Edit Profile (opens in new tab) Ponge, Raphaël S. Co-Author Distance Author ID: ponge.raphael-s Published as: Ponge, Raphaël; Ponge, Raphaël S. Documents Indexed: 52 Publications since 2001, including 1 Book and 10 Additional arXiv Preprints Co-Authors: 9 Co-Authors with 15 Joint Publications 190 Co-Co-Authors all top 5 Co-Authors 35 single-authored 5 Wang, Hang 3 Choi, Woocheol 3 Ha, Hyunsu 3 Lee, Gihyun 2 Canzani, Yaiza 2 Gover, Ashwin Rod 2 Jakobson, Dmitry 1 Loya, Paul A. 1 Moroianu, Sergiu all top 5 Serials 4 International Journal of Mathematics 4 Journal of Noncommutative Geometry 3 Journal of Geometry and Physics 2 Journal d’Analyse Mathématique 2 Journal of Mathematical Physics 2 Advances in Mathematics 2 Comptes Rendus de l’Académie des Sciences. Série I. Mathématique 2 Journal of Dynamical and Control Systems 2 Comptes Rendus. Mathématique. Académie des Sciences, Paris 1 Communications in Mathematical Physics 1 Letters in Mathematical Physics 1 Journal of Functional Analysis 1 Journal für die Reine und Angewandte Mathematik 1 Memoirs of the American Mathematical Society 1 Pacific Journal of Mathematics 1 Revista Matemática Iberoamericana 1 Differential Geometry and its Applications 1 IMRN. International Mathematics Research Notices 1 Mathematical Physics, Analysis and Geometry 1 SIGMA. Symmetry, Integrability and Geometry: Methods and Applications 1 Electronic Research Announcements in Mathematical Sciences 1 Journal of Pseudo-Differential Operators and Applications 1 Kyoto Journal of Mathematics all top 5 Fields 37 Global analysis, analysis on manifolds (58-XX) 20 Differential geometry (53-XX) 11 Partial differential equations (35-XX) 10 Several complex variables and analytic spaces (32-XX) 10 Functional analysis (46-XX) 8 \(K\)-theory (19-XX) 7 Operator theory (47-XX) 3 Topological groups, Lie groups (22-XX) 3 Algebraic topology (55-XX) 3 Quantum theory (81-XX) 2 Algebraic geometry (14-XX) 2 Group theory and generalizations (20-XX) 2 Abstract harmonic analysis (43-XX) 1 Associative rings and algebras (16-XX) 1 Real functions (26-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 35 Publications have been cited 300 times in 172 Documents Cited by ▼ Year ▼ Heisenberg calculus and spectral theory of hypoelliptic operators on Heisenberg manifolds. Zbl 1143.58014 Ponge, Raphaël S. 33 2008 Noncommutative geometry and lower dimensional volumes in Riemannian geometry. Zbl 1136.58017 Ponge, Raphaël 23 2008 Pseudodifferential calculus on noncommutative tori. I: Oscillating integrals. Zbl 1429.58016 Ha, Hyunsu; Lee, Gihyun; Ponge, Raphaël 18 2019 Tangent maps and tangent groupoid for Carnot manifolds. Zbl 1410.53034 Choi, Woocheol; Ponge, Raphaël 16 2019 A new short proof of the local index formula and some of its applications. Zbl 1191.58006 Ponge, Raphaël 16 2003 Noncommutative geometry and conformal geometry. II: Connes-Chern character and the local equivariant index theorem. Zbl 1343.58004 Ponge, Raphaël; Wang, Hang 15 2016 The tangent groupoid of a Heisenberg manifold. Zbl 1133.58010 Ponge, Raphaël 15 2006 Pseudodifferential calculus on noncommutative tori. II: Main properties. Zbl 1429.58017 Ha, Hyunsu; Lee, Gihyun; Ponge, Raphaël 14 2019 Spectral asymmetry, zeta functions, and the noncommutative residue. Zbl 1127.58030 Ponge, Raphaël 13 2006 Noncommutative residue for Heisenberg manifolds. Applications in CR and contact geometry. Zbl 1127.58024 Ponge, Raphaël 13 2007 Noncommutative geometry and conformal geometry: I. Local index formula and conformal invariants. Zbl 1417.58005 