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Lanthanides, like erbium and dysprosium, have emerged as powerful platforms for quantum-gas research due to their diverse properties, including a significant large spin manifold in their absolute ground state. However, effectively exploiting the spin richness necessitates precise manipulation of spin populations, a challenge yet to be fully addressed in this class of atomic species. In this work, we present an all-optical method for deterministically controlling the spin composition of a dipolar bosonic erbium gas, based on a clock-like transition in the telecom window at 1299 nm. The atoms can be prepared in just a few tens of microseconds in any spin-state composition using a sequence of Rabi-pulse pairs, selectively coupling Zeeman sublevels of the ground state with those of the long-lived clock-like state. Finally, we demonstrate that this transition can also be used to create spin-selective light shifts, thus fully suppressing spin-exchange collisions. These experimental results unlock exciting possibilities for implementing advanced spin models in isolated, clean and fully controllable lattice systems.

Electro-optic silicon-based modulators contribute to ease the integration of high-speed and low-power consumption circuits for classical optical communications or quantum computers. However, the inversion symmetry in the silicon crystal structure inhibits the use of Pockels effect. An electric field-induced optical modulation equivalent to a Pockels effect can nevertheless be achieved in silicon by the use of DC Kerr effect. Although some theoretical and experimental studies have shown its existence in silicon, the DC Kerr effect in optical modulation have led to a negligible contribution so far. This paper reports demonstration of high-speed optical modulation based on the electric field-induced linear electro-optic effect in silicon PIN junction waveguides. The relative contributions of both plasma dispersion and Kerr effects are quantified and we show that the Kerr induced modulation is dominant when a high external DC electric field is applied. Finally, the high-speed modulation response is analyzed and eye diagram up to 100 Gbits/s in NRZ format are obtained. This work demonstrates high speed modulation based on Kerr effect in silicon, and its potential for low loss, quasi-pure phase modulation., Comment: 7+6 pages, 5+4 figures

We consider a set of elementary compactifications of $D+1$ to $D$ spacetime dimensions on a circle: first for pure general relativity, then in the presence of a scalar field, first free then with a non minimal coupling to the Ricci scalar, and finally in the presence of gauge bosons. We compute the tree-level amplitudes in order to compare some gravitational and non-gravitational amplitudes. This allows us to recover the known constraints of the $U(1)$, dilatonic and scalar Weak Gravity Conjectures in some cases, and to show the interplay of the different interactions. We study the KK modes pair-production in different dimensions. We also discuss the contribution to some of these amplitudes of the non-minimal coupling in higher dimensions for scalar fields to the Ricci scalar., Comment: 35 pages, 7 figures. One typo in an equation corrected

Three-dimensional quantum gases of strongly dipolar atoms can undergo a crossover from a dilute gas to a dense macrodroplet, stabilized by quantum fluctuations. Adding a one-dimensional optical lattice creates a platform where quantum fluctuations are still unexplored, and a rich variety of new phases may be observable. We employ Bloch oscillations as an interferometric tool to assess the role quantum fluctuations play in an array of quasi-two-dimensional Bose-Einstein condensates. Long-lived oscillations are observed when the chemical potential is balanced between sites, in a region where a macrodroplet is extended over several lattice sites. Further, we observe a transition to a state that is localized to a single lattice plane$-$driven purely by interactions$-$marked by the disappearance of the interference pattern in the momentum distribution. To describe our observations, we develop a discrete one-dimensional extended Gross-Pitaevskii theory, including quantum fluctuations and a variational approach for the on-site wavefunction. This model is in quantitative agreement with the experiment, revealing the existence of single and multisite macrodroplets, and signatures of a two-dimensional bright soliton., Comment: 12 pages, 4+4 figures

The ability to exploit the on-chip nonlinear generation of new frequencies has opened the door to a plethora of applications in fundamental and applied physics. Excitation of dispersive waves is a particularly interesting process that allows efficient nonlinear wavelength conversion by phase-matching of a soliton and waves in the normal dispersion regime. However, controlling the wavelength of dispersive waves in integrated waveguides remains an open challenge, hampering versatile shaping of the nonlinear spectral response. Here, we show that metamaterial silicon waveguides release new degrees of freedom to select the wavelength of dispersive waves. Based on this concept, we experimentally demonstrate excitation of two dispersive waves near 1.55 {\mu}m and 7.5 {\mu}m allowing ultra-wideband supercontinuum generation, covering most of the silicon transparency window. These results stand as an important milestone for versatile nonlinear frequency generation in silicon chips, with a great potential for applications in sensing, metrology and communications.

