Juan González-Meneses
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1 Juan González-Meneses Curriculum Vitae February 25, current Experience Profesor Titular de Universidad, Universidad de Sevilla, Spain Profesor Titular de Escuela Universitaria, Universidad de Sevilla, Spain Profesor Asociado, Universidad de Sevilla, Spain PhD student with FPU Grant, Universidad de Sevilla, Spain & Université de Bourgogne, France Profesor Asociado, Universidad de Sevilla, Spain current Positions Head of the Department of Algebra, Universidad de Sevilla, Spain Deputy Head of the Department of Algebra, Universidad de Sevilla, Spain. Membership current current current current Research Committee of the University of Seville, Universidad de Sevilla, Spain. Academic Committee of the Doctorate Program Mathematics", Universidad de Sevilla, Spain. Institute of Research in Mathematics of the University of Seville (IMUS), Universidad de Sevilla, Spain. Centre Board of the Faculty of Mathematics, Universidad de Sevilla, Spain. Education 2000 PhD in Mathematics, Université de Bourgogne, France & Universidad de Sevilla, Spain, Advisor: Luis Paris Degree in Mathematics, Universidad de Sevilla, Spain. Publications Research papers [25] Juan González-Meneses, Pedro M. González Manchón. Closures of positive braids and the Morton-Franks-Williams inequality. Topology and its Applications 174 (2014), /10
2 [24] Juan González-Meneses. Geometric embeddings of braid groups do not merge conjugacy classes. Boletín de la Sociedad Matemática Mexicana 20, no. 2 (2014), [23] Juan González-Meneses, Enric Ventura. Twisted conjugacy in braid groups. Israel Journal of Mathematics 201, no. 1 (2014), [22] Volker Gebhardt, Juan González-Meneses. Generating random braids. Journal of Combinatorial Theory, Series A 120, No. 1 (2013), [21] Juan González-Meneses. Basic results on braid groups. Annales Mathématiques Blaise Pascal 18, no. 1 (2011), [20] Juan González-Meneses, Bert Wiest. Reducible braids and Garside theory. Algebraic and Geometric Topology 11 (2011), [19] Juan González-Meneses. On reduction curves and Garside properties of braids. Contemporary Mathematics 538 (2011), [18] Juan González-Meneses, Pedro M. González Manchón. A geometric characterization of the upper bound for the span of the Jones polynomial. J. Knot Theory Ramifications 20, no. 7 (2011), [17] Volker Gebhardt, Juan González-Meneses. Solving the conjugacy problem in Garside groups by cyclic sliding. Journal of Symbolic Computation 45 (6), 2010, [16] Volker Gebhardt, Juan González-Meneses. The cyclic sliding operation in Garside groups. Mathematische Zeitschrift 265 (1), 2010, [15] Juan González-Meneses, Volker Gebhardt. On the cycling operation in braid groups. Discrete Applied Mathematics 156 (16), 2008, [14] José Burillo, Juan González-Meneses. Bi-orderings on pure braided Thompson s groups. Quarterly Journal of Mathematics 59 (1), 2008, [13] Joan S. Birman, Volker Gebhardt, Juan González-Meneses. Conjugacy in Garside groups III: Periodic braids. Journal of Algebra 316 (2), 2007, [12] Joan S. Birman, Volker Gebhardt, Juan González-Meneses. Conjugacy in Garside groups II: Structure of the ultra summit set. Groups Geom. Dyn. 2 (1), 2008, [11] Joan S. Birman, Volker Gebhardt, Juan González-Meneses. Conjugacy in Garside groups I: Cyclings, powers and rigidity. Groups Geom. Dyn. 1 (3), 2007, [10] Juan González-Meneses. Improving an algorithm to solve multiple simultaneous conjugacy problems in braid groups. Contemp. Math. 372, 2005, [9] Juan González-Meneses, Bert Wiest. On the structure of the centralizer of a braid. Ann. Sci. Éc. Norm. Sup. 37 (5), 2004, [8] Jerónimo Díaz-Cantos, Juan González-Meneses, José María Tornero. On the singular braid monoid of an orientable surface. Proc. of the AMS 132 (10), 2004, [7] Juan González-Meneses, Luis Paris. Vassiliev invariants for braids on surfaces. Transactions of the AMS 356 (1), 2004, [6] Juan González-Meneses. The n-th root of a braid is unique up to conjugacy. Alg. and Geom. Topology 3, 2003, /10
![Generating random braids. Journal of Combinatorial Theory, Series A 120, No. 1 (2013), 111-128. [21] Juan González-Meneses. Basic results on braid groups. Annales Mathématiques Blaise Pascal 18, no.](/docs-images/43/8000027/images/page_2.jpg "1 (2011), 15-59. [20] Juan González-Meneses, Bert Wiest. Reducible braids and Garside theory. Algebraic and Geometric Topology 11 (2011), 2971-3010. [19] Juan González-Meneses.")
