Ana Bela Cruzeiro. Title of Agregado in Mathematics, 1991 by the University of Lisbon, Faculty of Sciences, PhD in Mathematics, 1985, by Université Pierre et Marie Curie. Full professor at Instituto Superior Técnico, Department of Mathematics. President of the Group of Matematical Physics, Instituto Superior Técnico (2024- ). Correspondant member of the Academy of Sciences Lisbon. Member of the General Council of the University of Lisbon (2021- ). Member of the Scientific Council of Instituto Superior Técnico. (2021-2024) Member of the Scientific Council for Exact Sciences and Engineering of FCT (2017-2023). President of the Portuguese Mathematical Society (2000-2004). Published 93 articles in specialized journals. Participated and was Principal Researcher in various projects. Organized/co-organized many scientific events. Area: Stochastic Analysis and applications in Mathematical Physics
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Personal identification

Full name
Ana Bela Cruzeiro

Citation names

  • Cruzeiro, Ana Bela

Author identifiers

Ciência ID
B417-3091-268B
ORCID iD
0000-0001-5256-1174

Email addresses

  • ana.cruzeiro@tecnico.ulisboa.pt (Professional)

Telephones

Telephone
  • 218417063 (Professional)

Addresses

  • Grupo de Física-Matemática e Dep. de Matemática IST. Av. Rovisco Pais, 1049-001, Lisboa, Lisboa, Portugal (Professional)

Websites

  • https://fisica-matematica.pt/people/ana-bela-cruzeiro/ (Professional)

Knowledge fields

  • Exact Sciences - Mathematics

Languages

Language Speaking Reading Writing Listening Peer-review
French Advanced (C1) Advanced (C1) Advanced (C1) Advanced (C1)
English Advanced (C1) Advanced (C1) Advanced (C1) Advanced (C1)
Portuguese (Mother tongue)
Degree Classification
1991
Concluded
 Matemática (Título de Agregado)
Universidade de Lisboa, Portugal
 Perguntar
1985/07
Concluded
 Matemática (Doutoramento)
Sorbonne Université Campus Pierre et Marie Curie, France
 Perguntar

Teaching in Higher Education

Category
Host institution 		Employer
2002/02/15 - Current Full Professor (University Teacher) Universidade de Lisboa Instituto Superior Técnico Departamento de Matemática, Portugal
Universidade de Lisboa Instituto Superior Técnico, Portugal
1995 - 2002 Associate Professor (University Teacher) Universidade de Lisboa Faculdade de Ciências, Portugal
1986 - 1995 Assistant Professor (University Teacher) Universidade de Lisboa Faculdade de Ciências, Portugal
1985/09/01 - 1986/02/28 Assistant Professor (University Teacher) Université Paris-Saclay Département de Mathématiques d'Orsay, France

Contract

Designation Funders
2018/10/01 - 2021/09/30 Schroedinger problem and Optimal Transport: a multidisciplinary perspective
PTDC/MAT-STA/28812/2017
Researcher
Fundação da Faculdade de Ciências da Universidade de Lisboa, Portugal
Ongoing
2016/05/15 - 2019/06/09 From Stochastic Geometric Mechanics to Mass Transportation Problems
PTDC/MAT-STA/0975/2014
Principal investigator
Fundação da Faculdade de Ciências da Universidade de Lisboa, Portugal
 Fundação para a Ciência e a Tecnologia
Concluded
2012/02/01 - 2015/01/31 Probability and Partial Differential Equations in Mathematical Physics
PTDC/MAT/120354/2010
Researcher
Concluded
2013 - 2015 Desenvolvimentos em EDPs não lineares: das equações não degeneradas ao controlo estocástico e aos jogos de campo médio
PTDC/MATCAL/0749/2012
Researcher
Associação do Instituto Superior Técnico para a Investigação e Desenvolvimento, Portugal
Concluded
2011/06/09 - 2014/12/31 Análise Estocástica e Aproximações Numéricas em Matemática Financeira (SANAF)
UTA_CMU/MAT/0006/2009
Fundação Gaspar Frutuoso, Portugal

Universidade de Lisboa Instituto Superior Técnico, Portugal

Universidade Nova de Lisboa NOVAMath, Portugal

Universidade de Lisboa Centro de Matematica Aplicada à Previsão e Decisão Económica, Portugal
Fundação para a Ciência e a Tecnologia
Concluded
2009 - 2014 ANR ProbaGeo
ANR
Researcher
Université de Bourgogne, France
Concluded
2010/03/01 - 2013/06/30 Probabilistic approach to finite and infinite dimensional dynamical systems
info:eu-repo/grantAgreement/FCT/3599-PPCDT/104173/PT
Principal investigator
Fundação para a Ciência e a Tecnologia
2010/01/01 - 2012/12/31 Novos algoritmos numéricos paralelos para os actuais e futuros supercomputadores de alto desempenho
PTDC/EIA-CCO/098910/2008
Universidade Nova de Lisboa NOVAMath, Portugal

Universidade de Lisboa Instituto Superior Técnico, Portugal
Fundação para a Ciência e a Tecnologia
Concluded
2010/01/01 - 2012 New parallel numerical algorithms for current and future high performance supercomputers
info:eu-repo/grantAgreement/FCT/3599-PPCDT/98910/PT
Associação do Instituto Superior Técnico para a Investigação e Desenvolvimento, Portugal
 Fundação para a Ciência e a Tecnologia
2007/09/01 - 2011/02/28 Mathematical Physics
PTDC/MAT/69635/2006
Researcher
Fundação da Faculdade de Ciências da Universidade de Lisboa, Portugal
Concluded
2009/10/01 - 2011 Technology Management and Policy in the Telecommunications Industry
info:eu-repo/grantAgreement/FCT/3599-PPCDT/83918/PT
Universidade de Lisboa Instituto Superior Técnico, Portugal
 Fundação para a Ciência e a Tecnologia
2005 - 2008 Functional Integration and Applications
PPCDT/MAT/55977/2004
Researcher
Fundação da Faculdade de Ciências da Universidade de Lisboa, Portugal
Concluded
2000 - 2005 Classical versus quantum dynamics and their mathematical tools
POCTI/MAT/34924/1999
Researcher
Concluded
1997 - 2001 TMR Stochastic Analysis and Its Applications
ERBFMRXCT 960075
Co-Principal Investigator (Co-PI)
Universidade de Lisboa Grupo de Física Matemática, Portugal
Concluded
1996 - 1998 Análise Estocástica e Aplicações
PRAXIS/PCEX/P/MAT/42/96
Principal investigator
Concluded
1994 - 1996 Física-Matemática
PRAXISXXI/2/2.1/MAT/19/94
Researcher
Concluded
1992 - 1996 Stochastic Analysis
SC1*-CT92-0784
Researcher
European Union, Belgium
Concluded
1990 - 1992 Métodos probabilísticos em sistema Dinâmicos
PMCT/CEN/159/90
Principal investigator
Concluded

