Numerical Methods and Scientific Computing, CIRM (Centre International de Rencontres Mathématiques), Luminy, France, 2021.
  Nonreversible Markovian Monte Carlo 2021, Lorentz Center, Leiden, The Netherlands, 2021.
  Haussdorf School on MCMC: Recent Developments and New Connections, Haussdorf Center, Bonn, Germany, 2020.
  International Conference on Computational Mathematics and Scientific Computing, in Memory of Feng Kang on his Centenary Birthday, Beijing, China, 2020.
  The Fifth International Conference on Numerical Analysis and Optimization, Muscate, Oman, 2020.
  Geometric Numerical Integration of Differential Equations, Beijing, China, 2019.
  HA-LU 2019, International Conference in honor of Ernst Hairer and Christian Lubich, Gran Sasso Science Institute, L\'Aquila, Italia, 2019.
  Integrating the Integrators for Nonlinear Evolution Equations: from Analysis to Numerical Methods, High-Performance-Computing and Applications, Banff International Research Station, Banff, Canada, 2018.
  Computational Statistics and Molecular Simulation, A Practical Cross-Fertilization, Casa Matematica Oaxaca/Banff International Research Station, Oaxaca, Mexico, 2018.
  Algebraic and Geometric Aspects of Numerical Methods for Differential Equations, Institute Mittag-Leffler, Djursholm, Sweden, 2018.
  Méthodes Numériques Géométriques et Multi-échelles, Henri Lebesque Center, Rennes, France, 2018.
  From computation to information: recent advances in Numerical Analysis, Cambridge, UK, 2017.
  Averaging: New techniques and new applications, Morningside Center of Mathematics of the Chinees Academy of Sciences, Beijing, China, 2016. (Six one hour lectures.)
  Stochastic Numerical Algorithms, Multiscale Modeling and High-Dimensional Data Analytics, ICERM (Institute for Computational and Experimental Research in Mathematics), Brown University, Providence, USA, 2016. (35 minute talk.)
  SDIDE2016 (Stability and Discretization Issues in Differential Equations), Trieste, Italy, 2016. (30 minute talk.)
  Second Joint Conference of the Belgian, Royal Spanish and Luxembourg Mathematical Societies, Logroño, 2016. (60 minute talk.)
  Orthonet 2016, Albarracín (Teruel), 2016. (60 minute talk.)
  Geometric Numerical Integration, Oberwolfach, Germany, 2016. (35 minute talk.)
  Discretization in Geometry and Dynamics, Herrsching am Ammersee, Alemania, 2015. (60 minute talk.)
  Multiscale Numerical Methods for Differential Equations, Rennes, Francia, 2015. (60 minute talk.)
  8th International Conference on Industrial and Applied Mathematics (ICIAM 2015), Beijing, China, 2015. (60 minute talk.)
  Workshop in Stochastic Dynamics, Beijing, China, 2015. (60 minute talk.)
  New Developments in Discrete Mechanics, Geometric Integration and Lie-Butcher Series, Madrid, Spain, 2015. (90 minute talk.)
  An International Conference on Nonlinear Dynamics Complexity, La Manga, Murcia, Spain, 2015. (50 minute talk.)
  Algorithms and Complexity in Mathematics, Epistemology and Science, London, Ontario, Canada, 2015. (60 minute talk.)
  Foundations of Computational Mathematics, Montevideo, Uruguay, 2014. (55 minute semiplenary talk.)
  Fourth International Conference on Numerical Analysis of Differential Equations, Nanjing, China, 2014. (45 minute talk.)
  Eleventh International Conference of Numerical Analysis and Applied Mathematics (ICNAAM 2013), Rodas, Grecia, 2013. (55 minute talk.)
  19th World Congress of the International Association for Mathematics and Computers in Simulation, El Escorial (Madrid), 2013. (60 minute talk.)
  Topics in Numerical Analysis of Differential Equations, TNADE 2013, Madrid, 2013. (60 minute talk.)
  Auckland Numerical Ordinary Differential Equations ANODE 2013, Auckland, Nueva Zelanda, 2013. (60 minute talk.)
  Tenth International Conference of Numerical Analysis and Applied Mathematics (ICNAAM 2012), Cos, Grecia, 2012. (55 minute talk.)
