Simetría e forma
Segundo Felix Klein, a xeometría é o estudo daquelas propiedades dun espazo que son invariantes pola acción dun grupo de transformacións. En Xeometría de Riemann o grupo de transformacións do espacio chámase o grupo de isometrías, aínda que o espacio pode ás veces ter propiedades adicionais que xorden de requisitos físicos ou matemáticos que tamén teñen que ser preservados polo grupo de transformacións. Este é o caso das subvariedades nas que xeometría é influenciada pola estructura do espacio ambiente.
Intuitivamente, a simetría é a correspondencia da forma en cada punto do espacio. Un problema importante en xeometría e en varias ciencias físicas é o de determinar as simetrías dun espacio en termos da súa forma. As subvariedades que son invariantes baixo as isometrías do espacio ambiente chámanse extrinsecamente homoxéneas, ou soamente homoxéneas cando non hai posibilidade de confusión. A idea principal do meu proxecto de investigación é a de clasificar subvariedades homoxéneas dunha variedade de Riemann dada, estudia-las súas propiedades xeométricas, e determinar se a súa forma é característica delas.
Financiamento
Esta liña de investigación foi financiada polos seguintes proxectos e bolsas:
- Simetría, curvatura y ecuaciones geométricas, Ministerio de Economía y Competitividad PID2019-105138GB-C21 (62920 euros), 1 de xuño de 2020 - 31 de maio de 2023. Investigador principal: José Carlos Díaz Ramos, Eduardo García Río.
- Simetría, curvatura y ecuaciones diferenciales en geometría, Ministerio de Economía y Competitividad MTM2016-75897-P (72963 euros), 30 de decembro de 2016 - 29 de decembro de 2019. Investigador principal: José Carlos Díaz Ramos, Eduardo García Río.
- Homoxeneidade e curvatura de variedades e subvariedades, Xunta de Galicia ED431F 2017/03 (40000 euros), 1 de xaneiro de 2017 - 30 de novembro de 2018. Investigador principal: José Carlos Díaz Ramos.
- Simetría, homoxeneidade e curvatura, Xunta de Galicia EM2014/009 (93000 euros), 14 de maio de 2014 - 14 de maio de 2017. Investigador principal: José Carlos Díaz Ramos.
- Simetría, curvatura y rigidez de estructuras geométricas, Ministerio de Economía y Competitividad MTM2013-41335-P (47700 euros), 1 de xaneiro de 2014 - 31 de decembro de 2016. Investigador principal: José Carlos Díaz Ramos, Eduardo García Río.
- Isometric actions, Unión Europea PERG04-GA-2008-239162 (45000 euros), 1 de abril de 2009 - 31 de marzo de 2012. Investigador principal: José Carlos Díaz Ramos.
- Symmetry and shape, Unión Europea MEIF-CT-2006-038754 (147640,42 euros), 1 de marzo de 2007 - 28 de decembro de 2008. Investigador principal: Jürgen Berndt.
Dirección de traballos de investigación
Fun director de tese dos seguintes alumnos de doctoramento:
- Olga Pérez Barral: Ruled hypersurfaces and homogeneous submanifolds in semi-Riemannian manifolds, tese doutoral, Universidade de Santiago de Compostela, .
- Víctor Sanmartín López: Homogeneous submanifolds and isoparametric hypersurfaces in symmetric spaces of noncompact type, tese doutoral, Universidade de Santiago de Compostela, .
- Cristina Vidal Castiñeira: Submanifolds in complex projective and hyperbolic planes, tese doutoral, Universidade de Santiago de Compostela, .
- Mohammad Javad Vanaei: Cohomogeneity one Lorentzian Manifolds of Constant Curvature, tese doutoral, Tarbiat Modares University, .
- Miguel Domínguez Vázquez: Isoparametric foliations and polar actions on complex space forms, tese doutoral, Universidade de Santiago de Compostela, .
Tamén fun o director dos seguintes traballos:
- Juan Manuel Lorenzo Naveiro: Foliaciones polares homogéneas en espacios simétricos, traballo de fin de máster, Universidade de Santiago de Compostela, .
- Alberto Rodríguez Vázquez: Hipersuperficies con curvaturas principais constantes en variedades Kähler con curvatura seccional holomorfa constante, traballo de fin de máster, Universidade de Santiago de Compostela, .
- Olga Pérez Barral: Acciones isométricas en el espacio-tiempo de Minkowski, traballo de fin de máster, Universidade de Santiago de Compostela, .
- Víctor Sanmartín López: Hipersuperficies isoparamétricas en el espacio hiperbólico complejo, traballo de fin de máster, Universidade de Santiago de Compostela, .