Publications

Book
  1. Cruzeiro, Ana Bela. Stochastic Analysis and Mathematical Physics. Birkhäuser Basel. 2003.
    Published • 10.1007/978-3-0348-8018-3 • Editor
Book chapter
  1. Bhauryal, Neeraj; Cruzeiro, Ana Bela. "On a forward and a backward stochastic Euler equation". In Nonlinear Differential Equations and Applications. Springer-CIM, 2024.
  2. Cruzeiro, Ana Bela. "Stochastic Geodesics". In Geometry and Invariance in Stochastic Dynamics. 2021.
    Published
  3. Cruzeiro, Ana Bela. "Invariant and Quasi-invariant Measures for Equations in Hydrodynamics". 101-120. Springer, Cham, 2019.
    Published
  4. Lassalle, Rémi; Cruzeiro, Ana Bela. "Symmetries and Martingales in a Stochastic Model for the Navier-Stokes Equation". In From Particle Systems to Partial Differential Equations III, 185-194. Springer International Publishing, 2016.
    10.1007/978-3-319-32144-8_9
  5. Arnaudon, Marc; Cruzeiro, Ana Bela. "Stochastic Lagrangian Flows and the Navier–Stokes Equations". In Stochastic Analysis: A Series of Lectures, 55-75. Springer Basel, 2015.
    10.1007/978-3-0348-0909-2_2
  6. Cruzeiro, Ana Bella; Lassalle, Remi. "On the Stochastic Least Action Principle for the Navier-Stokes Equation". In Springer Proceedings in Mathematics & Statistics, 163-184. Springer International Publishing, 2014.
    10.1007/978-3-319-11292-3_6
  7. Cruzeiro, Ana Bela; Shamarova, Evelina. "On a Forward-backward Stochastic System Associated to the Burgers Equation". In Stochastic Analysis with Financial Applications, 43-59. Springer Basel, 2011.
    10.1007/978-3-0348-0097-6_4
  8. Cruzeiro, Ana Bela. "Stochastic parallel transport on the d-dimensional torus". In Stochastic Analysis in Mathematical Physics. 2008.
  9. Cruzeiro, Ana Bela. "Variational principle for diffusions on the homeomorphism group with the H2 metric". In Mathematical Analysis of Random Phenomena. World Scientific, 2007.
    Published
  10. Cruzeiro, Ana Bela. "Malliavin Calculus". In Encyclopedia of Mathematical Physics. United Kingdom: Elsevier, 2006.
    Published
  11. Cruzeiro, Ana Bela. "On some probabilistic estimates of heat kernels and applications". Spain: Publicaciones de la Real Sociedad Matematica Espanola, 2005.
    Published
  12. Cruzeiro, Ana Bela. "A Littlewood-Paley type inequality on the path space". In Seminar on Stochastic Analysis, Random Fields and Applications IV. Birkhäuser Basel, 2004.
    Published
  13. Cruzeiro, Ana Bela. "On metrics for tangent processes on the path space". In Stochastic Analysis and Related Topics VIII. Birkhauser, 2003.
    Published
  14. Cruzeiro, Ana Bela. "Riemannian Geometry on the Path Space". In Stochastic Partial Differential Equations and Applications. Marcel Decker, 2002.
    Published
  15. Cruzeiro, A. B.; Wu, Liming; Zambrini, J. C.. "Bernstein Processes Associated with a Markov Process". In Stochastic Analysis and Mathematical Physics, 41-72. Birkhäuser Boston, 2000.
    Published • 10.1007/978-1-4612-1372-7_4
  16. Cruzeiro, Ana Bela. "Riesz Transforms, Commutators and Stochastic Integrals". In Perspectives in Partial Differential Equations, Harmonic Analysis and Applications. United States, 1999.
    Published
  17. Cruzeiro, A. B.; Malliavin, P.. "Energy Identities and Estimates for Anticipative Stochastic Integrals on a Riemannian Manifold". In Stochastic Analysis and Related Topics VI, 221-233. Birkhäuser Boston, 1998.
    10.1007/978-1-4612-2022-0_8
  18. Cruzeiro, Ana Bela. "Invariant measure for a wave equation on a Riemannian manifold". In Stochastic Differential and Difference Equations. Birkhäuser Boston, 1997.
    Published
  19. Cruzeiro, Ana Bela. "Singular differential operators and associated processes". World Scientific, 1995.
    Published
  20. Cruzeiro, Ana Bela. "Bernstein Diffusions and Euclidean Quantum Field Theory". In Proceedings Monte Verita meeting. Birkhauser, 1995.
    Published
  21. Cruzeiro, Ana Bela. "Euclidean Quantum Mechanics: an outline". In Stochastic Analysis and Applications in Physics. Acad. Publ., 1994.
    Published
  22. Cruzeiro, Ana Bela. "Ornstein-Ulhenbeck processes as Bernstein diffusions". In Proceedings of the Conference on Stochastic Analysis. Birkhauser, 1993.
    Published
  23. Bela Cruzeiro, Ana. "Invariant measures in hydrodynamic systems with random perturbations". In Dynamics and Stochastic Processes Theory and Applications, 107-113. Springer Berlin Heidelberg, 1990.
    Published • 10.1007/3-540-52347-2_26
  24. Cruzeiro, Ana Bela. "Flows in infinite dimensions and associated transformations of Gaussian measures". In Stochastic Methods in Mathematics and Physics. World Scientific, 1989.
    Published
  25. Cruzeiro, Ana Bela. "Invariant measures for Euler and Navier-Stokes systems". In Stochastic Analysis, Path Integration and Dynamics. Pitman, 1989.
Conference paper
  1. Cruzeiro, Ana. "Hydrodynamics, Probability and the Geometry of the Diffeomorphisms Group". 2011.
  2. Cruzeiro, Ana. "Non adapted transformations of the Wiener measure". 2004.
    10.1142/9789812702364_0014
  3. Cruzeiro, Ana. "Ornstein-Uhlenbeck semigroups on Riemannian path spaces". 2003.
    10.1142/9789812702241_0009
Edited book
  1. Cruzeiro, Ana Bela. Stochastic Geometric Mechanics. Springer International Publishing. 2017.
    Published • 10.1007/978-3-319-63453-1
  2. Cruzeiro, Ana Bela. Stochastic Analysis in Mathematical Physics. 2008.
    Published • Editor
  3. Cruzeiro, Ana Bela. Mathematical Analysis of Random Phenomena. 2007.
    Published • Editor
  4. Cruzeiro, Ana Bela. Stochastic Analysis and Applications. Birkhäuser Boston. 1991.
    Published • 10.1007/978-1-4612-0447-3 • Editor
Journal article
  1. Xin Chen; Ana Bela Cruzeiro; Tudor S. Ratiu. "Stochastic Variational Principles for Dissipative Equations with Advected Quantities". Journal of Nonlinear Science 33 1 (2023): 1-62. https://doi.org/10.1007/s00332-022-09846-1.
    Published • 10.1007/s00332-022-09846-1
  2. Ana Bela Cruzeiro; Carlos Oliveira; Jean-Claude Zambrini. "Time-symmetric optimal stochastic control problems in space-time domains". Optimization 71 11 (2022): 3241-3275. https://doi.org/10.1080/02331934.2021.2017430.
    Published • 10.1080/02331934.2021.2017430
  3. Ana Bela Cruzeiro. "Stochastic Approaches to Deterministic Fluid Dynamics: A Selective Review". Water (2020): https://doi.org/10.3390/w12030864.
    10.3390/w12030864
  4. Cruzeiro, Ana Bela; Symeonides, Alexandra. "On a Non-Periodic Modified Euler Equation: Well-Posedness and Quasi-Invariant Measures". Potential Analysis (2020): http://dx.doi.org/10.1007/s11118-020-09841-9.
    10.1007/s11118-020-09841-9
  5. Cruzeiro, Ana Bela; Arnaudon, Marc; Zambrini, J.C.. "An entropic interpolation problem for incompressible viscid fluids". Ann. Inst. Henri Poincaré 56 3 (2020): 2211-2235. https://projecteuclid.org/euclid.aihp/1593137325.
    Published
  6. Rémi Lassalle; Ana Bela Cruzeiro. "An intrinsic calculus of variations for functionals of laws of semi-martingales". Stochastic Processes and their Applications 129 10 (2019): 3585-3618. https://doi.org/10.1016/j.spa.2018.10.001.
    10.1016/j.spa.2018.10.001
  7. Bela Cruzeiro, Ana. "Navier-Stokes and stochastic Navier-Stokes equations via Lagrange multipliers". Journal of Geometric Mechanics 11 4 (2019): 553-560. http://dx.doi.org/10.3934/jgm.2019027.
    10.3934/jgm.2019027
  8. Cruzeiro, Ana Bela; Symeonides, Alexandra. "Invariant measures for the non-periodic two-dimensional Euler equation". Bulletin des Sciences Mathématiques 148 (2018): 33-52. http://dx.doi.org/10.1016/j.bulsci.2018.06.006.
    Published • 10.1016/j.bulsci.2018.06.006
