# Seminari de Teoria de Nombres de Barcelona

LUIS VICTOR DIEULEFAIT

Position: Catedrático de Álgebra (Full Professor)

Departament de Matemàtiques e Informàtica

Facultat de Matemàtiques e Informàtica

Universitat de Barcelona

Gran Via de les Corts Catalanes, 585

(08007) Barcelona, Spain

e-mail: ldieulefait@ub.edu

### List of publications:

Articles in international journals and proceedings:

1. Blanco-Chacón, I.; Dieulefait, L.V.: Potentially diagonalizable modular lifts of large weight, submitted.

2. Billerey, N.; Chen, I.; Dieulefait, L.V.; Freitas, N.: A multi-Frey approach to Darmon's Program for Fermat equations of signature (7,7,n), preprint.

3. Dieulefait, L.V.; Jimenez Urroz, J.: Factorization and malleability of RSA modules, and counting points on elliptic curves modulo N, submitted.

4. Dieulefait, L.V.; Soto, E.: Solving a x^p + b y^p = c z^p with abc containing an arbitrary number of prime factors, submitted.

5. Arias de Reyna, S.; Dieulefait, L.V.: Automorphy of GL(2) ⊗ GL(n) in the self-dual case, submitted.

6. Dieulefait, L.V.: Demostración simplificada de la Conjetura de Modularidad de Serre (letter from September 2018, with P.S. added on January 2019), available at ArXiv (in Spanish, not to be published in a journal until preliminary sections are added).

7. Dieulefait, L.V.; Pacetti, A.; Rodriguez Villegas, F.: Representaciones de Galois, notes from a course at the CIMPA-ICTP school "AGRA 3" (Córdoba, Argentina, July 2018), to appear.

8. Dieulefait, L.V.; Soto, E.: Raising the level at your favorite prime, Rendiconti Lincei - Mat. e Appl., to appear.

9. Billerey, N.; Chen, I.; Dembélé, L.; Dieulefait, L.V.; Freitas, N.: Some extensions of the modular method and Fermat equations of signature (13,13,n), submitted.

10. Billerey, N.; Chen, I.; Dieulefait, L.V.; Freitas, N.: A multi-Frey approach to Fermat equations of signature (r, r, p), Trans. AMS 371 (2019), p 8651-8677.

11. Dieulefait, L.V.; Zenteno, A.: On the images of the Galois representations attached to generic automorphic representations of GSp(4), Annali della Scuola Normale Superiore di Pisa, to appear.

12. Billerey, N.; Chen, I.; Dieulefait, L.V.; Freitas, N.: A result on the equation x^p + y^p = z^r using Frey abelian varieties, Proc. AMS 145 (2017), p 4111-4117.

13. Dieulefait, L.V.; Soto, E.: On congruences between normalized eigenforms with different sign at a Steinberg prime, Rev. Mat. Iberoamericana 34 (2018), p 413-421.

14. Dieulefait, L.V.; Freitas, N.: Base change for elliptic curves over real quadratic fields, C. R. Math. Acad. Sci. Paris 353 (2015), p 1–4.

15. Dieulefait, L.V.; Pacetti, A., Tsaknias, P.: On the number of Galois orbits of newforms, J. European Math. Soc., to appear.

16. Dieulefait, L.V.; Zenteno, A.: Constructing Hilbert modular forms without exceptional primes, Math. Z. 288 (2018), p 199–215.

17. Dieulefait, L.V.; Tsaknias, P.; Vila, N.: Seven small simple groups not previously known to be Galois over Q, preprint.

18. Dieulefait, L.V.; Pacetti, A.: Connectedness of Hecke algebras and the Rayuela conjecture: a path to functoriality and modularity. Arithmetic and Geometry (Proceedings of the trimester organized at the Hausdorff Institute during 2013). Dieulefait, L.; Faltings, G.; Heath-Brown, R.; Manin, Y.; Moroz, B.; Wintenberger, J.-P. (eds.), LMS Lecture Notes Series 420, Cambridge U. P., 2015.

