Anber, Mohamed: "The SU(3)/Z_3 QCD (adj) Deconfinement Transition via the Gauge Theory/"Affine" XY-Model Duality"
Previously, it was shown that some 4d gauge theories, compactified on a small spatial circle and considered at temperatures near deconfinement, are dual to 2d "affine" XY-spin models. We exploit this duality to study the deconfining phase transition of SU(3)/Z_3 gauge theories with n_f massless adjoint Weyl fermions.  The"affine" XY-model describes two "spins"  scalars taking values in the SU(3) root lattice, with nearest-neighbor interactions and subject to an "external field" preserving the topological Z_3^t and a discrete Z_3^chi subgroup of the chiral symmetry of the 4d gauge theory. We study the nature of the transition via Monte Carlo simulations of the dual spin model. Interestingly enough, we find that the transition is a first-order, as has been seen in earlier simulations of the full 4d QCD(adj) theory. This finding, along with others, may open the door into a new paradigm to tackle complicated strong coupling problems. 

Balitsky, Ian:  “NLO BFKL and Anomalous Dimensions of Light-Ray Operators”
The anomalous dimensions of light-ray operators of twist two are obtained by analytical continuation of the anomalous dimensions of corresponding local operators. I demonstrate that the asymptotics of these anomalous dimensions at the ``BFKL point'' $j\rightarrow 1$ can be obtained by comparing the light-cone operator expansion with the high-energy expansion in Wilson lines. 

Banerjee, Debasish: “Simulating Quantum Dynamics of Lattice Gauge Theories”
Quantum Link models are generalizations of Wilson's formulation of Lattice Gauge theories, but with discrete degrees of freedom which still implement an exact continuous gauge symmetry. These are amenable to quantum simulation using ultra-cold atomic gases in optical lattices. Sinc  quantum simulators do not suffer from the notorious sign problem, this offers a fresh approach to tackle problems otherwise intractable with conventional simulation methods. Examples include real time dynamics of string breaking to chiral symmetry restoration at finite density presently formulated with simple model systems. Some of these models also display unconventional phases which have been uncovered only recently using a newly developed cluster algorithm. 

Bender, Carl:  "PT-Symmetric Interpretation of Double-Scaling"
The conventional double-scaling limit of an O(N)-symmetric quarticquantum field theory is inconsistent because the critical coupling constant is negative. Thus, at the critical coupling the Lagrangian defines a quantum theory with an upside-down potential whose energy appears to be unbounded below. Worse yet, the integral representation of the partition function of the theory does not exist. It is shown that one can avoid these difficulties if one replaces the original theory by its PT-symmetric analog. For a zero-dimensional O(N)-symmetric quartic vector model the partition function of the PT-symmetric analog is calculated explicitly in the double-scaling limit.

Bilandzic, Ante:  "Anisotropic Flow in ALICE at LHC"
The measurement of azimuthal anisotropy in the momentum distribution of produced particles in heavy-ion collisions allows to study the properties of the produced matter. The highlights of anisotropic flow measurements in Pb- Pb collisions at √s NN = 2.76 TeV by the ALICE collaboration at the LHC will be presented, with an emphasis on results obtained via multi-particle correlation techniques. 

Britto, Ruth:  “Discontinuities of Loop Integrals”
Feynman integrals and loop amplitudes can be characterized by their discontinuities.  I will review applications of unitarity cut methods, discuss issues arising with massive particles, and explore the values and interpretations of the discontinuities associated to generalized cuts.

Broniowski, Wojciech:  “Collective Dynamics of the p+Pb Collisions”
We present predictions of hydrodynamics initialized with the Glauber model for the features of the p+Pb collisions recently measured at the LHC. In particular, the large values of the harmonic flow coefficients v_2 and v_3, as well as the natural appearance of the near-side ridge indicate a large degree of collectivity in this system. Predictions for other quantities, such as the p_t spectra and femtoscopic radii are also shown.