  9. Sousa, Rúben; Cruzeiro, Ana Bela; Guerra, Manuel. "Barrier option pricing under the 2-hypergeometric stochastic volatility model". Journal of Computational and Applied Mathematics 328 (2018): 197-213. http://dx.doi.org/10.1016/j.cam.2017.06.034.
    10.1016/j.cam.2017.06.034
  10. Cruzeiro, Ana Bela. "Momentum Maps and Stochastic Clebsch Action Principles". Communications in Mathematical Physics (2018):
  11. Cruzeiro, Ana Bela. "Generalized stochastic Lagrangian paths for the Navier-Stokes equation". ANNALI DELLA SCUOLA NORMALE SUPERIORE DI PISA - CLASSE DI SCIENZE (2018):
  12. Ana Bela Cruzeiro; Guoping Liu. "A stochastic variational approach to the viscous Camassa–Holm and Leray-alpha equations". Stochastic Processes and their Applications 127 1 (2017): 1-19. http://dx.doi.org/10.1016/j.spa.2016.05.006.
    10.1016/j.spa.2016.05.006
  13. Cruzeiro, Ana Bela; Liu, Guo Ping. "A stochastic variational approach to viscous Burgers equations". Acta Mathematica Sinica, English Series 32 9 (2016): 1027-1034. http://dx.doi.org/10.1007/s10114-016-5773-z.
    10.1007/s10114-016-5773-z
  14. Cruzeiro, Ana Bela. "Forward-backward systems of stochastic differential equations generated by Bernstein diffusions". Stochastic Analysis and Applications (2015):
    Published
  15. Cruzeiro, Ana Bela. "On a 2D stochastic Euler equation of transport type: existence and energy transfer". Stochastics and Dynamics (2015):
    Published
  16. Arnaudon, Marc; Chen, Xin; Cruzeiro, Ana Bela. "Stochastic Euler-Poincaré reduction". Journal of Mathematical Physics 55 8 (2014): 081507. http://dx.doi.org/10.1063/1.4893357.
    10.1063/1.4893357
  17. Cruzeiro, A.B.; Qian, Z.M.. "Backward stochastic differential equations associated with the vorticity equations". Journal of Functional Analysis 267 3 (2014): 660-677. http://dx.doi.org/10.1016/j.jfa.2014.05.011.
    10.1016/j.jfa.2014.05.011
  18. Cruzeiro, Ana Bela; Gomes, André de Oliveira; Zhang, Liangquan. "Asymptotic properties of coupled forward–backward stochastic differential equations". Stochastics and Dynamics 14 03 (2014): 1450004. http://dx.doi.org/10.1142/s021949371450004x.
    10.1142/s021949371450004x
  19. Cruzeiro, Ana. "Generalized stochastic flows and applications to incompressible viscous fluids". Bulletin des Sciences Mathematiques (2014): http://www.scopus.com/inward/record.url?eid=2-s2.0-84886959093&partnerID=MN8TOARS.
    10.1016/j.bulsci.2013.10.006
  20. Cruzeiro, Ana Bela. "Stochastic geodesics and stochastic backward equations on Lie groups". Discrete and Continuous Dynamical Systems (2013):
    Published
  21. Arnaudon, M.; Cruzeiro, A.B.. "Lagrangian Navier-Stokes diffusions on manifolds: Variational principle and stability". Bulletin des Sciences Mathematiques 136 8 (2012): 857-881. http://www.scopus.com/inward/record.url?eid=2-s2.0-84869156696&partnerID=MN8TOARS.
    10.1016/j.bulsci.2012.06.007
  22. Arnaudon, M.; Cruzeiro, A.B.. "Stochastic Lagrangian flows on some compact manifolds". Stochastics 84 2-3 (2012): 367-381. http://www.scopus.com/inward/record.url?eid=2-s2.0-84860324056&partnerID=MN8TOARS.
    10.1080/17442508.2010.498916
  23. Cruzeiro, A.B.. "Stochastic calculus of variations for the diffeomorphisms group". Bulletin des Sciences Mathematiques 135 6-7 (2011): 557-564. http://www.scopus.com/inward/record.url?eid=2-s2.0-80053295405&partnerID=MN8TOARS.
    10.1016/j.bulsci.2011.05.001
  24. Arnaudon, M.; Cruzeiro, A.B.; Galamba, N.. "Lagrangian Navier-Stokes flows: A stochastic model". Journal of Physics A: Mathematical and Theoretical 44 17 (2011): http://www.scopus.com/inward/record.url?eid=2-s2.0-79954567846&partnerID=MN8TOARS.
    10.1088/1751-8113/44/17/175501
  25. Cruzeiro, A.B.; Shamarova, E.. "Navier-Stokes equations and forward-backward SDEs on the group of diffeomorphisms of a torus". Stochastic Processes and their Applications 119 12 (2009): 4034-4060. http://www.scopus.com/inward/record.url?eid=2-s2.0-70350622586&partnerID=MN8TOARS.
    10.1016/j.spa.2009.09.011
  26. Cruzeiro, A.B.; Malliavin, P.. "Renormalized stochastic calculus of variations for a renormalized infinite-dimensional Brownian motion". Stochastics 81 3-4 (2009): 385-399. http://www.scopus.com/inward/record.url?eid=2-s2.0-70450182032&partnerID=MN8TOARS.
    10.1080/17442500902919652
  27. Cruzeiro, A.B.; Malliavin, P.. "Corrigendum to "Nonergodicity of Euler fluid dynamics on tori versus positivity of the Arnold-Ricci tensor" [J. Funct. Anal. 254 (7) (2008) 1903-1925] (DOI:10.1016/j.jfa.2007.08.002)". Journal of Functional Analysis 256 12 (2009): http://www.scopus.com/inward/record.url?eid=2-s2.0-64549095528&partnerID=MN8TOARS.
    10.1016/j.jfa.2009.02.022
  28. Cruzeiro, A.-B.; Malliavin, P.. "Stochastic Calculus of Variations on complex line bundle and construction of unitarizing measures for the Poincaré disk". Journal of Functional Analysis 256 2 (2009): 385-408. http://www.scopus.com/inward/record.url?eid=2-s2.0-56549108783&partnerID=MN8TOARS.
    10.1016/j.jfa.2008.03.011
  29. Cruzeiro, A.B.; Malliavin, P.. "Non-existence of infinitesimally invariant measures on loop groups". Journal of Functional Analysis 254 7 (2008): 1974-1987. http://www.scopus.com/inward/record.url?eid=2-s2.0-39849108749&partnerID=MN8TOARS.
    10.1016/j.jfa.2007.11.019
  30. Cruzeiro, A.-B.; Malliavin, P.. "Nonergodicity of Euler fluid dynamics on tori versus positivity of the Arnold-Ricci tensor". Journal of Functional Analysis 254 7 (2008): 1903-1925. http://www.scopus.com/inward/record.url?eid=2-s2.0-39749200946&partnerID=MN8TOARS.
    10.1016/j.jfa.2007.08.002
  31. Alves, C.J.S.; Cruzeiro, A.B.. "Monte-Carlo simulation of stochastic differential systems - a geometrical approach". Stochastic Processes and their Applications 118 3 (2008): 346-367. http://www.scopus.com/inward/record.url?eid=2-s2.0-38649101285&partnerID=MN8TOARS.
    10.1016/j.spa.2007.04.009
  32. Cruzeiro, A.-B.; Flandoli, F.; Malliavin, P.. "Brownian motion on volume preserving diffeomorphisms group and existence of global solutions of 2D stochastic Euler equation". Journal of Functional Analysis 242 1 (2007): 304-326. http://www.scopus.com/inward/record.url?eid=2-s2.0-33750520544&partnerID=MN8TOARS.
    10.1016/j.jfa.2006.06.010
  33. Cipriano, F.; Cruzeiro, A.B.. "Navier-Stokes equation and diffusions on the group of homeomorphisms of the torus". Communications in Mathematical Physics 275 1 (2007): 255-269. http://www.scopus.com/inward/record.url?eid=2-s2.0-34547864305&partnerID=MN8TOARS.
    10.1007/s00220-007-0306-3
  34. Cruzeiro, A.B.; Zhang, X.. "Bismut type formulae for diffusion semigroups on Riemannian manifolds". Potential Analysis 25 2 (2006): 121-130. http://www.scopus.com/inward/record.url?eid=2-s2.0-33746701904&partnerID=MN8TOARS.
    10.1007/s11118-006-9010-8
  35. Cruzeiro, A.B.; Malliavin, P.. "Numerical approximation of diffusions in Rd using normal charts of a Riemannian manifold". Stochastic Processes and their Applications 116 7 (2006): 1088-1095. http://www.scopus.com/inward/record.url?eid=2-s2.0-33744539902&partnerID=MN8TOARS.
    10.1016/j.spa.2006.02.004
  36. Cruzeiro, A.B.; Zhang, X.C.. "L p -gradient estimates of symmetric Markov semigroups for 1 < p = 2". Acta Mathematica Sinica, English Series 22 1 (2006): 101-104. http://www.scopus.com/inward/record.url?eid=2-s2.0-29144495826&partnerID=MN8TOARS.
    10.1007/s10114-005-0538-0
  37. Cipriano, F.; Cruzeiro, A.B.. "Flows associated with irregular Rd - Vector fields". Journal of Differential Equations 219 1 (2005): 183-201. http://www.scopus.com/inward/record.url?eid=2-s2.0-27944453583&partnerID=MN8TOARS.
    10.1016/j.jde.2005.02.015
  38. Cruzeiro, A.B.; Malliavin, P.; Thalmaier, A.. "Geometrization of Monte-Carlo numerical analysis of an elliptic operator: Strong approximation". Comptes Rendus Mathematique 338 6 (2004): 481-486. http://www.scopus.com/inward/record.url?eid=2-s2.0-1542318575&partnerID=MN8TOARS.