3 [5] Nuno Franco, Juan González-Meneses. Computation of Centralizers in Braid groups and Garside groups. Rev. Mat. Iberoamericana 19 (2), 2003, [4] Nuno Franco, Juan González-Meneses. Conjugacy problem for braid groups and Garside groups. Journal of Algebra 266 (1) 2003, [3] Juan González-Meneses. Presentation for the monoid of singular braids on closed surfaces. Comm. in Algebra 30 (6), 2002, [2] Juan González-Meneses. Ordering pure braid groups on compact, connected surfaces. Pacific J. of Math. 203 (2), 2002, [1] Juan González-Meneses. New presentations os surface braid groups. J. of Knot Theory Ramifications 10 (3), 2001, Books [1] Juan González-Meneses, Martin Lustig, Enric Ventura (eds.), Extended Abstracts Fall 2012, Trends in Mathematics 1, Birkhäuser, Talks at conferences Invited talks [26] Inyecciones geométricas de grupos de trenzas. Congreso RSME Granada, Spain, 2-6 February [25] Geometry and algebra to study braids. IV Seminario Atlántico de Geometría. Castro Urdiales, Spain, 2-5 October [24] Garside meets Thurston. Groups in Galway. Galway (Ireland), May [23] Combinatorics of Garside monoids. Garside theory: State of the art and prospects. Cap Hornu (France). 30 May - 2 June [22] Reconociendo representantes lexicográficos de trenzas positivas. II Encuentro Conjunto RSME-SMM. Torremolinos (Spain) January [21] Growth functions of braid monoids and generation of random braids. Geometric and Asymptotic Group Theory with Applications (GAGTA-5). Manresa (Spain), July [20] Growth functions of braid monoids and generation of random braids. Workshop Braids and Applications". Pisa (Italy), June [19] Growth functions of Artin-Tits monoids and generation of random braids. Autour de la Thorie de Garside. Amiens (France), May [18] Generating random braids Joint Mathematics Meetings. New Orleans (USA), 6-9 January [17] Generating random braids. Workshop on Complexity and Group-based Cryptography. Montreal (Canada), 27 August - 3 September [16] Detecting reducibility of braids. Fifth Barcelona Weekend in Group Theory. Barcelona (Spain), April [15] Nielsen-Thurston theory and braids. Topology and computer Tokyo, 31 August-2 September [14] The conjugacy problem in the braid group. Topology and computer Tokyo, 31 August-2 September [13] Problème de conjugaison dans les catégories de Garside. Journées Garside. Caen (France), 30 June /10
![in Algebra 30 (6), 2002, 2829-2836. [2] Juan González-Meneses. Ordering pure braid groups on compact, connected surfaces. Pacific J. of Math. 203 (2), 2002, 369-378. [1] Juan González-Meneses.](/docs-images/43/8000027/images/page_3.jpg "New presentations os surface braid groups. J. of Knot Theory Ramifications 10 (3), 2001, 431-451. Books [1] Juan González-Meneses, Martin Lustig, Enric Ventura (eds.")
