Miguel Domínguez Vázquez
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1 Instituto de Ciencias Matemáticas ICMAT Calle Nicolás Cabrera Madrid (Spain) miguel.dominguez()icmat.es miguel.dominguezv BIOGRAPHICAL Born September 29, 1985, in Ourense (Spain). EMPLOYMENT Marie Skłodowska-Curie Fellow. ICMAT-CSIC, Madrid, January 2018 present. Profesor Ayudante Doctor. Universidad Autónoma de Madrid, September 2017 January Marie Skłodowska-Curie Fellow. ICMAT-CSIC, Madrid, April 2017 September Juan de la Cierva-training Fellow. ICMAT-CSIC, Madrid, January 2016 April Iberoamerican Visiting Researcher. IMPA, Rio de Janeiro, November 2013 December Postdoctoral Researcher. Universidade de Santiago de Compostela, July 2013 October FPU Fellow of the Spanish Ministry of Education. Univ. Santiago de Compostela, August 2009 July EDUCATION PhD in Mathematics. Universidade de Santiago de Compostela, March Thesis: Isoparametric foliations and polar actions on complex space forms. Advisor: José Carlos Díaz Ramos Graduate in Mathematics (with average grade 9.92 out of 10). Univ. Santiago de Compostela, July RESEARCH INTERESTS Riemannian geometry and geometric analysis: submanifold theory, symmetric spaces, Lie group isometric actions, isoparametric foliations, polar actions, cohomogeneity one actions, overdetermined boundary problems of partial differential equations. PUBLICATIONS J. C. Díaz-Ramos, M. Domínguez-Vázquez, A. Kollross: On homogeneous manifolds whose isotropy actions are polar, arxiv: v1, 20 pp. M. Domínguez-Vázquez, J. M. Manzano: Isoparametric surfaces in E(κ, τ)-spaces, arxiv: v1, 13 pp. M. Domínguez-Vázquez, O. Pérez-Barral: Ruled hypersurfaces with constant mean curvature in complex space forms, arxiv: v1, 7 pp. M. Domínguez-Vázquez, A. Enciso, D. Peralta-Salas: Solutions to the overdetermined boundary problem for semilinear equations with position-dependent nonlinearities, arxiv: v1, 36 pp. M. Domínguez-Vázquez, C. Gorodski: Polar foliations on quaternionic projective spaces, Tohoku Math. J., to appear, 22 pp. J. C. Díaz-Ramos, M. Domínguez-Vázquez, C. Vidal-Castiñeira: Strongly 2-Hopf hypersurfaces in complex projective and hyperbolic planes, Ann. Mat. Pura Appl. (4) 197 (2018), no. 2, J. C. Díaz-Ramos, M. Domínguez-Vázquez, C. Vidal-Castiñeira: Isoparametric submanifolds in twodimensional complex space forms, Ann. Global Anal. Geom. 53 (2018), no. 2, J. C. Díaz-Ramos, M. Domínguez-Vázquez, A. Kollross: Polar actions on complex hyperbolic spaces, Math. Z. 287 (2017), no. 3-4, J. C. Díaz-Ramos, M. Domínguez-Vázquez, V. Sanmartín-López: Isoparametric hypersurfaces in complex hyperbolic spaces, Adv. Math. 314 (2017), J. C. Díaz-Ramos, M. Domínguez-Vázquez, C. Vidal-Castiñeira: Real hypersurfaces with two principal curvatures in complex projective and hyperbolic planes, J. Geom. Anal. 27 (2017), no. 1, M. Domínguez-Vázquez: Isoparametric foliations on complex projective spaces, Trans. Amer. Math. Soc. 368 (2016), no. 2, M. Domínguez-Vázquez: Canonical extension of submanifolds and foliations in noncompact symmetric spaces, Int. Math. Res. Not. (IMRN) 2015 (2015), no. 22, J. Berndt, M. Domínguez-Vázquez: Cohomogeneity one actions on some noncompact symmetric spaces of rank two, Transform. Groups 20 (2015), no. 4, J. C. Díaz-Ramos, M. Domínguez-Vázquez: Isoparametric hypersurfaces in Damek-Ricci spaces, Adv. Math. 239 (2013), J. C. Díaz-Ramos, M. Domínguez-Vázquez: Inhomogeneous isoparametric hypersurfaces in complex hyperbolic spaces, Math. Z. 271 (2012), J. C. Díaz-Ramos, M. Domínguez-Vázquez: Non-Hopf real hypersurfaces with constant principal curvatures in complex space forms, Indiana Univ. Math. J. 60 (2011), no. 3, Page 1 of 6