Das, Sumit:  “Quantum Quench and Holographic Critical Points”

De Forcrand, Philippe: “Scale Hierarchy in High-Temperature QCD”
Because of asymptotic freedom, QCD becomes weakly interacting at high  temperature: this is the reason for the transition to a deconfined  phase in Yang-Mills theory at temperature T_c. At high temperature  T >> T_c, the smallness of the coupling g induces a hierachy betwen  the "hard", "soft" and "ultrasoft" energy scales T, g T and g^2 T. This  hierarchy allows for a very successful effective treatment where the  "hard" and the "soft" modes are successively integrated out. However,  it is not clear how high a temperature is necessary to achieve such  a scale hierarchy.  By numerical simulations, we show that the required temperatures are  extremely high. Thus, the quantitative success of the effective theory  down to temperatures of a few T_c appears surprising a posteriori.

De Teramond, Guy:  “Systematics of the Hadron Spectrum from Conformal Quantum Mechanics and Holographic QCD”
A complementary approach, derived from (a) higher dimensional AdS space, (b) light-front quantization and (c) the invariance properties of the one-dimensional representation of the full conformal group leads to a nonperturbative relativistic light-front wave equation which incorporates essential characteristics of the hadron spectrum. The mass scale for hadrons appears from spontaneous breaking of dilatation invariance in the light-front Hamiltonian, while retaining the conformal invariance of the action. Remarkably, the specific form of the confinement interaction is uniquely determined.

Detmold, William:  “Exclusive Decays of Heavy Baryons”
In combination with experimental measurements, lattice QCD calculations of exclusive decays of hadrons provide opportunities to explore and test the Standard Model in the flavour sector. This has long been exploited in the case of bottom meson decays such as $B -> K \gamma and B -> \pi l \nu. Recent work, in which  we have considered the analogous flavour-changing neutral current decay \Lambda_b -> \Lambda mu^+ mu^- and results for other exclusive decays will be discussed.

 Djuric, Marko:  “Odderon in Gauge/String Duality”
At high energies, elastic hadronic cross sections are dominated by vacuum exchange, which in leading order of the $1/N_c$ expansion has been identified as the BFKL Pomeron or its strong AdS dual the closed string Reggeized graviton, also known as the BPST Pomeron. However the difference between particle-particle and particle anti-particle cross sections is given by a so-called Odderon, carrying C = -1 vacuum quantum numbers identified in weak coupling with odd numbers of exchanged gluons. Here we show that in the dual description the Odderon is the Reggeized Kalb-Ramond field ($B_{\mu\nu}$) in the Neveu-Schwartz sector of closed string theory. To first order in strong coupling, the high energy contribution of Odderon is evaluated for ${\cal N} = 4$ Super Yang-Mills by a generalization of the gravity dual analysis for the Pomeron. The consequence of confinement on the Odderon are estimated in the confining QCD-like $AdS^5$ hardwall model.

Dudal, David:   Some Insights Into the Magnetic QCD Phase Diagram from the Sakai-Sugimoto Model
In recent years, we witnessed an increasing number of papers studying the effects of a (strong) magnetic field B on the QCD phase diagram. This booming interest is supported by the potential occurrence of such a magnetic field in the extreme circumstances of heavy ion collisions. Since the relevant physics is highly nonperturbative, approximate treatments are in order.  In this talk, I’ll give a short overview of how we used the Sakai-Sugimoto model to study holographically the influence of B on the chiral transition temperature and on the possible condensation of charged vector mesons.   These results can be interpreted as the holographic analogues of quenched QCD in the chiral limit.

Dumitru, Adrian:  "Magnetic Vortices in High-Energy Heavy-Ion Collisions"
I discuss the structure of longitudinal chromomagnetic fields which develop in heavy-ion collisions. Rather than being homogeneous, Bz is found to exhibit domain-like structures in the transverse plane. The expectation values of spatial Wilson loops exhibit area law scaling for radii larger than the inverse saturation momentum, indicating uncorrelated magnetic flux fluctuations at such scales. The corresponding spatial string tension is approximately invariant under a Z(2) projection of the SU(2) Wilson loops. I discuss the failure of a naive perturbative expansion to reproduce area law scaling and the role of magnetic screening.

