Raphaël Ponge

Research Interests

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

Personal Information

• Vita (pdf) (updated 4/15/09)

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

• Summer Semester 2009:

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

• Winter Semester 2009-2010:

  • Introduction to Noncommutative Geometry. II (901-68). Fridays, from 10:40am-12:10pm in Room 122 of Math. Sci. Bldg (first lecture October 2).

Research Articles

- Recent Preprints:


1. A New hypoelliptic operator on almost CR manifolds (pdf). 18 pages, submitted.
   
   
2. Logarithmic singularities of Schwartz kernels and local invariants of conformal and CR structures operators (pdf). 44 pages, submitted.
   
   
   - Published and Accepted Papers:
   
   
3. Traces on pseudodifferential operators and sums of commutators. (pdf). 22 pages. To appear in J. Anal. Math..
   
   
4. Noncommutative geometry and lower dimensional volumes in Riemannian geometry. (pdf). Lett. Math. Phys. 83 (2008) 19-32.
   
   
5. Noncommutative residue invariants for CR and contact manifolds (pdf). J. Reine Angew. Math. (Crelle's Journal) 614 (2008) 117-151.
   
   
6. Heisenberg calculus and spectral theory of hypoelliptic operators on Heisenberg manifolds (pdf). Mem. Amer. Math. Soc. 194 (2008) no. 906, 140 pages.
   
   
7. Noncommutative residue for Heisenberg manifolds and applications in CR and contact geometry (pdf). J. Funct. Anal. 252 (2007) 399-463.
   
   
8. Spectral asymmetry, zeta functions and the noncommutative residue (pdf). Int. J. Math. 17 (2006) 1065-1090.
   
   
9. The tangent groupoid of a Heisenberg manifold (pdf). Pacific J. Math. 227 (2006) 151-175.
   
   
10. A new proof of the local regularity of the eta invariant of a Dirac operator (pdf). J. Geom. Phys. 56 (2006) 1654-1665.
    
    
11. On the asymptotic completeness of the Volterra calculus (pdf). J. Anal. Math. 94 (2004) 249-263.
    
    
12. A new short proof of the local index formula and some of its applications (pdf). Comm. Math. Phys. 241 (2003) 215--234.
    
    
13. 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.
    
    
14. 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.
    
    
    - Conference Proceedings:
    
    
15. A microlocal approach to Fefferman's program in conformal and CR geometry (pdf). To appear in the proceedings of the conference Motives, Quantum Field Theory and Pseudodifferential Operators (Boston University, USA, June 1-14, 2008), 20 pages.
    
    
16. 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.
    
    
17. Analogues of the holomorphic Morse inequalities in CR geometry (with George Marinescu, pdf). Proceedings of the Hayama symposium in several complex variables, Hayama, Japan, Dec. 18-21, 2005, T. Oshawa et al. eds., 6 pages.
    
    
18. 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.
    
    
19. 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.
    
    
    - Unpublished Manuscript:
    
    
20. 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).
    
    

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.