2 M. Domínguez-Vázquez: Real hypersurfaces with constant principal curvatures in complex space forms, Differential Geom. Appl. 29 (2011), suppl. 1, CONFERENCE PROCEEDINGS J. C. Díaz-Ramos, M. Domínguez-Vázquez, V. Sanmartín-López: Anti-De Sitter spacetimes and isoparametric hypersurfaces in complex space forms, Lorentzian Geometry and Related Topics, GELOMA 2016, Málaga, Springer Proceedings in Mathematics & Statistics, Vol. 211, M. Domínguez-Vázquez: On the existence of inhomogeneous isoparametric foliations of higher codimension on complex projective spaces, Pure and Applied Differential Geometry PADGE 2012 (In Memory of Franki Dillen), , Shaker Verlag, Aachen, M. Domínguez-Vázquez: Some interesting families of non-hopf real hypersurfaces in complex space forms, Proceedings of the 17th International Workshop on Differential Geometry and Related Fields, , NIMS (Daejeon), Vol. 17, M. Domínguez-Vázquez: On isoparametric hypersurfaces in complex hyperbolic spaces, International Meeting on Differential Geometry (Córdoba 2010), 71 92, M. Domínguez-Vázquez: On an inhomogeneous isoparametric family of hypersurfaces with constant principal curvatures in the Cayley hyperbolic plane, XX International Fall Workshop on Geometry and Physics, , AIP Conf. Proc., 1460, Amer. Inst. Phys., OTHER PUBLICATIONS M. Domínguez-Vázquez: Isoparametric foliations and polar actions on complex space forms. PhD thesis, Publicaciones del Departamento de Geometría y Topología 126, Univ. Santiago de Compostela, M. Domínguez Vázquez, A. Martínez Calvo, J. Seoane Bascoy (editors): As matemáticas do veciño. Actas do Seminario de Iniciación á Investigación 2010, Institute of Mathematics, Univ. Santiago de Compostela (2011). M. Domínguez Vázquez, A. Martínez Calvo, J. Seoane Bascoy (editors): As matemáticas do veciño. Actas do Seminario de Iniciación á Investigación 2009, Institute of Mathematics, Univ. Santiago de Compostela (2010). M. Domínguez-Vázquez: Hipersuperficies con curvaturas principais constantes nos espazos proxectivo e hiperbólico complexos. Advanced Studies Diploma thesis, Publicaciones del Departamento de Geometría y Topología 118, Univ. Santiago de Compostela, INVITED TALKS (CONFERENCES) Hiroshima Differential Geometry Day 2018, Hiroshima (Japan), 21/04/2018. Isoparametric surfaces in homogeneous 3-manifolds. Primer Encuentro Conjunto RSME-UMA, Buenos Aires (Argentina), 14/12/2017. Isoparametric hypersurfaces in the complex hyperbolic space. IV Encuentro Conjunto RSME-SMM, Valladolid (Spain), 22/07/2017. Isoparametric hypersurfaces in complex hyperbolic spaces. XXV International Fall Workshop on Geometry and Physics, IEM-CSIC, Madrid (Spain), 02/09/2016. Isoparametric submanifolds of complex space forms. First Joint Meeting Brazil-Spain in Mathematics (SBM-SBMAC-RSME), Fortaleza (Brazil), 08/12/2015. Classification of isoparametric hypersurfaces in complex hyperbolic spaces. Congreso de la RSME 2015, Granada (Spain), 03/02/2015. Two construction methods of isoparametric hypersurfaces in noncompact symmetric spaces. The second Japanese-Spanish workshop on Differential Geometry, Tokyo Institute of Technology (Japan), 10/02/2014. Isoparametric submanifolds of complex projective spaces. 17th International Workshop on Differential Geometry, NIMS, Daejeon (South Korea), 02/10/2013. Some interesting families of non-hopf real hypersurfaces in complex space forms. Geometric Analysis Seminar GAS-UV13, Valencia (Spain), 05/09/2013. The horospherical decomposition and new isoparametric hypersurfaces in noncompact symmetric spaces. Geometry Meeting 2012, Ferrol (Spain), 26/10/2012. Polar foliations for beginners. Differential Geometry Days in honour of Luis A. Cordero, Santiago de Compostela (Spain), 28/06/2012. Isoparametric foliations on complex projective spaces. Conference in Geometry and Global Analysis, celebrating P. Gilkey s 65th birthday, Santiago de Compostela (Spain), 16/12/2010. Principal curvatures of isoparametric hypersurfaces in complex hyperbolic spaces. Page 2 of 6