El-Showk, S.:  "Bootstrapping Conformal Field Theories"
The existence of a positive linear functional acting on the space of (differences between) conformal blocks has been shown to rule out regions in the parameter space of conformal field theories (CFTs). We argue that at the boundary of the allowed region the extremal functional contains, in principle, enough information to determine the dimensions and OPE coefficients of an infinite number of operators appearing in the correlator under analysis. Based on this idea we develop the Extremal Functional Method (EFM), a numerical procedure for deriving the spectrum and OPE coefficients of CFTs lying on the boundary (of solution space). We test the EFM by using it to rederive the low lying spectrum and OPE coefficients of the 2d Ising model based solely on the dimension of a single scalar quasi-primary – no Virasoro algebra required. Our work serves as a benchmark for  interesting, less known CFTs (such as the 3d Ising model) in the near future.

Epelbaum, Thomas: "The Early Stages of Heavy Ion Collisions”
In recent years, the problem of thermalization in Heavy Ion Collision has received much attention, but has yet to be solved.  The issue is the following: on the one hand, viscous hydrodynamics simulations suggest that the matter produced in such collisions (called the Quark Gluon Plasma, or QGP) behaves like a nearly perfect fluid, and does so very shortly after the collision (around 1 fm/c). Since hydrodynamics require local thermal equilibrium, this tends to show that the QGP has thermalized during the very early stages of the collision. On the other hand, theoretical models (like the Color Glass Condensate, or CGC) predict that the QGP is very far from local thermal equilibrium at the initial time (its energy-momentum is very anisotropic). One of the approaches developed to study this non-perturbative problem in QCD is a resummation scheme that amounts to averaging over classical fields, with random initial conditions. Its numerical implementation is presented here for the case of a scalar field theory with quartic coupling, that shares some important features with QCD (scale invariance at the classical level and the presence of instabilities). In particular, we will show the relevance of this resummation in capturing the physics relevant for thermalization. First analytical results concerning QCD will also be presented".

Evans, Nick:  “Holographic Vector Mesons and Low x Production”
Gauge/gravity duality can provide a description of chiral symmetry breaking and the q qbar meson masses. I review top down and bottom up models of the vector mesons and their holographic wave functions. A good test of these models is provided by low x vector meson production - I describe how a holographic computation of these processes using a regge-graviton pomeron proceeds. I present fits to the HERA H1 data for these processes which have a chi-squared fit of better than 1 per degree of freedom.

Filip, Peter:  "Magnetic Quenching of Quarkonium Decay".
In very strong magnetic fields created in relativistic heavy ion collisions a quantum mixing of spin-triplet and singlet states of heavy quarkonium might take place.  Based on the analogy with magnetic quenching of ortho-Positronium decay (observed in 1955), we shall  discuss the possibility of a similar behaviour for J/Psi and Upsilon mesons in relation to the specific signatures of quark gluon plasma formation.

Frasca, Marco: "QCD, Wilson Loop and the Interquark Potential"
Wilson loop is discussed for a pure Yang-Mills theory using a decoupling solution for the gluon propagator, in close agreement with lattice computations. At one-gluon exchange level it is shown how the potential cannot yield a linear rising contribution as expected for a confining theory. Then, next-to-leading order correction is computed giving rise to a quartic term for momenta in the gluon propagator. This contribution, in agreement with Gribov's view, yields a linear confining term. Such a correction is due to a two-loop or sunrise integral that we need to evaluate in the low-momenta limit. In the infrared regime, the physical consistency of the theory is determined by a natural cut-off, arising from the integration of the classical equations of the theory, fixing in this way the regularization scheme.

Fried, Herb:  “Inflation as the Precursor of Dark Energy”
A QED-based model of a new version of Vacuum Energy is suggested, which leads to a simple, finite, one-parameter representation of Dark Energy. An elementary, obvious, but somewhat radical generalization is then able to describe both Dark Energy and Inflation in the same Vacuum Energy framework, as well as the origins of Dark Matter, Ultra-High Energy Cosmic Rays, including GeV Gammas, with and without X-ray and Optical radiation tails. One further, obvious generalization then leads to a relation between Inflation and the Big Bang, and to a possible understanding of the Birth and Death of a Universe.

