Assegnista di ricerca, ERC Diophantine Problems, Scuola Normale Superiore di Pisa.

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Scuola Normale Superiore di Pisa Piazza die Cavalieri, 7

56126 Pisa, Italia.

Born on September 17th, 1973 in San Jos´e,Costa Rica.

Current position

Assegnista di ricerca, ERC Diophantine Problems, Scuola Normale Superiore di Pisa. Employment and Grants

2012-2014 Lehrauftrag at the University of Basle.

2009-2012 Ambizione Fund of the Swiss National Science Foundation, University of Basle. 2006-2009 Marie Curie IEF Fellowship at the ETH1 of Zurich and the University Roma 2

Tor Vergata (oct. 2006-avril 2009).

2005-2006 Assistant position at the EPF1, Lausanne (oct. 2005-sept. 2006). 2004-2005 Assistant position at the ETH, Zurich (january-september 2005).

Post-doc GTEM2 at the Universit`a degli Studi di Roma 2 (oct-dec 2004). 2002-2004 ATER (Research and teaching position) at the Universit´e Paris VI. 1999-2002 Allocation de recherche (Research fellowship) at the Universit´e Paris VI.

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Swiss Federal Institute of Technology, at Zurich or at Lausanne 2

European Network Galois Theory and Explicit Methods

Education

2003 PhD. in Mathematics (with distinction). Universit´e Pierre et Marie Curie, Paris VI

- PhD. dissertation :Transcendental methods and Diophantine geometry

Defended the 1st December 2003. Advisors : Marc Hindry and Michel Waldschmidt Others members of the committee : Daniel Bertrand (president), Yuri Bilu

(referee), Fran¸cois Gramain (referee), Joseph Oesterl´e (examinator).

1999 Diplˆome d’ ´Etudes Approfondies (Post-graduate diploma) in Algebraic methods. Universit´e Pierre et Marie Curie, Paris VI

A course on transcendental numbers (M. Waldschmidt) (second semester) A course on algebraic independence (Yu. Nesterenko) (second semester)

Modular forms and transcendence (D. Bertrand) (minicourse, second semester) Diophantine geometry (M. Hindry) (first semester)

- Dissertation of D.E.A. :Baker’s method and applications. 1998 Master’s degree (Licence and Maˆıtrise) of Pures mathematics.

Universit´e Pierre et Marie Curie, Paris VI

- First Dissertation of maˆıtrise :Margulis proof of the Oppenheim’s conjecture. - Second Dissertation of maˆıtrise :

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Research interests Number theory Diophantine geometry

Transcendental number theory Height theory

Counting points on varieties

Integral points on algebraic varieties

Algebraic values of transcendental functions Abelian varieties

Publications

– [8] Elliptic logarithms, diophantine approximation and the Birch and Swinnerton-Dyer conjecture, joint with Vincent Bosser. Bull. Soc. Math. Brazil, New Series (2014) ; Vol. 45, Issue 1, pp. 1-23. DOI 10.1007/s00574-014-0038-x.

– [7] A quantitative Chevalley-Weil theorem for curves, joint with Yuri Bilu and Marco Strambi. Monatsh. Math. 171 (1) :1-32, 2013. DOI 10.1007/s00605-013-0507-0.

– [6] Upper bound for the height of S-integral points on elliptic curves, joint with Vincent Bosser. Ramanujan J.(2013), Vol. 32, Issue 1, pp. 125-141. DOI 10.1007/s11139-012-9440-4.

– [5] Sur l’effectivit´e du th´eor`eme de Siegel et la conjecture abc, J. Number Theory 124 (2007), 267-290.

– [4] Valeurs alg´ebriques de fonctions transcendantes, Int. Math. Res. Not. (2006), Art. ID 16834, 31 pages.

– [3] Siegel’s theorem and the abc conjecture, Riv. Mat. Univ. Parma (7) 3 (2004) 323-332, Proceedings of the “Secondo Convegno Italiano di Teoria dei Numeri”, 13-15 nov. 2003. – [2] M´ethodes de transcendance et g´eom´etrie diophantienne, PhD. dissertation at the

Uni-versity of Paris VI, defended the 1st December 2003 in Paris (100 pages).

– [1] Sur le nombre de points alg´ebriques o`u une fonction analytique transcendante prend des valeurs alg´ebriques,C. R. Acad. Sci. Paris, Ser. I 334 (2002) 721-725.