19. Dieulefait, L.V.: Automorphy of m-fold tensor products of GL(2), Rev. Mat. Iberoamericana, to appear.

20. Dieulefait, L.V.: Automorphy of Symm^5(GL(2)) and base change (with Appendix A by R. Guralnick and Appendix B by L. Dieulefait and T. Gee), J. Math. Pures et Appl. 104 (2015), p 619-656. Corrigenda at this link: https://drive.google.com/file/d/0B28D-2SlXlB3YWdNaldGNXdmbzh5dEQ3MWtFczVTWFNIZzhn/view?usp=sharing

21. Dieulefait, L.V.; Jimenez, J.; Ribet, K.: Modular forms with large coefficient fields via congruences, Research in Number Theory (2015), 1: 2.

22. Arias de Reyna, S.; Dieulefait, L.V.; Shin, S.W.; Wiese, G.: Compatible systems of symplectic Galois representations and the inverse Galois problem III. Automorphic construction of compatible systems with suitable local properties, Math. Annalen 361 (2015), p 909-925.

23. Arias de Reyna, S.; Dieulefait, L.V.; Wiese, G.: Compatible systems of symplectic Galois representations and the inverse Galois problem II. Transvections and huge image, Pacific J. Math. 281 (2016), p 1–16.

24. Arias de Reyna, S.; Dieulefait, L.V.; Wiese, G.: Compatible systems of symplectic Galois representations and the inverse Galois problem I. Images of projective representations, Trans. AMS 369 (2017), p 887-908.

25. Arias de Reyna, S.; Dieulefait, L.V.; Wiese, G.: Classification of subgroups of symplectic groups over finite fields containing a transvection, Demonstratio Mathematica 49 (2016), p 129-148.

26. Dieulefait, L.V., Freitas, N.: Fermat-type equations of signature (13,13,p) via Hilbert cuspforms, Math. Annalen 357 (2013), p 987–1004.

27. Billerey, N.; Dieulefait, L.V.: Explicit large image theorems for modular forms, J. London Math. Soc. 89 (2014), p 499-523.

28. Dieulefait, L.V., Freitas, N.: The Fermat-type equations x^5+y^5 = 2 z^p or 3 z^p solved through Q-curves, Math. Comp. 83 (2014), p 917-933.

29. Dieulefait, L.V.: Langlands Base Change for GL(2), Annals of Math. 176 (2012), p 1015-1038.

30. Dieulefait, L.V.; Pacetti, A.; Schütt, M.: Modularity of the Consani-Scholten quintic (with an appendix by J. Burgos and A. Pacetti), Documenta Math. 17 (2012), p 953-987.

31. Dieulefait, L.V.; Mink, M.; Moroz, B.Z.: On an elliptic curve defined over $\Q(\sqrt{-23})$, St. Petersburg Math. J. 24 (2013), p 575-589.

32. Dieulefait, L.V.: A non-solvable extension of Q unramified outside 7, Compositio Math. 148 (2012), p 669-674.

33. Dieulefait, L.V.; Vila, N.: On the classification of geometric families of 4-dimensional Galois representations, Math. Res. Letters 18 (2011), p 805-814.

34. Dieulefait, L.V. : Remarks on Serre's modularity conjecture, Manuscripta Math. 139 (2012), p 71-89 (N.B.: this paper gives a proof of Serre's conjecture in the odd level case which avoids working in characteristic 2, a proof I gave in the period March-May 2006, using results of Kisin, Caruso, Schoof, and the switching-the-prime strategy already used in my previous work on the level 1 weight 2 case).

35. Burhanuddin, I.; Dieulefait, L.V.: On projectively rational lifts of mod 7 Galois representations, JP Journal of Algebra, Number Theory and Appl. 20 (2011), p 109-119.

36. Dieulefait, L.V.; Gonzalez-Jimenez, E.; Jimenez, J.: On fields of definition of torsion points of elliptic curves with complex multiplication, Proc. AMS 139 (2011), p 1961-1969.

37. Dieulefait, L. V.: On the modularity of rigid Calabi-Yau threefolds: Epilogue, "Proceedings of the trimester on Diophantine Equations at the Hausdorff Institute", Zapiski POMI of the Steklov Math. Inst. St. Petersbourg 377 (2010), p 44-49, also in J. Math. Sciences. 171 (2010), p 725-727.

