) and non-rational CFTs.

I shall discuss the structure of supersymmetry invariants in N=4 supergravity coupled to n vector multiplets, and in particular their transformation properties with respect to duality symmetry. This will permit to discuss the anomalous Ward identities for the duality symmetry, and their consequences on the logarithmic divergences of the theory.

In the first part of my talk, I will present a general classification of Riemannian three-manifolds on which one can put 3d N=2 supersymmetric field theories while preserving some amount of supersymmetry. This formalism clarifies the relationship between the extra couplings necessary to preserve supersymmetry in curved space, on the one hand, and various operators of the flat space theory, on the other hand. In the second part of the talk I will present some simple applications of this formalism. In particular I will present exact results for various two-point functions of N=2 SCFTs which were hitherto out of reach.

I will present a series of new results on classical and quantum properties of maximal supergravity in 4 dimensions, emphasizing the role of the recently discovered "new SO(8) theories". I will explain how this changes our understanding of some general properties of supergravity theories and comment on the impact of these results on the gauge/gravity correspondence.

We study N=2 ADE quiver gauge theories in presence of a non-trivial Omega background along a two dimensional plane. In particular we perform a saddle point analysis to the partition function and derive an epsilon-deformed version of Seiberg-Witten like equations. The result can be interpreted as a non-commutative version of the standard Seiberg-Witten curves associated to the quiver theories.