Work in progress

– [9]On some conjectures on the Mordell-Weil and the Tate-Shavarevich groups of an abelian variety, 22 pages, work in progress.

Pre-print of first version : http://math.unibas.ch/institut/personen

Talks in conferences

– Diophantine problems, Besan¸con, October 2013.

– Heights, Tossa de Mar, UAB, Barcelona, Avril 2011 (Invited speaker). – First Annual Meeting GTEM, Leiden, Septembre 2007 (Invited speaker). – Journ´ees Arithm´etiques, Edimburgh, Juillet 2007 (Contributed talk).

– Journ´ee Approximation diophantienne, Grenoble, Juin 2007 (Invited speaker). – Diophantine geometry, Scuola Normale Superiore di Pisa, Juillet 2005.

– Secondo Convegno Italiano di Teoria dei Numeri, Parme, Novembre 2003. – Colloque Jeunes Chercheurs en Th´eorie des Nombres, Besan¸con, March 2002.

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Teaching experience

– Bachelor lecture at the University of Basle, 2014 : Group theory (48 h).

– Master lectures at the University of Basle, 2012-2014 : Galois theory (24 h).

Some topics on modular functions, elliptic functions and transcendence (42 h). – Lecture at the University of Costa Rica, July 2007 :

Introduction to Diophantine geometry (5 hours). – As assistantat the EPF of Lausanne, 2005-2006 :

Exercises for 3rd year undergrte. students :Introduction to number theory (24 h). Ex. for 3-4th year undergrte. students :Algebra for digital communications (12 h). Exercises for 1st year undergraduate students :Linear algebra (24 heures).

– As assistant at the ETH Zurich, 2004-2005 :

Exercises for 1st year undergraduate students :Linear algebra and Statistics (13 h). – As ATER, at the University Pierre et Marie Curie, Paris VI :

2003-2004 Exercises in D.E.U.G. SCM 11, 1st year :Linear algebra (96 hours). 2002-2003 Exercises in D.E.U.G. SCM 11, 1st year :Analysis (96 hours). – As “vacataire” at the University Denis Diderot, Paris VII :

2001-2002 et 2000-2001 Pr´e-stage of D.A.E.U. (32 hours). 1999-2000 Courses and exercises of D.A.E.U. (27 hours). – As “vacataire”, at the University Pierre et Marie Curie, Paris VI :

1999-2001 Tutorials in D.E.U.G. M.I.A.S. 1st year.

* EPFL 2006 Dissertation of a 3rd year undergraduate student : Rational points of elliptic curves.

Talks in seminars

– On the Mordell-Weil and Tate-Shafarevich groups of an abelian variety :

IRMA Strasbourg (April 2009) ; Autour de la g´eom´etrie d’Arakelov Institut Math. Jussieu (June 2007) ; Probl`emes diophantiens Institut Math. Jussieu (May 2007).

– Linear forms in elliptic logarithms, the BSD-conjecture and the abc-conjecture :

Basle (March 2009) ; EPF Lausanne (November 2007) ; Roma 2 (April 2007) ; Bordeaux S´eminaire th´eorie des nombres jeunes (April 2007) ; Caen (March 2007) ; Probl`emes dio-phantiens Institut Math. Jussieu (March 2007).

– On the abc-conjecture and Siegel’s theorem :

Humbolt Universit¨at Berlin (May 2006) ; Besan¸con (February 2006) ; EPFL Lausanne (March 2005) ; UAB Barcelone (March 2005) ; Roma 2 (November 2004) ; Basle (June 2004) ; ETH, Z¨urich (April 2004) ; Nancy (April 2004) ; Lille (April 2004) ; Caen (April 2004) ; IRMA, Strasbourg (March 2004) ; Probl`emes diophantiens, Institut Math. Jussieu (October 2003).

– Algebraic values of transcendental functions :

Bordeaux (April 2006) ; Basle (February 2005) ; Saint- ´Etienne (January 2005). – Upper bound for the number of algebraic values of transcendental functions :

IRMA Strasbourg (March 2002) ; S´eminaire Jeune d’Arithm´etique et g´eometrie Or-say (December 2001) ; Probl`emes diophantiens Institut Math. Jussieu (November 2001) ; Universit´e du Costa Rica (Decembrer 2000).