38. Dieulefait, L.V.; Wiese, G.: On Modular Forms and the Inverse Galois Problem, Trans. AMS 363 (2011), p 4569-4584.(N.B.: In this paper we prove that the groups PSL(2, p^n), if n is any integer, and PGL(2,p^n), if n is odd, are Galois groups over Q for a positive density set of primes p. We also construct infinitely many modular forms not having exceptional primes).

39. Berrone, L.; Dieulefait, L.V.: A functional equation related to the product in a quadratic number field, Aequationes Math. 81 (2011), p 167-175.

40. Berrone, L.; Dieulefait, L.V.: Finite mappings and the topology of their stable sets, Demonstratio Mathematica 44 (2011), p 201-211.

41. Dieulefait, L.V.; Guerberoff, L.; Pacetti, A.: Proving modularity for a given elliptic curve over an imaginary quadratic field, Math. Comp. 79 (2010), p 1145-1170.

42. Dieulefait, L.V.; Jimenez, J.: Small primitive roots and malleability of RSA moduli, J. Comb. and Number Theory 2 (2010).

43. Dieulefait; L.V.: The level 1 case of Serre's conjecture revisited, Rendiconti Lincei - Mat. e Appl. 20 (2009), p 339–346 (N.B.: in this paper we prove "existence of Galois conjugates" for "geometric" ell-adic Galois representations. Then we observe that in many cases a suitable Galois conjugation makes the residual Serre's weight smaller. This gives a new, rather elementary, proof of the level 1 case of Serre's conjecture by induction on the weight).

44. Billerey, N.; Dieulefait, L.V.: Solving Fermat-type equations x^5+y^5 = d z^p, Math.Comp. 79 (2010), p 535-544.

45. Dieulefait, L.V.; Taixes, X.: Congruences between modular forms and lowering the level mod l^n, Proceedings of the 25th Journées Arithmétiques, J. de Théorie des Nombres de Bordeaux 21 (2009), p 109-118.

46. Dieulefait, L.V.; Jimenez, J.: Solving Fermat-type equations x^4 + d y^2 = z^p via modular Q-curves over polyquadratic fields, J. Reine Angew. Math. 633 (2009), p 183-196.

47. Dieulefait, L.V.: How to facet a gemstone: from potential modularity to the proof of Serre's modularity conjecture, Proceedings of the conference "Segundas Jornadas de Teoría de Números", Biblioteca de la Rev. Mat. Iberoamericana, 2008.

48. Dieulefait, L.V.: Galois realizations of families of Projective Linear Groups via cusp forms, Proceedings of the conference "Modular Forms on Schiermonnikoog", Cambridge Univ. Press (2008).

49. Dieulefait, L.V.: A control theorem for the images of Galois actions on certain infinite families of modular forms, Proceedings of the conference "Modular Forms on Schiermonnikoog",Cambridge Univ. Press (2008).

50. Dieulefait, L.V.; Vila, N.: Geometric families of 4-dimensional Galois representations with generically large images, Math. Z. 259 (2008), p 879-893.

51. Dieulefait, L.V.: The level 1 weight 2 case of Serre's conjecture. Rev. Mat. Iberoamericana 23 (2007), no. 3, p 1115-1124. (N.B.: This paper contains the proof of the first cases of Serre's conjecture which I gave in the period February-October 2004).

52. Dieulefait, L.V.: Uniform behavior of families of Galois representations on Siegel modular forms and the Endoscopy Conjecture. Bol. Soc. Mat. Mexicana 13 (2007), no. 2, p 243-253.

53. Dieulefait, L.V.: A modularity criterion for integral Galois representations and Calabi-Yau threefolds, appendix to the article by K. Hulek and H. Verrill "On the modularity of Calabi-Yau threefolds containing elliptic ruled surfaces", Mirror Symmetry V . Noriko Yui et al. (eds.). AMS/IP Studies in Advanced Mathematics vol. 38, AMS, 2006.

54. Bars, F; Dieulefait, L.V.: Galois actions on Q-curves and Winding Quotients. Math. Z. 254 (2006), no. 3, p 531-538.

55. Dieulefait, L.V.: Galois characterization of endoscopy for rational Siegel modular forms. Math. Res. Lett. 13 (2006), no. 2, p 317-319.

56. Dieulefait, L.V.: Elliptic mod $\ell$ Galois representations which are not minimally elliptic. Bull. Belg. Math. Soc. Simon Stevin 13 (2006), p 455-457.