    10.1016/j.crma.2004.01.007
  39. Cruzeiro, A.B.; Zhang, X.. "Finite dimensional approximation of Riemannian path space geometry". Journal of Functional Analysis 205 1 (2003): 206-270. http://www.scopus.com/inward/record.url?eid=2-s2.0-0348159937&partnerID=MN8TOARS.
    10.1016/S0022-1236(02)00095-2
  40. Cruzeiro, A.-B.; Malliavin, P.. "Stochastic calculus of variations and Harnack inequality on Riemannian path spaces". Comptes Rendus Mathematique 335 10 (2002): 817-820. http://www.scopus.com/inward/record.url?eid=2-s2.0-0037715276&partnerID=MN8TOARS.
    10.1016/S1631-073X(02)02561-X
  41. Cruzeiro, A.B.. "Construction of some processes on the Wiener space associated to second order operators". Journal of the Korean Mathematical Society 38 2 (2001): 311-320. http://www.scopus.com/inward/record.url?eid=2-s2.0-52549095688&partnerID=MN8TOARS.
  42. Cruzeiro, A.B.; Fang, S.. "Weak Levi-Civita connection for the damped metric on the Riemannian path space and vanishing of Ricci tensor in adapted differential geometry". Journal of Functional Analysis 185 2 (2001): 681-698. http://www.scopus.com/inward/record.url?eid=2-s2.0-0035484986&partnerID=MN8TOARS.
    10.1006/jfan.2001.3765
  43. Cruzeiro, A.-B.; Fang, S.. "Une formule de Weitzenböck pour l'opérateur d'Ornstein-Ulhenbeck amorti em géométrie différentielle adaptée | A Weitzenböck formula for the damped Ornstein-Uhlenbeck operator in adapted differential geometry". Comptes Rendus de l'Academie des Sciences - Series I: Mathematics 332 5 (2001): 447-452. http://www.scopus.com/inward/record.url?eid=2-s2.0-0345878081&partnerID=MN8TOARS.
    10.1016/S0764-4442(01)01861-4
  44. Cruzeiro, A.-B.; Malliavin, P.. "A class of anticipative tangent processes on the Wiener space | Une classe de processus tangents anticipatifs sur l'espace de Wiener". Comptes Rendus de l'Academie des Sciences - Series I: Mathematics 333 4 (2001): 353-358. http://www.scopus.com/inward/record.url?eid=2-s2.0-0042369905&partnerID=MN8TOARS.
    10.1016/S0764-4442(01)02055-9
  45. Cruzeiro, A.-B.; Malliavin, P.; Taniguchi, S.. "Ground state estimations in gauge theory". Bulletin des Sciences Mathematiques 125 6-7 (2001): 623-640. http://www.scopus.com/inward/record.url?eid=2-s2.0-0346508865&partnerID=MN8TOARS.
    10.1016/S0007-4497(01)01102-2
  46. Cruzeiro, A.-B.; Malliavin, P.. "Frame Bundle of Riemannian Path Space and Ricci Tensor in Adapted Differential Geometry". Journal of Functional Analysis 177 1 (2000): 219-253. http://www.scopus.com/inward/record.url?eid=2-s2.0-0000889771&partnerID=MN8TOARS.
    10.1006/jfan.2000.3634
  47. Cruzeiro, A.B.; Fang, S.; Malliavin, P.. "A probabilistic weitzenböck formula on Riemannian path space". Journal d'Analyse Mathematique 80 (2000): 87-100. http://www.scopus.com/inward/record.url?eid=2-s2.0-0003008746&partnerID=MN8TOARS.
  48. Cipriano, F.; Cruzeiro, A.B.. "Flows Associated to Tangent Processes on the Wiener Space". Journal of Functional Analysis 166 2 (1999): 310-331. http://www.scopus.com/inward/record.url?eid=2-s2.0-0005474197&partnerID=MN8TOARS.
    10.1006/jfan.1999.3418
  49. Cruzeiro, A.-B.; Malliavin, P.. "Non perturbative construction of invariant measure through confinement by curvature". Journal des Mathematiques Pures et Appliquees 77 6 (1998): 527-537. http://www.scopus.com/inward/record.url?eid=2-s2.0-0032084130&partnerID=MN8TOARS.
  50. Cruzeiro, A.B.; Fang, S.. "An l2 estimate for riemannian anticipative stochastic integrals". Journal of Functional Analysis 143 2 (1997): 400-414. http://www.scopus.com/inward/record.url?eid=2-s2.0-0031067197&partnerID=MN8TOARS.
  51. Cruzeiro, A.-B.; Malliavin, P.. "Renormalized differential geometry on path space: Structural equation, curvature". Journal of Functional Analysis 139 1 (1996): 119-181. http://www.scopus.com/inward/record.url?eid=2-s2.0-0030578297&partnerID=MN8TOARS.
    10.1006/jfan.1996.0081
  52. Gaxie, Daniel; Michel, Hélène; Weber, Louis. "Diffusions sur l'espace de Wiener". Comptes Rendus de l Académie des Sciences - Series I - Mathematics 302 8 (1996): http://dx.doi.org/10.3917/sava.009.0065.
    Published • 10.3917/sava.009.0065
  53. Cruzeiro, A.B.; Zambrini, J.C.. "Malliavin Calculus and Euclidean Quantum Mechanics II. Variational Principle for Infinite Dimensional Processes". Journal of Functional Analysis 130 2 (1995): 450-476. http://www.scopus.com/inward/record.url?eid=2-s2.0-0012265339&partnerID=MN8TOARS.
    10.1006/jfan.1995.1077
  54. Cruzeiro, Ana Bela. "Une inégalité L2 pour des integrales stochastiques anticipatives sur une varieté Riemannienne". Comptes Rendus de l Académie des Sciences - Series I - Mathematics 321 (1995):
    Published
  55. Vernière, Marc. "Courbures de l'espace de probabilité d'un Brownien Riemannien". Comptes Rendus de l Académie des Sciences - Series I - Mathematics 320 (1995):
    Published • 10.3406/spgeo.1973.1386
  56. Janet, Maurice. "Repère mobile et Géométrie Riemannienne sur les espaces de chemins". Comptes Rendus de l Académie des Sciences - Series I - Mathematics 319 (1994): 165-186. http://dx.doi.org/10.24033/asens.897.
    Published • 10.24033/asens.897
  57. Cruzeiro, A.B.; Zambrini, J.-C.. "Malliavin calculus and Euclidean quantum mechanics. I. Functional calculus". Journal of Functional Analysis 96 1 (1991): 62-95. http://www.scopus.com/inward/record.url?eid=2-s2.0-0040181612&partnerID=MN8TOARS.
  58. Albeverio, S.; Cruzeiro, A.-B.. "Global flows with invariant (Gibbs) measures for Euler and Navier-Stokes two dimensional fluids". Communications in Mathematical Physics 129 3 (1990): 431-444. http://www.scopus.com/inward/record.url?eid=2-s2.0-0000701064&partnerID=MN8TOARS.
    10.1007/BF02097100
  59. Bertrand-Mathis, Anne. "Solutions et mesures invariantes pour des équations d'évolution stochastiques du type Navier-Stokes". Expositiones Mathematicae 7 (1989): http://dx.doi.org/10.1007/pl00004734.
    Published • 10.1007/pl00004734
  60. Cruzeiro, A.B.. "Processus sur l'espace de Wiener associés à des opérateurs elliptiques à coefficients dans certains espaces de Sobolev". Journal of Functional Analysis 72 2 (1987): 346-367. http://www.scopus.com/inward/record.url?eid=2-s2.0-45949113547&partnerID=MN8TOARS.
  61. Gaxie, Daniel; Michel, Hélène; Weber, Louis. "Estimations capacitaires sur l'espace de Wiener". Bulletin des Sciences Mathématiques 110 (1986):
    Published • 10.3917/sava.009.0065
  62. Cruzeiro, A.B.. "Unicité de solutions d'équations différentielles sur l'espace de Wiener". Journal of Functional Analysis 58 3 (1984): 335-347. http://www.scopus.com/inward/record.url?eid=2-s2.0-0000177015&partnerID=MN8TOARS.
  63. Cruzeiro, A.B.. "Équations différentielles ordinaires: Non explosion et mesures quasi-invariantes". Journal of Functional Analysis 54 2 (1983): 193-205. http://www.scopus.com/inward/record.url?eid=2-s2.0-0038968010&partnerID=MN8TOARS.
  64. Cruzeiro, A.B.. "Équations différentielles sur l'espace de Wiener et formules de Cameron-Martin non-linéaires". Journal of Functional Analysis 54 2 (1983): 206-227. http://www.scopus.com/inward/record.url?eid=2-s2.0-0001494371&partnerID=MN8TOARS.
  65. Cruzeiro, Ana Bela. "Convergence quasi partout dans des domaines paraboliques des fonctions d'intégrale de Dirichlet finie". Comptes Rendus de l Académie des Sciences - Series I - Mathematics (1982):
    Published
  66. Cruzeiro, Ana Bela. "Convergence au bord pour les fonctions harmoniques dans Rd de la classe de Sobolev Wd,1". Comptes Rendus de l Académie des Sciences - Series I - Mathematics 294 (1982):
    Published
Newsletter article
  1. Cruzeiro, Ana Bela. "Probabilidades e Hidrodinâmica", Boletim da SPE, 2018