Ponge, Raphaël; Wang, Hang 9 2018 Traces on pseudodifferential operators and sums of commutators. Zbl 1194.58029 Ponge, Raphaël 9 2010 Privileged coordinates and nilpotent approximation for Carnot manifolds. II: Carnot coordinates. Zbl 1432.53047 Choi, Woocheol; Ponge, Raphaël 8 2019 Privileged coordinates and nilpotent approximation of Carnot manifolds. I: General results. Zbl 1410.53033 Choi, Woocheol; Ponge, Raphaël 7 2019 Conformal invariants from nodal sets. I: Negative eigenvalues and curvature prescription. With an appendix by Rod Gover and Andrea Malchiodi. Zbl 1321.58022 Canzani, Yaiza; Gover, Rod; Jakobson, Dmitry; Ponge, Raphaël 7 2014 Weyl’s laws and Connes’ integration formulas for matrix-valued \(L\!\log \!L\)-Orlicz potentials. Zbl 1486.35445 Ponge, Raphaël 7 2022 Laplace-Beltrami operators on noncommutative tori. Zbl 1437.53026 Ha, Hyunsu; Ponge, Raphaël 7 2020 Noncommutative residue invariants for CR and contact manifolds. Zbl 1140.58010 Ponge, Raphaël 6 2008 Functional calculus for elliptic operators on noncommutative tori. I. Zbl 1455.58010 Lee, Gihyun; Ponge, Raphaël 6 2020 Connes’ integration and Weyl’s laws. Zbl 07722571 Ponge, Raphaël 6 2023 The cyclic homology of crossed-product algebras. I. (L’homologie cyclique des algèbres produits-croisés, I.) Zbl 1380.46054 Ponge, Raphaël 5 2017 Noncommutative geometry and conformal geometry. III: Vafa-Witten inequality and Poincaré duality. Zbl 1311.53037 Ponge, Raphaël; Wang, Hang 5 2015 Connes’s trace theorem for curved noncommutative tori: application to scalar curvature. Zbl 1443.58017 Ponge, Raphaël 5 2020 Noncommutative residue and canonical trace on noncommutative tori. Uniqueness results. Zbl 1471.58033 Ponge, Raphaël 5 2020 The logarithmic singularities of the Green functions of the conformal powers of the Laplacian. Zbl 1350.53053 Ponge, Raphaël 4 2014 Sub-elliptic functional calculus and non-commutative residue on Heisenberg manifolds. (Calcul fonctionnel sous-elliptique et résidu non commutatif sur les variétés de Heisenberg.) Zbl 0989.58013 Ponge, Raphaël 4 2001 Spectral geometry and local index formulae for CR and contact manifolds. (Géométrie spectrale et formules d’indices locales pour les variétés CR et contact.) Zbl 0987.58012 Ponge, Raphaël 4 2001 The cyclic homology of crossed-product algebras. II. (Homologie cycliques des algèbres produits-croisés, II.) Zbl 1380.46055 Ponge, Raphaël 4 2017 Cyclic homology and group actions. Zbl 1468.19003 Ponge, Raphaël 3 2018 Nullspaces of conformally invariant operators. Applications to \(Q_k\)-curvature. Zbl 1282.53027 Canzani, Yaiza; Gover, A. Rod; Jakobson, Dmitry; Ponge, Raphaël 3 2013 Cwikel estimates and negative eigenvalues of Schrödinger operators on noncommutative tori. Zbl 1507.35124 McDonald, Edward; Ponge, Raphaël 3 2022 On the asymptotic completeness of the Volterra calculus. With an appendix by H. Mikayelyan and R. Ponge. Zbl 1090.47036 Ponge, Raphaël 2 2004 Dixmier trace formulas and negative eigenvalues of Schrödinger operators on curved noncommutative tori. Zbl 1504.58006 McDonald, Edward; Ponge, Raphaël 2 2023 Index map, \(\sigma\)-connections, and Connes-Chern character in the setting of twisted spectral triples. Zbl 1361.46055 Ponge, Raphaël; Wang, Hang 2 2016 On the singularities of the zeta and eta functions of an elliptic operator. Zbl 1256.58010 Loya, Paul; Moroianu, Sergiu; Ponge, Raphaël 1 2012 Connes’ integration and Weyl’s laws. Zbl 07722571 Ponge, Raphaël 6 2023 Dixmier trace formulas and negative eigenvalues of Schrödinger operators on curved noncommutative tori. Zbl 1504.58006 McDonald, Edward; Ponge, Raphaël 2 2023 Weyl’s laws and Connes’ integration formulas for matrix-valued \(L\!