Raphaël Ponge







Department of Mathematical Sciences
Seoul National University
1 Gwanak-ro, Gwanak-gu
Seoul, 08826
Republic of Korea

Room: 129-402 (Bldg 27, Room 314).
Phone: (82) (2) 880-5736
Fax: (82) (2) 887-4694
E-mail: ponge [dot] snu [at] gmail [dot] com


In Summer 2015 I organized a workshop on Noncommutative Geometry and Spectral Invariants in Montréal, Canada.

Research Interests


Personal Information


Travel in 2018:

Travel in 2017:

Travel in 2016:


Teaching


Lecture Notes


Research Articles

  1. Privileged coordinates and tangent groupoid for Carnot manifolds (with Woocheol Choi) (arXiv) (v2: September 2017). Submitted, 40 pages.

  2. Privileged coordinates and nilpotent approximation for Carnot manifolds, II. Carnot coordinates (with Woocheol Choi) (arXiv) (v2: September 2017). Submitted, 36 pages.

  3. Privileged coordinates and nilpotent approximation for Carnot manifolds, I. General results (with Woocheol Choi) (arXiv) (v1: September 2017). Submitted, 40 pages.

  4. Cyclic homology and group actions (arXiv) (doi). J. Geom. Phys. 123 30-52.

  5. Noncommutative geometry and conformal geometry. I. Local index formula and conformal invariants (with Hang Wang) (arXiv). (v2: April 2017). To appear in J. Noncomm. Geom., 39 pages.

  6. The cyclic homology of crossed-product algebras, I (pdf). C. R. Acad. Sci. Paris, sér. I, 355 (2017), 618-622

  7. The cyclic homology of crossed-product algebras, II (pdf). C. R. Acad. Sci. Paris, sér. I, 355 (2017), 623-627.

  8. Noncommutative geometry and conformal geometry. II. Connes-Chern character and the local equivariant index theorem (with Hang Wang) (pdf). J. Noncomm. Geom. 10 (2016), 307-378.

  9. Index map, σ-connections, and Connes-Chern character in the setting of twisted spectral triples (with Hang Wang) (pdf). Kyoto J. Math. 56 (2016), 347-399.

  10. Noncommutative geometry and conformal geometry. III. Vafa-Witten inequality and Poincaré duality (with Hang Wang) (pdf). Adv. Math. 272 (2015), 761-819.

  11. The Logarithmic singularities of the Green functions of the conformal powers of the Laplacian (pdf). Contemp. Math. Vol. 630 (2014), pp. 247-273.

  12. Conformal invariants from nodal sets (with Yaiza Canzani, Rod Gover and Dmitry Jakobson) (Appendix by Rod Gover and Andrea Malchiodi) (pdf). Int. Math. Res. Notices 2014 (2014), 2356-2400.

  13. Nullspaces of conformally invariant operators. Applications to Q-curvature (with Yaiza Canzani, Rod Gover and Dmitry Jakobson) (pdf). Electron. Res. Announc. Math. Sci. 20 (2013), 43-50.

  14. On the singularities of the zeta and eta functions of an elliptic operator (with Paul Loya and Sergiu Moroianu) (pdf). Int. J. Math. 23 (2012), no. 6, 1-26.

  15. A New hypoelliptic operator on almost CR manifolds (pdf). Rev. Mat. Iberoamericana 27 (2011), no. 2, 393-414.

  16. A microlocal approach to Fefferman's program in conformal and CR geometry (pdf). Clay Math. Proc., 12, Amer. Math. Soc., Providence, RI, 2011, pp. 219-242.

  17. Traces on pseudodifferential operators and sums of commutators. (pdf). J. Anal. Math. 110 (2010), 1-30.

  18. Logarithmic singularities of Schwartz kernels and local invariants of conformal and CR structures operators (pdf). 44 pages.

  19. Noncommutative residue and new invariants for CR and contact manifolds (pdf). Traces in Geometry, Number Theory and Quantum Fields (Max Planck Institute, Bonn, Germany, Oct. 24 - 28, 2005), pp. 179-186. S. Albeverio, M. Marcolli and S. Paycha eds., Aspects of Mathematics, Vieweg Verlag, 2008.

  20. Noncommutative geometry and lower dimensional volumes in Riemannian geometry. (pdf). Lett. Math. Phys. 83 (2008), 19-32.

  21. Noncommutative residue invariants for CR and contact manifolds (pdf). J. Reine Angew. Math. (Crelle's Journal) 614 (2008), 117-151.

  22. Heisenberg calculus and spectral theory of hypoelliptic operators on Heisenberg manifolds (pdf). Mem. Amer. Math. Soc. 194 (2008) no. 906, 140 pages.

  23. Noncommutative residue for Heisenberg manifolds and applications in CR and contact geometry (pdf). J. Funct. Anal. 252 (2007), 399-463.

  24. A new short proof of the Atiyah-Singer index formula (pdf). Noncommutative Geometry and Number Theory (Max Planck Institute, Bonn, Aug. 17-22, 2003), 361-372, Aspects of Mathematics, Vieweg Verlag, 2006.

  25. Spectral asymmetry, zeta functions and the noncommutative residue (pdf). Int. J. Math. 17 (2006), 1065-1090.

  26. The tangent groupoid of a Heisenberg manifold (pdf). Pacific J. Math. 227 (2006), 151-175.

  27. Comments on: "Operator K-theory for the group SU(n,1)" by P. Julg and G. Kasparov (pdf). Version of 4/17/06, 7 pages. Not intended for publication (will be included in a forthcoming paper).

  28. A new proof of the local regularity of the eta invariant of a Dirac operator (pdf). J. Geom. Phys. 56 (2006), 1654-1665.

  29. Analogues of the holomorphic Morse inequalities in CR geometry (pdf). Proceedings of the Hayama symposium in several complex variables, Hayama, Japan, Dec. 18-21, 2005, T. Oshawa et al. eds., 6 pages.

  30. Szegö projections and new invariants for CR and contact manifolds (pdf). Proceedings of the workshop "Analytic geometry of the Bergman kernel and related topics", RIMS, Kyoto University, Japan, Dec. 12-16, 2005, T. Oshawa et al. eds., 14 pages.

  31. On the asymptotic completeness of the Volterra calculus (Appendix by Hayk Mikayelyan and myself) (pdf). J. Anal. Math. 94 (2004), 249-263.

  32. A new short proof of the local index formula and some of its applications (pdf). Comm. Math. Phys. 241 (2003), 215--234.

  33. Géométrie spectrale et formules d'indices locales pour les variétés CR et contact (in French) (pdf). C. R. Acad. Sci. Paris, sér. I, 332 (2001), 735-738.

  34. Calcul fonctionnel sous elliptique et résidu non commutatif pour les variétés de Heisenberg (in French) (pdf). C. R. Acad. Sci. Paris, sér. I, 332 (2001), 611-614.


Theses