Senior Research Associate

Dr Raphael Ponge

Science
Sch of Mathematics & Statistic

Publications

  • Journal articles | 2020
    Dr Raphael Ponge
    Ponge R, 2020, 'Noncommutative residue and canonical trace on noncommutative tori. Uniqueness results', Symmetry, Integrability and Geometry: Methods and Applications (SIGMA), vol. 16, pp. 1 - 31, http://dx.doi.org/10.3842/SIGMA.2020.061
    Journal articles | 2020
    Dr Raphael Ponge
    Lee G; Ponge R, 2020, 'Functional calculus for elliptic operators on noncommutative tori, I', Journal of Pseudo-Differential Operators and Applications, vol. 11, pp. 935 - 1004, http://dx.doi.org/10.1007/s11868-020-00337-z
    Journal articles | 2020
    Dr Raphael Ponge
    Ponge R, 2020, 'Connes's trace theorem for curved noncommutative tori: Application to scalar curvature', JOURNAL OF MATHEMATICAL PHYSICS, vol. 61, http://dx.doi.org/10.1063/5.0005052
    Journal articles | 2020
    Dr Raphael Ponge
    Ha H; Ponge R, 2020, 'Laplace–Beltrami operators on noncommutative tori', Journal of Geometry and Physics, vol. 150, http://dx.doi.org/10.1016/j.geomphys.2019.103594
    Journal articles | 2019
    Dr Raphael Ponge
    Choi W; Ponge R, 2019, 'Privileged Coordinates and Nilpotent Approximation of Carnot Manifolds, I. General Results', Journal of Dynamical and Control Systems, vol. 25, pp. 109 - 157, http://dx.doi.org/10.1007/s10883-018-9404-0
    Journal articles | 2019
    Dr Raphael Ponge
    Choi W; Ponge R, 2019, 'Privileged Coordinates and Nilpotent Approximation for Carnot Manifolds, II. Carnot Coordinates', Journal of Dynamical and Control Systems, vol. 25, pp. 631 - 670, http://dx.doi.org/10.1007/s10883-019-09434-9
    Journal articles | 2019
    Dr Raphael Ponge
    Choi W; Ponge R, 2019, 'Tangent maps and tangent groupoid for Carnot manifolds', Differential Geometry and its Application, vol. 62, pp. 136 - 183, http://dx.doi.org/10.1016/j.difgeo.2018.11.002
    Journal articles | 2019
    Dr Raphael Ponge
    Ha H; Lee G; Ponge R, 2019, 'Pseudodifferential calculus on noncommutative tori, I. Oscillating integrals', International Journal of Mathematics, vol. 30, http://dx.doi.org/10.1142/S0129167X19500332
    Journal articles | 2019
    Dr Raphael Ponge
    Ha H; Lee G; Ponge R, 2019, 'Pseudodifferential calculus on noncommutative tori, II. Main properties', International Journal of Mathematics, vol. 30, http://dx.doi.org/10.1142/S0129167X19500344
    Journal articles | 2018
    Dr Raphael Ponge
    Ponge R; Wang H, 2018, 'Noncommutative geometry and conformal geometry. I. Local index formula and conformal invariants', Journal of Noncommutative Geometry, vol. 12, pp. 1573 - 1639, http://dx.doi.org/10.4171/JNCG/280
    Journal articles | 2018
    Dr Raphael Ponge
    Ponge R, 2018, 'Cyclic homology and group actions', Journal of Geometry and Physics, vol. 123, pp. 30 - 52, http://dx.doi.org/10.1016/j.geomphys.2017.08.014
    Journal articles | 2017
    Dr Raphael Ponge
    Ponge R, 2017, 'The cyclic homology of crossed-product algebras, II', Comptes Rendus Mathematique, vol. 355, pp. 623 - 627, http://dx.doi.org/10.1016/j.crma.2017.04.013
    Journal articles | 2017
    Dr Raphael Ponge
    Ponge R, 2017, 'The cyclic homology of crossed-product algebras, I', Comptes Rendus Mathematique, vol. 355, pp. 618 - 622, http://dx.doi.org/10.1016/j.crma.2017.04.012
    Journal articles | 2016
    Dr Raphael Ponge
    Ponge R; Wang H, 2016, 'Indexmap, Σ-connections, and Connes-Chern character in the setting of twisted spectral triples', Kyoto Journal of Mathematics, vol. 56, pp. 347 - 399, http://dx.doi.org/10.1215/21562261-3478907
    Journal articles | 2016
    Dr Raphael Ponge
    Ponge R; Wang H, 2016, 'Noncommutative geometry and conformal geometry, II. Connes-Chern character and the local equivariant index theorem', Journal of Noncommutative Geometry, vol. 10, pp. 307 - 378, http://dx.doi.org/10.4171/JNCG/235
    Journal articles | 2015
    Dr Raphael Ponge
    Ponge R; Wang H, 2015, 'Noncommutative geometry and conformal geometry: III: Vafa-Witten inequality and Poincaré duality', Advances in Mathematics, vol. 272, pp. 761 - 819, http://dx.doi.org/10.1016/j.aim.2014.12.009
    Journal articles | 2014