Oral presentation

Presentation title Event name
Host (Event location)
2023/11 Stochastic Euler-Poincaré reduction and some applications
Ritsumeikan Univ. (Japan)
2023/11 On a pathwise stochastic contro problem Stochastic Analysis
RIMS (Kyoto, Japan)
2023/11 On pathwise stochastic control problems Mathematics Colloquium
Institut de Mathématiques de Bourgogne (Dijon, France)
2023/09 Stochastic variational principles on Lie groups
UNIV. SANTIAGO DE COMPOSTELA (Spain)
2023/06 Stochastic variational principles on Lie groups
University Milan (Italy)
2023/06 Pathwise stochastic control problems
Univ. du Luxembourg (Luxembourg)
2023/04 Brownian motion and some of its applications to fluid dynamics
Universidade Aberta (Portugal)
2023/03 On a pathwise stochastic control problem
École Les Houches (France)
2022/07 Generalized solutions for the Navier-Stokes equations
Universidade de Évora (Portugal)
2021/11 On the shortest path problem for Navier-Stokes stochastic flows Leipzig Seminar
(Germany)
2021/11 About the Brownian motion Communication
Academia das Ciências de Lisboa (Portugal)
2021/10 Optimal stochastic control problems in space-time domains
Ritsumeikan University (Japan)
2021/10 The Schroedinger problem in space-time domains
Ritsumeikan Univ. (Japan)
2021/09 Bernstein processes in infinite dimensions
Barcelona Univ. (Barcelona, Spain)
2021/07 Stochastic variational principles for the Navier- Stokes equation in bounded domains ENSPM
Sociedade Portuguesa de Matemática (Portugal)
2021/07 A stochastic view on the deterministic Navier-Stokes equation GDM Seminar
University of Padova (Italy)
2021/06 A stochastic view on the deterministic Navier-Stokes equation
Universite de Rennes (France)
2021/03 On stochastic Clebsch variational principles Stochastics and Geometry
BIRS (Canada)
2021/02 Optimal stochastic control problems in space-time domains
Imperial College London (United Kingdom)
2020/02 Navier-Stokes via variational principles with Lagrange multipliers Workshop on manifold and shape stochastics
(Denmark)
2019/07 On some stochastic partial differential equations obtained by a variational approach IWOTA 2019
Instituto Superior Técnico (Lisboa, Portugal)
2019/06 Stochastic Clebsch variational principles Workshop on Stochastic Analysis and Applications
Nanyang Technological University (Singapore)
2019/04 A stochastic approach to (deterministic) Hydrodynamics CIM Colloquium
CIM (Portugal)
2019/03 An entropic interpolation problem for incompressible viscid fluids Conf. Random transformations and invariance in stochastic dynamics,
Universita Milano (Italy)
2019/03 An entropic minimization problem for incompressible viscid fluids Colloquium in Interacting Particle Systems @ Tecnico,
Instituto Superior Técnico (Portugal)
2018/12 On some relations between Optimal Transport and Stochastic Geometric Mechanics BIRS Workshop Shape Analysis, Stochastic Mechanics and Optimal Transport,
Banff (Canada)
2018/07 Stochastic variational principles for some equations in Hydrodynamics Encontro Nacional da Sociedade Portuguesa de Matemática
SPM (Portugal)
2018/06 Stochastic Clebsch action principles Workshop Stochastic Analysis and applications LSAA2018,
Linnaeus University (Sweden)
2018/04 Solutions and invariant measures for Euler equations on the plane Workshop Gibbs Measures for Nonlinear Dispersive Equations,
Oberwalfach Inst. (Germany)
2018/01 Stochastic variational principles on Lie groups Intern. Scientific Conf. ”Infinite-dimensional Analysis and control theory, centenary of S.V. Fomin,
Moscow State University (Russia)
2017/12 An entropic interpolation problem for incompressible viscid fluids CIM-WIAS Workshop
Universidade de Lisboa (Portugal)
2017/10 An entropic interpolation problem for incompressible viscid fluids Classic and Stochastic Approaches to Mathematical Fluid Dynamics
Imperial College London (United Kingdom)
2017/07 Stochastic variational principles on Lie groups and semi-direct products” LMS Durham Research Symposium Stochastic Analysis
Durham University (United Kingdom)
2017/07 Camassa-Holm and Leray-alpha equations: a stochastic approach GeoProb 2017
Univ. Luxembourg (Luxembourg)
2017 Camassa-Holm and Leray-alpha equations: a stochastic approach Workshop ¿Irregular transport: analysis and applications¿
Univ. Bâle (Switzerland)
2016/12 Stochastic variational principles on Lie groups and semi-direct products Workshop Heat kernels, stochastic processes and functional inequalities,
Mathematisches Forschungsinstitut Oberwolfach (Germany)
2016/07 Forward-backward stochastic systems and Navier-Stokes equations Asian Mathematical Conference (AMC2016), Indonesia
(Indonesia)
2016/01 Navier-Stokes equation and stochastic forward-backward systems Stochastic Analysis, Rough paths, Geometry
Imperial College London (United Kingdom)
2016/01 Stochastic variational approach to the viscous Camassa–Holm and Leray-alpha equations Classic and Stochastic Geometric Mechanics UK-Japan Winter School,
Imperial College London (United Kingdom)
2015/10 On the shortest path problem for Navier-Stokes stochastic flows Stochastics and Symmetry: theory and applications from Mechanics to Finance
University of Milano (Italy)
2014/12 Stochastic variational principles for the Navier-Stokes equation, Particle Systems and Partial Differential Equations III
Universidade do Minho (Portugal)
2014/12 Forward-backward differential systems and the Navier-Stokes equation Stochastic analysis and numerical approximations in mathematical finance,
ISEG (Portugal)
2014/09 Théorème de réduction d'Euler-Poincaré stochastique Rencontres de Probabilités 2014,
Université de Rouen (France)
2014/06 Navier-Stokes equation and forward-backwars stochastic differential systems ProbaGeo
Université de Bordeaux (France)
2014/04 Stochastic variational principles on Lie groups Mathematics Colloquium
Institut de Mathématiques de Bourgogne (Dijon, France)
2013/09 Forward-backward stochastic differential systems and the Navier-Stokes equation Stochastic Analysis and Applications
Oxford-Man Institute Of Quantitative Finance (United Kingdom)
2013/07 Lagrangian Navier-Stokes stochastic flows Conference on Random Dynamical Systems
Chern Institute of Mathematics (China)
2013/05 A stochastic variational approach to the Navier-Stokes equation Probability and PDE's
Scula Normale Superiore Pisa (Italy)
2013/05 Stochastic variational principles and Fbsde's on Lie groups Heat Kernels, Stochastic Processes and Functional Inequalities
Mathematisches Forschungsinstitut Oberwolfach (Germany)
2013/03 On stochastic variational principles CIM-MPE 2013: Mathematics of Energy and Climate Change
CIM (Portugal)
2012/07 A stochastic approach to the deterministic NavierStokes equations UT-Austin Portugal Workshop in Mathematics (Mathematical Finance and Stochastic Control)
Universidade Nova de Lisboa (Portugal)
2012/07 Stochastic Euler-Poincaré reduction on Lie groups 9ª AIMS Conference, Orlando
