Raphaël Ponge

Research Interests

• Noncommutative geometry, index theory, Fefferman's program, CR and conformal geometry, pseudodifferential operators.

Personal Information

• Vita (pdf) (last update: August 14, 2011)

Travel Plans in 2011:

• Sep. 8 - Sep. 17: Australian National University, Canberra, Australia.
• Aug. 8 - Sep. 1: IPMU (Institute for the Physics and Mathematics of the Universe), University of Tokyo, Kashiwa, Japan.
• Jul. 30 - Aug. 8: Seoul National University, Seoul, South Korea.
• July 19 - July 22: Kyoto Symposium on Complex Analysis in Several Variables, Kyoto University, Kyoto, Japan.
• June 3 - June 5: Takagi Lectures, Kyoto University, Kyoto, Japan.
• May 26 - June 2: CIMPA Spring School "Spectral Triples and Applications", Chulalongkorn University, Bangkok, Thailand.
• May 9 - May 19: Spring Institute on Noncommutative Geometry and Operator Algebras, Vanderbilt University, Nashville, USA.
• April 25 - May 5: Academica Sinica, Taipei, Taiwan.
• Apr. 1 - Jul. 30: IPMU (Institute for the Physics and Mathematics of the Universe), University of Tokyo, Kashiwa, Japan.
• Mar. 1 - Mar. 5: University of Victoria, Victoria, BC, Canada.
• Feb. 28 - Mar. 1: University of British Columbia, Vancouver, BC, Canada.
• Feb. 20 - Feb. 22: Columbus, OH, USA.
• Feb. 13 - Feb. 15: University of Western Ontario, London, ON, Canada.
• Feb. 10 - Feb. 12: Princeton University, Princeton, NJ, USA.
• Feb. 7: University of Toronto, Toronto, ON, Canada.
• Jan. 18 - Jan. 27: San Francisco and Berkeley, CA, USA.
• Jan. 15 - Feb. 26: McGill University, Montréal, QC, Canada.

Travel Plans in 2010:

• Dec. 19 - Jan. 5: Ecole normale supérieure, Paris, France.
• Nov. 28 - Nov. 30: Seoul National University, Seoul, South Korea.
• Nov. 22 - Nov. 25: Takagi Lectures and Workshop on Noncommutative Geometry and Number Theory, Kyoto University, Kyoto, Japan.
• Nov. 5 - Nov. 13: Perspectives in Deformation Quantization and Noncommutative Geometry, RIMS, Kyoto University, Kyoto, Japan.
• Oct. 16 - Oct. 21: University of Auckland, Auckland, New Zealand.
• Sep. 17: Seoul National University, Seoul, South Korea.
• Sep. 16: Sungkyunkwan University, Suwon, South Korea.
• Sep. 3 - Sep. 18: Korean Institute for Advanced Study, Seoul, South Korea.
• Jul. 14 - Sep. 2: McGill University, Montréal, QC, Canada.
• Apr. 27 - May 10: UC Berkeley, CA, USA.
• Feb. 17- Mar. 14: Ohio State University, Columbus, OH, USA.

Travel Plans in 2009:

• Oct. 30 - Nov. 5: Academica Sinica, Taipei, Taiwan.
• Sep. 10 - Oct. 3: Université du Québec à Montréal, Montréal, QC, Canada.
• Aug. 14 - Sep. 1: University of Toronto, Toronto, ON, Canada.
• June 29-July 3: Conference "Noncommutative geometric methods in global analysis" (in honor of Henri Moscovici's 60th birthday). Hausdorff Center, Bonn, Germany.
• May 3-9: Conference "The Power of Analysis" (in honor of the 60th birthday of Charles Fefferman). Princeton University, Princeton, NJ, USA.
• Apr. 26 - May 3: University of Toronto, Toronto, ON, Canada.
• Mar. 19-22: McGill University, Montréal, QC, Canada.
• Feb. 12-22: Université du Québec à Montréal, Montréal, QC, Canada.