Flexible control of the modal confinement in silicon photonic waveguides is an appealing feature for many applications, including sensing and hybrid integration of active materials. In most cases, strip waveguides are the preferred solution to maximize the light interaction with the waveguide surroundings. However, the only two degrees of freedom in Si strip waveguides are the width and thickness, resulting in limited flexibility in evanescent field control. Here, we propose and demonstrate a new strategy that exploits metamaterial engineering of the waveguide core and cladding to control the index contrast in the vertical and horizontal directions, independently. The proposed dual-material geometry yields a substantially increased calculated overlap with the air (0.35) compared to the best-case scenario for a strip waveguide (0.3). To experimentally demonstrate the potential of this approach, we have implemented dual-metamaterial ring resonators, operating with the transverse-magnetic polarized mode in 220-nm-thick waveguides with air as upper-cladding. Micro-ring resonators implemented with strip and dual-metamaterial waveguides exhibit the same measured quality factors, near 30,000. Having similar measured quality factors and better calculated external confinement factors than strip waveguides, the proposed dual-metamaterial geometry stands as a promising approach to control modal confinement in silicon waveguides.

Einstein-Maxwell-dilaton theory with non-trivial dilaton potential is known to admit asymptotically flat and (Anti-)de Sitter charged black hole solutions. We investigate the conditions for the presence of horizons as function of the parameters mass $M$, charge $Q$ and dilaton coupling strength $\alpha$. We observe that there is a value of $\alpha$ which separate two regions, one where the black hole is Reissner-Nordstr\"om-like from a region where it is Schwarzschild-like. We find that for de Sitter and small non-vanishing $\alpha$, the extremal case is not reached by the solution. We also discuss the attractive or repulsive nature of the leading long distance interaction between two such black holes, or a test particle and one black hole, from a world-line effective field theory point of view. Finally, we discuss possible modifications of the Weak Gravity Conjecture in the presence of both a dilatonic coupling and a cosmological constant., Comment: 40 pages, 6 figures. Matches the published version: one typo corrected and one paragraph added for clarifications

Complex 3D integration of photonic and electronic integrated circuits is of particular interest to carry the photonics roadmap and to address challenges but involves mechanical stress, often detrimental for the behavior of optical components. Existing experiments failed to carefully analyze the stress in such integrated optical devices due to the requirement in terms of feature sizes, few hundreds of nanometers, and 3D-stacked integration. We present for the first time the characterization of the stress tensor of a silicon waveguide using Integrated Raman Spectroscopy (IRS). This experimental technique is directly sensitive to the effective stress, which involves changes in optical properties of the guided mode, at the working wavelength and polarization state of the photonic component. The experimental stress tensor is in good agreement with simulations.

Tiny values for gauge couplings of dark photons allow to suppress their kinetic mixing with ordinary photons. We point out that the Weak Gravity Conjecture predicts consequently low ultraviolet cut-offs where new degrees of freedom might appear. In particular, a mixing angle of $\mathcal{O}(10^{-15})$, required in order to fit the excess reported by XENON1T, corresponds to new physics below $\mathcal{O}(100)$ TeV, thus accessible at a Future Circular Collider. We show that possible realizations are provided by compactifications with six large extra dimensions and a string scale of order $\mathcal{O}(100)$ TeV., Comment: 9 pages. A few comments and references improved. This version matches the one published

We revisit the Scalar Weak Gravity Conjecture and investigate the possibility to impose that scalar interactions dominate over gravitational ones. More precisely, we look for consequences of assuming that, for leading scalar interactions, the corresponding gravitational contribution is sub-dominant in the non-relativistic limit. For a single massive scalar particle, this leads us to compare four-point self-interactions in different type of potentials. For axion-like particles, we retrieve the result of the Axion Weak Gravity Conjecture: the decay constant $f$ is bounded by the Planck mass, $f < {M_{Pl}}$. Similar bounds are obtained for exponential potentials. For quartic, power law and Starobinsky potentials, we exclude large trans-Planckian field excursions. We then discuss the case of moduli that determine the scalars masses. We retrieve the exponential dependence as requested by the Swampland Distance Conjecture. We also find extremal state masses with field dependence that reproduces both the Kaluza-Klein and winding modes behaviour. In particular cases, our constraints can be put in the form of the Refined de Sitter Conjecture., Comment: 21 pages, 1 figure. References and few comments added