\log \!L\)-Orlicz potentials. Zbl 1486.35445 Ponge, Raphaël 7 2022 Cwikel estimates and negative eigenvalues of Schrödinger operators on noncommutative tori. Zbl 1507.35124 McDonald, Edward; Ponge, Raphaël 3 2022 Laplace-Beltrami operators on noncommutative tori. Zbl 1437.53026 Ha, Hyunsu; Ponge, Raphaël 7 2020 Functional calculus for elliptic operators on noncommutative tori. I. Zbl 1455.58010 Lee, Gihyun; Ponge, Raphaël 6 2020 Connes’s trace theorem for curved noncommutative tori: application to scalar curvature. Zbl 1443.58017 Ponge, Raphaël 5 2020 Noncommutative residue and canonical trace on noncommutative tori. Uniqueness results. Zbl 1471.58033 Ponge, Raphaël 5 2020 Pseudodifferential calculus on noncommutative tori. I: Oscillating integrals. Zbl 1429.58016 Ha, Hyunsu; Lee, Gihyun; Ponge, Raphaël 18 2019 Tangent maps and tangent groupoid for Carnot manifolds. Zbl 1410.53034 Choi, Woocheol; Ponge, Raphaël 16 2019 Pseudodifferential calculus on noncommutative tori. II: Main properties. Zbl 1429.58017 Ha, Hyunsu; Lee, Gihyun; Ponge, Raphaël 14 2019 Privileged coordinates and nilpotent approximation for Carnot manifolds. II: Carnot coordinates. Zbl 1432.53047 Choi, Woocheol; Ponge, Raphaël 8 2019 Privileged coordinates and nilpotent approximation of Carnot manifolds. I: General results. Zbl 1410.53033 Choi, Woocheol; Ponge, Raphaël 7 2019 Noncommutative geometry and conformal geometry: I. Local index formula and conformal invariants. Zbl 1417.58005 Ponge, Raphaël; Wang, Hang 9 2018 Cyclic homology and group actions. Zbl 1468.19003 Ponge, Raphaël 3 2018 The cyclic homology of crossed-product algebras. I. (L’homologie cyclique des algèbres produits-croisés, I.) Zbl 1380.46054 Ponge, Raphaël 5 2017 The cyclic homology of crossed-product algebras. II. (Homologie cycliques des algèbres produits-croisés, II.) Zbl 1380.46055 Ponge, Raphaël 4 2017 Noncommutative geometry and conformal geometry. II: Connes-Chern character and the local equivariant index theorem. Zbl 1343.58004 Ponge, Raphaël; Wang, Hang 15 2016 Index map, \(\sigma\)-connections, and Connes-Chern character in the setting of twisted spectral triples. Zbl 1361.46055 Ponge, Raphaël; Wang, Hang 2 2016 Noncommutative geometry and conformal geometry. III: Vafa-Witten inequality and Poincaré duality. Zbl 1311.53037 Ponge, Raphaël; Wang, Hang 5 2015 Conformal invariants from nodal sets. I: Negative eigenvalues and curvature prescription. With an appendix by Rod Gover and Andrea Malchiodi. Zbl 1321.58022 Canzani, Yaiza; Gover, Rod; Jakobson, Dmitry; Ponge, Raphaël 7 2014 The logarithmic singularities of the Green functions of the conformal powers of the Laplacian. Zbl 1350.53053 Ponge, Raphaël 4 2014 Nullspaces of conformally invariant operators. Applications to \(Q_k\)-curvature. Zbl 1282.53027 Canzani, Yaiza; Gover, A. Rod; Jakobson, Dmitry; Ponge, Raphaël 3 2013 On the singularities of the zeta and eta functions of an elliptic operator. Zbl 1256.58010 Loya, Paul; Moroianu, Sergiu; Ponge, Raphaël 1 2012 Traces on pseudodifferential operators and sums of commutators. Zbl 1194.58029 Ponge, Raphaël 9 2010 Heisenberg calculus and spectral theory of hypoelliptic operators on Heisenberg manifolds. Zbl 1143.58014 Ponge, Raphaël S. 33 2008 Noncommutative geometry and lower dimensional volumes in Riemannian geometry. Zbl 1136.58017 Ponge, Raphaël 23 2008 Noncommutative residue invariants for CR and contact