Grandou, Thierry: “On Casimir Operators Scaling Laws in QCD”
In eikonal and quenched approximations at least, it is argued that the non-perturbative fermionic QCD amplitudes obtained with the help of the newly discovered Effective Locality property, depart from ordinary scaling laws in $C_2({\cal{R}})$, where $C_2({\cal{R}})$ is the $SU_c(3)$ quadratic Casimir operator, evaluated on some relevant gauge group representation ${\cal{R}}$. This result, at variance with most customary ones accounts for the full content of the rank-2 $SU_c(3)$ Lie algebra, as it involves not only the quadratic but also the cubic Casimir operator $C_3({\cal{R}})$.

Hansen, Hubert:  “A Detailed Analysis of the Phase Diagram of QCD in the High Density and Temperature Region”
In this talk we will present the detailed behavior of the mean field parameter and mesonic excitations of the Polyakov -- Nambu -- Jona-Lasinio (PNJL) model in the high density/intermediate temperature phase.  This effective model of the Quantum Chromodynamic contains quarks as fundamental degrees of freedom and exhibits a spontaneous chiral symmetry breaking. Besides, the coupling to the Polyakov loop allows the model to describe the (statistical) confinement/deconfinement phase transition by taking into account a static gluonic field in which quarks propagate. The PNJL model is well known to give a good description of QCD thermodynamics at zero density when compared to lattice QCD calculations. We will present an extended analysis of this model with two flavors at the mean field level and beyond, with a special interest in the high density phase. At this level of approximation the order parameters indicate that a confined phase where the chiral symmetry is restored is possible. We also study the very high density phase and show that the deconfinement cannot be described anymore by a sharp crossover between confined and deconfined phase du to the Fermi motion.

Hautmann, Francesco: “Planckian Scattering and Higher-Dimensional Gravity Fixed Points”
Gravitational high-energy scattering is studied in models with extra dimensions under the hypothesis that quantum corrections to planckian scattering are controlled by ultraviolet fixed points in the gravity coupling.

Jia, Jiangyong:  “Event-by-Event Flow and Initial Geometry at the LHC”
In recent years, the measurement of harmonic flow coefficients vn has provided important information on the hot and dense matter created in heavy ion collisions. These coefficients are now understood to reflect the hydrodynamic response to the collision geometry in the initial state. I present recent results from LHC on  event by event vn and correlation between their phases.  I will discuss the insights from these results on the  the initial geometry fluctuation and the hydrodynamic  response of the produced medium.

Johansson, Henrik:  "Supergravity from 2 and 3-Algebra Gauge Theory"
Supergravity scattering amplitudes in general space-time dimension have the remarkable property that they can be constructed out of double copies of Yang-Mills interactions. In three dimensions, they can also be built out of double copies of Chern-Simons-matter  interactions. This holds when these gauge theories exhibit a duality between color and kinematics, which predicts the existence of a novel kinematic Lie 2-algebra in Yang-Mills theory, and similarly a kinematic Lie 3-algebra for Chern-Simons-matter theory.

Korchemsky, Gregory: "Energy Flow in N=4 SYM".

Marquet, Cyrille:  “Multi-Particle Production in Proton-Nucleus Collisions in the CGC Framework”
Within the Color Glass Condensate (CGC) framework, I will discuss particle production in the collision of a dilute projectile with a dense hadronic target. For years CGC studies focused on the dipole scattering amplitude, and it's evolution towards high energies or small x. One has now reached an accuracy sufficient to quantitatively describe single inclusive particle production in p+A type collisions, at least in the forward rapidity region, sensitive to the smallest values of x. Recently the focus has turned to the quadrupole amplitude, necessary to compute the two-particle inclusive case. Actually in the large-Nc limit, only dipoles and quadrupoles contribute, and I will show that this is the case irrespectively of the numbers of particles measured in the final state.