Up to date, inertial migration of particles in microflows has demonstrated a great potential for a wide range of applications. In particular, this phenomenon is used to achieve particle separation or sorting in a suspension. Recent works reported that the focusing mode of particles can be modified in a polydisperse suspension. Nevertheless, the impact of the particle sizes in a mixture on their inertial migration has been rarely studied up to now. Thus, we have investigated in this work the influence of bidispersity on the lateral migration of the particles towards equilibrium positions and on their longitudinal ordering into trains. Different changes in the particles behavior were observed when the ratio between the particle sizes (dp1/dp2) varied from 1.64 to 4.58.

We explain how an $SU(2)_R$ R-symmetry allows alignment of the vacuum expectation value and the mass eigenstates in the Higgs bosons squared-mass matrix. More important, we discuss how our parametrization of the breaking of this global symmetry allows to quantitatively apprehend the diverse sources of misalignment, which are kept, by supersymmetry, small., Comment: 13 pages. Contribution to the Workshop on the Standard Model and Beyond, Corfu, 31 Aug - Sept 9, 2018. arXiv admin note: text overlap with arXiv:1812.02208

KEY WORDS suspensions, inertial focusing, particle-laden flows, high Reynolds numbers SHORT SUMMARY The inertial migration of particles in square channel flows at the micro-scale has been deeply investigated in the last two decades. The well-known four equilibrium positions are located near the center of each channel face at moderate Reynolds numbers [1]. More recently, Miura et al. [2] revealed experimentally the presence of eight equilibrium positions in millimetric square channels for Reynolds numbers higher than 250. The aim of the present work is to extend these results obtained at millimeter scale to the micrometer scale. To this end, in situ visualization of particles flowing in square micro-channels at Reynolds numbers ranging from 5 to 300 have been conducted and analyzed.

We show that a non-abelian global $SU(2)_R$ acting on the quartic part of the two Higgs Doublet Model leads, at tree-level, to an automatic alignment without decoupling. An example of phenomenologically viable model with this feature is the the low energy effective field theory of the Minimal Dirac Gaugino Supersymmetric Model in the limit where the adjoint scalars are decoupled. We discuss here how the $SU(2)_R$ can be identified with the R-symmetry of the $N=2$ supersymmetry in the gauge and Higgs sectors. We also review how the radiative corrections lead to a very small misalignment., Comment: 12 pages, 1 figure. Contribution to the proceedings of the 7th International Conference on New Frontiers in Physics (ICNFP 2018), 4-12 July 2018, Crete, Greece. Typos corrected. Some explanations added. Corresponds to the published version

Stochastic gravitational waves can be produced during the preheating when out-of-equilibrium particles are produced with an anisotropic stress-tensor. We discuss the case where these particles carry spin 3/2. We compute the spectrum of the gravitational waves generated by the transverse and longitudinal components. We find a different scaling of the spectrum near the peak and the longitudinal components lead to an enhancement when compared to spin-1/2 fermions with Yukawa couplings. We note, as expected, that the corresponding typical frequency is too high for the current observation and calls for ultra-high frequency gravitational wave detectors in the future., Comment: 13 pages, 1 figure. v3: one equation corrected

It has been observed that an automatic alignment without decoupling is predicted at tree-level in a Two-Higgs Doublet Model (2HDM) with extended supersymmetry in the gauge and Higgs sectors. Moreover, it was found that radiative corrections preserve this alignment to a very good precision. We show that it is the non-abelian global $SU(2)_R$ R-symmetry that is at the origin of this alignment. This differs from previously considered Higgs family symmetries as it is present only in the quartic part of the Higgs potential. It can not be imposed to the quadratic part which has to be generated by $N=1$ supersymmetry breaking sectors. This absence of symmetry does not spoil alignment at the minimimum of the potential. We show how the (small) misalignment induced by higher order corrections can be described as the appearance of non-singlet representations of $SU(2)_R$ in the quartic potential., Comment: 13 pages. Matches the version accepted for publication