manifolds. Zbl 1140.58010 Ponge, Raphaël 6 2008 Noncommutative residue for Heisenberg manifolds. Applications in CR and contact geometry. Zbl 1127.58024 Ponge, Raphaël 13 2007 The tangent groupoid of a Heisenberg manifold. Zbl 1133.58010 Ponge, Raphaël 15 2006 Spectral asymmetry, zeta functions, and the noncommutative residue. Zbl 1127.58030 Ponge, Raphaël 13 2006 On the asymptotic completeness of the Volterra calculus. With an appendix by H. Mikayelyan and R. Ponge. Zbl 1090.47036 Ponge, Raphaël 2 2004 A new short proof of the local index formula and some of its applications. Zbl 1191.58006 Ponge, Raphaël 16 2003 Sub-elliptic functional calculus and non-commutative residue on Heisenberg manifolds. (Calcul fonctionnel sous-elliptique et résidu non commutatif sur les variétés de Heisenberg.) Zbl 0989.58013 Ponge, Raphaël 4 2001 Spectral geometry and local index formulae for CR and contact manifolds. (Géométrie spectrale et formules d’indices locales pour les variétés CR et contact.) Zbl 0987.58012 Ponge, Raphaël 4 2001 all cited Publications top 5 cited Publications all top 5 Cited by 178 Authors 28 Ponge, Raphaël S. 20 Wang, Yong 9 Sukochev, Fedor Anatol’evich 8 Wang, Jian 6 Bao, Kaihua 6 Wang, Hang 5 McDonald, Edward Andrew 5 Zanin, Dmitriy V. 4 Booss-Bavnbek, Bernhelm 4 Haller, Stefan 4 Lee, Gihyun 3 Choi, Woocheol 3 Dave, Shantanu 3 Fischer, Véronique 3 Ha, Hyunsu 3 Julg, Pierre 3 Lesch, Matthias 3 Liu, Siyao 3 Rozenblum, Grigori V. 3 Sun, Aihui 3 van Erp, Erik 3 Xiong, Xiao 3 Yuncken, Robert 2 Aribi, Amine 2 Battisti, Ubertino 2 Braverman, Maxim 2 Brodzki, Jacek 2 Coriasco, Sandro 2 Debord, Claire 2 El Soufi, Ahmad 2 Engliš, Miroslav 2 Ewert, Eske Ellen 2 Fathizadeh, Farzad 2 Gayral, Victor 2 Goffeng, Magnus 2 Gover, Ashwin Rod 2 Jakobson, Dmitry 2 Junge, Marius 2 Kaad, Jens 2 Karpukhin, Mikhail A. 2 Latrémolière, Frédéric 2 Lescure, Jean-Marie 2 Ludewig, Matthias 2 Maalaoui, Ali 2 Ouedraogo, Marie Françoise 2 Paycha, Sylvie 2 Pérez-Ayala, Samuel 2 Rennie, Adam 2 Rosenberg, Steven 2 Rumin, Michel 2 Ruzhansky, Michael V. 2 Savin, Anton Yur’evich 2 Seshadri, Neil 2 Wei, Sining 2 Zhu, Chaofeng 1 Abanov, Alexander G. 1 Bansil, Mohit 1 Barilari, Davide 1 Baudoin, Fabrice 1 Bauer, Wolfram 1 Beltrán, Carlos E. 1 Beschastnyi, Ivan Yu. 1 Bhattacharjee, Suvrajit 1 Biquard, Olivier 1 Boggiatto, Paolo 1 Bohlen, Karsten 1 Boltachev, A. V. 1 Carey, Alan L. 1 Carrillo-Rouse, Paulo 1 Chen, Guoyuan 1 Corral, Nuria 1 Couchet, Nathan 1 Cox, Graham 1 Criado del Rey, Juan G. 1 Cruz, Flávio Franca 1 Cruz, Tiarlos 1 Dabrowski, Ludwik 1 Delgado, Julio 1 Deng, Chao 1 Don, Sebastiano 1 Dong, Rui 1 Ducourtioux, Catherine 1 Fahrenwaldt, Matthias Albrecht 1 Faifman, Dmitry 1 Falk, Kévin 1 Gaarde, Anders 1 Gabriel, Olivier 1 Gao, Li 1 Ghorbanpour, Asghar 1 Gimperlein, Heiko 1 Gomez-Aparicio, Maria-Paula 1 Gorokhovsky, Alexander 1 Grong, Erlend 1 Guo, Kunyu 1 Gursky, Matthew J. 1 Haj Saeedi Sadegh, Ahmad Reza 1 Herzlich, Marc 1 Higson, Nigel 1 Hu, Kunming 1 Inahama, Yuzuru ...and 78 more Authors all top 5 Cited in 70 Serials 14 Advances in Mathematics 13 Journal of Geometry and Physics 12 Journal of Noncommutative Geometry 9 Journal of Functional Analysis 8 Journal of Mathematical Physics 6 Journal of Pseudo-Differential Operators and Applications 5 Annals of Global Analysis and Geometry 5 International Journal of Geometric Methods in Modern Physics 4 Communications in Mathematical Physics 4 International Journal of Mathematics 4 Journal of Nonlinear Mathematical Physics 3 The Journal of Geometric Analysis 3 Comptes