4 [12] On a relation between algebraic and geometric properties of braids. Lib60ber. Topology of Algebraic Varieties. Jaca (Spain), June [11] Bi-orderings on pure braided Thompson s groups. Les groupes de Thompson: nouveaux dévelopements et interfaces. Luminy (France), 2-6 June [10] A project to find a polynomial solution to the conjugacy problem in braid groups. I Congreso Hispano Francés de Matemáticas. Zaragoza (Spain), 9-13 July 2007 [9] Towards a polynomial solution to the conjugacy problem in braid groups. Braids. Singapore, June [8] A project to find a polynomial solution to the conjugacy problem in braid groups. The many strands of the braid group. BIRS, Banff (Canada), April [7] Rigidity of braids: A new tool for studying conjugacy in braid groups. Barcelona weekend in Group Theory. Barcelona (Spain), May [6] Conjugacy problem for braid groups and Garside groups. Marie Curie Training Site Closing Conference. Liverpool (UK), April [5] Conjugacy problem for pseudo-anosov braids. Braid groups and applications. BIRS. Banff (Canada), October [4] Trenzas: de los automorfismos de superficies a la criptografía. XI Encuentro de Topología. Barcelona (Spain), March [3] Braids and Nielsen-Thurston theory. Joint meeting AMS-RSME. Sevilla (Spain), June [2] Braids and Cryptography: New algorithms for conjugacy problems. Workshop Complexity-theoretical and Algebraic Methods in Cryptography". Bochum (Germany), 7-8 November [1] Ordering pure braid groups on closed surfaces. Canadian Mathematical Society Winter 2000 Meeting. Vancouver (Canada), December Contributed talks [15] Geometric techniques in braid groups. Closing Workshop on Automorphisms of Free Groups. CRM Barcelona (Spain), December [14] Autómatas que reconocen representantes lexicográficos en ciertos monoides. IX Encuentro en Teoría de Grupos. ICMAT Madrid (Spain) June, [13] Algorithmics in braid groups. Trenzas: Jornada temática interdisciplinar de la Red Española de Topología. Barcelona, October [12] Conjugación torcida en los grupos de trenzas. VIII encuentro en Teoría de Grupos. Bilbao, June [11] Twisted conjugacy in braid groups. Braids in Paris. Paris (France), September [10] On a relation between algebraic and geometric properties of braids. Workshop Braids, Groups and Topology". Málaga (Spain), 31 January [9] Unifying cycling and decycling in Garside groups. Noeuds, arrangements d hyperplans et groupes de Coxeter. CIRM Luminy (France), 4-8 June [8] The conjugacy problem in braid groups. Advanced Course on The Geometry of the Word Problem for Finitely Generated Groups. CRM Barcelona (Spain), 5-15 July /10
![I Congreso Hispano Francés de Matemáticas. Zaragoza (Spain), 9-13 July 2007 [9] Towards a polynomial solution to the conjugacy problem in braid groups. Braids. Singapore, 25-29 June 2007.](/docs-images/43/8000027/images/page_4.jpg "[8] A project to find a polynomial solution to the conjugacy problem in braid groups. The many strands of the braid group. BIRS, Banff (Canada), 22-27 April 2007.")
5 [7] A new algorithm to solve the conjugacy problem in braid groups. Groupes de tresses, invariants quantiques et géométrie des varietés de dimension 3. CIRM Luminy (Francia), 6-10 June [6] The n-th root of a braid is unique up to conjugacy. Journées tresses. CIRM Luminy (France), June [5] Minimal set of generators for the centraliser of a braid. Tresses à Lacanau. Lacanau (France), September [4] Minimal Simple Elements in Garside Groups (Poster). Braids in Cortona. Cortona (Italy), June [3] L ordre dans les groupes de tresses des surfaces. Colloque GDR Tresses à Marne-la-Vallée. Marne-la-Vallée (France), November [2] Vassiliev invariants for braids on surfaces. Journées Toulousaines autour des Tresses et des Noeuds. Toulouse (France), 5-8 June [1] Presentation of surface braid groups. Journées Groupes de Tresses. CIRM Luminy (France), 7-11 June Advanced courses (lecturer) [5] Geometric approaches to Artin-Tits groups. Winter Braids V. Pau (France), February [4] Algebraic and geometric aspects of braid groups and Artin groups. Tresses in Pau. Pau (France), 5-8 October [3] Conjugación en los grupos de trenzas. Introducción y aplicaciones. Universidad Politécnica de Madrid. Madrid (Spain), November [2] Conjugacy problem in braid groups and other Garside groups. Problèmes algorithmiques liés aux tresses et à la topologie de basse dimension. Berder (France), November [1] Cryptosystems based on conjugacy Problem. EMS Summer School: Braid Groups - Applications to Geometry, Cryptography and Computation. Eilat (Israel), February Seminars and talks [30] Inyecciones geométricas de grupos de trenzas. Seminario del Departamento de Álgebra. Universidad de Sevilla (Spain). 30 September [29] Growth function of braid monoids and generation of random braids. UWS seminar. University of western Sydney. Sydney (Australia), 11 April [28] Generación de trenzas aleatorias. Seminario del Grupo de Criptografía Matemática de la URJC. Universidad Rey Juan Carlos. Madird (Spain), 3 March [27] On a relation between algebraic and geometric properties of braids. Pure Colloquium of the School of Mathematics. University of Southampton. Southampton (UK), 15 January [26] Pero, >A quién le interesan las trenzas? Seminario del Departamento de Álgebra. Universidad de Sevilla (Spain), 20 May [25] Pero, >A quién le interesan las trenzas? Universidad Politécnica de Madrid. Madrid (Spain), 27 November /10
![Lacanau (France), 23-26 September 2002. [4] Minimal Simple Elements in Garside Groups (Poster). Braids in Cortona. Cortona (Italy), 19-22 June 2002.](/docs-images/43/8000027/images/page_5.jpg "[3] L ordre dans les groupes de tresses des surfaces. Colloque GDR Tresses à Marne-la-Vallée. Marne-la-Vallée (France), 16-18 November 2000. [2] Vassiliev invariants for braids on surfaces.")