- Cristina Vidal Castiñeira: Hipersuperficies reais con dúas curvaturas principais nos planos proxectivo e hiperbólico complexos, traballo de fin de máster, Universidade de Santiago de Compostela, .
- Miguel Domínguez Vázquez: Hipersuperficies con curvaturas principais constantes nos espazos proxectivo e hiperbólico complexos, DEA, Universidade de Santiago de Compostela, .
Publicacións
A continuación preséntase unha lista de publicacións relacionada con esta liña de investigación. Para a miña lista completa de publicacións (xunto cos pdf dalgúns dos meus artigos) prema aquí.
Artículos de investigación
- J. C. Díaz-Ramos, M. Domínguez-Vázquez, T. Otero-Casal: Cohomogeneity one actions on symmetric spaces of noncompact type and higher rank, arXiv:2202.05138 [math.DG].
- J. C. Díaz-Ramos, M. Domínguez-Vázquez, T. Hashinaga: Homogeneous Lagrangian foliations on complex space forms, arXiv:2010.11877 [math.DG].
- J. C. Díaz-Ramos, M. Domínguez-Vázquez, O. Pérez-Barral: Homogeneous CR submanifolds of complex hyperbolic spaces, a aparecer en Publ. Mat.
- M. Domínguez-Vázquez, V. Sanmartín López: Isoparametric hypersurfaces in symmetric spaces of non-compact type and higher rank, arXiv:2109.03850.
- J. Berndt, V. Sanmartín-López: Submanifolds with constant principal curvatures in Riemannian symmetric spaces, a aparecer en Comm. Anal. Geom.
- J. M. Lorenzo-Naveiro, I. Solonenko: Sections of polar actions, arXiv:2111.05280 [math.DG].
- J. C. Díaz-Ramos, M. Domínguez-Vázquez, A. Rodríguez-Vázquez: Homogeneous and inhomogeneous isoparametric hypersurfaces in rank one symmetric spaces, J. Reine Angew. Math. 779 (2021), 189-222.
- M. Domínguez-Vázquez, O. Pérez-Barral: Existence and uniqueness of inhomogeneous ruled hypersurfaces with shape operator of constant norm in the complex hyperbolic space, Internat. J. Math. 32 (2021), 2150049, 4 pp.
- M. Domínguez-Vázquez, V. Sanmartín López: Codimension one Ricci soliton subgroups of solvable Iwasawa groups, J. Math. Pures Appl. 152 (2021), 69-93.
- M. Domínguez-Vázquez, J. M. Manzano: Isoparametric surfaces in E(κ, τ)-spaces, Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) 22 (2021), 269-285.
- J. C. Díaz-Ramos, M. Domínguez-Vázquez, A. Kollross: On homogeneous manifolds whose isotropy actions are polar, Manuscripta Math. 161 (2020), 15-34.
- O. Pérez-Barral: Some problems on ruled real hypersurfaces in non flat complex space forms, Results Math., 75, 167 (2020).
- M. Domínguez-Vázquez, O. Pérez-Barral: Ruled hypersurfaces with constant mean curvature in complex space forms, J. Geom. Phys. 144 (2019), 121-125.
- A. Rodríguez-Vázquez: A nonisoparametric hypersurface with constant principal curvatures, Proc. Amer. Math. Soc. 147 (2019), 5417-5420.
- J. C. Díaz-Ramos, M. Domínguez-Vázquez, C. Vidal-Castiñeira: Strongly 2-Hopf hypersurfaces in complex projective and hyperbolic planes, Ann. Mat. Pura Appl. 197 (2018), 469-486.
- J. C. Díaz-Ramos, M. Domínguez-Vázquez, C. Vidal-Castiñeira: Isoparametric submanifolds in two-dimensional complex space forms, Ann. Global Anal. Geom. 53 (2018), 205-216.
- M. Domínguez-Vázquez, C. Gorodski: Polar foliations on quaternionic projective spaces, Tohoku Math. J. 70 (2018), 353-375.
- J. C. Díaz-Ramos, M. Domínguez-Vázquez, V. Sanmartín-López: Isoparametric hypersurfaces in complex hyperbolic spaces, Adv. Math. 314 (2017), 756-805.
- J. C. Díaz-Ramos, M. Domínguez-Vázquez, A. Kollross: Polar actions on complex hyperbolic spaces, Math. Z. 287 (2017), 1183-1213.
- 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), 442-465.
- J. Berndt, J. C. Díaz-Ramos, M. Vanaei: Cohomogeneity one actions on Minkowski spaces, Monatsh. Math. 184 (2017), 185-200.
- J. C. Díaz-Ramos, S. M. B. Kashani, M. Vanaei: Cohomogeneity one actions on anti de Sitter spacetimes, Results Math. 72 (2017), 515-536.