Rendus. Mathématique. Académie des Sciences, Paris 3 SIGMA. Symmetry, Integrability and Geometry: Methods and Applications 2 Journal d’Analyse Mathématique 2 Letters in Mathematical Physics 2 Geometriae Dedicata 2 Journal für die Reine und Angewandte Mathematik 2 Mathematische Zeitschrift 2 Differential Geometry and its Applications 2 Communications in Partial Differential Equations 2 Journal de Mathématiques Pures et Appliquées. Neuvième Série 2 Calculus of Variations and Partial Differential Equations 2 Documenta Mathematica 2 Abstract and Applied Analysis 2 Geometry & Topology 2 Acta Mathematica Sinica. English Series 2 Journal of Dynamical and Control Systems 2 Journal of the Australian Mathematical Society 2 Oberwolfach Reports 2 Journal of \(K\)-Theory 2 Journal of Spectral Theory 1 Archive for Rational Mechanics and Analysis 1 Mathematical Notes 1 Studia Mathematica 1 American Journal of Mathematics 1 Annales de l’Institut Fourier 1 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série 1 Bulletin of the London Mathematical Society 1 Bulletin de la Société Mathématique de France 1 Functional Analysis and its Applications 1 Illinois Journal of Mathematics 1 Integral Equations and Operator Theory 1 Journal of Approximation Theory 1 Journal of the Mathematical Society of Japan 1 Kyungpook Mathematical Journal 1 Manuscripta Mathematica 1 Mathematische Annalen 1 Mathematische Nachrichten 1 Memoirs of the American Mathematical Society 1 Pacific Journal of Mathematics 1 Proceedings of the American Mathematical Society 1 Proceedings of the London Mathematical Society. Third Series 1 Results in Mathematics 1 Ergodic Theory and Dynamical Systems 1 \(K\)-Theory 1 Revista Matemática Iberoamericana 1 Publicacions Matemàtiques 1 NoDEA. Nonlinear Differential Equations and Applications 1 Journal of Lie Theory 1 Bulletin des Sciences Mathématiques 1 Mathematical Physics, Analysis and Geometry 1 Annales Henri Poincaré 1 Journal of Mathematical Physics, Analysis, Geometry 1 Communications in Mathematical Analysis 1 Advances in Mathematical Physics 1 Kyoto Journal of Mathematics 1 Forum of Mathematics, Sigma 1 Complex Analysis and its Synergies 1 Advances in Operator Theory all top 5 Cited in 34 Fields 125 Global analysis, analysis on manifolds (58-XX) 53 Differential geometry (53-XX) 50 Functional analysis (46-XX) 41 Partial differential equations (35-XX) 38 Operator theory (47-XX) 20 \(K\)-theory (19-XX) 20 Several complex variables and analytic spaces (32-XX) 14 Topological groups, Lie groups (22-XX) 9 Quantum theory (81-XX) 8 Manifolds and cell complexes (57-XX) 7 Algebraic geometry (14-XX) 6 Abstract harmonic analysis (43-XX) 5 Associative rings and algebras (16-XX) 3 Algebraic topology (55-XX) 2 General and overarching topics; collections (00-XX) 2 Number theory (11-XX) 2 Commutative algebra (13-XX) 2 Group theory and generalizations (20-XX) 2 Real functions (26-XX) 2 Dynamical systems and ergodic theory (37-XX) 1 Combinatorics (05-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Measure and integration (28-XX) 1 Functions of a complex variable (30-XX) 1 Potential theory (31-XX) 1 Sequences, series, summability (40-XX) 1 Approximations and expansions (41-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Calculus of variations and optimal control; optimization (49-XX) 1 Convex and discrete geometry (52-XX) 1 General topology (54-XX) 1 Probability theory and stochastic processes (60-XX) 1 Mechanics of deformable solids (74-XX) 1 Relativity and gravitational theory (83-XX) Citations by Year