6 [24] On the Garside structure and the Nielsen-Thurston reducibility of braids. Centre de Recerca Matematica (CRM). Barcelona (Spain), 19 september [23] Transmitiendo información secreta: Las matemáticas detrás de la criptografía. Obra social de Caixa Manresa. Manresa (Spain), 4 October [22] On periodic braids. Centre de Recerca Matematica (CRM). Barcelona (Spain), 3 October [21] The conjugacy problem in braid groups and Garside groups. New York Group Theory Seminar. City University of New York. New York (USA), 7 April [20] The conjugacy problem in braid groups and Garside groups. Geometric Topology Seminar. Columbia University. New York (USA), 31 March [19] Nudos, trenzas y criptografía. Conferències per a estudiants universitaris. Universitat Autònoma de Barcelona. Barcelona (Spain), 3 March [18] Nudos, trenzas y criptografía. Conferències per a estudiants universitaris. Universitat Politècnica de Catalunya. Barcelona (Spain), 2 March [17] The n-th root of a braid is unique up to conjugacy. Summer Geometric Topology Seminar. Columbia University. New York (USA), 9 July [16] Teoría de Nielsen-Thurston aplicada a las trenzas. Seminario del Departamento de Álgebra. Universidad de Sevilla (Spain). 3 April [15] Criptografía y trenzas: Última hora. Seminario del Departamento de Álgebra. Universidad de Sevilla (Spain). 4 March [14] Tresses et Cryptographie. Invited seminar. Université de Rennes 1. Rennes (France), February [13] Criptografía y trenzas. Seminario de Topología computacional y Matemática Aplicada. Universidad de Sevilla. Sevilla (Spain), 19 November [12] Conjugación, trenzas y criptografía. Seminario del Departamento de Álgebra. Universidad de Sevilla (Spain), 23 October [11] Algorithme pour le problème de conjugaison dans le groupe de tresses. Séminaire AGT. Université de Bourgogne. Dijon (France), June [10] Grupos ordenables. Seminario del Departamento de Álgebra. Universidad de Sevilla (Spain), 22 January [9] Vassiliev invariants for braids. Grupo de trabalho Singularidades. Universidade de Lisboa. Lisboa (Portugal), 16 November [8] Vassiliev invariants for knots. Grupo de trabalho Singularidades. Universidade de Lisboa. Lisboa (Portugal), 9 November [7] Introducción a los invariantes de Vassiliev. Seminario del Departamento de Álgebra. Universidad de Sevilla (Spain), 27 April [6] Invariants de Vassiliev des tresses de surfaces. Séminaire de Topologie. Université de Provence. Marseille (France), 3 April [5] Invariants de Vassiliev des tresses de surfaces. éminaire AGT. Université de Bourgogne. Dijon (France), 16 march [4] Surface braid groups. Séminaire de Topologie. Université de Provence. Marseille (France), 13 June [3] Introducción a los grupos automáticos. Seminario del Departamento de Álgebra. Universidad de Sevilla (Spain), 11 February /10
![Centre de Recerca Matematica (CRM). Barcelona (Spain), 3 October 2006. [21] The conjugacy problem in braid groups and Garside groups. New York Group Theory Seminar. City University of New York.](/docs-images/43/8000027/images/page_6.jpg "New York (USA), 7 April 2006. [20] The conjugacy problem in braid groups and Garside groups. Geometric Topology Seminar. Columbia University. New York (USA), 31 March 2006.")