We prove that, over any elliptic global Langlands parameter $\sigma$, the cuspidal cohomology groups of moduli stacks of shtukas are given by a formula involving a finite dimensional representation of the centralizer of $\sigma$. It is a first step in the direction of Arthur-Kottwitz conjectures., Comment: in French

Finite-size neutrally buoyant particles in a channel flow are known to accumulate at specific equilibrium positions or spots in the channel cross-section if the flow inertia is finite at the particle scale. Experiments in different conduit geometries have shown that while reaching equilibrium locations, particles tend also to align regularly in the streamwise direction. In this paper, the Force Coupling Method was used to numerically investigate the inertia-induced particle alignment, using square channel geometry. The method was first shown to be suitable to capture the quasi-steady lift force that leads to particle cross-streamline migration in channel flow. Then the particle alignment in the flow direction was investigated by calculating the particle relative trajectories as a function of flow inertia and of the ratio between the particle size and channel hydraulic diameter. The flow streamlines were examined around the freely rotating particles at equilibrium, revealing stable small-scale vortices between aligned particles. The streamwise inter-particle spacing between aligned particles at equilibrium was calculated and compared to available experimental data in square channel flow (Gao {\it et al.} Microfluidics and Nanofluidics {\bf 21}, 154 (2017)). The new result highlighted by our numerical simulations is that the inter-particle spacing is unconditionally stable only for a limited number of aligned particles in a single train, the threshold number being dependent on the confinement (particle-to-channel size ratio) and on the Reynolds number. For instance, when the particle Reynolds number is $\approx1$ and the particle-to-channel height size ratio is $\approx0.1$, the maximum number of stable aligned particles per train is equal to 3. This agrees with statistics realized on the experiments of (Gao {\it et al.} Microfluidics and Nanofluidics {\bf 21}, 154 (2017))., Comment: 13 pages, 13 figures

High-performance optical beam splitters are of fundamental importance for the development of advanced silicon photonics integrated circuits. However, due to the high refractive index contrast of the silicon-on-insulator platform, state of the art Si splitters are hampered by trade-offs in bandwidth, polarization dependence and sensitivity to fabrication errors. Here, we present a new strategy that exploits modal engineering in slotted waveguides to overcome these limitations, enabling ultra-wideband polarization-insensitive optical power splitters, with relaxed fabrication tolerances. The proposed splitter relies on a single-mode slot waveguide which is transformed into two strip waveguides by a symmetric taper, yielding equal power splitting. Based on this concept, we experimentally demonstrate -3$\pm$0.5 dB polarization-independent transmission in an unprecedented 390 nm bandwidth (1260 - 1650 nm), even in the presence of waveguide width deviations as large as $\pm$25 nm.

We discuss recent developments in the Langlands program for function fields, and in the geometric Langlands program. In particular we explain a canonical decomposition of the space of cuspidal automorphic forms for any reductive group G over a function field, indexed by global Langlands parameters. The proof uses the cohomology of G-shtukas with multiple modifications and the geometric Satake equivalence., Comment: ICM report

We associate to every irreducible representation of a reductive group over a local field of equal characteristics a local Langlands parameter up to semisimplification and prove the compatibility with the global parameterization constructed by the second author. Our method involves stacks of restricted shtukas (which are analogues of truncated Barsotti-Tate groups) and nearby cycles over arbitrary bases., Comment: in French

We prove that any hyperbolic group admits a proper affine isometric action on a quotient space of a $\ell^p$ Banach space, for all $p>1$ sufficiently close to 1., Comment: in French

We give a simple and relatively short proof of the following fact: any hyperbolic group admits a proper affine isometric action on a $\ell^p$-space for $p$ large enough. A first proof of this result was given by Guoliang Yu., Comment: in French

We give a new construction, based on categorical logic, of Nori's $\mathbb Q$-linear abelian category of mixed motives associated to a cohomology or homology functor with values in finite-dimensional vector spaces over $\mathbb Q$. This new construction makes sense for infinite-dimensional vector spaces as well, so that it associates a $\mathbb Q$-linear abelian category of mixed motives to any (co)homology functor, not only Betti homology (as Nori had done) but also, for instance, $\ell$-adic, $p$-adic or motivic cohomology. We prove that the $\mathbb Q$-linear abelian categories of mixed motives associated to different (co)homology functors are equivalent if and only a family (of logical nature) of explicit properties is shared by these different functors. The problem of the existence of a universal cohomology theory and of the equivalence of the information encoded by the different classical cohomology functors thus reduces to that of checking these explicit conditions., Comment: 30 pages