(United States)
2012/06 On stochastic variational principles ProbaGeo
Université de Strasbourg (France)
2012/04 Stochastic calculus of variations on the diffeomorphisms group EPSRC Symposium-Workshop Stochastic analysis and stochastic PDEs
Warwick University (United Kingdom)
2012/01 Stochastic least action principle and related Brenier-type Navier-Stokes flows Workshop Recent Developments in Stochastic Analysis
EPFL (Switzerland)
2011/09 Generalized stochastic Navier-Stokes flows GDIS 2011 (Geometry, Dynamics, Integrable Systems)
Universidade de Lisboa (Portugal)
2011/09 Generalized stochastic Navier-Stokes flows 5th International Conference on Stochastic Analysis and its Applications
Hausdorff Center, Univ. Bonn (Germany)
2011/05 Stochastic forward-backward equations associated with Navier-Stokes equations Seventh Seminar on Stochastic Analysis, Random Fields and Applications
ETH (Switzerland)
2010/10 Non existence of Haar-type measures on some spaces of maps Conference in Memory of Paul Malliavin
Université de Dijon (France)
2010/09 Stochastic Navier-Stokes flows: stability and rotation Geometry Dynamics Integrable Systems GDIS2010
University of Belgrade (Serbia)
2010/07 Non existence of Haar-type invariant measures on some spaces of maps XXIX Workshop on Geometric Methods in Physics
(Poland)
2009/12 Stochastic Lagrangian Navier-Stokes flows on Riemannian manifolds Symposium Analysis, probability and geometry in quantum physics and classical mechanics
KTH (Sweden)
2009/11 Stochastic Lagrangian Navier-Stokes flows on Riemannian manifolds XI CLAPEM (Congresso Latino-Americano de Probabilidad y Estadistica Matematica)
(Venezuela)
2009/07 Some results on Lagrangian Navier-Stokes flows 7 th Intern. ISAAC Congress (Stochastic Analysis Session)
Imperial College London (United Kingdom)
2009/07 Non ergodicity of diffusions on the diffeomorphisms group Workshop on Stochastic Analysis and Finance
City University of Hong-Kong (Hong Kong SAR China)
2008/05 Hydrodynamics, probability and the geometry of the diffeomorphisms group Sixth Seminar on Stochastic Analysis, Random Fields and Applications,
ETH (Switzerland)
2008/04 Hydrodynamics and the geometry of the diffeomorphims group - some results Symposium on Stochastic Analysis
University Bonn (Germany)
2007/11 Non ergodicity of the Euler flow on the torus Workshop on Stochastic partial differential equations”
Institut Mittag-Leffler (Sweden)
2006/09 On a stochastic Euler equation DMV meeting, Probability and Geometry
University Bonn (Germany)
2006/07 “Brownian motion on the diffeomorphisms group and global solution of a 2D stochastic Euler equation” Stochastic Fluid Mechanics and SPDEs
Centro De Giorgi (Italy)
2006/01 Approximations géométriques d’équations différentielles stochastiques Colloque "Discrétisation de processus"
INRIA Sophia Antipolis (France)
2005/09 Differential equations on invariant manifolds: a Malliavin calculus approach Journées de Probabilité
Institut Élie Cartan, Nancy (France)
2005/09 Diffusions on the group of homeomorphisms in the torus and the Navier-Stokes equation
Tunis (Tunisia)
2005/05 Geometrical numerical schemes for s.d.e.’s Fifth Seminar on Stochastic Analysis, Random Fields and Applications
ETH (Switzerland)
2004/09 Riemannian path space geometry XIII Encontro de Outono de Geometria e Física
(Spain)
2003/09 Finite dimensional approximation of Riemannian path space geometry
Université de Toulouse (Toulouse, France)
2002/09 The heat semigroup on the Riemannian path space 1st. Sino-German Conference on Stochastic Analysis (Satellite of ICM 2002)
Beijing University (China)
2002/05 An asymptotic estimate for the vertical derivatives of the heat kernel associated with the horizontal Laplacian
(Ascona, Switzerland)
2001/07 Tangent processes on the Wiener space 27th. Conf. On Stochastic Processes and their Applications
Cambridge University (Cambridge, United Kingdom)
2001/07 Ricci tensors on the path space
Berlin University (Berlin, Germany)
2001/06 Tangent processes and applications
Euler Institute (St Petersbourg, Russia)
2000/07 Geometry of path spaces
Warwick University (Warwick, United Kingdom)
2000/01 Tangent processes – some applications
Univ. Trento (Trento, Italy)
1999/08 On a method of constructing invariant measures for elliptic operators
(Norway)
1999/07 Construction of some diffusion processes on the Wiener space
Yonsei University (Seoul)
1998/10 Equations of motion for a class of time-symmetric processes associated to a Markov process
(Santiago, Chile)
1997/11 Weitzenböck formulae and estimates for anticipative stochastic integrals
MSRI Berkely (United States)
1997/09 Calcul Stochastique anticipatif et analyse sur l’espace des chemins d’une variété Riemanniene
Université Paul Sabatier (Toulouse, France)
1997/06 Some Aspects of the Geometry of Path Spaces European conference on Stochastic Analysis
Univ. Barcelona (Barcelona, Spain)
1996/08 Invariant measure for a wave equation on a Riemannian manifold Stochastic Differential Equations and Difference Equations ( Satellite Bernoulli Society Congress)
(Hungary)
1996/07 Energy identities and estimates for anticipative stochastic integrals on a Riemannian manifold
(Geilo, Norway)
1995/07 Energy identities on the path space of a Riemannian manifold VI European on Symposium Stochastic Analysis
Swansea Univ. (Swansea, United Kingdom)
1994/10 Curvature on the Path Space of a Riemannian Manifold IV European on Symposium Stochastic Analysis
Bonn Univ. (Bonn, Germany)
1993/12 A class of stochastic processes in Quantum Physics Stochasic Analysis
Warsow Univ. (Warsow, Poland)
1993/07 Bernstein processes and Dirichlet forms NATO (ARW) Conf. Classical and Modern Potential Theory and Applications
(France)
1993/04 Invariant measures on Wiener spaces Stochastic Analysis
Université de Metz (Metz, France)
1991/06 Singular differential operators and associated processes
(Locarno, Switzerland)
1991/03 Bernstein processes in infinite dimensions European conference on Stochastic Analysis
Bielefeld Univ. (Bielefeld, Germany)
1989/11 Differential Equations on Wiener spaces and action of the associated flows on Wiener measure
(Poland)
1989/08 Invariant measures for the Euler flow in two dimensions
KTH (Stockholm, Sweden)
1989/07 Infinite-dimensional diffusions Dirichlet forms
MFO (Oberwalfach, Germany)
1988/07 Wiener measure preserving maps
(Ascona, Switzerland)
1987/09 About some evolution equations in infinite dimensional spaces Rencontre Internat. de Math.
(Greece)
1986/08 Infinite Dimensional Stochastic processes associated to some elliptic operators
Swansea Univ. (Swansea, United Kingdom)
1986/01 Some elliptic operators on the Wiener space Stochastic Analysis and Applications
IMA (Minneapolis, United States)
1985/07 Differential equations on the Wiener space and Capacitary estimates on the Wiener space Stochastic Analysis
Warwick University (United Kingdom)