3 Geometry Meeting 2010, Ferrol (Spain), 07/10/2010. The classification problem of isoparametric hypersurfaces. Workshop on Hypersurface Geometry and Integrable Systems, Tohoku University, Sendai (Japan), 25/08/2010. Real hypersurfaces with constant principal curvatures in complex projective and hyperbolic spaces. INVITED TALKS (SEMINARS) Universidade de Santiago de Compostela, Vidal Abascal Seminar, Santiago (Spain), 07/06/2018. Isoparametric surfaces in homogeneous spaces. Universidad de Murcia, Rey Pastor Seminar, Murcia (Spain), 25/05/2017. Cohomogeneity one actions on symmetric spaces of noncompact type. Universidade de Santiago de Compostela, Vidal Abascal Seminar, Santiago (Spain), 21/07/2016. Isoparametric hypersurfaces in overdetermined PDE problems. Universidade de Santiago de Compostela, Vidal Abascal Seminar, Santiago (Spain), 03/03/2016. Classification of polar foliations in the quaternionic projective space. Universidade de São Paulo, Geometry Seminar, São Paulo (Brazil), 23/10/2015. Polar foliations on quaternionic projective spaces. IMPA, Differential Geometry Seminar, Rio de Janeiro (Brazil), 01/10/2015. Canonical extension of submanifolds in noncompact symmetric spaces. Universidade de São Paulo, Geometry Seminar, São Paulo (Brazil), 03/07/2015. Extending submanifolds in the symmetric spaces of noncompact type. IMPA, Differential Geometry Seminar, Rio de Janeiro (Brazil), 09/10/2014. Polar foliations on complex projective spaces. Universidade de São Paulo, Geometry Seminar, São Paulo (Brazil), 30/05/2014. Inhomogeneous isoparametric foliations and prime numbers. Universidade de Brasília, Geometry Seminar, Brasilia (Brazil), 31/03/2014. Homogeneity of isoparametric submanifolds and prime numbers. IMPA, Differential Geometry Seminar, Rio de Janeiro (Brazil), 16/01/2014. Hypersurfaces with two principal curvatures in nonflat complex space forms. Universidade Federal Fluminense, Geometry Seminar, Rio de Janeiro (Brazil), 07/11/2013. A geometric characterisation via prime numbers. King s College London and University College London, Geometry Seminar, London (UK), 07/05/2013. Inhomogeneous isoparametric foliations. ICMAT, Geometry Seminar, Madrid (Spain), 11/02/13. The classification problem of isoparametric foliations. Universität Stuttgart, Geometry and Topology Seminar, Stuttgart (Germany), 19/06/2012. Inhomogeneous isoparametric families on complex projective spaces. Universität zu Köln, Geometry Seminar, Cologne (Germany), 19/04/2011. Homogeneous and isoparametric hypersurfaces in non-compact rank-one symmetric spaces. OTHER TALKS Pure and Applied Differential Geometry - PADGE 2017, Leuven (Belgium), 23/08/2017. Overdetermined boundary value problems on Riemannian manifolds. Geometry and Dynamics of Foliations, ICMAT, Madrid (Spain), 02/09/2014. Classification of isoparametric foliations on complex projective spaces. XVIII Escola de Geometria Diferencial, Brasília (Brazil), 28/07/2014. Polar actions on complex hyperbolic spaces. Congreso de Jóvenes Investigadores de la RSME, Seville (Spain), 19/09/2013. Isoparametric families in Damek-Ricci spaces. Conference on Pure and Applied Differential Geometry PADGE 2012, Leuven (Belgium), 28/08/2012. On the existence of inhomogeneous isoparametric foliations of higher codimension on complex projective spaces. VI International Meeting on Lorentzian Geometry Gelogra 2011, Granada (Spain), 08/09/2011. Families of parallel CMC hypersurfaces in noncompact rank-one symmetric spaces. International Meeting on Differential Geometry, Córdoba (Spain), 15/11/2010. On isoparametric hypersurfaces in complex hyperbolic spaces. Page 3 of 6
4 DGA 2010 Differential Geometry and its Applications, Brno (Czech Republic), 30/08/2010. Real hypersurfaces with constant principal curvatures in complex space forms. POSTERS International Fall Workshop on Geometry and Physics, ICMAT, Madrid (Spain), 31/08/2011. Some results on isoparametric hypersurfaces in nonflat complex space forms. Conference in Geometry and Global Analysis, celebrating P. Gilkey s 65th birthday, Santiago de Compostela (Spain), 13/12/2010. Principal curvatures of isoparametric hypersurfaces in complex hyperbolic spaces. Lectures on Lorentzian Geometry, Granada (Spain), 08/02/2010. Hypersurfaces with constant principal curvatures in complex projective and hyperbolic spaces. GRANTS AND AWARDS RESEARCH STAYS PARTICIPATION IN RESEARCH PROJECTS Marie Skłodowska-Curie Individual Fellowship (Standard EF). European Commission, Extraordinary PhD Award. University of Santiago de Compostela (Spain), Juan de la