This is a translation in English of version 5 of the article arXiv:1404.3998, which is itself an introduction to arXiv:1209.5352. We explain all the ideas of the proof of the following theorem. For any reductive group G over a global function field, we use the cohomology of G-shtukas with multiple modifications and the geometric Satake equivalence to prove the global Langlands correspondence for G in the "automorphic to Galois" direction. Moreover we obtain a canonical decomposition of the spaces of cuspidal automorphic forms indexed by global Langlands parameters. The proof does not rely at all on the Arthur-Selberg trace formula.

This is an introduction to the article "Chtoucas pour les groupes r\'eductifs et param\'etrisation de Langlands globale", arXiv:1209.5352. We explain all the ideas of the proof. For any reductive group G over a global function field, we use the cohomology of G-shtukas with multiple modifications and the geometric Satake equivalence to prove the global Langlands correspondence for G in the "automorphic to Galois" direction. Moreover we obtain a canonical decomposition of the spaces of cuspidal automorphic forms indexed by global Langlands parameters. The proof does not rely at all on the Arthur-Selberg trace formula., Comment: in French. arXiv admin note: substantial text overlap with arXiv:1209.5352

It is shown that for every $p\in (2,\infty)$ there exists a doubling subset of $L_p$ that does not admit a bi-Lipschitz embedding into $\R^k$ for any $k\in \N$.

Let $\H= < a,b | a[a,b]=[a,b]a \wedge b[a,b]=[a,b]b>$ be the discrete Heisenberg group, equipped with the left-invariant word metric $d_W(\cdot,\cdot)$ associated to the generating set ${a,b,a^{-1},b^{-1}}$. Letting $B_n= {x\in \H: d_W(x,e_\H)\le n}$ denote the corresponding closed ball of radius $n\in \N$, and writing $c=[a,b]=aba^{-1}b^{-1}$, we prove that if $(X,|\cdot|_X)$ is a Banach space whose modulus of uniform convexity has power type $q\in [2,\infty)$ then there exists $K\in (0,\infty)$ such that every $f:\H\to X$ satisfies {multline*} \sum_{k=1}^{n^2}\sum_{x\in B_n}\frac{|f(xc^k)-f(x)|_X^q}{k^{1+q/2}}\le K\sum_{x\in B_{21n}} \Big(|f(xa)-f(x)|^q_X+\|f(xb)-f(x)\|^q_X\Big). {multline*} It follows that for every $n\in \N$ the bi-Lipschitz distortion of every $f:B_n\to X$ is at least a constant multiple of $(\log n)^{1/q}$, an asymptotically optimal estimate as $n\to\infty$.

For any reductive group G over a global function field, we use the cohomology of G-shtukas with multiple modifications and the geometric Satake equivalence to prove the global Langlands correspondence for G in the "automorphic to Galois" direction. Moreover we obtain a canonical decomposition of the spaces of cuspidal automorphic forms indexed by global Langlands parameters. The proof does not rely at all on the Arthur-Selberg trace formula., Comment: in French

In this article, we apply the methods of our work on Fontaine's theory in equal characteristics to the $\varphi/\mathfrak S$-modules of Breuil and Kisin. Thanks to a previous article of Kisin, this yields a new and rather elementary proof of the theorem "weakly admissible implies admissible" of Colmez-Fontaine.

This paper gives a proof of the Baum-Connes conjecture with coefficients for hyperbolic groups. More precisely the injectivity of the Baum-Connes map was established by Kasparov and Skandalis and we prove the surjectivity., Comment: published by the European Mathematical Society

Let X be a smooth projective curve. Write Bun_{SO_{2n}} for the moduli stack of SO_{2n}-torsors on X. We give a geometric interpretation of the automorphic function f on Bun_{SO_{2n}} corresponding to the minimal representation. Namely, we construct a perverse sheaf K on Bun_{SO_{2n}} such that f should be equal to the trace of Frobenius of K plus some constant function. We also calculate K explicitely for curves of genus zero and one. The construction of K is based on some explicit geometric formulas for the Fourier coefficients of f on one hand, and on the geometric theta-lifting on the other hand. Our construction makes sense for more general simple algebraic groups, we formulate the corresponding conjectures. They could provide a geometric interpretation of some unipotent automorphic representations in the framework of the geometric Langlands program., Comment: LaTeX2e, 69 pages, final version, to appear in Representation theory (electronic J. of AMS)