- V. Sanmartín-López: Spacelike isoparametric hypersurfaces, Differential Geom. Appl., 54, Part A (2017), 53-58.
- M. Domínguez-Vázquez: Isoparametric foliations on complex projective spaces, Trans. Amer. Math. Soc. 368 (2016), 1211-1249.
- J. C. Díaz-Ramos, C. Vidal-Castiñeira: Examples of real hypersurfaces with two principal curvatures in complex projective planes, Int. J. Geom. Meth. Mod. Physics 12 (2015), 1560013 (6 pages).
- M. Domínguez-Vázquez: Canonical extension of submanifolds and foliations in noncompact symmetric spaces, Int. Math. Res. Not. (IMRN) 22 (2015), 12114-12125.
- J. Berndt, M. Domínguez-Vázquez: Cohomogeneity one actions on some noncompact symmetric spaces of rank two, Transform. Groups 20 (2015), 921-938.
- J. C. Díaz-Ramos, M. Domínguez-Vázquez: Isoparametric hypersurfaces in Damek-Ricci spaces, Adv. Math. 239 (2013), 1-17.
- J. Berndt, J. C. Díaz-Ramos: Polar actions on the complex hyperbolic plane, Ann. Global Anal. Geom. 43 (2013), 99-106.
- J. Berndt, J. C. Díaz-Ramos: Homogeneous polar foliations of complex hyperbolic spaces, Comm. Anal. Geom. 20 (2012), 435-454.
- J. C. Díaz-Ramos, M. Domínguez-Vázquez: Inhomogeneous isoparametric hypersurfaces in complex hyperbolic spaces, Math. Z. 271 (2012), 1037-1042.
- 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), 859-882.
- J. C. Díaz-Ramos, A. Kollross: Polar actions with a fixed point, Differential Geom. Appl. 29 (2011), 20-25.
- M. Domínguez-Vázquez: Real hypersurfaces with constant principal curvatures in complex space forms, Differential Geom. Appl. 29 (2011), 65-70.
- J. Berndt, J. C. Díaz-Ramos, H. Tamaru: Hyperpolar homogeneous foliations on symmetric spaces of noncompact type, J. Differential Geom. 86 (2010), 191-235.
- J. Berndt, J. C. Díaz-Ramos: Homogeneous hypersurfaces in complex hyperbolic spaces, Geom. Dedicata 138 (2009), 129-150.
- J. Berndt, J. C. Díaz-Ramos: Real hypersurfaces with constant principal curvatures in the complex hyperbolic plane, Proc. Amer. Math. Soc. 135 (2007), 3349-3357.
- J. Berndt, J. C. Díaz-Ramos: Real hypersurfaces with constant principal curvatures in complex hyperbolic spaces, J. London Math. Soc. 74 (2006), 778-798.
Actas de congresos
- J. C. Díaz-Ramos, M. Domínguez-Vázquez, V. Sanmartín-López: Submanifold geometry in symmetric spaces of noncompact type, Sao Paulo J. Math. Sci., (Special Section: An Homage to Manfredo P. do Carmo), 2021, 75-110.
- J. C. Díaz-Ramos, M. Domínguez-Vázquez, V. Sanmartín-López: Anti-De Sitter spacetimes and isoparametric hypersurfaces in complex hyperbolic spaces, Lorentzian Geometry and Related Topics, Springer Proceedings in Mathematics & Statistics 211, GeLoMa 2016, Málaga, Spain, September 20-23, Springer, 2017, 87-101.
- J. C. Díaz-Ramos: Polar Actions on Symmetric Spaces, Recent Trends in Lorentzian Geometry, Springer Proceedings in Mathematics & Statistics, Springer, 2013, 315-334.
- 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, 2013, 114-125.
- M. Domínguez-Vázquez: Some interesting families of non-Hopf real hypersurfaces in complex space forms, Proceedings of The Seventeenth International Workshop on Differential Geometry and related fields 17, 2013, 113-124.
- M. Domínguez-Vázquez: On isoparametric hypersurfaces in complex hyperbolic spaces, International Meeting on Differential Geometry (Córdoba 2010), Universidad de Córdoba, 2013, 71-92.
- J. C. Díaz-Ramos: Polar actions on complex space forms, Proceedings of The Sixteenth International Workshop on Differential Geometry and related fields 16, 2012, 69-88.
- 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 Conference Proceedings 1460, Amer. Inst. Phys., 2012, 169-173.
- J. C. Díaz-Ramos: The orbits of cohomogeneity one actions on complex hyperbolic spaces, Proceedings of the VIII International Colloquium on Differential Geometry, World Sci. Publ. Co., 2009, 146-155.
Conferencias
Esta é unha lista de conferencias e charlas relacionadas con esta liña de investigación. Para unha lista completa das miñas charlas prema aquí.