Cierva-training Fellowship. Ministry of Economy and Competitiveness (Spain), January 2016 December Iberoamerican Visiting Researcher Grant. IMPA (Brazil), November 2013 December Doctor Europeus. University of Santiago de Compostela, Grant of the National Programme for the Formation of University Professors (FPU). Ministry of Education (Spain), August 2009 July Grant for postgraduate studies. Galician Government (Spain), October 2008 July Third position in the National Graduation Award. Ministry of Education (Spain), Galician Graduation Award. Galician Government (Spain), Extraordinary Graduation Award. University of Santiago de Compostela, Departmental collaboration grant. Galician Government (Spain), October 2007 July Galician Extraordinary Award of pre-university education. Galician Government, Gold medal in the National Chemistry Olympiad. Spanish Government, Silver medal in the Spanish Physics Olympiad. Spanish Government, Silver medal in the Spanish Mathematical Olympiad. Spanish Government, University of Hiroshima (Japan), 3 weeks, 12/04/ /05/2018. Universidad de Murcia (Spain), 1 week, 21/05/ /05/2017. Universidade de São Paulo (Brazil), 2 weeks, 27/03/ /04/2017. Instituto Nacional de Matemática Pura e Aplicada IMPA (Brazil), 2 weeks, 13/03/ /03/2017. Universidade de São Paulo (Brazil), 2 months, 23/06/ /07/2014 and 10/06/ /07/2015. King s College London (United Kingdom), 3 months, 01/04/ /07/2013. Universität Stuttgart (Germany), 1 week, 17/06/ /06/2012. Universität zu Köln (Germany), 3 months, 01/04/ /07/2011. Homogeneity and curvature of manifolds and submanifolds (ED431F 2017/03). Galician Government (Spain), , e40.000, 7 researchers. Principal investigator: J. C. Díaz-Ramos. Symmetry, curvature and differential equations in geometry (MTM P). Ministry of Economy and Competitiveness (Spain), , e72.963, 12 researchers. Principal investigators: José Carlos Díaz- Ramos, Eduardo García-Río. Symmetry, homogeneity and curvature (EM2014/009). Galician Government (Spain), , e93.000, 7 researchers. Principal investigator: J. C. Díaz-Ramos. Symmetry, curvature and rigidity of geometric structures (MTM P). Ministry of Economy and Competitiveness (Spain), , e47.700, 11 members. Principal investigators: J. C. Díaz-Ramos, E. García-Río. Consolidation of competitive research units of the Galician university system (GRC ). Galician Government (Spain), , e , 10 researchers. Principal investigator: E. García-Río. Curvature and symmetry in semi-riemannian geometry (MTM ). Ministry of Science and Innovation (Spain), , e , 14 researchers. Principal investigator: E. García-Río. Page 4 of 6
5 Curvature and structure of Lorentzian manifolds (09PXIB207151PR). Galician Government (Spain), , e99.710, 12 researchers. Principal investigator: E. García-Río. SERVICE ADVISORSHIP OF STUDENTS SCIENCE OUTREACH TEACHING EXPERIENCE Referee for The Journal of Geometric Analysis (x3); Proceedings of the Royal Society of Edinburgh A; Revista Matemática Iberoamericana; Publicacions Mathemàtiques; Journal of Geometry and Physics; Differential Geometry and its Applications (x4); Archiv der Mathematik; Houston Journal of Mathematics (x4); Mathematical Physics, Analysis and Geometry; Mediterranean Journal of Mathematics (x2); Journal of Geometry; Publicationes Mathematicae Debrecen; Tsukuba Journal of Mathematics; Bulletin of the Korean Mathematical Society (x2); Extracta Mathematicae; Bulletin of the Malaysian Mathematical Sciences Society. Reviewer for Mathematical Reviews of the American Mathematical Society (x21). Member of the PhD thesis committee of Benigno Alves. Advisors: M. M. Alexandrino and M. Á. Javaloyes. University of São Paulo, 13/11/2017. Member of the PhD thesis committee of Francisco J. Gozzi. Advisors: L. A. Florit and W. Ziller. IMPA, 1/12/2014. Co-organiser of the Seminario Vidal Abascal (Seminar of the Department of Geometry and Topology of the University of Santiago de Compostela), November 2009 October Co-organiser and editor of the proceedings of the Seminario de Iniciación á Investigación (Seminar of PhD students at the University of Santiago de