Xavier Guitart
Departament de Matemàtiques i Informàtica
Universitat de Barcelona
Gran Via de les Corts Catalanes, 585(08007) Barcelona, Spainemail: xevi.guitart@gmail.com
office phone: +34 934 021 619
http://www.maia.ub.es/∼guitart/

EMPLOYMENTUniversitat de Barcelona.
Associate professor (in Catalan: professor agregat), September 2019, present.
Universitat de Barcelona.
Tenure-track 1 lecturer (in Catalan: professor lector), September 2015, present.
Universitat de Barcelona.
Juan de la Cierva Fellowship, December 2014-August 2015.
Institut für Experimentelle Mathematik, Universität Duisburg-Essen.
Postdoctoral Fellowship, September 2013-November 2014.
Universitat Politècnica de Catalunya
Adjunct Lecturer (Professor Ajudant), January-August 2013.
Max Planck Institute for Mathematics, Bonn.
Postdoctoral visiting researcher. January-December 2012.
Universitat Politècnica de Catalunya
Adjunct Lecturer (Professor Ajudant), June 2010-December 2012.
EDUCATION
Universitat Politècnica de Catalunya, Barcelona.
Phd in Mathematics, June 2010.
Universitat Politècnica de Catalunya, Barcelona
Degree in Mathematics, June 2005.
Universitat Politècnica de Catalunya, Barcelona
Degree in Telecomunications Engineering, September 2005.
AWARDS
Juan de la Cierva Fellowship (Spanish Ministry of Education and Science), 2013.
Predoctoral fellowship FPU (Spanish Ministry of Education and Science)
Universitat Politècnica de Catalunya, September 2007-August 2009.
Predoctoral Fellowship FI (Government of Catalonia)
Universitat Politècnica de Catalunya, January 2006-September 2007.
RESEARCH STAYS
University of Duisburg–Essen, Essen. Research stay visiting Professor Ulrich Goertz. April
1–June 30, 2016.
Hausdorff Research Institute for Mathematics, Bonn. Trimester program on Arithmetic andGeometry. January 2, 2013–February 2, 2013.
Max Planck Institute for Mathematics, Bonn. Postdoctoral visiting researcher. JanuaryDecember 2012.
McGill University, Montreal.
December 2010.

Research stay visiting Professor Henri Darmon.

September-Xavier Guitart
PUBLICATIONS
On the elliptic Stark Conjecture in higher weight
F. Gatti, X. Guitart. Publ. Mat. 64 (2020), 577-619.
Endomorphism algebras of geometrically split abelian surfaces over Q (with F. Fité).
F. Fité, X. Guitart. Algebra and Number Theory Vol. 14 (2020), No. 6, 1399-1421.
An automorphic approach to Darmon points
X. Guitart, M. Masdeu, S. Molina. Indiana Univ. Math. J. 69 (2020), no. 4, 1251-1274.
Computing p-adic periods of abelian varieties
X. Guitart, M. Masdeu. Contemporary Mathematics, Volume 732, 2019.
On the rank and the convergence rate towards the Sato-Tate measure
F. Fité, X. Guitart. Int. Math. Res. Not., Vol. 2019 I. 13, July 2019, Pages 4081-4118
Periods of modular GL2 -type varieties and p-adic integration
X. Guitart, M. Masdeu. Exp. Math. 27 (2018), no. 3, 344-361.
Fields of definition of elliptic k-curves and the realizability of all genus two Sato-Tate groups.
F. Fité, Xavier Guitart. Trans. Amer. Math. Soc. 370 (2018), 4623-4659
Darmon points on elliptic curves over fields of arbitrary signature.
X. Guitart, M. Masdeu, H. Sengun. P. Lond. Math. Soc. (3) 111 (2015), no. 2, 484–518.
Uniformization of modular elliptic curves via p-adic periods.
X. Guitart, M. Masdeu, H. Sengun. J. Algebra 445 (2016), 458–502.
A p-adic construction of ATR points.
X. Guitart, M. Masdeu. Publ. Mat. 59 (2015), 511–545
Overconvergent cohomology and quaternionic Darmon points.
X. Guitart, M. Masdeu. J. Lond. Math. Soc. (2) 90 (2014), no. 2, 495–524
Elementary matrix decomposition and the computation of Darmon points with higher conductor.
X. Guitart, M. Masdeu. Math. Comp. 84 (2015), 875–893
Computation of ATR Darmon points on non-geometrically modular elliptic curves.
X. Guitart, M. Masdeu. Experimental Mathematics, 22:1, 85–98
Almost totally complex points on elliptic curves.
X. Guitart, V. Rotger, Y. Zhao. Trans. Amer. Math. Soc. 336 (2014) 2773–2802
Modular abelian varieties over number fields.
X. Guitart, J. Quer. Canad. J. Math. 36 (2014) 170–196
Continued fractions in 2-stage euclidean quadratic fields .
X. Guitart, M. Masdeu. Math. Comp. 82 (2013), no. 282, 1223–1233.
Fields of definition of definition of building blocks with quaternionic multiplication.
X. Guitart. Acta Arith. 153 (2012), 1–14
Abelian varieties with many endomorphisms and their absolutely simple factors.
X. Guitart. Rev. Mat. Iberoam. 28 (2012), no. 2, 591–601
Remarks on strongly modular Jacobian surfaces.
X. Guitart, J. Quer. J. Théor. Nombres Bordeaux, 23 no. 1 (2011), 171-182

