CURRICULUM VITAE

1. Personal Data

Name: César Leopoldo Camacho Manco Date of birth: April 15, 1943 Place of birth: Lima, Peru

Nationality: Brazilian and Peruvian Present Position: General Director and Full Professor at the Instituto

Nacional de Matemática Pura e Aplicada – IMPA

Professional address: IMPA Estrada Dona Castorina 110, Jardim Botânico 22460-320 - Rio de Janeiro, RJ - Brazil Email camacho@impa.br

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2. Academic Data

- Ph.D. (Mathematics), 1971

University of California, Berkeley Doctoral Thesis: On Rk x Zl-actions. Research Area: Dynamical Systems Adviser: Stephen Smale - Master in Mathematics, 1966 Instituto de Matemática Pura e Aplicada (IMPA) Rio de Janeiro 3. Research Papers

Extension theorems for analytic objects associated to foliations. Bulletin des Sciences Mathématiques (Paris. 1885), v. 136, p. 54-71, 2012. Jointly with B. Scárdua Nondicritical C*-actions on two-dimensional Stein manifolds. Manuscripta Mathematica, v. 129, p. 91-98, 2009. Jointly with B. Scárdua On the limit of families of algebraic subvarieties with unbounded volume. Astérisque, v. 323, p. 41-59, 2009. Jointly with L.H. Figueiredo The moduli of quasi-homogeneous Stein surface singularities. The Journal of Geometric Analysis, v. 19, p. 244-255, 2009. Jointly with B. Scárdua and H. Movasati Actions of the groups C and C* on Stein varieties. Geometriae Dedicata, v. 139, p. 5-12, 2009. Jointly with B. Scárdua On foliations with Morse singularities. Proceedings of the American Mathematical Society, v. 136, p. 4065-4073, 2008. Jointly with B. Scárdua Dicritical holomorphic flows on Stein manifolds. Archiv der Mathematik, v. 1, p. 1-12, 2007. Jointly with B. Scárdua

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A characterization of the three-sphere by means of foliations. Topology and its Applications, v. 154, p. 1032-1040, 2007. Jointly with B. Scárdua Residues of holomorphic foliations relative to a general submanifold. Bulletin of the London Mathematical Society - v. 37, p. 433-445, 2005. Jointly with D. Lehmann Neighborhoods of analytic varieties. Monografias del IMCA, nº 35, 2003. Jointly with H. Movasati Fibered neighborhoods of complex curves in surfaces. The Journal of Geometric Analysis, vol. 13, nº 1, pp. 55-66, 2003. Jointly with H.Movasati and P.Sad

The dynamics of the Jouanolou foliation on the complex projective 2-space. Ergodic Theory and Dynamical Systems, Vol. 21, 757-766, 2001. Jointly with L.H.Figueiredo

Holomorphic foliations with Liouvillian first integrals. Ergodic Theory and Dynamical Systems, vol. 21, pp. 717-756, 2000. Jointly with B. Scárdua Local first integrals, from holomorphic to transcendent. Contemporary Mathematics AMS, nº 269, pp 39 – 46, 2000. Foliations on complex projective spaces with algebraic limit sets. Asteristique, nº 261, pp. 57 – 87, 2000. Jointly with B. Scárdua Holomorphic foliations and Kupka singularities. Communications in Analysis and Geometry, Vol. 7, nº 3, pp 623-640, 1999. Jointly with B. Scárdua Beyond Liouvillian transcendence. Mathematical Research Letters, 6, 31-41, 1999. Jointly with B. Scárdua The transcendence of solutions of complex differential equations. Ecuaciones Diferenciales. Singularidades. Valladolid, Serie Ciencias no. 15, 79-102, 1997. Jointly with B. Scárdua

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Four problems on the structure of complex foliations. Revista del Seminario de Singularidades. Tordesillas. Fascículo VI. 1997. Perspectivas en singularidades de foliaciones holomorfas. Ecuaciones Diferenciales Singularidades, Valladolid, Serie Ciencias No. 15, 451-454, 1997. Generalización de un Teorema de Painlevé. Volumen en homenaje a J. Tola. Pro Mathematica vol. IX, 1995, 35-43. Jointly with B. Scárdua Complex foliations arising from polynomial differential equations, bifurcations and periodic orbits of vector fields. Edited by D. Schlomiuk, Nato ASI Series C: Mathematical and Physical Sciences – Vol. 408, 1993, 1-18.