The {\em overlap number} of a finite $(d+1)$-uniform hypergraph $H$ is defined as the largest constant $c(H)\in (0,1]$ such that no matter how we map the vertices of $H$ into $\R^d$, there is a point covered by at least a $c(H)$-fraction of the simplices induced by the images of its hyperedges. In~\cite{Gro2}, motivated by the search for an analogue of the notion of graph expansion for higher dimensional simplicial complexes, it was asked whether or not there exists a sequence $\{H_n\}_{n=1}^\infty$ of arbitrarily large $(d+1)$-uniform hypergraphs with bounded degree, for which $\inf_{n\ge 1} c(H_n)>0$. Using both random methods and explicit constructions, we answer this question positively by constructing infinite families of $(d+1)$-uniform hypergraphs with bounded degree such that their overlap numbers are bounded from below by a positive constant $c=c(d)$. We also show that, for every $d$, the best value of the constant $c=c(d)$ that can be achieved by such a construction is asymptotically equal to the limit of the overlap numbers of the complete $(d+1)$-uniform hypergraphs with $n$ vertices, as $n\rightarrow\infty$. For the proof of the latter statement, we establish the following geometric partitioning result of independent interest. For any $d$ and any $\epsilon>0$, there exists $K=K(\epsilon,d)\ge d+1$ satisfying the following condition. For any $k\ge K$, for any point $q \in \mathbb{R}^d$ and for any finite Borel measure $\mu$ on $\mathbb{R}^d$ with respect to which every hyperplane has measure $0$, there is a partition $\mathbb{R}^d=A_1 \cup \ldots \cup A_{k}$ into $k$ measurable parts of equal measure such that all but at most an $\epsilon$-fraction of the $(d+1)$-tuples $A_{i_1},\ldots,A_{i_{d+1}}$ have the property that either all simplices with one vertex in each $A_{i_j}$ contain $q$ or none of these simplices contain $q$.

For any 1\leq p \leq \infty different from 2, we give examples of non-commutative Lp spaces without the completely bounded approximation property. Let F be a non-archimedian local field. If p>4 or p<4/3 and r\geq 3 these examples are the non-commutative Lp-spaces of the von Neumann algebra of lattices in SL_r(F) or in SL_r(\R). For other values of p the examples are the non-commutative Lp-spaces of the von Neumann algebra of lattices in SL_r(F) for r large enough depending on p. We also prove that if r \geq 3 lattices in SL_r(F) or SL_r(\R) do not have the Approximation Property of Haagerup and Kraus. This provides examples of exact C^*-algebras without the operator space approximation property., Comment: v3; Minor corrections according to the referees

We prove that the global geometric theta-lifting functor for the pair (H, G) is compatible with the Whittaker normalization, where (H,G) is one of the pairs (SO_{2n}, Sp_{2n}), (Sp_{2n}, SO_{2n+2}) or (GL_{n},GL_{n+1}). That is, the composition of the theta-lifting functor from H to G with the Whittaker functor for G is isomorphic to the Whittaker functor for H., Comment: 13 pages, final version to appear in Bulletin SMF

Let k be an algebraically closed field of characteristic >2, F=k((t)) and Mp(F) denote the metaplectic extension of Sp_{2d}(F). In this paper we propose a geometric analog of the Weil representation of Mp(F). This is a category of certain perverse sheaves on some stack, on which Mp(F) acts by functors. This construction will be used in math.RT/0701170 (and subsequent publications) for a proof of the geometric Langlands functoriality for some dual reductive pairs., Comment: LaTeX2e, 37 pages

The report below describes the applications of Banach KK-theory to a conjecture of P. Baum and A. Connes about the K-theory of group $C^*$-algebras, and a new proof of the classification by Harish-Chandra, the construction by Parthasarathy and the exhaustion by Atiyah and Schmid of the discrete series representations of connected semi-simple Lie groups.

Cet expos\'e est consacr\'e \`a la preuve de la correspondance de Langlands pour les groupes $\GL_r$ sur les corps de fonctions. ----- This article is devoted to the proof of the Langlands correspondence for the groups $GL_r$ over function fields.