7 [2] Grupos de trenzas de superfiies. Seminario del Departamento de Álgebra. Universidad de Sevilla (Spain), 7 January [1] Présentation des groupes de tresses de surfaces. Séminaire AGT. Université de Bourgogne. Dijon (France), 26 November Research projects As principal investigator MTM P, Trenzas: Nudos, Grupos de Garside y Mapping Class Groups, Ministerio de Economía y Competitividad, Spain. No. of researchers: MTM , Propiedades Algebraicas y Topológicas de Trenzas y Nudos, Ministerio de Ciencia e Innovación, Spain. No. of researchers: P09-FQM-5112, Aspectos geométricos y Computacionales de los grupos de trenzas, Consejería de Innovación, Ciencia y Empresas, Junta de Andalucía, Andalousia, Spain. No. of researchers: 5 As researcher DP , Algorithmic approaches to braids and their generalisations, Ministry for Innovation, Industry, Science and Research, Australia. No. of researchers: 3 Principal investigator: Volker Gebhardt MTM , D-Módulos, singularidades y geometría algebraica aritmética, Ministerio de Educación y Ciencia, Spain. no. of researchers: 17 Principal investigator: Luis Narváez Macarro MTM C02-01, Variedades algebraicas o analíticas, D-módulos, sistemas dinámicos y foliaciones: singularidades y aspectos globales. Aplicaciones e interacciones con otros campos, Ministerio de Ciencia y Tecnología, Spain. No. of researchers: 14 Principal investigator: Luis Narváez Macarro BFM , D-módulos y cohomología de variedades, Ministerio de Ciencia y Tecnología, Spain. No. of researchers: 11 Principal investigator: Luis Narváez Macarro DGSIC PB , Métodos y estructuras diferenciales en Álgebra, Geometría y Singularidades, Ministerio de Educación y Cultura, Spain. Principal investigator: Luis Narváez Macarro Organization of research events International events X Encuentro en Teoría de Grupos, International Conference, Universidad de Sevilla, Sevilla (Spain). Main organizer and member of the scientific committee Cool-down week for the International Conference, Workshop, Centre de Recerca Matematica, Barcelona (Spain). Main organizer. 7/10
8 Conference on Automorphisms of free groups: Algorithms, Geometry and Dynamics, International conference, Centre de Recerca Matematica, Barcelona (Spain) Summer school on Automorphism of free groups, Advanced course, Centre de Recerca Matematica, Barcelona (Spain) Automorphisms of free groups: Algorithms, Geometry and Dynamics, Research Program, Centre de Recerca Matematica, Barcelona (Spain) Topología de bajas dimensiones, Special Session of the II Joint Meeting RSME-SMM, Torremolinos (Spain) Braids in Seville, International conference, Universidad de Sevilla, Sevilla (Spain). Main organizer and member of the scientific committee Congreso Internacional sobre Álgebra Conmutativa, Combinatoria y Computacional, en memoria de Pilar Pisón Casares, International conference, Universidad de Sevilla, Sevilla (Spain) Combinatorial, algorithmic and cryptographic aspects of Group Theory, International conference, CIRM, Luminy (France). Member of the scientific committee Geometric and Asymptotic Group Theory with Applications, International conference (Satellite of ICM 2006), Manresa (Spain). Member of the organizing committee National events RSME Imaginary, Exhibition, Universidad de Sevilla, Sevilla (Spain) Encuentro de Topología, National conference, Universidad de Sevilla, Sevilla (Spain). Member of the organizing and scientific committees Trenzas: Jornada temática Interdisciplinar de la Red Española de Topología, National meeting with international participants, Universitat de Barcelona, Barcelona (Spain). Member of the organizing and scientific committees Problemas diofánticos y variedades abelianas, National meeting, Universidad de Sevilla, Sevilla (Spain) Singularidades de ecuaciones algebraicas y de ecuaciones diferenciales: Métodos valorativos, homológicos y analíticos, National meeting, Universidad de Sevilla, Sevilla (Spain) Seminario del Departamento de Álgebra, Periodic seminar, Universidad de Sevilla, Sevilla (Spain). Main organizer. 8/10