  Ai65, Conference in Numerical Analysis to celebrate Arieh Iserles\'s 65th birthday, Lom, Noruega, 2012. (45minute talk.)
  9th AIMS International Conference on Dynamical Systems, Differential Equations and Applications, Orlando, USA, 2012. (50 minute talk.)
  Multiscale systems: theory and applications, Warwick, UK, 2011. (50 minute talk.)
  Equadiff 2011, Loughborough, UK, 2011. (45 minute talk.)
  Current challenges in stability issues for numerical differential equations (CIME, Centro Internazionale Matematico Estivo), Cetraro, Italia, 2011. (Five 50 minute lectures.)
  KAM theory and Geometric Integration, Banff, Canada, 2011. (60 minute talk.)
  Geometric Numerical Integration, Oberwolfach, Germany, 2011. (35 minute talk.)
  Verwer65, Amsterdam, The Netherlands, 2011. (45 minute talk.)
  Eighth International Conference of Numerical Analysis and Applied Mathematics (ICNAAM 2010), Rodos, Greece, 2010. (60 minute talk.)
  Highly Oscillatory Problems: From Theory to Applications, Cambridge, England, 2010. (60 minute talk.)
  19th Scottish Computational Mathematics Symposium, Edinburgh, Scotland, 2010. (50 minute talk.)
  I Jaen Conference on Approximation Theory, Ubeda, 2010. (60 minute talk.)
  Emerging Topics in Dynamical Systems and Partial Differential Equations, SIAM, RSME, SCM, SEMA, Barcelona, 2010. (50 minute talk.)
  Numerical Methods for Highly-Oscillatory ODEs and PDEs, Dinard, France, 2010. (45 minute talk.)
  Numerical Analysis of Multiscale Computations, Banff International Research Station, Canada, 2009. (45 minute talk.)
  NUMDIFF-12 (Numerical treatment of differential equations.), Halle, Germany, 2009. (45 minute talk.)
  Calv(6)5 (conference to celebrate M. Calvo\'s 65th birthday), Zaragoza, 2009. (30 minute talk.)
  23rd Biennial Conference on Numerical Analysis, Glasgow, Scotland, 2009. (60-minute talk.)
  NSD09 International Conference on Non-autonomous and Stochastic Dynamical Systems and Multidisciplinary Applications, Seville, Spain, 2009. (45-minute talk.)
  Conference on Scientific Computing, Celebrating Ernst Hairer s 60th Birhtday, Geneva, Switzerland, 2009. (45-minute talk.)
  Workshop on Numerics in Dynamical Systems, Helsinki, Finland, 2009. (40-minute talk.)
  III Encuentros sobre Modelización de Sistemas Complejos, Móstoles, 2008. (60-minute inaugural talk.)
  XIII Escuela Jacques-Louis Lions Hispano-Francesa sobre Simulación en Física e Ingeniería, Valladolid, 2008. (60-minute talk.)
  Foundations of Computational Mathematics, Hong Kong, China, 2008. (Semiplenary 45-minute talk.)
  Numerical Modeling of Complex Dynamical Systems, Leiden The Netherlands, 2008. (35-minute talk.)
  Geometric Integration: where are we heading next?, Bath, England, 2007. (30-minute talk.)
  1st Internacional Summer School on Geometry, Mechanics and Control, Castro Urdiales, 2007. (7-hour course.)
  Applying Geometric Integrators, Edinburgh, Scotland, 2007. (30-minute talk.)
  The theory of highly oscillatory problems, Cambridge, England, 2007. (30-minute talk.)
  XII Escuela Jacques-Louis Lions Hispano-Francesa de Simulacion Numerica en Fisica e Ingenieria, Castro Urdiales, 2006. (Three 60-minute lectures.)
  XIX CEDYA, Leganes (Madrid), 2005. (Debate with J L Vazquez on La matematica aplicada en el sistema de investigacion español.)
  MAT ES 2005, Valencia, 2005. (60-minute opening talk.)
  Simposio Internacional: La matemática como base conceptual de la ciencia y la tecnología, Madrid, 2000. (60-minute talk.)