57. Dieulefait, L.V.; Dimitrov, M.: Explicit determination of the images of the Galois representations attached to Hilbert modular forms. J. Number Theory 117 (2006), p 397-405.

58. Dieulefait, L.V.: Modular congruences, Q-curves, and the diophantine equation x^4+y^4=z^p. Bull. Belg. Math. Soc. Simon Stevin 12 (2005), p 363-369.

59. Dieulefait. L.V.; Rotger V.: On abelian surfaces with potential quaternionic multiplication. Bull. Belg. Math. Soc. Simon Stevin 12 (2005), p 617-624.

60. Dieulefait, L.V.: Solving diophantine equations x^4 + y^4 = q z^p. Acta Arithmetica 117 no.3 (2005), p 207-211.

61. Dieulefait, L.V.: Computing the Level of a Modular Rigid Calabi-Yau threefold. Experiment. Math. 13, no.2 (2004), p 75-80.

62. Dieulefait, L.V.: Existence of families of Galois representations and new cases of the Fontaine-Mazur conjecture. J. Reine Angew. Math. 577 (2004), p 147-151. (N.B.: This paper contains the proof of "existence of compatible families" and of the first cases of the Fontaine-Mazur conjecture in dimension 2).

63. Dieulefait, L.V.: Existence of non-elliptic mod \ell Galois representations for every \ell > 5. Experiment. Math. 13, no. 3 (2004), p 327-329.

64. Dieulefait, L.V. : Irreducibility of Galois actions on level 1 Siegel cusp forms . Modular Curves and Abelian Varieties. Cremona et al. (eds.). Birkhauser, Progress in Mathematics vol. 224; p 75-80. 2004.

65. Dieulefait, L.V.; Rotger, V.: The arithmetic of QM-abelian surfaces through their Galois representations. J. Algebra 281 (2004), p 124-143.

66. Dieulefait, L.V.; Vila, N.: On the images of modular and geometric three-dimensional Galois representations. Amer. J. Math. 126 (2004), p 335-361.

67. Dieulefait, L.V.; J. Manoharmayum: Modularity of rigid Calabi-Yau threefolds over Q. Calabi-Yau Varieties and Mirror Symmetry. N. Yui, J. Lewis et al. (eds.). Fields Institute Communications vol. 38; AMS, p 159-166. 2003. (N.B.: This paper contains the proof of the modularity conjecture for rigid Calabi-Yau threefolds over Q, under mild conditions)

68. Dieulefait, L.V.: Modularity of Abelian Surfaces with Quaternionic Multiplication. Math. Research Letters 10 nos.2,3 (2003), p 145-150.

69. Dieulefait, L. V.: Medida de Jordan; Miscelánea Matemática (2003).

70. Dieulefait, L.V.: Explicit determination of the images of the Galois representations attached to abelian surfaces with End(A) = Z. Experiment. Math. 11, no.4 (2002), p 503-512.

71. Dieulefait, L.V.: On the images of the Galois representations attached to genus 2 Siegel modular forms. J. Reine Angew. Math. 553 (2002), p 183-200.

72. Dieulefait, L.V.: Newforms, Inner Twists, and the Inverse Galois Problem for Projective Linear Groups. J. de Théorie des Nombres de Bordeaux 13 (2001), p 395-411.

73. Dieulefait, L.V.; Vila, N.: Projective linear groups as Galois groups over Q via modular representations. J. Symbolic Comput. 30 (2000), p 799-810.

74. Dieulefait, L.V.; Guzmán, A.W.: Teorema de la Integral de Cauchy. Premios "Miguel Herrera" (Primer y Segundo Premio). Trabajos de Matemática, Serie B, 1993/20 (1993), FAMAF, Córdoba, Argentina.

### Books:

1. Darmon, H.; Diamond, F.; Dieulefait, L.V.; Edixhoven, B.; Rotger, V. (eds.): Elliptic curves, Hilbert modular forms and Galois deformations. Advanced Courses in Mathematics CRM Barcelona, Birkhauser, 2013. This book contains the notes of some of the Advanced Courses from the special year on Arithmetic Geometry at Barcelona's CRM (2009-2010). Authors: Dimitrov, M.; Dokchitser, T.; Berger, L.; Böckle, G.; Dembélé, L.; Voight, J.