9 Student supervision PhD students Matthieu Calvez, Problèmes algorithmiques dans les groupes des tresses", Université de Rennes I & Universidad de Sevilla. Co-advised with Bert Wiest (Université de Rennes I) In preparation In preparation In preparation Marta Aguilera Gómez del Castillo, Universidad de Sevilla. Dolores Valladares García, Universidad de Sevilla. Marithania Silvero Casanova, Universidad de Sevilla. Grants and awards Grants Beca FPU, (Doctoral grant), Ministerio de Educación y Cultura, Spain, Unversidad de Sevilla. Apr Sept 2000 Oct Dec 1999 Oct Dec 1998 Oct Dec 1997 Research Stay Grant, Université de Bourgogne, Dijon, France, Awarded by Ministerio de Educación y Cultura, Spain. Research Stay Grant, Université de Bourgogne, Dijon, France, Awarded by Ministerio de Educación y Cultura, Spain. Research Stay Grant, Université de Bourgogne, Dijon, France, Awarded by Ministerio de Educación y Cultura, Spain. Research Stay Grant, Université Joseph Fourier, Grenoble, France, Awarded by Ministerio de Educación y Cultura, Spain Mathematical Olympiad Grant, Universidad de Sevilla, Spain, Awarded by Ministerio de educación y Cultura, Spain. Awards 2006 Diploma de Excelencia Docente, (Teaching Excellence Diploma), Curso 2005/2006, Universidad de Sevilla, Spain Diploma de Excelencia Docente, (Teaching Excellence Diploma), Curso 2002/2003, Universidad de Sevilla, Spain Primer Premio Extraordinario de Doctorado, (Extraordinary Award PhD in Mathematics), Convocatoria 2000/2001, Universidad de Sevilla, Spain Primer Premio Extraordinario de Licenciatura en Matemáticas, (Extraordinary Award Degree in Mathematics), Curso 1995/1996, Facultad de Matemáticas. Universidad de Sevilla, Spain Premio Mejor Expediente, (Best academic record award), Promoción 1991/1996, Facultad de Matemáticas. Opción Puras. Universidad de Sevilla, Spain Premio Real Maestranza de Caballería de Sevilla al Mejor Expediente, (Best academic record award), Promoción 1991/96, Facultad de Matemáticas. Universidad de Sevilla, Spain Premio Ayuntamiento de Sevilla al Mejor Expediente, (Best academic record award), Promoción 1991/96, Facultad de Matemáticas. Universidad de Sevilla, Spain.. 9/10
10 Research stays Sep Dec 2012 Apr 2011 Sep 2007 Jun 2007 Mar Apr 2006 Jul 2004 Feb 2002 Jun 2001 Nov 2000 Apr-Sep 2000 Oct-Dec 1999 Oct-Dec 1998 Oct-Dec 1997 Sep 1995 Jun 1996 Centre de Recerca Matemàtica (CRM). Barcelona, Spain. 3 months. University of Western Sydney. Siydney, Australia. 2 weeks. Centre de Recerca Matemàtica (CRM). Barcelona, Spain. 2 weeks. National University of Singapore. Singapore. 2 weeks. Columbia University. New York, USA. 2 weeks. Columbia University. New York, USA. 2 weeks. Université de Rennes I. Rennes, France. 1 week. Université de Bourgogne. Dijon, France. 1 month. Universidade de Lisboa. Lisboa, Portugal. 1 month. Predoctoral stays Université de Bourgogne. Dijon, France. 6 months. Université de Bourgogne. Dijon, France. 3 months. Université de Bourgogne. Dijon, France. 3 months. Université Joseph Fourier. Grenoble, France. 3 months. University of Kent at Canterbury. Canterbury, UK. Erasmus grant. 9 months. Other merits 2012 Marker at the XLVIII Spanish Mathematical Olympiad. Santander, Spain Marker at the XLVII Spanish Mathematical Olympiad. Pamplona, Spain Marker at the XLV Spanish Mathematical Olympiad. Sant Feliú de Guixols, Spain Coordinator (marker) at the 49th International Mathematical Olympiad, IMO Madrid, Spain Winner at the XXVII Spanish Mathematical Olympiad (Local round, province of Seville). Sevilla, Spain Winner at the III Mathematical Olympiad Thales (Regional round, Andalousia). El Rocío, Spain Winner at the III Mathematical Olympiad Thales (Local round, province of Seville). Sevilla, Spain. 10/10
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