Comunicacións en congresos
- J. C. Díaz-Ramos: Homogeneous Lagrangian foliations in complex spaces forms, Workshop on Manifolds with Symmetries, Stuttgart, Alemania, 28-30 de marzo de 2022.
- M. Domínguez-Vázquez: Extension of submanifolds in symmetric spaces of noncompact type, Workshop on Manifolds with Symmetries, Stuttgart, Alemania, 28-30 de marzo de 2022.
- V. Sanmartín López: Codimension one Ricci solitons in Iwasawa groups, Workshop on Manifolds with Symmetries, Stuttgart, Alemania, 28-30 de marzo de 2022.
- A. Rodríguez-Vázquez: Totally geodesic submanifolds in products of rank one symmetric spaces, Workshop on Manifolds with Symmetries, Stuttgart, Alemania, 28-30 de marzo de 2022.
- T. Otero-Casal: Homogeneous hypersurfaces of symmetric spaces of noncompact type, Workshop on Manifolds with Symmetries, Stuttgart, Alemania, 28-30 de marzo de 2022.
- J. M. Lorenzo-Naveiro: Polar actions on some noncompact symmetric spaces, Workshop on Manifolds with Symmetries, Stuttgart, Alemania, 28-30 de marzo de 2022.
- J. C. Díaz-Ramos: Cohomogeneity one actions on rank one symmetric spaces of noncompact type, Geometry of symmetric spaces and group actions, online, Xapón, 17-19 de febreiro de 2022.
- M. Domínguez-Vázquez: Cohomogeneity one actions on symmetric spaces of noncompact type and higher rank, Geometry of symmetric spaces and group actions, online, Xapón, 17-19 de febreiro de 2022.
- A. Rodríguez-Vázquez: Totally geodesic submanifolds and Kähler angle in symmetric spaces, Symmetry and Shape, Santiago de Compostela, España, 15-18 de outubro de 2021.
- T. Otero-Casal: Cohomogeneity one actions on irreducible and reducible symmetric spaces of noncompact type, Symmetry and Shape, Santiago de Compostela, España, 15-18 de outubro de 2021.
- J. M. Lorenzo-Naveiro: Polar homogeneous foliations on SL(3,R)/SO(3), Symmetry and Shape, Santiago de Compostela, España, 15-18 de outubro de 2021.
- A. Rodríguez-Vázquez: Symmetric spaces: holonomy and totally geodesic submanifolds, PG Forum, Lancaster, Reino Unido, .
- M. Domínguez-Vázquez: Cohomogeneity one actions and inhomogeneous isoparametric hypersurfaces in quaternionic hyperbolic spaces, Differential Geometry Seminar, online, Alemania, .
- O. Pérez-Barral: Subvariedades CR homogéneas en el espacio hiperbólico complejo, Congreso de Jóvenes Investigadores RSME, Castelló, España, 27-31 de xaneiro de 2020.
- A. Rodríguez-Vázquez: Isoparametricidad e isospectralidad del operador forma, Congreso de Jóvenes Investigadores RSME, Castelló, España, 27-31 de xaneiro de 2020.
- A. Rodríguez-Vázquez: Homogeneous and inhomogeneous isoparametric hypersurfaces in quaternionic hyperbolic spaces, Workshop on Geometric Analysis IEMATH-GR, Granada, España, .
- J. C. Díaz-Ramos: Homogeneous submanifolds in complex space forms, Symmetry and shape, Celebrating the 60th birthday of Prof. J. Berndt, Santiago de Compostela, España, 28-31 de outubro de 2019.
- O. Pérez-Barral: Homogeneous CR submanifolds in complex hyperbolic spaces, Symmetry and shape: Celebrating the 60th birthday of Prof. J. Berndt, Santiago de Compostela, España, 28-31 de outubro de 2019.
- M. Domínguez-Vázquez: Cohomogeneity one isometric actions on quaternionic hyperbolic spaces, Encuentro de Topología 2019, Santiago de Compostela, España, 18-19 de outubro de 2019.
- A. Rodríguez-Vázquez: A non isoparametric hypersurface with constant principal curvatures, Differential Geometry and its Applications, Hradrec Králové, República Checa, 1-7 de setembro de 2019.
- M. Domínguez-Vázquez: Homogeneous and inhomogeneous isoparametric hypersurfaces in symmetric spaces of noncompact type, Workshop on the Isoparametric Theory, Beijing , China, 2-6 de xuño de 2019.
- M. Domínguez-Vázquez: Isoparametric surfaces in E(κ, τ)-spaces, Encuentro de la Red Española de Análisis Geométrico, Murcia, España, .