Supervision

Thesis Title
Role 		Degree Subject (Type)
Institution / Organization
2022 - 2023/12 Fractional Brownian motion and Applications
Supervisor
 Mathematics (Master)
Universidade de Lisboa Instituto Superior Técnico, Portugal
2019/01 - 2019/12 Derivation of the Navier-Stokes Equations from a Stochastic Variational Principle
Supervisor
 Matemática (Master)
Universidade de Lisboa Instituto Superior Técnico, Portugal
2015/09 - 2019/02 Statistical solutions and invariant measures in Hydrodynamics
Co-supervisor
 Matemática (PhD)
Universidade de Lisboa Faculdade de Ciências, Portugal
2015 - 2019/02 Statistical solutions and invariant measures in Hydrodynamics
Co-supervisor
 Mathematics
Universidade de Lisboa Faculdade de Ciências, Portugal
2014 - 2018 Statistical solutions and invariant measures in Hydrodynamics
Co-supervisor
 Mathematics (PhD)
Universidade de Lisboa Faculdade de Ciências, Portugal
2014/10 - 2017/05 Stochastic Characterization for Navier-Stokes and Camassa-Holm Equations and Existence and Uniqueness of Solutions for Camassa-Holm Equations
Co-supervisor
 Matemática (PhD)
Chinese Academy of Sciences Institute of Applied Mathematics, China
2014 - 2017 Stochastic characterization for Navier-Stokes and Camassa-Holm equations
Co-supervisor
 Mathematics (PhD)
Chinese Academy of Sciences Beijing Advanced Sciences and Innovation Center, China
2015/10 - 2016/07 Financial derivatives and stochastic calculus
Co-supervisor
 Matemática (Master)
Universidade de Lisboa Instituto Superior Técnico, Portugal
2011/01 - 2011/12 Stochastic forward-backward differential systems and large deviations
Co-supervisor
 Ensino de Matemática no 3.º Ciclo do Ensino Básico e no Secundário (Master)
Universidade de Lisboa Faculdade de Ciências, Portugal
2008/10 - 2009/09 Diferenças Finitas na Valoração de Opções Europeias e Americanas
Co-supervisor
 Matemática (Master)
Universidade de Lisboa Instituto Superior Técnico, Portugal
2008/08 - 2009/09 Equações Diferenciais Estocásticas em Modelos Financeiros
Co-supervisor
 Matemática (Master)
Universidade de Lisboa Instituto Superior Técnico, Portugal
2003/10 - 2004/07 Equações diferenciais estocásticas e aplicações
Supervisor
 Matemática (Master)
Universidade de Lisboa Instituto Superior Técnico, Portugal
2003 - 2004 Equações diferenciais estocásticas
Supervisor
 Matemática (Master)
Universidade de Lisboa Instituto Superior Técnico, Portugal
2002 - 2003 O integral de Skorohod
Supervisor
 Matemática (Master)
Universidade de Lisboa Faculdade de Ciências, Portugal
1998 - 2001 Aplicação de Métodos de Análise Estocástica ao Estudo de Certas Equações da Hidrodinâmica
Supervisor
 Matemática (PhD)
Universidade de Lisboa Faculdade de Ciências, Portugal
1997 - 1999/08 Análise em espaços de caminhos
Co-supervisor
 Matemática (PhD)
Universidade de Lisboa Faculdade de Ciências, Portugal
1995 - 1996/01 Equações diferenciais em espaços de Wiener
Supervisor
 Matemática (Master)
Universidade de Lisboa Faculdade de Ciências, Portugal