  International Conference on New Applications of Multisymplectic Field Theory, Salamanca, 1999. (60-minute talk.)
  1998 New Zealand Mathematics Colloquium, Wellington, New Zealand, 1998. (60-minute talk.)
  Auckland Numerical Ordinary Differential Equations, Auckland, New Zealand, 1998. (Six 60-minute lectures.)
  2nd Meeting on Numerical Methods for Differential Equations, Coimbra, Portugal, 1998. (45-minute lecture.)
  SYNODE Workshop, Oppdal, Norway, 1998. (Three 60-minute lectures.)
  XV CEDYA/V CMA, Vigo, 1997. (60-minute talk.)
  SCICADE, Grado, Italy, 1997. (50-minute talk.)
  Large time behaviour in dynamical systems: analysis and numerics, Oberwolfach, Germany, 1997. (45-minute talk.)
  17th Biennial Conference on Numerical Analysis, Dundee, Scotland, 1997. (45-minute talk.)
  Numerical Analysis of Hamiltonian Problems, NSF/CBMS Conference, Golden, Colorado, USA, 1997. (Principal lecturer, 10 60-minute talks.)
  Foundations of Computational Mathematics FOCM\'97, Rio de Janeiro, Brazil, 1997. (60-minute talk.)
  Recent Advances in Partial Differential Equations, in honour of P. D. Lax and L. Nirenberg on their 70th birthday, Venice, Italy, 1996. (60-minute talk.)
  The State of the Art in Numerical Analysis, York, England, 1996. (60-minute talk.)
  Differential-algebraic equations, related fields of theory and application, Oberwolfach, Germany, 1995. (60-minute talk.)
  16th Dundee Biennial Numerical Analysis Conference, Dundee, Scotland, 1995. (45-minute talk.)
  SCICADE, Stanford, California, USA, 1995. (45-minute talk.)
  III Granada Seminar on Computational Physics, Granada, 1994. (Five 50-minute lectures.)
  International Congress of Mathematicians, ICM 94, Zurich, Switzerland, 1994. (45-minute talk.)
  Integration Algorithms for Classical Mechanics, Fields Instute, Waterloo, Canada, 1993. (50-minute talk.)
  Geometric, Analytic and Computational Aspects of Mechanics, Oberwolfach, Germany, 1993. (45-minute talk.)
  Chaotic Numerics, Geelong, Australia, 1993. (60-minute talk.)
  14th Biennial Conference on Numerical Analysis, Dundee, Scotland, 1993. (45-minute talk.)
  Numerical Treatment of Differential Equations, NUMDIFF-6, Halle, Germany, 1992. (60 minute talk.)
  Physics Computing 82, 4th International Conference on Computational Pysics. Prague, Czech Republic, 1992. (35-minute talk.)
  London Mathematical Society Durham Research Symposium on Evolutionary Problems: Continuous and Discretized Nonlinear Systems, Durham, England, 1992. (Three 60-minute talks.)
  Fisica Estadistica 91, Gijon, 1991. (30-minute talk.)
  Equadiff 1991, Barcelona, 1991. (30-minute talk.)
  14th Biennial Conference on Numerical Analysis, Dundee, Scotland, 1991. (45-minute talk.)
  Experimental Mathematics: Computational Issues in Nonlinear Science, Los Alamos, New Mexico, USA, 1991. (50-minute talk.)
  Dutch Numerical Mathematics Conference, Zeist, The Netherlands, 1990. (Two 45-minute talks.)
  XV Jornadas Lusoespanholas de matematica, Evora, Portugal, 1990. (60-minute opening lecture.)
  Dynamics of Numerics and Numerics of Dynamics, Bristol, England, 1990. (60-minute talk.)
  SERC Summer School in Numerical Analysis, Lancaster, England, 1990. (Five 60-minute lectures.)
  Computational Ordinary Differential Equations, London, England, 1989. (50-minute talk.)
  Numerical Treatment of Differential Equations (NUMDIFF), Halle, East Germany, 1989. (45-minute talk.)
  Dynamics of Numerics and Numerics of Dynamics, Cambridge, England, 1988. (45-minute talk.)
  Third International Conference on Computational Mathematics, Benin City, Nigeria, 1998. (45-minute talk.)