Mehtar-Tani, Yacine: “Generating Functional for Jet Observables in Heavy Ion Collisions”
The recent jet measurements at the LHC have challenged the heavy-ion community to a better understanding of jet fragmentation in the presence of the Quark-Gluon-Plasma (QGP).   Almost 30 years ago, the theory of jet fragmentation in vacuum was established in the framework of perturbative QCD yielding a very good agreement with the data in $e^+e^-$, hadron-hadron collisions, etc.  However, in the presence of the QGP, just a little is known, and only the single gluon emission probability at leading order in the coupling constant has been achieved from first principle calculations.  Only recently, color coherence effects between multiple partons in a shower have been considered. In particular it was show that jet-medium interactions lead to the decoherence of partons all along the patron cascade. In this work, we studied jet evolution through a dense QCD medium such as the quark-gluon plasma (QGP) formed in heavy Ion Collisions (HIC). We established a factorization scheme where we focus on relatively soft gluons emitted at large angles for which the formation time is much smaller than the overall size of the medium. We show that multiple emissions are important even at weak coupling because the smallness of the coupling constant is compensated by the large available phase-space, which is proportional to the longitudinal size of the medium. We show that successive emissions of this type are typically independent from each other and can be factorized. Indeed, coherence effects are restricted to time intervals of the order of the formation time and hence are parametrically suppressed. Ultimately, we propose a probabilistic description of in-medium multiple soft gluon emission. A generating functional is constructed and can be implemented as a Monte Carlo to study jet observables in HIC

Mukhopadhyay, Ayan:  “AdS/CFT Imprints on the ALICE Fireball?”
In the classical gravity approximation and at strong coupling, AdS/CFT predicts a generalization of the non-equilibrium fluctuation-dissipation relation, which holds universally for any non-equilibrium state. We will briefly sketch how this relation can be derived. We will then investigate it's imprints on ALICE experiments. We will consider a general semi-holographic model for heavy ion collisions, where non-perturbative degrees of freedom are holographic and perturbative degrees of freedom are the glasma fields which dominate the initial stage of evolution after the collision. We will show that the holographic non-equilibrium fluctuation-dissipation relation can indeed be tested by the event-by-event fluctuations in collective flow which arise as response to quantum fluctuations in initial conditions. We will also discuss universal aspects of the dynamics of thermalization in these semi-holographic models.

Nesterenko, Alexander: “Dispersive Approach to QCD and Hadronic Vacuum Polarization Function”
Hadronic vacuum polarization function is studied within dispersive approach to QCD. The latter embodies intrinsically nonperturbative constraints, which originate in the kinematic restrictions on the function on hand, and incorporates the effects due to hadronization, which play valuable role in the analysis of the strong interaction processes in the infrared domain. The hadronic vacuum polarization function obtained within developed approach proves to be in a good agreement with relevant low-energy lattice simulation data. A number of other applications of the dispersive approach are briefly discussed

Nitti, Francesco:  The Trailing String in Confining Holographic Theories”
The gravity dual of a single heavy probe quark in AdS/CFT is a fundamental string trailing behind the quark in the bulk geometry, with the quark  as its UV endpoint.  In the deconfined, black hole phase, this  configuration allows to compute holographically the energy loss and   diffusion parameters for the quark trajectory. In this talk I will  discuss the trailing string dynamics in a confining geometry, which  displays new and unexpected features such as an emergent temperature and dissipative dynamics in the vacuum.  

Ollitrault,  Jean-Yves:  “Introduction to the Heavy-Ion Session”
Nucleus-nucleus collisions at the LHC create a drop of strongly-coupled  quark-gluon plasma which expands into the vacuum like a fluid.  I briefly review the experimental observations which have led to this conclusion, and list some of the pending issues to be discussed during the session.

Orginos, Kostas:  “Nuclear Physics From Lattice QCD”
Quantum Chromodynamcs (QCD) is now established as the theory of strong interactions. A plethora of hadronic physics phenomena can be explained and described by QCD. From the early days of QCD, it was clear that low energy phenomena require a non-perturbative approach. Lattice QCD is a non perturbative formulation of QCD that is particularly suited for numerical calculations. Today, supercomputers are capable of performing calculations that explore  nuclear physics and its connection to QCD. In this talk I will review  recent lattice QCD results, relevant to Nuclear Physics. 