- J. C. Díaz-Ramos: Cohomogeneity one actions on Minkowski spaces, II joint meeting Brazil-Spain in Mathematics, Cádiz, España, 11-14 de decembro de 2018.
- M. Domínguez-Vázquez: Nonlinear overdetermined boundary problems in Riemannian manifolds, II joint meeting Brazil-Spain in Mathematics, Cádiz, España, 11-14 de decembro de 2018.
- M. Domínguez-Vázquez: Subvariedades e accións isométricas en espazos simétricos de tipo non compacto, Seminario Vidal Abascal, Santiago de Compostela, España, 29-31 de outubro de 2018.
- M. Domínguez-Vázquez: Isoparametric surfaces in homogeneous 3-spaces, Preliminary talks of the ICM Satellite Conference Modern Trends in Differential Geometry, São Paulo, Brasil, .
- M. Domínguez-Vázquez: Cohomogeneity one actions on symmetric spaces of noncompact type, Seminar, Rio de Janeiro, Brasil, .
- O. Pérez-Barral: Ruled hypersurfaces with constant mean curvature in complex space forms are minimal, First BYMAT Conference: Bringing Young Mathematicians Together, Madrid, España, 7-9 de maio de 2018.
- V. Sanmartín-López: Isospectral submanifolds in non-compact symmetric spaces, Hiroshima Differential Geometry Day 2018, Hiroshima, Xapón, .
- V. Sanmartín-López: Homogeneous and isoparametric hypersurfaces in complex hyperbolic spaces, Geometry of Submanifolds and Integrable Systems, Osaka, Xapón, 26-30 de marzo de 2018.
- M. Domínguez-Vázquez: Isoparametric hypersurfaces in the complex hyperbolic space, Primer Encuentro Conjunto RSME-UMA, Buenos Aires, Arxentina, 11-15 de decembro de 2017.
- J. C. Díaz-Ramos: Homogeneous submanifolds of complex space forms, The third Japanese-Spanish workshop on Differential Geometry, Madrid, España, 18-22 de setembro de 2017.
- M. Domínguez-Vázquez: Isoparametric hypersurfaces in complex hyperbolic spaces, IV Encuentro Conjunto RSME-SMM, Valladolid, España, 19-22 de xuño de 2017.
- V. Sanmartín-López: Description and classification of isoparametric submanifolds in the complex hyperbolic space, Differential Geometry, Bedlewo, Polonia, 18-24 de xuño de 2017.
- M. Domínguez-Vázquez: Submanifolds and isometricactions on symmetric spaces of noncompact type, Seminar, São Paulo, Brasil, 27 de marzo - 9 de abril de 2017.
- J. C. Díaz-Ramos: Cohomogeneity one actions on Minkowski spaces, 8th International Meeting on Lorentzian Geometry, Málaga, Spain, 20-23 de setembro de 2016.
- M. Domínguez-Vázquez: Isoparametric submanifolds of complex space forms, XXV International Fall Workshop on Geometry and Physics, Madrid, España, 29 de agosto - 2 de setembro de 2016.
- V. Sanmartín-López: Anti-De Sitter and complex hyperbolic spaces: their isoparametric hypersurfaces, Differential Geometry and its Applications, Brno, República Checa, 11-15 de xullo de 2016.
- J. C. Díaz-Ramos: Isoparametric hypersurfaces in complex hyperbolic spaces, Second joint Conference of the Belgian, Royal Spanish and Luxembourg Mathematical Societies, Logroño, España, 6-8 de xuño de 2016.
- J. C. Díaz-Ramos: Non-proper cohomogeneity one actions on Minkowski spaces, First joint meeting Brazil-Spain in Mathematics, Fortaleza, Brasil, 7-10 de decembro de 2015.
- M. Domínguez-Vázquez: Classification of isoparametric hypersurfaces in complex hyperbolic spaces, First joint meeting Brazil-Spain in Mathematics, Fortaleza, Brasil, 7-10 de decembro de 2015.
- C. Vidal-Castiñeira: Hipersuperficies de cohomogeneidad uno en los planos proyectivo e hiperbólico complejos, Congreso de Jóvenes Investigadores, Murcia, España, 7-11 de setembro de 2015.
- V. Sanmartín López: Clasificación de hipersuperficies isoparamétricas en el espacio hiperbólico complejo, Congreso de Jóvenes Investigadores, Murcia, España, 7-11 de setembro de 2015.
- C. Vidal-Castiñeira: Cohomegeneity one hypersurfaces in the complex projective and hyperbolic planes, XXIV International Fall Workshop on Geometry and Physics, Zaragoza, España, 1-4 de setembro de 2015.
- V. Sanmartín-López: Hipersuperficies isoparamétricas en el espacio hiperbólico complejo, XI Encuentro Andaluz de Geometría, Sevilla, España, .