Foliations with algebraic limit sets. Annals of Mathematics 136 (1993), 429-446. Jointly with A. Lins Neto and P. Sad Problems on limit sets of foliations of complex projective spaces. Proceedings of the International Congress of Mathematicians, Kyoto, Springer-Verlag, pp. 1235-1239, 1990. Absolutely isolated singularities of holomorphic vector field. Inventiones Mathematicae 98, pp. 351-369, 1990. Jointly with F. Cano and P. Sad Minimal sets of foliations on complex projective spaces. Publications Mathématiques de l'IHES, 68, pp l87-203, 1988. Colloque en l'honneur de René Thom. Jointly with A. Lins N. and P.Sad

Quadratic forms and holomorphic foliations on singular surfaces. Matematische Annalen, 282 , 177-184, 1988.

Topological invariants and equidesingularization for holomorphic vector fields. Journal of Differential Geometry, 20, pp. 143-174, 1984. Jointly with A. Lins Neto and P. Sad

Singularities of holomorphic differential equations. Singularities and Dynamical Systems, Creta. North Holland, 1983.

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An extension of Peixoto's structural stability theorem. Geometric Dynamics, Lectures Notes in Mathematics, Springer Verlag, v° 1007, pp.

60-88, 1983. Jointly with R. Mañé, M. Krych and L. Nitecki.

Topological classification and bifurcation of holomorphic vector fields with resonances. Inventiones Mathematicae, 67, pp. 447-472, 1982. Jointly with P. Sad Invariant varieties through singularities of holomorphic vector fields. Annals of Mathematics, 115, pp 579-595, 1982. Jointly with P. Sad The topology of integrable differential forms near a singularity. Publications Mathematiques de l'IHES, n° 55, pp.05-35, 1981.

Jointly with A. Lins Neto

Sur l'existence de courbes analytiques complexes invariants d’un champ de vecteurs holomorphe. C.R.A. - Acad.Sc.Paris, 6 p. 291, pp.311-312, 1980. Jointly with P. Sad Local structure of conformal mappings and holomorphic vector fields in C2. Asterisque, 59-60 (Société Mathématique de France), pp. 83-94, 1979. Cr Structural stability of germs of integrable 1-forms. Sociedade Brasileira de Matemática, pp. 65-67, 1978. Structural stability of integrable 1-forms on 3-manifolds. Topology, vol. 17, n° 2, pp 143-155, 1978.

Structural stability of foliations with singularities. Differential Topology, Foliations and Gelfand-Fuks Cohomology. Lecture Notes in Mathematics. Springer Verlag, vol. 652, pp 43-51, 1978. The topology of holomorphic flows with singularity. Publications Mathematiques de l' I.H.E.S., 48 pp. 5-38, 1978. Jointly with N. Kuiper and J. Palis

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La topologie du feuilletage d’un champ de vecteurs holomorphes prés d'une s singularité. C.R. Acad. Sciences, Paris, T. 282, pp. 959-961, 1977. Jointly with N.H. Kuiper and J. Palis Orbit preserving diffeomorphisms and the stability of Lie group actions and singular foliations. Geometry and Topology. Lectures Notes in Mathematics, Springer-Verlag, vol. 597, pp. 82-103, 1977. Jointly with A. Lins Neto Poincaré-Bendixson theorem for R2-actions. Boletim da Sociedade Brasileira de Matemática, vol. 5, n° 1, 1973.

Stability theorems for R2-actions. International Congress of Global Analysis. International Centre for Theoretical Physics, Trieste, 1972. Morse-Smale R2-actions on two manifolds. Annals of the International Symposium on Dynamical Systems. Editor M.Peixoto. Academic Press, 1971.

On Rk x Zl- Actions. Annals of the International Symposium on Dynamical Systems. Editor M.Peixoto. Academic Press, 1971.

4. Books

- Tópicos de una Variable Compleja

Monografias del IMCA, n 1, 1997

- Complex Analytic Methods in Dynamical Systems. Asterisque 222, Soc. Math. de France 1993. Jointly with A. Lins N., R. Moussu and P. Sad. - Seminário de Superfícies de Riemann – Volumes I e II IMPA, 1986.

- Singular Points of Analytic Differential Equations Summer School on Dynamical Systems International Centre for Theoretical Physics, Trieste, 1990 Jointly with P.Sad

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- Pontos Singulares de Equações Diferenciais Analíticas IMPA, 1988 Jointly with P.Sad. - Holomorphic Dynamical Systems Summer School on Dynamical Systems International Centre for Theoretical Physics, Trieste, 1983

- Geometric Theory of Foliations Birkhäuser, 1985 Jointly with A. Lins Neto - Teoria Geométrica das Folheações Projeto Euclides, IMPA, 1976 Jointly with A. Lins Neto

5. Advisor in the following Doctoral Thesis

1. Alcides Lins Neto

Instituto de Matemática Pura e Aplicada “Generalized gradient fields and electrical circuits”, 1974.