2. Dieulefait, L.V. ; Vila, N. (eds.): Representacions de Galois de dimensió 2: Conjectures d'Artin, de Serre i de Fontaine-Mazur. Seminari de Teoria de Nombres (UB-UAB-UPC) vol. 11; Barcelona, 2004. ISBN: 84-934244-1-2.

3. Dieulefait, L.; Faltings, G.; Heath-Brown, R.; Manin, Y.; Moroz, B.; Wintenberger, J.-P. (eds.): Arithmetic and Geometry (Proceedings of the trimester organized at the Hausdorff Institute during 2013), LMS Lecture Notes Series 420, Cambridge U. P., 2015.

### Other Publications:

1. Dieulefait, L.V.: Criba de Selberg; Una cota superior. Métodes de Garbell . Notes del Seminari de Teoria de Nombres (UB-UAB-UPC) vol 13; p 29 - 48; Barcelona 2005.

2. Dieulefait, L.V.; Vila N.: Modularitat potencial de representacions de Galois. Representacions de Galois de dimensió 2: Conjectures d'Artin, de Serre i de Fontaine-Mazur. Notes del Seminari de Teoria de Nombres (UB-UAB-UPC) vol. 11 ; p 97- 110 ; Barcelona, 2005.

3. Dieulefait, L. V. : Isogenias, Reducción y Módulos de Tate . Mòduls de Drinfeld . Notes del Seminari de Teoria de Nombres (UB-UAB-UPC) vol. 6; p 41- 51; Barcelona 2005.

My PhD Thesis (in case you are interested):

It can be downloaded from William Stein's webpage, clicking here. Its five non-trivial chapters "correspond" to the papers that appear in my list of publications (starting from below) in positions 2,3,4,5 and 9. The main differences are the following. First, computations in the chapter on Siegel modular forms are more detailed in the thesis. Second, some interesting results in the chapter on 3-dimensional Galois representations have dissapeared from the published version: in particular the main theorem (="large image for almost every prime") has a nice "corollary" saying that "the set of primes p such that the trace a_p gives a generator of the field of coefficients has DENSITY 1", and this corollary follows automatically from some technical results proved in my thesis that were removed from the published version to save space. In short, if we focus on the results (and not on the presentation) the thesis is better than the published papers, but it is longer, thus it will take you more time!

### Lectures:

• Safe chains of congruences and base change for some real quadratic base fields, ICM Satellite Conference on Automorphic Forms, Galois representations and L-functions, Rio de Janeiro, Brasil, July 2018

• Galois Representations, joint course with F. Rodriguez Villegas and A. Pacetti, Escuela CIMPA-ICTP AGRA III "Aritmética, Grupos y Análisis", Universidad Nacional de Córdoba and Academia Nacional de Ciencias, Córdoba, Argentina, July 2018

• Ecuaciones diofánticas de tipo Fermat y el método modular, Seminar of Mathematics, Facultad de Ciencias Exactas, Ingeniería y Agrimensura, Universidad Nacional de Rosario, Rosario, Argentina, July 2018

• Chains of congruences linking Hilbert modular forms, Workshop on Bianchi modularity, Luxembourg, July 2016

• Automorphy for GL(2) ⊗ GL(n) in the self-dual case, Frontiers in Serre’s Modularity Conjecture: Torsion and Low Weights, Luxembourg, June 2015

• Cambio de base para GL(2) y otros casos de funtorialidad de Langlands, Plenary Speaker, Biannual Meeting of the RSME (Real Sociedad Matemática Española), Granada, Spain, January 2015

• Advances on base change, symmetric powers and tensor product functoriality, Number Theory Seminar, Caltech, Los Angeles, USA, October 2014

• Safe chains of automorphic congruences and new cases of Langlands functoriality, Research Seminar, MSRI, Berkeley, USA, October 2014

• Advances on Langlands functoriality: base change, symmetric powers and tensor products, Journées arithmétiques à Villetaneuse, Université Paris 13, Villetaneuse, France, June 2014

• The future of modularity, Number Theory Days, Lille, France, June 2014

• Grupos de Galois lineales y formas automorfas: El sueño de Langlands, Plenary talk at the Reunión Anual de la Unión Matemática Argentina, Rosario, Argentina, September 2013