- J. C. Díaz-Ramos: Polar actions on symmetric spaces, Congreso da RSME 2015, Granada, España, 2-6 de febreiro de 2015.
- M. Domínguez-Vázquez: Two construction methods of isoparametric hypersurfaces in noncompact symmetric spaces, Congreso da RSME 2015, Granada, España, 2-6 de febreiro de 2015.
- C. Vidal Castiñeira: Hipersuperficies con dos curvaturas principales en CP^2 y CH^2, Congreso da RSME 2015, Granada, España, 2-6 de febreiro de 2015.
- M. Domínguez-Vázquez: Classification of isoparametric foliations on complex projective spaces, Geometry and Dynamics of Foliations, Madrid, España, 1 de setembro - 5 de agosto de 2014.
- C. Vidal-Castiñeira: Real hypersurfaces with two constant principal curvatures in the complex projective and hyperbolic planes, XXIII International Fall Workshop on Geometry and Physics, Granada, España, 1-6 de setembro de 2014.
- M. Domínguez-Vázquez: Polar actions on complex hyperbolic spaces II, XVIII Escola de Geometria Diferencial, Brasilia, Brasil, 28 de xullo - 1 de agosto de 2014.
- J. C. Díaz-Ramos: Real hypersurfaces in complex space forms, The second Japanese-Spanish workshop on Differential Geometry, Tokyo, Xapón, 5-10 de febreiro de 2014.
- M. Domínguez-Vázquez: Isoparametric submanifolds of complex projective spaces, The second Japanese-Spanish workshop on Differential Geometry, Tokyo, Xapón, 5-10 de febreiro de 2014.
- M. Domínguez-Vázquez: Some interesting families of non-Hopf real hypersurfaces in complex space forms, 17th International Workshop on Differential Geometry, Daejeon, Corea do Sur, 30 de setembro - 2 de outubro de 2013.
- M. Domínguez-Vázquez: Familias isoparamétricas en espacios de Damek-Ricci, Congreso de Jóvenes Investigadores de la RSME, Sevilla, España, 16-20 de setembro de 2013.
- M. Domínguez-Vázquez: The horospherical decomposition and new isoparametric hypersurfaces in noncompact symmetric spaces, Geometric Analysis Seminar GAS-UV13, Valencia, España, 4-7 de setembro de 2013.
- J. C. Díaz-Ramos: Polar actions on complex space forms II, The 16th International Workshop on Differential Geometry & Related Topics, Daegu, Corea do Sur, 1-3 de novembro de 2012.
- J. C. Díaz-Ramos: Polar actions on complex space forms I, Pre-joint Meeting of The 16th International Workshop on Differential Geometry, Daegu, Corea do Sur, .
- M. Domínguez-Vázquez: Polar foliations for beginners, Geometry Meeting 2012, Ferrol, España, .
- M. Domínguez-Vázquez: On the existence of inhomogeneous isoparametric foliations of higher codimension on complex projective spaces, Conference on Pure and Applied Differential Geometry PADGE 2012, Leuven, Bélxica, 27-30 de agosto de 2012.
- J. C. Díaz-Ramos: Polar actions on complex hyperbolic spaces, Differential Geometry Days, Santiago de Compostela, España, 27-29 de xuño de 2012.
- M. Domínguez-Vázquez: Isoparametric foliations on complex projective spaces, Differential Geometry Days, Santiago de Compostela, España, 27-29 de xuño de 2012.
- J. C. Díaz-Ramos: Polar actions on noncompact symmetric spaces, 2nd European Young and Mobile Workshop, Geometric Analysis and Partial Differential Equations, Granada, España, 28-30 de novembro de 2011.
- J. C. Díaz-Ramos: Polar actions on symmetric spaces of noncompact type, VI International Meeting on Lorentzian Geometry, Granada, España, 6-9 de setembro de 2011.
- M. Domínguez-Vázquez: Families of parallel CMC hypersurfaces in noncompact rank-one symmetric spaces, VI International Meeting on Lorentzian Geometry, Granada, España, 6-9 de setembro de 2011.
- M. Domínguez-Vázquez: Principal curvatures of isoparametric hypersurfaces in complex hyperbolic spaces, Conference in Geometry and Global Analysis, Santiago de Compostela, España, 13-17 de decembro de 2010.
- M. Domínguez-Vázquez: On isoparametric hypersurfaces in complex hyperbolic spaces, International Meeting on Differential Geometry, Córdoba, España, 15-17 de novembro de 2010.
- M. Domínguez-Vázquez: O problema da clasificación das hipersuperficies isoparamétricas, Encontro de Xeometría 2010, Ferrol, España, .