Xavier Guitart
On the modularity level of modular abelian varieties over number fields.
E. González-Jiménez, X. Guitart. J. Number Theory 130, no. 4, 1560-1570 (2010).
Parametrization of abelian K-surfaces with quaternionic multiplication.
X. Guitart, S. Molina. C. R. Math. Acad. Sci. Paris 347 (2009), no. 23-24, 1325-1330.
SEMINAR AND CONFERENCE TALKS
Endomorphism algebras of geometrically split abelian surfaces over Q. Octavas Jornadas de Teorı́ade Números. June 25-28, 2019, Vilanova i la Geltrú.
Modular forms over number fields of mixed signature and algebraic points on elliptic curves. Building Bridges: 4th EU–US Summer School + Workshop on Automorphic Forms and Related Topics.
July 20, 2018. Budapest.
Fields of definition of elliptic k-curves with CM and Sato–Tate groups of abelian surfaces. 4th Conference of young researchers in Mathematics (RSME), September 4, 2017. University of Valencia.
Fields of definition of elliptic k-curves with CM and Sato–Tate groups of abelian surfaces. Septimas
Jornadas de teorı́a de números. June 26, 2017. Universitat de Lleida.
Modular forms over number fields of mixed signature and algebraic points on elliptic curves. Meetingof the Catalan, Spanish, Swedish Math Societies. June 12, 2017. Umea (Sweden).
Fields of definition of elliptic k-curves with CM and Sato–Tate groups of abelian surfaces. HISTRUCT- Workshop on higher structures. December 13–16, 2016, University of Luxembourg
Modular forms over number fields of mixed signature and algebraic points on elliptic curves. Automorphic forms: theory and computation. King’s College, London, September 6, 2016.
Fields of definition of elliptic k-curves with CM and Sato-Tate groups of abelian surfaces. Warwich
Number Theory Seminar, February 2016.
Fields of definition of elliptic k-curves with CM and Sato-Tate groups of abelian surfaces. York
Number Theory Seminar, February 2016.
Modular forms over fields of mixed signature and rational points on elliptic curves. Barcelona Fall
Number Theory Workshop, November 2015.
Computation and some new instances of Darmon points. Séminaire de théorie des nombres deJussieu-PRG, March 2015.
Computing equations of elliptic curves over number fields via p-adic methods. Barcelona Number
Theory Seminar, January 2015.
Computing equations of elliptic curves over number fields via p-adic methods. Conference for Young
Researchers in Arithmetic and Algebraic Geometry. University of Bonn, 6–8 October 2014
Modular forms over cubic fields and algebraic points on elliptic curves. First Joint International
Meeting RSME-SCM-SEMA-SIMAI-UMI. Bilbo, July 2014.
Effective computation and some new instances of Darmon points. Arithmetic geometry seminar.
Essen, April 2014.
Computation of quaternionic p-adic Darmon points. Bielefeld Arithmetic Geometry Seminar. Bielefeld, January 2014.
Computation of quaternionic p-adic Darmon points. Algebra and Number Theory Seminar. Heidelberg, December 2013.