2. Airton Von Sohsten de Medeiros

Instituto de Matemática Pura e Aplicada “Structural stability of integrable differential forms,”, 1974.

3. Guilherme Lincoln Aguiar Ellery

Instituto de Matemática Pura e Aplicada “Sobre a Estabilidade Estrutural Global de Ações do R2”, 1979.

4. Sérgio Rodrigues

Instituto de Matemática Pura e Aplicada “Quasihyperbolic R2-actions”, 1979.

5. Maria Lúcia Alvarenga Peixoto

Instituto de Matemática Pura e Aplicada “The closing Lemma for generalized recurrence in the plane”, 1985

6. Júlio César Canille Martins

Instituto de Matemática Pura e Aplicada “Holomorphic flows in C3 with resonances”, 1985.

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7. Bruno Cesar Azevedo Scárdua

Instituto de Matemática Pura e Aplicada “Transversely affine and transversely projective holomorphic foliations”, 1994

8. Renato Mario Benazic Tomé

Instituto de Matemática Pura e Aplicada “A resolution theorem for absolutely isolated singularities of holomorphic vector

fields”, 1996.

9. Rogerio Santos Mol Instituto de Matemática Pura e Aplicada

“Meromorphic first integrals: Some extension results”, 1998

10. Renata Nunes Ostwald Instituto de Matemática Pura e Aplicada

“On the existence of Levi foliations”, 2000

11. Fabio Enrique Brochero Martínez Instituto de Matemática Pura e Aplicada

“Groups of Germs of Analytic Diffeomorphisms”, 2001

12. Percy Fernández Instituto de Matemática Pura e Aplicada

“Automorphism Groups of Holomorphic Foliations”, 2001

13. Jorge Vitório Bacelar Pereira Instituto de Matemática Pura e Aplicada

“Global Stability for Holomorphic Foliations on Kähler Manifolds”, 2001

14. Rudy Rosas Bazán Instituto de Matemática Pura e Aplicada

“On the topological invariance of the algebraic multiplicity of a holomorphic vector field”, 2005

15. Mahdi Teymuri Garakani Instituto Nacional de Matemática Pura e Aplicada

“On the deformation of holomorphic foliations and complex hypersurfaces”, 2006

16. Jesus Abad Zapata Samanez Instituto Nacional de Matemática Pura e Aplicada

Anti-Self-Dual Geometry, Twistor spaces and Painlevé VI equation.. 2007.

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17. Gabriela Verónica Fernández Lamilla Instituto Nacional de Matemática Pura e Aplicada “Holomorphic Actions on Stein Manifolds”, 2010

6. Invited Talks

2 0 1 2 - Guanajuato, México Fracciones continuas y soluciones de la ecuación hypergeométrica de Gauss. March 2 0 1 1 - Guanajuato, México Extension theorems associated to foliations. August 2 0 1 0 - Colloque em l’honneur de Marc Chaperon Singularities of holomorphic vector fields. January 2 0 0 8 - Congrès à la mémoirie d’Adrien Douady, Institut Henri Poincaré The moduli C*-actions on 2-dimensional Stein analytic spaces. May 2 0 0 7 - Cuernavaca - Mexico

Classification of C* - actions on Stein surfaces with singularity. The Geometry and Topology of singularities.

2 0 0 6

- Satellite Conference on Differential Equations and Singularities, in honor of J. M. Aroca’s 60th birthday, Tordesilhas, Espanha Foliation with Morse Singularities, Ecuaciones Diferenciales y Singularidades. May

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2 0 0 4 - International Congress on Dynamical Systems, in honor of J.L. Massera Fibered Neighborhoods of Curves in Complex Surfaces. May 2 0 0 3 - University of Valladolid Linearización de fibrações holomorfas sobre superfícies de Riemann February 2 0 0 2 - Centre International de Rencontres Mathématiques – Marseille Fibered embeddings of Riemann surfaces. April - University of Tokyo Singularities of differential equations and the fibered embedding of Riemann Surfaces November - University of Kyoto Fibered embedding of riemman surfaces in complex surfaces November 2 0 0 1 - Instituto de Matemática y Ciencias Afines – IMCA Residue theorems for dicritical singularities February - Universidade Católica do Rio de Janeiro Three lectures on complex foliations August - Instituto de Matemática y Ciencias Afines – IMCA Immersiones fibradas en superficies complejas November

