Semisimple types for p -adic classical groups

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On the elliptic nonabelian Fourier transform for unipotent representations of p-adic groups

In this paper, we consider the relation between two nonabelian Fourier transforms. The first one is defined in terms of the Langlands-Kazhdan-Lusztig parameters for unipotent elliptic representations of a split p-adic group and the second is defined in terms of the pseudocoefficients of these representations and Lusztig's nonabelian Fourier transform for characters of finite groups of Lie type. We exemplify this relation in the case of the p-adic group of type G_2.Comment: 17 pages; v2: several minor corrections, references added; v3: corrections in the table with unipotent discrete series of G

Motion corrected 3D reconstruction of the fetal thorax from prenatal MRI

In this paper we present a semi-automatic method for analysis of the fetal thorax in genuine three-dimensional volumes. After one initial click we localize the spine and accurately determine the volume of the fetal lung from high resolution volumetric images reconstructed from motion corrupted prenatal Magnetic Resonance Imaging (MRI). We compare the current state-of-the-art method of segmenting the lung in a slice-by-slice manner with the most recent multi-scan reconstruction methods. We use fast rotation invariant spherical harmonics image descriptors with Classification Forest ensemble learning methods to extract the spinal cord and show an efficient way to generate a segmentation prior for the fetal lung from this information for two different MRI field strengths. The spinal cord can be segmented with a DICE coefficient of 0.89 and the automatic lung segmentation has been evaluated with a DICE coefficient of 0.87. We evaluate our method on 29 fetuses with a gestational age (GA) between 20 and 38 weeks and show that our computed segmentations and the manual ground truth correlate well with the recorded values in literature

The subconvexity problem for \GL_{2}

Generalizing and unifying prior results, we solve the subconvexity problem for the $L$-functions of \GL_{1} and \GL_{2} automorphic representations over a fixed number field, uniformly in all aspects. A novel feature of the present method is the softness of our arguments; this is largely due to a consistent use of canonically normalized period relations, such as those supplied by the work of Waldspurger and Ichino--Ikeda.Comment: Almost final version to appear in Publ. Math IHES. References updated

Eisenstein series for infinite-dimensional U-duality groups

We consider Eisenstein series appearing as coefficients of curvature corrections in the low-energy expansion of type II string theory four-graviton scattering amplitudes. We define these Eisenstein series over all groups in the E_n series of string duality groups, and in particular for the infinite-dimensional Kac-Moody groups E9, E10 and E11. We show that, remarkably, the so-called constant term of Kac-Moody-Eisenstein series contains only a finite number of terms for particular choices of a parameter appearing in the definition of the series. This resonates with the idea that the constant term of the Eisenstein series encodes perturbative string corrections in BPS-protected sectors allowing only a finite number of corrections. We underpin our findings with an extensive discussion of physical degeneration limits in D<3 space-time dimensions.Comment: 69 pages. v2: Added references and small additions, to be published in JHE

Sur les paquets d'Arthur des groupes classiques et unitaires non quasi-d\'eploy\'es

15 pages, in FrenchNous \'etendons aux groupes orthogonaux et unitaires non quasi-d\'eploy\'es sur un corps local des r\'esultats de J. Arthur et de la premi\`ere auteure \'etablis dans le cas quasi-d\'eploy\'e. En particulier, nous obtenons une classification de Langlands compl\`ete pour les repr\'esentations temp\'er\'ees dans le cas $p$-adique. Nous en d\'eduisons en utilisant l'involution d'Aubert-Schneider-Stuhler un r\'esultat de multiplicit\'e un dans les paquets unipotents, et par des m\'ethodes globales, le m\^eme r\'esultat pour les paquets unipotents dans le cas archim\'edien. We extend to non quasi-split orthogonal and unitary groups over a local field some results of J. Arthur and the first author established in the quasi-split case. In particular, we obtain a full Langlands classification for tempered representations in the $p$-adic case. Using Aubert-Schneider-Stuhler involution, we deduce from this a multiplicity one result for unipotent packets, and by global methods, the same result for unipotent packets in the archimedean case