Compostela), PhD Thesis of Olga Pérez Barral (co-advised jointly with J. C. Díaz-Ramos). University of Santiago de Compostela, scheduled for PhD Thesis of Víctor Sanmartín López (co-advised jointly with J. C. Díaz-Ramos). University of Santiago de Compostela, scheduled for December Master Thesis of Alberto Rodríguez Vázquez (co-advised jointly with J. C. Díaz-Ramos). University of Santiago de Compostela, scheduled for July Undergraduate research project Submanifolds in symmetric spaces by Alberto Rodríguez Vázquez. Severo Ochoa Initiation to Research Programme, ICMAT, 06/ /2017. Undergraduate research project Singular Riemannian foliations in spheres by Miguel Ángel Berbel López. Severo Ochoa Initiation to Research Programme, ICMAT, 06/ /2016. PhD Thesis of Cristina Vidal Castiñeira (co-advised jointly with J. C. Díaz-Ramos), entitled Submanifolds in complex projective and hyperbolic planes. University of Santiago de Compostela, 22/07/2016. It deserved the highest mark (Cum Laude) and the international distinction awarded by the university. Supervision of the research stays of the PhD students Cristina Vidal Castiñeira (23/02/ /05/2015) and Víctor Sanmartín López (15/09/ /12/2015) at IMPA. Master Thesis of Cristina Vidal Castiñeira (co-advised jointly with J. C. Díaz-Ramos), entitled Hipersuperficies reais con dúas curvaturas principais nos planos proxectivo e hiperbólico complexos. University of Santiago de Compostela, 22/07/2013. It deserved the highest mark (Matrícula de Honor). Symmetry, isoparametric hypersurfaces and prime numbers. Abroad, A Coruña (Spain), 28/12/2017. VIII Galician Meeting of Young Researchers Workshop on soap bubbles, minimal surfaces and shortest paths (jointly with M. M. González, aimed at high school students). Science week at UAM, Madrid, 14/11/2017. Profile: Miguel Domínguez Vázquez (authored by E. Del Pozo). ICMAT Newsletter, no. 12, 03/2016. Equations with symmetry. 12/12/2012. Talk and article, Initiation to Research Seminar, Santiago de Compostela, Differential Geometry... what and why? Talk in the Seminar of Young Researchers, Santiago, 30/11/2011. The skeleton of a Lie group. 19/10/2011. Talk and article, Initiation to Research Seminar, Santiago de Compostela, Isoparametric hypersurfaces in spheres. Talk and article, Initiation to Research Seminar, Santiago de Compostela, 28/04/2010. Poincaré s hyperbolic world. 22/04/2009. Talk and article, Initiation to Research Seminar, Santiago de Compostela, Algebraic structures. Degree in Mathematics (3rd semester), Universidad Autónoma de Madrid, 60 hours, 2017/2018. Students satisfaction: 4.72 out of 5. Page 5 of 6
6 Mathematics I. Degree in Chemical Engineering (1st semester), Universidad Autónoma de Madrid, 60 hours, 2017/2018. Students satisfaction: 4.53 out of 5. Submanifolds and isometric actions in symmetric spaces of noncompact type. Postgraduate Mathematics course, Universidade de São Paulo, 6 hours, Algebraic structures. Degree in Mathematics (3rd semester), Universidad Autónoma de Madrid, 60 hours, 2016/2017. Students satisfaction: 4.64 out of 5. Introduction to isoparametric foliations. Postgraduate Mathematics course, Universidade de São Paulo, 10 hours, Riemannian Geometry. Doctorate course, IMPA, 48 hours, Students satisfaction: 4.9 out of 5. Member of the teaching innovation group in Algebra and Geometry GrID-A/XD. Universidade de Santiago de Compostela. Coordinator: María Elena Vázquez Abal. Mathematics and Statistics. Degree in Pharmacy (2nd semester), Universidade de Santiago de Compostela, 60 hours, 2012/2013. Topology of Euclidean spaces. Degree in Mathematics (2nd semester), Universidade de Santiago de Compostela, 60 hours, 2011/2012. Certificate of Pedagogical Aptitude. Universidade de Santiago de Compostela, HABILITATIONS Acreditación para Profesor Contratado Doctor, ANECA (Spain), 20/04/2016. LANGUAGES Native speaker of Spanish and Galician. Fluent in English (Certificate in Advanced English) and Portuguese. Reading skills in French and German (Zertifikat Deutsch). Page 6 of 6
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