- M. Domínguez-Vázquez: Real hypersurfaces with constant principal curvatures in complex space forms, DGA 2010 - Differential Geometry and its Applications, Brno, República Checa, 27-31 de agosto de 2010.
- J. C. Díaz-Ramos: Homogeneous hyperpolar foliations on symmetric spaces of noncompact type, Workshop on Hypersurface Geometry and Integrable Systems, Sendai, Xapón, 24-27 de agosto de 2010.
- M. Domínguez-Vázquez: Real hypersurfaces with constant principal curvatures in complex projective and hyperbolic spaces, Workshop on Hypersurface Geometry and Integrable Systems, Sendai, Xapón, 24-27 de agosto de 2010.
- J. C. Díaz-Ramos: Acciones hiperpolares en espacios simétricos no compactos, Geometry Meeting 2009, Ferrol, España, 29-30 de outubro de 2009.
- J. C. Díaz-Ramos: Hyperpolar actions on noncompact symmetric spaces, II Congreso latinoamericano de grupos de Lie en geometría, La Falda, Arxentina, 25-29 de setembro de 2008.
- J. C. Díaz-Ramos: Hypersurfaces with constant principal curvatures in the complex hyperbolic space, VIII International Colloquium on Differential Geometry, Santiago de Compostela, España, 7-11 de xullo de 2008.
- J. C. Díaz-Ramos: A characterisation of real hypersurfaces with constant principal curvatures, Differential Geometry, Bedlewo, Polonia, 22-28 de xuño de 2008.
- J. C. Díaz-Ramos: Homogeneous hypersurfaces in the complex hyperbolic space, Irish Geometry Conference, Galway, Irlanda, 24-25 de maio de 2007.
- A. Rodríguez-Vázquez: Homogeneous and inhomogeneous isoparametric hypersurfaces in symmetric spaces, Junior Geometry Seminar KCL/UCL, Londres, Reino Unido, .
Charlas invitadas de seminario
- J. C. Díaz-Ramos: Cohomogeneity one actions on quaternionic hyperbolic spaces, Symmetric spaces seminar, online, Reino Unido, .
- M. Domínguez-Vázquez: On isoparametric hypersurfaces in noncompact symmetric spaces, Seminar, Norman, Estados Unidos, .
- M. Domínguez-Vázquez: Overdetermined elliptic problems in Riemannian manifolds, Seminar, South Bend, Estados Unidos, .
- M. Domínguez-Vázquez: Isoparametric surfaces in homogeneous 3-manifolds, Seminar, St. Louis, Estados Unidos, .
- M. Domínguez-Vázquez: Polar foliations on symmetric spaces, Colloquium, St. Louis, Estados Unidos, .
- M. Domínguez-Vázquez: Isoparametric surfaces in homogeneous spaces, Seminario Vidal Abascal, Santiago de Compostela, España, .
- V. Sanmartín-López: Description of isoparametric hypersurfaces in the complex hyperbolic space, Seminario de Geometría, Madrid, España, .
- V. Sanmartín-López: On the classification of isoparametric hypersurfaces, Geometry Seminar, Colonia, Alemania, .
- J. C. Díaz-Ramos: Isoparametric hypersurfaces in complex space forms, Department of Mathematics Seminar, Stuttgart, Alemania, .
- V. Sanmartín-López: Isoparametric hypersurfaces in the anti-De Sitter space and the complex hyperbolic space, Geometry Seminar, Londres, Reino Unido, .
- M. Domínguez-Vázquez: Isoparametric hypersurfaces in overdetermined PDE problems, Seminario Vidal Abascal, Santiago de Compostela, España, .
- M. Domínguez-Vázquez: Clasificación das foliacións polares no espazo proxectivo cuaterniónico, Seminario Vidal Abascal, Santiago de Compostela, España, .
- J. C. Díaz-Ramos: On the classification of polar actions on complex hyperbolic spaces, Workshop on submanifolds in complex space forms, Londres, Reino Unido, .
- C. Vidal Castiñeira: Strongly 2-Hopf hypersurfaces in complex projective and hyperbolic planes, Workshop on submanifolds in complex space forms, Londres, Reino Unido, .
- V. Sanmartín-López: On the classification of isoparametric hypersurfaces in complex hyperbolic spaces, Workshop on submanifolds in complex space forms, Londres, Reino Unido, .
- M. Domínguez-Vázquez: Isoparametric families of hypersurfaces in complex hyperbolic spaces, Geometry Seminar, São Paulo, Brasil, .
- J. C. Díaz-Ramos: Cohomogeneity one actions on the Minkowski space, Seminario, Rio de Janeiro, Brasil, .
- J. C. Díaz-Ramos: Foliaciones polares e isoparamétricas, Seminario del Departamento de Matemáticas, Bilbao, España, .