    Dr Raphael Ponge
    Gover R; Canzani Y; Jakobson D; Ponge R; Malchiodi A, 2014, 'Conformal invariants from nodal sets. I. negative eigenvalues and curvature prescription', International Mathematics Research Notices, vol. 2014, pp. 2356 - 2400, http://dx.doi.org/10.1093/imrn/rns295
    Journal articles | 2013
    Dr Raphael Ponge
    Canzani Y; Gover AR; Jakobson D; Ponge R, 2013, 'NULLSPACES OF CONFORMALLY INVARIANT OPERATORS. APPLICATIONS TO Q(k)-CURVATURE', ELECTRONIC RESEARCH ANNOUNCEMENTS IN MATHEMATICAL SCIENCES, vol. 20, pp. 43 - 50, http://dx.doi.org/10.3934/era.2013.20.43
    Journal articles | 2012
    Dr Raphael Ponge
    Loya P; Moroianu S; Ponge R, 2012, 'On the singularities of the zeta and eta functions of an elliptic operator', International Journal of Mathematics, vol. 23, http://dx.doi.org/10.1142/S0129167X11007616
    Journal articles | 2011
    Dr Raphael Ponge
    Ponge R, 2011, 'A new hypoelliptic operator on almost CR manifolds', Revista Matematica Iberoamericana, vol. 27, pp. 393 - 414, http://dx.doi.org/10.4171/RMI/641
    Journal articles | 2010
    Dr Raphael Ponge
    Ponge R, 2010, 'Traces on pseudodifferential operators and sums of commutators', Journal d'Analyse Mathematique, vol. 110, pp. 1 - 30, http://dx.doi.org/10.1007/s11854-010-0001-8
    Journal articles | 2008
    Dr Raphael Ponge
    Ponge R, 2008, 'Noncommutative geometry and lower dimensional volumes in Riemannian geometry', Letters in Mathematical Physics, vol. 83, pp. 19 - 32, http://dx.doi.org/10.1007/s11005-007-0199-2
    Journal articles | 2008
    Dr Raphael Ponge
    Ponge R, 2008, 'Noncommutative residue invariants for CR and contact manifolds', Journal fur die Reine und Angewandte Mathematik, pp. 117 - 151, http://dx.doi.org/10.1515/CRELLE.2008.004
    Journal articles | 2007
    Dr Raphael Ponge
    Ponge R, 2007, 'Noncommutative residue for Heisenberg manifolds. Applications in CR and contact geometry', Journal of Functional Analysis, vol. 252, pp. 399 - 463, http://dx.doi.org/10.1016/j.jfa.2007.07.001
    Journal articles | 2006
    Dr Raphael Ponge
    Ponge R, 2006, 'The tangent grupoid of a Heisenberg manifold', Pacific Journal of Mathematics, vol. 227, pp. 151 - 175, http://dx.doi.org/10.2140/pjm.2006.227.151
    Journal articles | 2006
    Dr Raphael Ponge
    Ponge R, 2006, 'Spectral asymmetry, zeta functions, and the noncommutative residue', International Journal of Mathematics, vol. 17, pp. 1065 - 1090, http://dx.doi.org/10.1142/S0129167X06003825
    Journal articles | 2006
    Dr Raphael Ponge
    Ponge R, 2006, 'A new proof of the local regularity of the eta invariant of a Dirac operator', Journal of Geometry and Physics, vol. 56, pp. 1654 - 1665, http://dx.doi.org/10.1016/j.geomphys.2005.09.003
    Journal articles | 2004
    Dr Raphael Ponge
    Ponge R; Mikayelyan H, 2004, 'On the asymptotic completeness of the Volterra calculus', Journal d'Analyse Mathematique, vol. 94, pp. 249 - 263, http://dx.doi.org/10.1007/BF02789049
    Journal articles | 2004
    Dr Raphael Ponge
    Ponge R, 2004, 'Erratum: A new short proof of the local index formula and some of its applications (Communications in Mathematical Physics (2003) 241 (215-234))', Communications in Mathematical Physics, vol. 248, pp. 639, http://dx.doi.org/10.1007/s00220-004-1109-4
    Journal articles | 2003
    Dr Raphael Ponge
    Ponge R, 2003, 'A New Short Proof of the Local Index Formula and Some of Its Applications', Communications in Mathematical Physics, vol. 241, pp. 215 - 234, http://dx.doi.org/10.1007/s00220-003-0915-4
    Journal articles | 2001
    Dr Raphael Ponge
    Ponge R, 2001, 'Spectral geometry and local index formulae for CR and contact manifolds', Comptes Rendus de l'Academie des Sciences - Series I: Mathematics, vol. 332, pp. 735 - 738, http://dx.doi.org/10.1016/S0764-4442(01)01891-2
    Journal articles | 2001
    Dr Raphael Ponge
    Ponge R, 2001, 'Sub-elliptic functional calculus and non-commutative residue on Heisenberg manifolds', Comptes Rendus de l'Academie des Sciences - Series I: Mathematics, vol. 332, pp. 611 - 614, http://dx.doi.org/10.1016/S0764-4442(01)01890-0

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