  Numerical Treatment of Differential Equations (NUMDIFF), Halle, East Germany, 1987. (45-minute talk.)
  Dutch Numerical Mathematics Conference, Zeist, The Netherlands, 1986. (Two 45-minute talks.)
  SCICADE, Albuquerque, New Mexico, USA, 1986. (45 talk presented by my coauthor J. G. Verwer.)
  Colloquium Werkgemeenschap Numerieke Wiskunde, Leiden, The Netherlands, 1985. (50-minute talk.)
  Dundee Biennial Conference on Numerical Analysis, Dundee, Scotland, 1985. (50-minute talk.)
  VII Congreso de Ecuaciones Diferenciales y Aplicaciones (CEDYA), Granada, 1984. (Two 60-minute talks.)
  I Jornadas de Mecanica y Fisica Matematica, El Escorial, 1983. (60-minute talk.)

  One-World Numerical Analysis Seminar, 15 November 2021.
  Casa de la Ciencia, Consejo Superior de Investigaciones Científicas, Valencia, 21 October 2021.
  Bristol University, UK, 26 March 2021.
  Chalmers University, Sweden, 14 October, 2020.
  Rothschild Seminar as a Rothschild Distinguished Visiting Fellow, Isaac Newton Institute, Cambridge, 6 December 2019.
  Potsdam Universitaet, Alemania, 25 October 2019.
  Isaac Newton Institute, Cambridge, UK, 5 September 2019.
  University of Edinburgh, 8 May 2019.
  Coloquio de Matemáticas RSME-IUMA, Zaragoza, 17 mayo 2018.
  Universidad Jaume I, Ciclo Matemáticas y Sociedad en Castellón, "Ciegos ante el azar", 25 enero 2018.
  Ateneo IMUVA, "La cuadratura Gaussiana según Gauss", 18 enero 2018.
  Rutgers University-Camden, 2017.
  Instituto de Matemática Pura y Aplicada, Universidad Politécnica de Valencia, 2017.
  Oxford University, 2017.
  University of Edinburgh, 2017.
  Real Academia de Ciencias, 2016.
  University of Bristol, UK, 2016.
  Chinese Academy of Sciences, Beijing, China, 2016.
  Beijing Computational Science Reserach Center CSRC, 2016.
  Tuebingen Universitaet, Germany, 2016.
  Chinese Academy of Sciences, Beijing, China, 2015.
  Escuela JAE, ICMAT, 2015 (10 hour lecture course).
  Real Academia de Medicina y Cirugía de Valladolid, 2015.
  Conferencia de clausura, Olimpiada Regional de Matemáticas, Castilla y León, 2015.
  Universidad Rey Juan Carlos, Madrid, 2015.
  Universidad Autonoma de Madrid, Madrid, 2015.
  ICMAT (ICMAT-China Exploratory Workshop), Madrid, 2014.
  Universidad del País Vasco, Bilbao, 2014.
  BCAM (Basque Center for Applied Mathematics), 2014.
  Universidad Complutense de Madrid, Departamento de Matemática Aplicada, seminario inaugural del curso 2014-2015.
  Nanjing Agricultural University (China), 2014.
  Chinese Academy of Sciences, Beijing (China), 2014.
  ICMAT, Madrid, 2014 (Seminario de Probabilidad aplicada y Estadística)
  M4TEMOZIOA 2014: Matematikaren Hitzordua, Bilbao, 2014.
  Universität Zürich (Suiza), 2013.
  University of Bergen (Noruega), 2013.
  ICMAT (Madrid), ciclo 10 conferencias, 2013.
  BCAM (Basque Center for Applied Mathematics), 2013.
  Programa de Promoción de la Cultura Científica, Universidad de Castilla-La Mancha, 2013.
  Academia de Ciencias (Ciclo Ciencia Para Todos), Madrid, 2013.
  Ramanujan Institute, University of Madras (India), 2013.
  Universidad de Cantabria, 2012.
  Universidad Carlos III de Madrid, 2012.
  BCAM EHU/UPV Basque Colloquium in Mathematics and its applications (7th edition), Bilbao, 2012.
  Ecole Polytechnique Fédérale de Lausanne, Lausanne, 2012.