Paulos, Miguel:  “Loops and Splines”
We uncover an unexpected connection between the physics of loop integrals and the mathematics of spline functions. One loop integrands are Laplace transforms of splines. This clarifies the geometry of the associated loop integrals, since a n-node spline has support on an n-vertex polyhedral cone. One-loop integrals are integrals of splines on a hyperbolic slice of the cone, yielding polytopes in AdS space. Splines thus give a geometrical counterpart to the rational function identities at the level of the integrand. Spline technology also allows for a clear, simple, algebraic decomposition of higher point loop integrals in lower dimensional kinematics in terms of lower point integrals - e.g. an hexagon integral in 2d kinematics can be written as a sum of scalar boxes. Higher loops can also be understood directly in terms of splines - they map onto spline convolutions, leading to an intriguing representation in terms of hyperbolic simplices integrated over other hyperbolic simplices. We finish with speculations on the interpretation of one-loop integrals as partition functions, inspired by the use of splines in counting points in polytopes.

Peter, Patrick:  “The Quantum Measurement Problem in Cosmology”
It is sometimes argued that decoherence solves the quantum measurement problem in the cosmological setup, whereas it actually is nowhere as acute as in this ultimate closed system. I will discuss the problem itself and two of its possible solutions; they both require some amount of extension of the quantum mechanical framework, with the bonus that these extension also provide a natural basis for a dynamical understanding of the otherwise arbitrary Born rules.

Petreczky, Peter: ``The Chiral and Deconfinement Transitions in QCD at Non-Zero Temperature and QGP”
I will present recent lattice QCD results on various observables that are sensitive to the deconfinement and chiral transitions in QCD at non-zero temperature.  I will compare results obtained with staggered fermion formulation and with Domain Wall fermion formulation for quantities sensitive to the chiral transition. Fluctuations of conserved charges will be discussed in connection with the deconfinement transition and the effective degrees of freedom for different temperature regions.

Plumari, Salvatore:  “Anisotropic Flows and Shear Viscosity from a Beam Energy Scan”
We employ a relativistic transport theory to describe the fireball expansion of the matter created in ultra-relativistic heavy-ion collisions (uRHICs). Developing an approach to fix locally the shear viscosity to entropy density $\eta/s$, we study the impact of a temperature dependent $\eta/s(T)$ on the build-up of the elliptic flow, $v_2$, a measure of the angular anisotropy in the particle production. Beam Energy Scan from $\sqrt{s_{NN}}= \rm 62.4 GeV$ at RHIC up to 2.76 TeV at LHC has shown that the $v_2(p_T)$ as a function of the transverse momentum $p_T$ appears to be nearly invariant with energy. We show that such a surprising behavior is determined by a rise and fall of $\eta/s(T)$ with a minimum at $T\sim T_c$, as one would expect if the matter undergoes a phase transition or a cross-over. This provides a first constraint on the temperature dependence of $\eta/s$. In particular, a constant $\eta/s$ at all temperatures or a too strong T-dependence would cause a breaking of the scaling of $v_2(p_T)$ with the energy.

Poppitz, Erich:  “Continuity, Deconfinement, and Super-Yang-Mills theory"
Supersymmetry, while still the subject of an intensive search at the LHC, has another impact on particle physics, affecting our understanding of difficult issues in non-perturbative gauge dynamics. In this talk, I will argue that a quantum phase transition in softly-broken pure super-Yang-Mills theory, which can be studied using reliable semiclassical tools, is continuously connected to the thermal deconfinement transition in pure Yang-Mills theory. The mechanism governing the phase transition is universal and valid for all simple groups: monopole-instantons and the perturbative one-loop potential generate attraction among the eigenvalues of the Wilson line, which is counter-acted by ``neutral bions"---novel topological excitations generating  eigenvalue repulsion. The transition is driven by a competition between these three effects, occurs for gauge groups with or without center symmetry, and exhibits interesting theta-angle dependence. In the end, I will compare results with recent lattice studies and discuss directions of current and future research. (Based on work with Thomas Schaefer and Mithat Unsal and ongoing work with Tin Sulejmanpasic.)