- M. Domínguez-Vázquez: Polar foliations on complex projective space, Seminar, Rio de Janeiro, Brasil, .
- M. Domínguez-Vázquez: Introduction to isoparametric foliations, Seminar, Sao Paulo, Brasil, 23-30 de xuño de 2014.
- M. Domínguez-Vázquez: Inhomogeneous isoparametric foliations and prime numbers, Seminar, Sao Paulo, Brasil, .
- M. Domínguez-Vázquez: Homogeneity of isoparametric submanifolds and prime numbers, Seminar, Brasilia, Brasil, .
- M. Domínguez-Vázquez: Hypersurfaces with two principal curvatures in nonflat complex space forms, Department of Mathematics Seminar, IMPA, Rio de Janeiro, Brasil, .
- M. Domínguez-Vázquez: A geometric characterization via prime numbers, Department of Mathematics Seminar, Universidade Federal Fluminense, Rio de Janeiro, Brasil, .
- M. Domínguez-Vázquez: Inhomogeneous isoparametric foliations, Department of Mathematics Seminar, Londres, Reino Unido, .
- M. Domínguez-Vázquez: The classification problem of isoparametric foliations, ICMAT Seminar, Madrid, España, .
- M. Domínguez-Vázquez: Inhomogeneous isoparametric families on complex projective spaces, Department of Mathematics Seminar, Stuttgart, Alemania, .
- J. C. Díaz-Ramos: A classification of polar actions on complex hyperbolic spaces, Department of Mathematics Seminar, Colonia, Alemania, .
- J. C. Díaz-Ramos: Isoparametric hypersurfaces in complex space forms, Department of Mathematics Seminar, Darmstadt, Alemania, .
- J. C. Díaz-Ramos: Foliaciones polares homogéneas en espacios hiperbólicos complejos, Xornada de Xeometría (Seminario Vidal Abascal), Santiago de Compostela, España, .
- M. Domínguez-Vázquez: Homogeneous and isoparametric hypersurfaces in non-compact rank-one symmetric spaces, Department of Mathematics Seminar, Colonia, Alemania, .
- J. C. Díaz-Ramos: Non-Hopf real hypersurfaces with constant principal curvatures in complex space forms, Department of Mathematics Seminar, Colonia, Alemania, .
- J. C. Díaz-Ramos: Homogeneous hyperpolar foliations on symmetric spaces of noncompact type, Department of Mathematics Seminar, Colonia, Alemania, .
- J. C. Díaz-Ramos: Hyperpolar homogeneous foliations on noncompact symmetric spaces, Department of Mathematics Seminar, Augsburg, Alemania, .
- J. C. Díaz-Ramos: Hypersurfaces with constant principal curvatures in the complex hyperbolic space, Hiroshima University Topology-Geometry Seminar, Hiroshima, Japón, .
- J. C. Díaz-Ramos: Hipersuperficies homoxéneas no espazo hiperbólico real, Seminario de Xeometría e Topoloxía, Santiago de Compostela, España, .
Pósters
- A. Rodríguez-Vázquez: Non-Hopf hypersurfaces with constant principal curvatures in complex projective space and complex hyperbolic space, Congreso Bienal de la RSME, Santander, España, 4-8 de febreiro de 2019.
- O. Pérez-Barral: Ruled hypersurfaces with constant mean curvature in complex space forms, XXV Encuentro de Topología, Barcelona, España, 19-20 de outubro de 2018.
- A. Rodríguez-Vázquez: Hypersurfaces with constant principal curvatures in complex hyperbolic spaces, XXV Encuentro de Topología, Barcelona, España, 19-20 de outubro de 2018.
- J. C. Díaz-Ramos, M. Domínguez-Vázquez, C. Vidal-Castiñeira: Real hypersurfaces with two constant principal curvatures in complex projective and hyperbolic planes, XXIII International Fall Workshop on Geometry and Physics, Granada, España, 1-6 de setembro de 2014.
- M. Domínguez-Vázquez: Some results on isoparametric hypersurfaces in nonflat complex space forms, XX International Fall Workshop on Geometry and Physics, Madrid, España, 31 de agosto - 3 de setembro de 2011.
- J. C. Díaz-Ramos, M. Domínguez-Vázquez: Principal curvatures of isoparametric hypersurfaces in complex hyperbolic spaces II, Conference in Geometry and Global Analysis, Santiago de Compostela, España, 13-17 de decembro de 2010.
- J. C. Díaz-Ramos, M. Domínguez-Vázquez: Hypersurfaces with constant principal curvatures in complex projective and hyperbolic spaces, Lectures on Lorentzian Geometry, Granada, España, 8-11 de febreiro de 2010.