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2 0 0 0 - Universitá di Firenze Louvillian foliations June - Univerditá di Siena Algebraic invariants of complex differential equations June 1 9 9 9 - Scuola Normale Superiore di Pisa Dynamics of complex flows May - Université de Paris VI A Residue theorem for complex foliations May - Instituto de Matemática y Ciencias Afines (IMCA), Lima Una extensión de la fórmula de indice de campos holomorfos May - International Centre for Theoretical Physycs, Trieste Liouvillian first integrals of complex foliations November - Universidade Federal de Pernambuco Integrais primeiras de Liouville de equações diferenciais analíticas November

1 9 9 8 - State University of New York Germs of holomorphic foliations May. - Universidade de São Paulo A dinâmica global das folheações complexas November

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1 9 9 7 - Universidad de Valladolid Projective Holonomy and Riccati equation February. - Instituto de Estudios de Ibero America y Portugal El espacio de foliaciones de una variedad proyectiva. Tordesilhas, Spain February - Instituto de Matemática de Cuernavaca Liouvillan first integrals for holomorphic foliations April - Université de Rennes The Transcendence of non Liouvillian foliations May - Centre International de Rencontres Mathematiques, Luminy , France Foliations with solvable holonony June. - Université de Marseille Transcendent first integrals for complex foliations June 1 9 9 6 - Universidad de La Plata Six Conferences in Dynamical complex foliations. June - Universidad de Buenos Aires Determinación de una foliación compleja atraves de su holonomia. June 1 9 9 5 - Universidad de Valladolid The transverse structure of complex singular foliations. February

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- Universidade de São Paulo. Estruturas transversais projetivas de folheações complexas. April - Université de Paris XI, Orsay A Galois theorem for nonlinear holomorphic differential equations International Conference in honor of A. Douady. July - Medina del Campo Open problems on Complex foliations. September 1 9 9 4 - Université de Dijon The theory of complex foliations with singularities (5 conferences). May - Universidad Católica del Peru Una generalización de un Teorema de Painlevé. 1 9 9 3 - Université de Paris XI, Orsay Sur l'existence de varietés de Levi, d'après Lins N. January - Université de Dijon

Topologie des feuilletages complexes de CP(n), n 3. January - Universidad de Chile La dinâmica de foliaciones complejas. August 1 9 9 2 - International Centre for Theoretical Physics, Trieste School on Dynamical Systems. First Integrals of Algebraic Differential Equations. May

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- Université de Montreal Seminaire de Mathèmatiques Supèrieures Course: Five lectures on foliations induced by polynomial differential equations. July - Universidad de Valladolid Four conferences on recent results in Complex Dynamical Systems. December 1 9 9 1 - Université de Strasbourg The space of complex foliations of CP(n).

Conference in homage to C. Godbillon and J. Martinet. June - International Centre for Theoretical Physics, Trieste Singular points of analytic differential equations. September - Universitá de Bologna Limit sets and a global linearization theorem for holomorphic foliations. Conference in honor of V. Arnol’d. September 1 9 9 0 - Université de Toulouse The space of foliations of CP(n).

January - Université de Paris, Orsay Foliations with simple limit sets. January - Université de Dijon Foliations with algebraic limit sets. January - Universidad de Valladolid The limit set of complex foliations in projective spaces. February

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- International Congress of Mathematicians, Kyoto Three problems on the limit sets of foliations on complex projective spaces. August 1 9 8 8 - International Centre for Theoretical Physics, Trieste The contribution of Il'Yashenko to the solution of Dulac's problem. August - Institut Henri Poincaré, Paris Singular points of holomorphic foliations. September Colóquium in homage to René Thom. - Universidad del Cuzco Campos de vectores polinomiales en el Plano. El 16° problema de Hilbert.

December 1 9 8 7 - Institut Henri Poincaré, Paris Singularities of homogeneous integrable differential forms. May - E.T.H. - Zurich Chern classes and algebraic invariants of the resolution of singularities. June - Université de Strasbourg The construction of holomorphic vector fields with given holonomy. June 1 9 8 6 - École Normale Superieure - Paris Complex foliations without separatrices on singular surfaces. April - Université de Toulouse Singularities of complex differential equations April