Royon, Christophe:  “BFKL Tests at Hadronic Collider: forward Jets, Mueller Navelet Jets and Jet Gap Jets”
We will start by a description of the forward jet measurements at HERA using the BFKL NLL formalism. The same formalism leads to a good description of Mueller Navelet jet measuremnts at the Tevatron. We will finsih the talk by giving the predictions of jet gap jet events at the LHC, and a discussion of the jet veto measurement in ATLAS.

Ruggieri, Marco: “Kinetic Theory Computation of Elliptic Flow in Heavy Ion Collisions”
I review our recent results about the computation of the elliptic flow of the quark-gluon-plasma produced in heavy ion collisions at RHIC and LHC experiments. Our computations are based on Monte Carlo simulations of the expanding fireball created immediately after the collision, whose dynamical evolution is obtained by solving the kinetic Boltzmann  equation. Emphasis is put on new results for a special initial condition, known as the Glasma, and on the role of the nonequilibrium effects on the building up of the elliptic flow.

Spradlin, Marcus: "Introduction to the Amplitudes and String Session"

Stanev, Todor: “Extensive Air Showers and Particle Physics”
We describe the high energy cosmic ray energy spectrum that extends   above 10^{11} GeV in the Lab (220 TeV in cms) and the way the particle  energy is estimated. We give examples for the highest energy cosmic rays  that exceed significantly the current and future LHC energies.   We then give examples about the current work to generate new hadronic   interaction models for air shower analysis that describe correctly   the 7 and 8 TeV LHC data.

Tan, Chung-I:  "Anomalous Dimensions, Pomeron, and AdsS/CFT"

Tarrio, Javier:  “D3-D7 Plasma at Finite Charge and Temperature”In this talk we will consider a deformation at strong coupling of N=4SYM theory, with the addition of a large number of fields transforming in the fundamental representation (flavors) at finite charge density and temperature. This system is a top-down model used to study strong-coupling effects on a hot charged plasma of adjoint and fundamental matter. Having the phase diagram of QCD in mind, we will comment on instabilities and issues at low values of the temperature compared to the charge density.

Travaglini, Gabriele:

Vanhove, Pierre:  "Elliptic Dilogarithm and Two-Loop Amplitudes"
At two-loop order, Feynman integrals show the appearance of an elliptic curve. In this talk we will discuss the role of this elliptic curve and the kind of elliptic function entering in the expression for some particular two-loop integrals. On some example, we will show the appearance of some elliptic dilogarithm expressing the regulator map associated to the underlying algebraic geometrical setup for the two-loop graph.

Vennin, Vincent:  “Inflationary Models after Planck”
An unprecedented opportunity to constrain the inflationary theory is provided by the current flow of high accuracy astrophysical data, among which are the Cosmic Microwave Background measurements by the Planck satellite. This is however a challenging project given the size of the inflationary landscape which contains hundreds of different scenarios. A reasonable approach is to consider the simplest models first, namely the slow-roll single field models with minimal kinetic terms, unless the data drive us to more complicated ones. This still leaves us with a very populated landscape, the exploration of which requires new and efficient strategies. Recently the publicly available runtime library ASPIC has been developed to implement this approach, providing all routines needed to quickly derive reheating consistent observable predictions for each of the ~70 models within this class of scenarios. In this talk I will introduce cosmological inflation and present the status of this evolutive project, ultimately aimed at ranking the inflationary models by means of Bayesian inference. Depending on schedule, I will also show the first results of Bayesian evidences and posteriors for these models.

Wosiek, Jacek: "On Non-Trivial Spectra of Trivial, Two Dimensional Gauge Theories"
It is usually said that the two dimensional gauge theories are trivial, since there are no transverse degrees of freedom to sustain any dynamics. This picture is not fully correct. Beginning from the lattice solution, we will rederive the renown  Manton spectrum, and the effective Hamiltonian, of Quantum Maxwell Dynamics - the pure gauge U(1) theory. The effect of external charges on the spectrum and the structure of $\Theta$ vacua will be also given.