Raphaël Ponge

Research Area

Geometric analysis, including pseudodifferential operators, Connes' noncommutative geometry, index theory, CR and contact geometry, some aspects of Fefferman's program and the (fractional) Quantum Hall effect.

Personal Information

• Vita (pdf) (updated 11/18/07)

Travel Plans for 2008-2009

• Oct.3 - Oct. 6: AMS Meeting, University of British Columbia, Vancouver, BC, Canada.
• Aug. 20 - Dec. 19: Mathematical Science Research Institute, Berkeley, CA, USA.

Travel Plans for 2007-2008

• June 30 - July 4: Conference on Complex and CR Geometry, PDEs and Invariant Theory in honor of J.J. Kohn. Charles University, Prague, Czech Republic.
• June 6 - June 13: Conference on Motives, Quantum Field Theory, and Pseudodifferential Operators, Boston University, Boston, MA, USA.
• June 2 - June 5: Second congress Canada-France, University of Montreal, Montreal, QC, Canada.
• May 27 -May 31: Noncommutative Geometry Workshop, Fields Institute, Toronto, ON, Canada.
• May 1- June 30: McGill University, Montreal, QC, Canada.
• Apr. 14 - May 1: Boston University, Boston, MA, USA.
• Mar. 14 - Mar. 20: Conference on Geometry and Geometric Analysis, UC Santa Barbara, CA, USA.
• Feb. 15 - Feb. 26: Columbia University, New York, NY, USA.
• Dec. 8 - Dec. 10: CMS Winter Meeting, London, ON, Canada.
• Nov. 16 - Nov. 19: Conference on Current Development in Mathematics, Harvard University, Cambridge, MA, USA.

Travel Plans for 2006-2007

• Aug. 4 - Sep. 1: IHÉS, Bures-sur-Yvette, France.
• May 17- May 20: Midwest Geometry Conference 2007 (in memory of Thomas Branson), University of Iowa, Iowa City, USA.
• May 10 - May 15: Spring Institute in Noncommutative Geometry and Operator Algebras, Nashville, USA.
• May 3 - July 31: University of California at Berkeley, USA.
• Mar. 29 - Apr. 6: Conference in honor of Alain Connes, IHP, Paris, France.
• Dec. 17 - Dec. 22: Workshop "Trends in Noncommutative Geometry", Newton Institute, Cambridge, UK.

Travel Plans for 2005-2006

• July 31 - Aug. 4: Workshop "Noncommutative Geometry and Cyclic Cohomology", Newton Institute, Cambridge, UK.
• May 27 - June 1: Workshop "Spectral invariants and related topics", KIAS, Seoul, South Korea.
• May 19 - July 29: University of Tokyo, Japan.
• Jan. 3 - May 16: Max Planck Institute for Mathematics, Bonn, Germany.
• Dec. 18 - Dec. 21: Hayama symposium in several complex variables, Hayama, Japan.
• Dec. 11 - Dec 18: Workshop "Analytic geometry of the Bergman kernel and related topics", RIMS, Kyoto, Japan
• Nov. 1 - Dec. 11: University of Tokyo, Japan.
• Oct. 24 - Oct. 28: Workshop "Traces in geometry, number theory and quantum fields", Max Planck Institute for Mathematics, Bonn, Germany.
• Jul. 28 - Oct. 22: University of California at Berkeley, USA.

Teaching

• 2007-08:

  • MAT135 (Calculus I; year course, Fall and Winter terms).

  • MAT1314 (Introduction to Noncommutative Geometry; Winter term).

• 2006-07:

  • MAT135 (Calculus I; year course, Fall and Winter terms).

  • MAT234 (Differential Equations; Winter term).

Research Articles

- Recent Preprints:


1. A New hypoelliptic operator on almost CR manifolds (pdf). Preliminary draft, 10 pages.
   
   
2. Logarithmic singularities of Schwartz kernels and local invariants of conformal and CR structures operators (pdf). 44 pages, submitted.
   
   
3. 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).
   
   
   - Published and Accepted Papers:
   
   
4. Traces on pseudodifferential operators and sums of commutators. (pdf). 22 pages. To appear in J. Anal. Math..
   
   
5. Noncommutative geometry and lower dimensional volumes in Riemannian geometry. (pdf). Lett. Math. Phys. 83 (2008) 19-32.
   
   
6. Noncommutative residue invariants for CR and contact manifolds (pdf). J. Reine Angew. Math. (Crelle's Journal) 614 (2008) 117-151.
   
   
7. Heisenberg calculus and spectral theory of hypoelliptic operators on Heisenberg manifolds (pdf). Mem. Amer. Math. Soc. 194 (2008) no. 906, 140 pages.
   
   
8. Noncommutative residue for Heisenberg manifolds and applications in CR and contact geometry (pdf). J. Funct. Anal. 252 (2007) 399-463.
   
   
9. Spectral asymmetry, zeta functions and the noncommutative residue (pdf). Int. J. Math. 17 (2006) 1065-1090.
   
   
10. The tangent groupoid of a Heisenberg manifold (pdf). Pacific J. Math. 227 (2006) 151-175.
    
    
11. A new proof of the local regularity of the eta invariant of a Dirac operator (pdf). J. Geom. Phys. 56 (2006) 1654-1665.
    
    
12. On the asymptotic completeness of the Volterra calculus (pdf). J. Anal. Math. 94 (2004) 249-263.
    
    
13. A new short proof of the local index formula and some of its applications (pdf). Comm. Math. Phys. 241 (2003) 215--234.
    
    
14. 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.
    
    
15. 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:
    
    
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.
    
    
    

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.

Notes of talks

• Local index formulae for Heisenberg manifolds through non-commutative geometry. Workshop "Geometric scattering theoryand elliptic theory on noncompact and singular spaces" (T. Christiansen, C. Epstein, R. Mazzeo, R. Melrose), MSRI, Berkeley, May 2001; by going here you can view scanned written notes and a streaming video of my talk.

• Cohomologie cyclique des fonctions lisses sur une variété et du tore non commutatif (in French) ( pdf). Working seminar "Théorèmes d'indices, opérateurs de Dirac et géométrie non commutative" (E. Leichtnam, V. Maillot), Ecole normale supérieure, Paris, March 96.

• Opérateurs de Dirac (in French) ( pdf). Working seminar "Théorèmes d'indices, opérateurs de Dirac et géométrie non commutative" (E. Leichtnam, V. Maillot), Ecole normale supérieure, Paris, Dec. 95.