– On Baker’s method and applications :

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Participation in conferences

– September 2014 Diophantine Analysis and Transcendence, CIRM, Luminy.

– July 2014Integral points, Algebraic dynamics, Unlikely intersections, ERC, Cetraro, Italy. – March 2014 On the conjectures of Lang and Vojta, CIRM, Luminy.

– October 2013Diophantine problems, Besan¸con. – September 2013 Thue 150, Bordeaux.

– July 2013o-minimality and Diophantine geometry, Manchester. – March 2013 Number Theory Days, EPF Lausanne.

– June-July 2012 Autour des conjectures de Zilber-Pink, IMJ, Paris. – Mai 2011La conjecture de Zilber-Pink, CIRM Luminy.

– Mai 2011Number Theory Days, EPF Lausanne.

– Avril 2011Heights in Diophantine and Arakelov Geometry, UB, Tossa de Mar, Barcelona. – Avril 2010 Number Theory Days, ETH Zurich.

– April 2009Counting points in varieties, Lorentz Center, Leiden. – March 2009 Rencontre diff´erentio-diophantienne, IHP, Paris. – February 2009 Rencontre du projet ANR Diophante, Fribourg. – May 2008 Vari´et´es rationnellement connexes, IRMA, Strasbourg.

– October 2007D´eveloppements r´ecents en approximation diophantienne, CIRM, Luminy. – September 2007 Summer school in Arithmetic Geometry, CIME, Cetraro, Italy.

– September 2007 First Annual Meeting GTEM, Leiden (Invited speaker). – July 2007Journ´ees Arithm´etiques, Edimburgh (Contributed talk).

– June 2007 Journ´ee Approximation diophantienne, Institut Fourrier, Grenoble (Invited speaker).

– April 2007Number Theory Day, EPF Lausanne.

– Septembre 2006 Colloque sur l’Approximation diophantienne et nombres transcendants, CIRM, Luminy.

– Juillet 2006Arithmetic Geometry, Mathematisches Institut Georg August, Goettingen1. – Mars 2006 Number Theory Days, ETH Zurich.

– Juillet 2005Diophantine geometry, Scuola Normale Superiore di Pisa, Italie2. – March 2005 Number Theory Days, EPF Lausanne.

– April 2004Colloque sur l’Hyperbolicit´e et l’Arithm´etique, CIRM, Luminy. – November 2003Secondo Convegno Italiano di Teoria dei Numeri, Parma, Italy. – Jully 2002 Analytic number theory, CIME, Cetraro, Italie.

– March 2002 Colloque Jeunes Chercheurs en Th´eorie des Nombres, Besan¸con.

– September 2001 Higher Dimensional Varieties and Rational Points, R´enyi Institute of Mathematics, Budapest.

– May 2001 Arithm´etique des corps et des revˆetements,Universit´e de Saint- ´Etienne. – November 2000 G´eom´etrie alg´ebrique et applications aux codes correcteurs d’erreurs et `a

la cryptographie, CIMPA, Cuba.

– Jully 2000 Diophantine Approximation,CIME, Cetraro, Italy. – March 2000 Journ´ees revˆetements,Universit´e de Saint- ´Etienne.

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Research period funded by the Clay Mathematics Institut. 2

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Seminars and workshops

– Co-organization of a workshop onModular forms (based on the book of F. Diamond and J. Shurman) with the doctorants and post-doctorants, EPF Lausanne, 2005-2006. – Organization of the seminar of the PhD. students in Number Theory of the Institut de

Math´ematiques de Jussieu, Paris, from November 2001 until July 2003. Some talks : On the Chevalley-Weil theorem.

Theabc-conjecture and Siegel’s theorem : the case of P1\ {0,1,∞}.

Introduction to the height theory ; finiteness results on Diophantine geometry. abc implies Mordell, following Elkies.

Lectures attended during the doctorate (after the D.E.A.)

Specialized (post-graduate) courses of the D.E.A. on Algebraic Methods, Paris VI-VII : – 2001-2002On the Birch and Swinnerton-Dyer conjecture (J. Oesterl´e)

Arithmetic methods for alg groups and differential equations (D. Bertrand) – 2000-2001Diophantine geometry (S. David)

Languages (in decreasing order) : Spanish, French, Italian, English, German.

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