• New results on Langlands functoriality: non-solvable base change, symmetric powers and tensor products, London Number Theory Seminar, King's College, London, UK, June 2013

• Langlands functoriality and lifts of modular forms, course at the "1st Arithmetic-Geometric TANdeM in Anna", Anna, Valencia, Spain, June 2013

• Langlands functoriality for GL(2) ⊗ GL(n) and other related cases, Workshop "Explicit methods for modular forms", University of Warwick, Coventry, UK, March 2013

• Grupos de Galois lineales provenientes de la geometría, Jornada d'obertura del Curs Galois, Universitat Politecnica de Catalunya, Barcelona, March 2013

• Some new cases of Langlands functoriality solved, Workshop on Serre's conjecture in the Trimester Program "Arithmetic and Geometry", Hausdorff Institute for Mathematics, Bonn, Germany, February 2013

• Non-solvable base change for GL(2), Seminar of the Trimester Program "Arithmetic and Geometry", Hausdorff Institute for Mathematics, Bonn, Germany, January 2013

• Modularity and non-solvable base change for GL(2), Séminaire de Théorie de Nombres, Institut de Mathématiques de Bordeaux, Bordeaux, France, June 2012

• Compatible systems of Galois representations with generically large images and applications, 1st Latin American School of Algebraic Geometry and Applications (ELGA), La Cumbre, Córdoba, Argentina, August 2011

• Non-solvable base change for GL(2), LMS Durham Symposium "Automorphic forms and Galois representations", Durham, UK, July 2011

• Formes Automorfes i grups de Galois lineals: un camí d'anada i tornada, 14a Trobada Matemàtica, Societat Catalana de Matemàtiques, Barcelona, May 2011

• Two-dimensional Galois representations: the modularity quest, Seminar für Algebraische Geometrie und Arithmetik (Oberseminar), Universität Duisburg-Essen, Essen, Germany, April 2011

• The proof of Serre's modularity conjecture, course at the Winter School "Serre's Modularity Conjecture" (other courses by Boeckle, Savitt, Gee and Ribet), POSTECH, Pohang, South Korea, January 2011

• Modular Forms and Serre's conjectures, course at the Summer School "Arithmetic of Modular Forms and Elliptic curves" (other courses by Diamantis, T. Dokchitser and Movasati), IMPA, Rio de Janeiro, Brazil, January 2011

• Modularity by propagation: Serre's conjecture and non-solvable base change for GL(2), Forschungsseminar Arithmetische Geometrie, Humboldt Universität, Berlin, Germany, 2010

• Non-solvable base change for GL(2), plenary talk at the conference "Modular: Arithmetic of Modular Forms and Modularity results", final conference of the Research Programme in Arithmetic Geometry, CRM, Bellaterra, Barcelona, 2010

• Three lectures on the proof of Serre's conjecture, as part of the "Advanced Courses on Modularity" (other lecturers: Diamond, Boeckle, L. Berger and Wintenberger), CRM, Bellaterra, Barcelona, 2010

• Modularity over Q and non-solvable base change for GL(2), Algebra and Number Theory Seminar, EPFL, Lausanne, Switzerland, 2010

• Formas Automorfas y correspondencia de Langlands para GL(n), Thematic Day "The Geometric Langlands Correspondence III", CRM, Bellaterra, Barcelona, 2010

• Methods for weight reduction and level reduction in a proof of Serre's conjecture (plenary lecture), Annual Meeting of the GTEM European Research Network, Warwick Mathematics Institute, University of Warwick, Coventry, UK, 2009

• A proof of Serre's conjecture for odd levels: how to kill ramification, Number Theory Seminar, Institut für Experimentelle Mathematik, Essen, Germany, 2009

• Resultados de Modularidad: de Wiles a la actualidad, Col·loqui del Departament de Matemàtiques, Universitat Autònoma de Barcelona, 2009

• The proof of Serre's conjecture: the ubiquity of modular forms (plenary lecture), Final Conference of the Trimester on Diophantine Equations, Hausdorff Institute for Mathematics, Bonn, Germany, 2009

• Modularidad: ¿Cómo se establece?, Introductory talk to present CRM's "Research Programme on Arithmetic Geometry", Universidad Complutense de Madrid, 2009

