Raphaël Ponge
Department of Mathematical Sciences
Seoul National University
1 Gwanakro, Gwanakgu
Seoul, 08826
Republic of Korea
Room: 129402 (Bldg 27, Room 314).
Phone: (82) (2) 8805736
Fax: (82) (2) 8874694
Email: 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
 Geometric analysis (noncommutative geometry, microlocal
analysis, local index theory, spectral theory).
 Differential geometry
(conformal geometry, complex and CR geometry, contact geometry,
subRiemannian geometry).
 Homological algebra (cyclic homology).
Personal Information
 Vita
(pdf) (last update: October 1, 2017)
Travel in 2018:
 July 814: Workshop on "Noncommutative Geometry, Index Theory and
Mathematical Physics", Oberwolfach, Germany.
 Jan. 1Feb. 28: McGill University, Montréal, Canada.
Travel in 2017:
 Dec. 1231: McGill University, Montréal, Canada.
 Dec. 911: Winter meeting of Canadian Mathematical Society,
University of Waterloo, Waterloo, Canada.
 Sep. 28Oct. 10: Kyoto University, Kyoto, Japan.
 July 31Aug. 4: MCA Satellite Conference on Operator Algebras, Fields
Institute, Toronto, Canada.
 July 2428: Mathematical Congress of the Americas, McGill Univeristy,
Montréal, Canada.
 May 29June 2: Conference on "Index theory and Singular structures", University of
Toulouse, Toulouse, France.
 March 2327: Workshop on "Noncommutative Geometry: Index Theory and its Ramifications in Geometry,
Topology and Physics" (in honor of Alain Connes), Fudan University,
Shanghai, China.
 Jan. 22 Feb. 28: McGill University, Montréal, Canada.
 Jan. 1213: University of Montpellier, Montpellier, France.
 Jan. 911: Glasgow University, Glasgow, UK.
 Jan. 322: ParisDiderot University, Paris, France.
Travel in 2016:
 Dec. 1431: McGill University, Montréal, Canada.
 Dec. 1014: Kyoto University, Kyoto, Japan.
 Oct. 2030: Banach Center, IMPAN, Warsaw, Poland.
 July 1722: Conference on "Geometry, Representation Theory and the
BaumConnes Conjecture" (in honor of Paul Baum), Fields Institute,
Toronto, Canada.
 June 5  Sep. 1: McGill University, Montréal, Canada.
 Feb. 29 Mar. 4: University of Tokyo, Tokyo, Japan.
 Feb. 2526: Northeastern University, Boston, USA.
 Jan. 1  Feb. 28: McGill University, Montréal, Canada.
Teaching

Fall Semester 2017:

Spring Semester 2017:
 Functional Analysis 1.
Mondays and Wednesdays from 11am12:15pm. The first lecture will be on
March 6, 2017.

Fall Semester 2016:

Spring Semester 2016:
 Functional Analysis 1.
Tuesdays and Thursdays
from 2pm3:15pm. The first lecture will be on March 8, 2016.

Fall Semester 2015:
 Introduction to Linear Algebra. Tuesdays and Thursdays
from 12:30pm1:45pm.
 Differential Equations. Tuesdays and Thursdays from
3:30pm4:45pm.

Spring Semester 2014:
 Functional Analysis 1. Mondays and Wednesdays
from 2pm3:15pm.

Fall Semester 2013:
 Introduction to Linear Algebra. Mondays and Wednesdays
from 12:30pm1:45pm.
 Differential Equations. Mondays and Wednesdays from
5pm6:15pm.

Spring Semester 2013:
 Introduction to Quantum Groups. Tuesdays and Thursdays
from 11am12:15pm.

Fall Semester 2012:
 Functional Analysis 2 (Distributions and Spectral
Theory). Mondays and Wednesdays from 5pm6:15pm.
 Calculus 2 (Multivariable calculus). Mondays and Wednesdays from 11am11:50am.

Spring Semester 2012:

Fall Semester 2011:
 Introduction to Linear Algebra. Mondays and Wednesdays
from 9:30am10:45am.
 Calculus 2 (Multivariable calculus). Mondays and Wednesdays from 11am11:50am.
Lecture Notes
 Slides of my series of lectures on "Introduction to Noncommutative
Geometry" at UC Berkeley in Spring 2015. (Many thanks to Prof. Marc Rieffel
for letting me give these lectures in his Quantum Geometry seminar.)
 Part 1: Quantized Calculus (pdf).
 Part 2: Spectral Triples (pdf).
 Part 3: Cyclic Homology and Cohomology (pdf).
 Part 4: Index Theory and the ConnesChern Character (pdf).
 Slides of my short course on noncommutative geometry at Mathematical Science Center,
Tsinghua University, Beijing, P.R. China (October 2427, 2011), and
at Australian National University, Canberra, Australia (August 2012).
 Part 1: Introduction (Quantized Calculus) (pdf).
 Part 2: Spectral Triples and he AtiyahSinger
Index Theorem (pdf).
 Part 3: Cyclic Cohomology (pdf).
 Part 4: The Local Index Formula in
Noncommutative Geometry (pdf).
 Part 5: DiffeomorphismInvariant Geometry (pdf).
 Notes of my graduate course Introduction to Noncommutative
Geometry at the University of Tokyo, Oct. 2010  Jan.
2011.
 Chap. 17: Operator ideals, Connes' quantized
calculus, Dixmier trace, pseudodifferential operators, the
noncommutative residue, lower dimensional volumes in Riemannian
geometry (pdf).
 Chap. 8.: Clifford algebras, spinors, Dirac operators and the
AtiyahSinger index theorem (pdf).
 Chap. 912: Ktheory, cyclic cohomology, the local index formula in
NCG, the CM cocycle for Dirac spectral triples, ConnesMoscovici's index theorem in diffeomorphisminvariant
geometry (pdf).
Research Articles
 Privileged coordinates and tangent
groupoid for Carnot manifolds (with Woocheol Choi) (arXiv) (v2: September
2017). Submitted, 40 pages.
 Privileged coordinates and nilpotent
approximation for Carnot manifolds, II. Carnot coordinates (with Woocheol Choi)
(arXiv) (v2: September
2017). Submitted, 36 pages.
 Privileged coordinates and nilpotent
approximation for Carnot manifolds, I. General results (with Woocheol Choi)
(arXiv) (v1: September
2017). Submitted, 40
pages.
 Cyclic homology and group actions
(arXiv)
(doi). J. Geom. Phys. 123 3052.
 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.
 The cyclic homology of crossedproduct algebras, I (pdf).
C. R. Acad. Sci. Paris, sér. I, 355 (2017), 618622
 The cyclic homology of crossedproduct algebras, II (pdf). C. R. Acad. Sci. Paris, sér. I,
355 (2017), 623627.
 Noncommutative geometry and conformal
geometry. II. ConnesChern character and the local equivariant index
theorem (with Hang Wang)
(pdf). J. Noncomm.
Geom. 10 (2016), 307378.
 Index map, σconnections, and
ConnesChern character in the setting of twisted spectral triples (with Hang Wang)
(pdf). Kyoto J. Math. 56 (2016),
347399.
 Noncommutative geometry and conformal
geometry. III. VafaWitten inequality and Poincaré duality (with Hang Wang)
(pdf).
Adv. Math. 272 (2015), 761819.
 The Logarithmic singularities of the Green
functions of the conformal powers of the Laplacian (pdf). Contemp. Math. Vol. 630 (2014),
pp. 247273.
 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), 23562400.
 Nullspaces of conformally invariant operators. Applications to
Qcurvature (with Yaiza Canzani, Rod Gover and
Dmitry Jakobson)
(pdf).
Electron. Res. Announc. Math. Sci. 20 (2013), 4350.
 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, 126.
 A New hypoelliptic operator on almost CR manifolds
(pdf). Rev. Mat.
Iberoamericana 27 (2011), no. 2, 393414.
 A microlocal approach to Fefferman's program in conformal and CR
geometry (pdf).
Clay Math. Proc., 12, Amer. Math. Soc., Providence, RI, 2011, pp.
219242.
 Traces on pseudodifferential operators and
sums of commutators.
(pdf). J. Anal.
Math. 110 (2010), 130.
 Logarithmic singularities of Schwartz
kernels and local invariants of conformal and CR structures
operators
(pdf). 44 pages.
 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. 179186. S. Albeverio, M. Marcolli and S. Paycha eds., Aspects
of Mathematics, Vieweg Verlag, 2008.
 Noncommutative geometry and lower
dimensional volumes in Riemannian geometry.
(pdf). Lett.
Math. Phys. 83 (2008), 1932.
 Noncommutative residue invariants for CR and contact
manifolds
(pdf).
J. Reine Angew. Math. (Crelle's Journal) 614 (2008), 117151.
 Heisenberg calculus and spectral theory of
hypoelliptic operators on Heisenberg manifolds
(pdf). Mem. Amer. Math.
Soc. 194 (2008) no. 906, 140 pages.
 Noncommutative residue for Heisenberg
manifolds and applications in CR and contact geometry (pdf). J. Funct. Anal. 252 (2007), 399463.
 A new short proof of the AtiyahSinger index formula
(pdf). Noncommutative Geometry and Number
Theory (Max Planck Institute, Bonn, Aug. 1722, 2003), 361372, Aspects of Mathematics, Vieweg Verlag, 2006.
 Spectral asymmetry, zeta functions and the noncommutative residue
(pdf).
Int. J. Math. 17 (2006), 10651090.
 The tangent groupoid of a Heisenberg manifold
(pdf). Pacific J. Math. 227
(2006), 151175.

Comments on: "Operator Ktheory 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).
 A new proof of the local regularity of the
eta invariant of a Dirac operator
(pdf). J. Geom. Phys. 56 (2006), 16541665.
 Analogues of the holomorphic Morse
inequalities in CR geometry
(pdf). Proceedings of the
Hayama symposium in several complex variables,
Hayama, Japan, Dec. 1821, 2005, T. Oshawa et al. eds., 6 pages.
 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. 1216, 2005, T. Oshawa et
al. eds., 14 pages.
 On the asymptotic completeness of the
Volterra calculus (Appendix by Hayk Mikayelyan and myself)
(pdf). J. Anal. Math. 94 (2004), 249263.
 A new short proof of the local index formula and some of its
applications (pdf). Comm. Math. Phys.
241 (2003), 215234.
 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), 735738.
 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), 611614.
Theses
 Calcul hypoelliptique sur les variétés de
Heisenberg,
résidu non commutatif et géométrie
pseudohermitienne (in English)
( pdf ). PhD Thesis, Univ. ParisSud
(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 ParisSud, Orsay, Nov. 95.
 Formule de FeynmanKac (in French) ( pdf).
Senior thesis, Ecole normale supérieure, Paris, Sep. 94.