Teaching

• Winter Semester 2010-2011:

  • Introduction to Noncommutative Geometry (901-68). On Fridays from 1-2:30pm in Room 122 (first lecture October 1st).

• Summer Semester 2010:

  • Pseudodifferential Operators and Applications (901-69). On Tuesdays from 10:40am-12:10pm in Room 118 (first lecture April 6th.).

• Winter Semester 2009-2010:

  • Introduction to Noncommutative Geometry. II (901-68). On Fridays from 10:40am-12:10pm in Room 122 (first lecture October 9th).

• Summer Semester 2009:

  • Introduction to Noncommutative Geometry. I (901-46). On Thursdays from 10:40am-12:10pm in Room 118 (first lecture April 16th).

Research Articles

1. On the singularities of the zeta and eta functions of an elliptic operator (with Paul Loya and Sergiu Moroianu) (pdf). To appear in Int. J. Math., 20 pages.
   
   
2. A New hypoelliptic operator on almost CR manifolds (pdf). To appear in Rev. Mat. Iberoamericana 27 (2011), no. 2, 393-414.
   
   
3. 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.
   
   
4. Traces on pseudodifferential operators and sums of commutators. (pdf). J. Anal. Math. 110 (2010) 1-30.
   
   
5. Logarithmic singularities of Schwartz kernels and local invariants of conformal and CR structures operators (pdf). 44 pages.
   
   
6. 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.
   
   
7. Noncommutative geometry and lower dimensional volumes in Riemannian geometry. (pdf). Lett. Math. Phys. 83 (2008) 19-32.
   
   
8. Noncommutative residue invariants for CR and contact manifolds (pdf). J. Reine Angew. Math. (Crelle's Journal) 614 (2008) 117-151.
   
   
9. Heisenberg calculus and spectral theory of hypoelliptic operators on Heisenberg manifolds (pdf). Mem. Amer. Math. Soc. 194 (2008) no. 906, 140 pages.
   
   
10. Noncommutative residue for Heisenberg manifolds and applications in CR and contact geometry (pdf). J. Funct. Anal. 252 (2007) 399-463.
    
    
11. 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.
    
    
12. Spectral asymmetry, zeta functions and the noncommutative residue (pdf). Int. J. Math. 17 (2006) 1065-1090.
    
    
13. The tangent groupoid of a Heisenberg manifold (pdf). Pacific J. Math. 227 (2006) 151-175.
    
    
14. 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).
    
    
15. A new proof of the local regularity of the eta invariant of a Dirac operator (pdf). J. Geom. Phys. 56 (2006) 1654-1665.
    
    
16. 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.
    
    
17. 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.
    
    
18. On the asymptotic completeness of the Volterra calculus (pdf). J. Anal. Math. 94 (2004) 249-263.
    
    
19. A new short proof of the local index formula and some of its applications (pdf). Comm. Math. Phys. 241 (2003) 215--234.
    
    
20. Géométrie spectrale et formules d'indices locales pour les variétés CR et contact (in French) (pdf). C. R. Acad. Sci. Paris, t. 332, série I, pp. 735-738, 2001.
    
    
21. Calcul fonctionnel sous elliptique et résidu non commutatif pour les variétés de Heisenberg (in French) (pdf). C. R. Acad. Sci. Paris, t. 332, série I, pp. 611-614, 2001.
    
    

Theses

• Calcul hypoelliptique sur les variétés de Heisenberg, résidu non commutatif et géométrie pseudo-hermitienne (in English) ( pdf ). PhD Thesis, Univ. Paris-Sud (Orsay), December 2000 (Advisor: Alain Connes). You can also get an abstract either in French (html) or in English (html).
  
  
• Résidu de Wodzicki et géométrie non commutative (in French) ( pdf ). Mémoire de magistère (Master thesis), Ecole normale supérieure, Paris, Dec. 96.
  
  
• Trace de Dixmier (in French) ( pdf). Mémoire de DEA (Master thesis), University of Paris-Sud, Orsay, Nov. 95.
  
  
• Formule de Feynman-Kac (in French) ( pdf). Senior thesis, Ecole normale supérieure, Paris, Sep. 94.