Xavier Guitart
Algorithms for Darmon points. Quintas Jornadas de Teorı́a de Números. Sevilla, July 8-12, 2013.
Effective computation of Darmon points. Essen Seminar for Algebraic Geometry and Arithmetic.
University of Duisburg-Essen, November 29, 2012.
Darmon points: algorithms and numerical evidence. Number Theory Lunch Seminar, Max Planck
Institute for Mathematics, Bonn, November 14.
Problema del subgrup de congruència efectiu i càlcul de punts de Stark-Heegner. Third meetingof young researchers of the SCM (Catalan Society of Mathematics), Institut d’Estudis Catalans,
October 19, 2012
Numerical computation of Stark-Heegner points in higher level. Rational points on curves: A p-adic
and computational perspective, Mathematical Institute, University of Oxford, September 24-28,
2012
Cálculo de puntos ATR de Darmon en curvas elı́pticas no geométricamente modulares. Seminariode Teorı́a de Números, ICMAT, Madrid. May 8, 2012.
Effective computation of ATR Darmon points. Number theory lunch seminar, Max Planck Institutefor Mathematics, Bonn. May 2, 2012.
Rational points on elliptic curves over almost totally complex quadratic extensions. Seminarium z
Arytmetycznej Geometrii Algebraicznej, Adam Mickiewicz University, Poznan. November 9, 2011
Rational points on elliptic curves over almost totally complex quadratic extensions. Computations
with modular forms, Heidelberg. September 5, 2011.
Computing continued fractions on real quadratic fields. Cuartas Jornadas de Teorı́a de Números,Bilbao. July 13, 2011.
L-series of building blocks. Québec-Vermont Number Theory Seminar, University of Vermont.
October 21, 2010.
On the modularity level of modular abelian varieties over number fields. Conférence de théorie desnombres Québec-Maine, Université Laval, Québec. October 2, 2010.
On the modularity level of modular abelian varieties over number fields. Arithmetic geometry
seminar, Centre de Recerca Matemàtica, Bellaterra (Barcelona). May 19, 2010.
Modular abelian varieties over number fields. 26th Journées Arithmétiques, Saint-Étienne. July 8,2009.
Variedades abelianas modulares sobre cuerpos de números. Terceras jornadas de teorı́a de números,Salamanca. June 30, 2009.
Article de Ribet: Abelian varieties over Q and modular forms. Seminari de Teoria de Nombres deBarcelona, Barcelona. 2009.
Tipus de reduccions de corbes. Seminari de Teoria de Nombres de Barcelona. Barcelona, 2007.
MATHEMATICAL ACTIVITIES
Coorganizer (with C. de Vera) of the Number Theory session of the Barcelona Mathematical Days
2020 Conference, October 23-24, 2020.
Thesis defense committee member, Iago Giné, Albanese varieties of non-Archimedean uniformizedvarieties, student of Xavier Xarles (Universitat Autònoma de Barcelona), July 2017.

Xavier Guitart
Member of the Local Organizing Committee of the Foundations of Computational Mathematics
conference. July 10-19, 2017. Barcelona.
Co-organizer (with Daniel Barrera, Francesc Fité, Santiago Molina, and Victor Rotger) of theworkshop p-adic methods for modular forms and Galois representations, February 13–17, 2017.
Barcelona.
Thesis defense committee member, Laia Amorós, Images of Galois representations and p-adic models of Shimura curves, student of Gabor Wiese (University of Luxembourg) and Pilar Bayer (University of Barcelona), December 2016.
Co-organizer (with M. Masdeu) of the workshop Arithmetic of Euler Systems, to be held in Benasque, Spain, on August 22–30, 2015.
Co-organizer (with Paloma Bengoechea) of the Session on Number Theory of the Young Researchers
Conference of the Royal Spanish Mathematical Society, University of Murcia, September 7–11, 2015.
Co-organizer (with F. Fité, J.-C. Lario, M. Masdeu, and V. Rotger) of the workshop EffectiveMethods for Darmon Points, Benasque (Spain), August 26–30, 2013.
Heegner points on elliptic curves, 4 hours course to graduate students at the Universidad Autónomade Madrid, 7-9 May, 2012.
Master defense committee member, Carlos de Vera, Rational points on Atkin-Lehner quotients ofShimura curves, student of Victor Rotger (Universitat Politècnica de Catalunya), June 2011.
Ph.D. external examiner of the thesis The Birch and Swinnerton-Dyer conjecture for Q-curves,
by Yu Zhao (McGill University); student of Henri Darmon (McGill University) and Victor Rotger(Universitat Politècnica de Catalunya), 2011.
Co-organizer (with J.-C. Lario and M. Masdeu) of the workshop Sato-Tate in Higher dimension,
Benasque (Spain), Jul 25 – Aug 06, 2011.
Coordinator at the 49th International Mathematics Olympiad, July 10th to 22nd, 2008. Madrid,Spain
LANGUAGES
Catalan and Spanish. Mother tongues.
English. Fluent, spoken and written. Cambridge Certificate in Advanced English (CAE).