  Jornadas Técnicas Red Iris 2011. Conferencia inaugural, Valladolid, 2011.
  Residencia de Estudiantes (Ciclo Matemáticas en la Residencia), Madrid, 2010.
  Academia de Ciencias (Ciclo Ciencia Para Todos), Madrid, 2010.
  Ecole Nationale des Ponts et Chaussées, Paris, 2010.
  University of Warwick, 2009.
  II Escuela de Doctorado i-Math, Ecuaciones diferenciales y singularidades. Ecuaciones y singularidades, congreso de jóvenes investigadores iberoamericanos, Valladolid, 2009.
  Universidad de Castilla-La Mancha, Ciudad Real, 2009.
  Universidad del País Vasco, 2008.
  ACES (Applied Computational Engineering & Sciences),
University of Texas, Austin, 2008.
  Department of Mathematics, University of Texas, Austin, 2008.
  Instituto Madrileño de Estudios Avanzados, Lecciones magistrales, 2008.
  Universidad de las Islas Baleares, 2007.
  Instituto de España, 2007.
  Universitat Jaume I, 2007.
  Universidad Carlos III de Madrid, 2007.
  Donostia Physics Center, 2000.
  Conferencia Inaugural de la Reunión de Decanos de Matemáticas, Santiago de Compostela, 2000.
  Universidad Complutense, 1999.
  Universidad Carlos III de Madrid, 1998.
  Universitat de Barcelona, 1997.
  Universidad Complutense, 1996.
  Conversaciones Científicas de El Escorial, Universidad Complutense, 1996.
  Freie Universiaet Berlin/Konrad-Zuse-Zentrum/Weierstrass-Institute, 1996.
  Universidad de Cantabria, 1996.
  Universidad Autonoma de Madrid, 1995.
  Museo de la Ciencia de Barcelona, 1995.
  CWI, Mathematical Centre, Amsterdam 1994.
  Chalmers University of Technology, Gothenburg, 1994.
  Universite de Geneve, 1993.
  Universidad del Pais Vasco, 1993.
  University of Illinois, 1993.
  Universidad Autonoma de Madrid, 1993.
  Leopold-Franzens Universitaet Innsbruck, 1992.
  Technische Universitaet, Viena, 1992.
  Universidad Carlos III de Madrid, 1992.
  Universidad de Cantabria, 1991.
  Chalmers University of Technology, Gothenburg, 1991.
  Center for Nonlinear Studies, Los Alamos, 1991.
  Technical University Helsinki, 1990.
  Universidad de Oviedo, 1990.
  Universidad de Zaragoza, 1989.
  Escuela Tecnica Superior de Ingenieros Aeronauticos, Universidad Politecnica de Madrid, 1989.
  Escuela Tecnica Superior de Ingenieros de Minas, Universidad Politecnica de Madrid, 1989.
  Universidad de Santiago, 1989.
  Universidade de Coimbra, 1989.
  Oxford University, 1988.
  University of Cambridge, 1988.
  Fudan University, 1987.
  Shanghai Mathematical Society, 1987.
  Shanghai University of Science and Technology, 1987.
  Chinese Academy of Sciences, 1987.
  Technische Universitaet, Viena, 1987.
  MIT, Massachusetts Institute of Technology, 1987.
  Escuela Tecnica Superior de Ingenieros Aeronauticos, Universidad Politecnica de Madrid, 1986.
  Universidad de Sevilla, 1986.
  Universitaet Hamburg, 1985.
  Technische Hogeschool Twente, 1985.
  Katholieke Universiteit Nijmegen, 1985.
  Rijksuniversiteit Leiden, 1985.
  Rhein-West. Technische Hochschule, 1985.
  Oxford University, 1985.
  Universidad de Santander (Cantabria), 1985.
  Universidad del Pais Vasco, 1984.
  Rijksuniversiteit Leiden, 1983.
  Universidad de Santander (Cantabria), 1983.
  Universidad de Valencia, 1983.
  CWI, Amsterdam, 1983.
  Universidad del Pais Vasco, 1983.
  Colegio Universitario de Alava, 1981.
  University of the Witwatersrand, 1981.
  University of the Orange Free State, 1981.