• Formas modulares con cuerpos de coeficientes grandes via congruencias (joint work with J. Jimenez and K. Ribet), Seminario de Álgebra y Teoría de Numeros, Universidad Autónoma de Madrid, 2008

• The proof of Serre's modularity conjecture in the odd level case, Algebra, Number Theory, and Combinatorics Seminar, University of Texas at Austin, USA, 2008

• La conjetura de modularidad de Serre, resuelta.Seminario del Depto. de Matemática, Universidad de Buenos Aires, Argentina, 2008

• Lifts, compatible families, Galois conjugates: tools for the modularity of Galois representations. Joint Number Theory Workshop, Columbia University, New York, USA, 2008

• Representaciones de Galois y formas modulares: la conjetura de Serre resuelta. Coloquio de Matematica, UACM, Ciudad de Mexico, Mexico, 2008

• Remarks on Serre's modularity conjecture. Number Theory Seminar, Harvard University, Cambridge,USA, 2007

• How to facet a gemstone: From potential modularity to modularity and other modular excursions, Summer School on Serre's modularity conjecture, CIRM, Luminy, France 2007.

• Galois representations, modular elliptic curves and diophantine equations, Algebra Seminar, USC, Los Angeles (USA), 2006.

• Geometric familias of Galois representations: existence, ell-independence, modularity and other properties, Number Theory Seminar, UCLA, Los Angeles (USA), 2006

• Topics form Arithmetic of Elliptic Curves, Institute for Pure an Applied Mathematics, UCLA, Los Angeles (USA) 2006

• The proof of Serre’s modularity conjecture,Seminari de Teoria de Nombres, Universitat Politécnica de Catalunya, 2006

• Curso de nueve horas de duración sobre la demostración de la conjetura de Serre, Seminario sobre la conjetura de Serre, Universitat de Barcelona, 2006

• Galois representations: deformations, families, images and modularity, Seminaire de Geometrie Arithmetique, Université Paris 13 (Paris, France), March 2006.

• Existence of families, lowering the conductor and some cases of Serre's conjecture, Number Theory Seminar. University of California at Berkeley, Berkeley (U.S.A.), 2005.

• Serre's modularity conjecture in cases of small level and weight, Number Theory Seminar. Caltech, Los Angeles (U.S.A.), 2005.

• From potential modularity to the level 1 weight 2 case of Serre's conjecture, International conference Algebraic Geometry and Number Theory, Euler International Mathematical Institute, St Petersburg (Russia), 2005.

• Existence of families, Galois descent and the first cases of Serre's conjecture, Conférence "Galois Representations" (European Network Arithmetic Algebraic Geometry), IRMA , Strasbourg (France), 2005.

• From potential modularity to the level 1 weight 2 case of the conjectures of Serre and Fointane-Mazur. Seminario Teoria dei Numeri. Universita Tor Vergara, Roma (Italy), 2005.

• Existence of compatible families of Galois representations and the Fontaine-Mazur conjecture for elliptic curves. London Number Theory Seminar. Imperial College, London (U.K.), 2004.

• Existencia de familias de representaciones de Galois y nuevos casos de la conjetura de Fontaine-Mazur. Presentación de comunicación. Seminari de Teoria de Nombres de Barcelona. UPC, Barcelona, 2004.

• Uniform behavior, existence of families, and geometricity of Galois representations. Seminaire d'arithmetique et geometrie algebrique. Université de Paris Sud. Orsay (France), 2003.

• Curvas Elípticas. Impartición de un curso de 10 horas de duración. Universidad Nacional de Rosario, Rosario (Argentina), 2003.

• Modularidad de superficies abelianas con QM y de variedades de Calabi-Yau rígidas. Seminari de Teoria de Nombres (UB-UAB-UPC). Barcelona, 2003.

• Representaciones de Galois de dimensión dos, conjetura de Fontaine-Mazur y formas modulares. Centre de Recerca Matematica, Bellaterra (Barcelona), 2003.

• Uniform behavior of geometric families of four-dimensional Galois representations. International Conference on Arithmetic Algebraic Geometry. Max-Planck Inst. fur Math., Bonn (Germany), 2003.

• Uniformity for families of Galois representations on Siegel modular forms. Séminaire de Théorie des Nombres. Institut de Math. De Jussieu, Paris (France), 2003.