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- Technical University of Denmark, Copenhaguen Holomorphic dynamical systems May - Université de Grenoble Foliations in singular surfaces and the separatrix theorem May - International Centre for Theoretical Physics - Trieste Complex dynamical systems May - Congresso Internacional de Sistemas Dinâmicos Complejos, México. Desingularization theorems for absolutely isolated singularities. July 1 9 8 5 - Université de Strasbourg Topological invariants of complex dynamical systems. April & May - Université de Dijon The separatrix theorem in singular surfaces. May 1 9 8 4 - Université de Paris XI - Orsay Two talks on invariants associated to holomorphic vector fields. April - Institut des Hautes Études Scientifiques, Paris The topological invariance of the Milnor number and the algebraic multiplicity. April - Université de Dijon Newton diagrams and invariants for holomorphic vector fields. May - Université de Toulouse Generalized curves and the invariance of the algebraic multiplicity. May

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- Université de Lille Residue theory for holomorphic foliations. May - International Centre for Theoretical Physics Resolution of holomorphic vector fields. May

7. Special Conferences

- Colloque en l'honneur de Marc Chaperon Title: Singularities of holomorphic vector fields. Institut Henri Poincaré, Paris, January 2010 - Congrès à la mémoire d'Adrien Douady. Institut Henri Poincaré Title: The moduli of C*-actions on 2-dimensional Stein analytic spaces. 2008 - Conference on Differential Equations and Singularities, in honor of J. M. Aroca's 60th birthday Title: Foliation with Morse singularities, ecuaciones diferenciales y singularidades, Tordesilhas - Espanha 2006 - International Congress on Dynamical Systems, in honor of J. L. Massera Title: Fibered neighborhoods of curves in complex surfaces Montevideo – Uruguay March, 2004 - Singularities of Differential Equations Kyoto November, 2002 - Topologie et Singularitéis Colloque en Homage de D. Lehman Conferência: Fibered embeddings of Riemann surfaces Marseille April, 2002 - Conferência em homenagem a R. Moussu Lisboa May, 2001

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- Geometrie Complexe et Systemes Dynamiques En l'honneur de Adrien Douady Title: A Galois theorem for nonlinear holomorphic differential equations. Université de Paris XI, Orsay. July, 1995 - Conferencia en Homenaje a J. Tola Title: Una generalización de un teorema de Painlevé. Universidad Católica del Peru. December, 1994. - International Symposium in Honor of V. Arnol'd Title: Limit sets and a global linearization theorem for holomorphic foliations. Universitá de Bologna. September, 1991. - Colloque de Geometrie à la memoire de C. Godbillon et J.Martinet. Title: On the space of foliations of the complex projective space. Université de Strasbourg. June, 1991 - International Congress of Mathematicians “Invited Speaker”, 45 min. talk. Title: Three problems on the limit sets of foliations on complex projective spaces. Kyoto, August, 1990. - Colloque en l'honeur de René Thom Title: Singular points of holomorphic foliations. Institut Henri Poincaré, Paris September, 1988

8. Scientific - Administrative Positions

- Director of Instituto Nacional de Matemática Pura e Aplicada – IMPA Since 2003 - Deputy Director of Instituto Nacional de Matemática Pura e Aplicada – IMPA

1993 – 2003 - Member of the Special Advisory Committee of the Presidency of CNPq 1998 - 1999

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- President of the Scientific Council of the Instituto de Matemática y Ciencias

Afines (IMCA) Lima, Peru Since 1997 - Member of the Executive Committee of the Unión Matemática de America Latina y el Caribe, 1995-2005 - President of the Brazilian Mathematical Society 1991 - 1993 - Member of the Commission on Development and Exchange (CDE), of the International Mathematical Union 1990-1994 and 1995-1999. - Coordinator of the interchange agreement between Brazil and Peru with the support of the International Centre for Theoretical Physics, Trieste. Since 1989 - President of the Brazilian Mathematical Society l987 - l989

9. Other Titles

Member of the Brazilian Academy of Sciences, since 1992.

Miembro Numerario de la Academia Nacional de Ciencias del Perú, Lima, 2008

Honorary Professor, Pontifícia Universidad Católica del Peru, 1997.

Honorary Professor – Universidad Nacional Mayor de San Marcos, 1999.

Doctor Honoris Causa Universidad Nacional de Ingenieria, Lima, 1998

Doctor Honoris Causa, Universidad de Valladolid, Spain, 2007

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10. Other Honors and Distinctions

Prêmio Southern, Peru, 2006

Carlos Chagas Filho Medal, State of Rio de Janeiro, 2005

Prêmio Concytec, Peru, 2004

Ordem Nacional do Mérito Científico, categoria Gran Cruz - Brasil, 2000

Brazilian National Prize for Science and Technology, 1997

Third World Academy of Sciences Award, 1997

Chair Banco Bilbao Viscaya, 1996

Invited speaker, International Congress of Mathematicians, 1990