• Cuestiones de Reducibilidad en familias compatibles de representaciones de Galois. Presentación de comunicación. Seminari de Teoria de Nombres (UB-UAB-UPC) Barcelona, 2002.

• Images of four dimensional Galois representations of symplectic type. Differential and Arithmetic Galois groups. Oberwolfach (Germany), 2002.

• Irreducibility of symplectic four dimensional Galois representations. Euroconference “Modular Curves and Abelian Varieties". Centre de Recerca Matemática, Bellaterra (Barcelona) , 2002.

• Isogenias y Módulo de Tate. Seminari de Teoria de Nombres (UB-UAB-UPC): Mòduls de Drinfeld. Barcelona, 2002.

• Propriétés galoisiennes de formes de Siegel de genre 2. Institut de Math. de Jussieu, Paris (France), 2002.

• Cálculo efectivo de las imágenes de las representaciones de Galois asociadas a una superficie abeliana con End(A) = Z. Seminari de Teoria de Nombres (UB-UAB-UPC). Barcelona, 2001.

• Compatible families of Galois representations with large image. Université Paris 13. Paris (France), 2001.

• Explicit description of the local Langlands correspondence for GL_2 and $p \neq 2$. Euroconference “Modular Forms and p-adic Hodge Theory". Bellaterra, (Barcelona) 2001 .

• Geometric Galois representations with large images. IRMA, Strasbourg (France), 2001.

• Geometria Aritmética. Formas Modulares y el Problema Inverso de Galois. Annual Meeting of the UMA. Rosario (Argentina), 2000.

• Images of 3-dimensional Galois representations. Arithmetic Geometry. Mathematical Sciences Research Institute, Berkeley (U.S.A), 2000.

• Projective Linear Groups realized as Galois groups over Q using newforms with inner twists. Algorithmes en Théorie des Nombres. CIRM, Luminy (France), 2000.

• Images of 2 and 3-dimensional modular and geometric Galois Representations, Galois Representations Seminar, Mathematical Sciences Research Institute, Berkeley (U.S.A.), 1999

### Prizes, awards and alike:

1. Member of the Scientific Committee of RSME and SCM.

2. P.R. of the Number Theory Group at U.B. and Senior Researcher at the Number Theory area at BGSMath.

3. ICREA ACADEMIA 2010 Award for Excellence in Research, January 2011 to December 2015

4. Organizer with J. Cremona, S. Siksek, T. Gee and D. Loeffler of the workshop "Higher rank automorphic forms", University of Warwick, Coventry, UK, May 2013

5. Organizer with Jean-Pierre Wintenberger of the special session on Serre's conjecture at the Hausdorff Institute for Mathematics (Bonn, Germany) from January 15th to February 14th 2013. This activity is part of the Trimester Program "Arithmetic and Geometry" (January 2nd to April 19th, 2013), organized by Faltings, Manin, Heath-Brown and Moroz. During this session three mini-courses and a conference will take place, and we will host several senior visitors and post-doctoral fellows.

6. Organizer with Francesc Bars and Victor Rotger of the year-long Research Programme on Arithmetic Geometry at the Centre de Recerca Matematica (2009-2010). Member of the Scientific Committee of the subprogramme on Modular Forms and Modularity (with V. Rotger, F. Diamond, B. Edixhoven and H. Darmon). The Programme includes three periods of advanced courses, weekly seminars, several workshops and a final conference on Modularity. During this year we will host several long-term senior visitors and some post-doctoral fellows.

7. José Castillejo Mobility Research Grant (MEC). Harvard University, 2007/2008

8. Investigador Ramón y Cajal, Universitat de Barcelona. Barcelona, 2003/2006

9. Member of the European Research Training Networks “Arithmetic Algebraic Geometry” and "Galois Theory and Explicit Methods".

10. MECD/Fullbright Postdoctoral Fellowship. Centre de Recerca Matemàtica. Bellaterra (Barcelona), 2003.

11. Marie Curie Postdoctoral Fellowships at European Research Networks. Université Paris 13 and Inst. Math. Jussieu, 2001/2003.

12. Marie Curie Doctoral Fellowship. Universitat de Barcelona. Barcelona, 1998/2001.

13. Repsol-YPF Doctoral Fellowship. Universitat de Barcelona, Barcelona, 1997/98.