Event organisation

Event name
Type of event (Role) 		Institution / Organization
2023/08/30 - 2023/09/01 6th Conference on Geometric Science of Information (GSI2023) (2023/08/30 - 2023/09/01)
Conference (Member of the Scientific Committee)
2023/07/24 - 2023/07/28 SPA 2023 - 43th Conference on stochastic Processes and their Applications Bernoulli Society (2023/07/24 - 2023/07/28)
Conference (President of the Organising Committee)
2022/06/21 - 2022/06/24 Optimal transport, geometric and stochastic Hydrodynamics (2022/06/21 - 2022/06/24)
Conference (Co-organisor)
 Universidade de Lisboa Grupo de Física Matemática, Portugal
2021/09/14 - 2021/09/17 Schroedinger's problem and Optimal Transport (2021/09/14 - 2021/09/17)
Conference (Co-organisor)
 Universidade de Lisboa Grupo de Física Matemática, Portugal
2021/02 - 2021/02 Membro do Comité Científico da conferência Dynamic Control and Optimization, DCO (2021/02 - 2021/02)
Conference (Member of the Scientific Committee)
2021 - 2021 Membro do Comité Científico de GSI2021 (2021 - 2021)
Conference (Member of the Scientific Committee)
2019 - 2019 Membro do Comité Científico de GSI2019 (2019 - 2019)
Conference (Member of the Scientific Committee)
2018 - 2018 Membro do Comité Científico de GSI2018 (2018 - 2018)
Conference (Member of the Scientific Committee)
 Universidade de Lisboa Grupo de Física Matemática, Portugal
2018 - 2018 Workshop “From Stochastic Geometric Mechanics to Mass Transportation Problems (2018 - 2018)
Conference (Member of the Organising Committee)
2017/07 - 2017/07 Conference New trends in Applied Geometric Mechanics (2017/07 - 2017/07)
Conference (Member of the Scientific Committee)
 Instituto de Ciencias Matemáticas, Spain
2017/07 - 2017/07 3rd Int'l Conference on Probability and Stochastic Analysis (ICPSA 2017) (2017/07 - 2017/07)
Conference (Member of the Scientific Committee)
2017 - 2017 39 thConference on Stochastic processes and their applications, SPA 2017 (2017 - 2017)
Conference (Member of the Scientific Committee)
2016 - 2016 2nd Int'l Conference on Probability and Stochastic Analysis (ICPSA 2016) (2016 - 2016)
Conference (Member of the Scientific Committee)
2015/10 - 2015/10 International Conference on Stochastic Analysis and Applications (ICSAA-2015) (2015/10 - 2015/10)
Conference (Member of the Scientific Committee)
2015/01/01 - 2015/06/30 Co-organizadora do programa do Centre Bernoulli da EPFL “Geometric Mechanics, Variational and Stochastic Methods” (2015/01/01 - 2015/06/30)
Other (Co-organisor)
 École Polytechnique Fédérale de Lausanne, Switzerland
2015 - 2015 International Conference on Probability and Stochastic Analysis (ICPSA 2015) (2015 - 2015)
Conference (Member of the Scientific Committee)
2014/07 - 2014/07 Conferência “Advances in Mathematical Fluid Mechanics – Stochastic & deterministic methods (2014/07 - 2014/07)
Conference (Member of the Organising Committee)
 Universidade de Lisboa Grupo de Física Matemática, Portugal
2011/09 - 2011/09 Conferência GDIS 2011 (Geometry, Dynamics, Integrable Systems) (2011/09 - 2011/09)
Conference (Member of the Scientific Committee)
2010 - 2010 conferência SPA 2010, Osaka, Japão (2010 - 2010)
Conference (Member of the Scientific Committee)
2007/11 - 2007/11 International Conference on Stochastic Analysis and Applications (2007 - 2007)
Conference (Member of the Scientific Committee)
2006/09 - 2006/09 Stochastic Analysis in Mathematical Physics, Satellite conference of the International Congress of Mathematics (2006/09 - 2006/09)
Conference (Member of the Organising Committee)
 Universidade de Lisboa Grupo de Física Matemática, Portugal
2005/09 - 2005/09 International Conference on Mathematical Analysis of Random Phenomena (2005/09 - 2005/09)
Conference (Member of the Scientific Committee)
2003 - 2003 EMS Mathematical Weekend (2003 - 2003)
Conference (Member of the Organising Committee)
2003 - 2003 International Congress Mathematical Physics (2003 - 2003)
Congress (Member of the Organising Committee)
2002/09 - 2002/09 1st. Sino-German Conference on Stochastic Analysis (Satellite of the ICM 2002) (2002/09 - 2002/09)
Conference (Member of the Scientific Committee)
2001/09 - 2001/09 Workshop “From Brownian motion to infinite dimensional analysis” (2001/09 - 2001/09)
Conference (Member of the Organising Committee)
2000/09 - 2000/09 8 thSilivri-Magusa Workshop on Stochastic Analysis (2000/09 - 2000/09)
Conference (Member of the Scientific Committee)
1999/05 - 1999/05 International Conference on Stochastic Analysis and Mathematical Physics (1999/05 - 1999/05)
Conference (Member of the Organising Committee)
 Universidade de Lisboa Grupo de Física Matemática, Portugal
1998/06 - 1998/06 3º Encontro do Projecto PRAXIS “Física-Matemática" (1998/06 - 1998/06)
Meeting (Member of the Organising Committee)
1997/02 - 1997/02 2º Encontro do Projecto PRAXIS "Física-Matemática" (1997/02 - 1997/02)
Meeting (Member of the Organising Committee)
1996/02 - 1996/02 1º Encontro do Projecto PRAXIS "Física-Matemática" (1996/02 - 1996/02)
Meeting (Member of the Organising Committee)
1993/09 - 1993/09 4 th European Symposium on Stochastic Analysis (1993/09 - 1993/09)
Conference (Member of the Organising Committee)
1989/09 - 1989/09 Stochastic Analysis and Applications (1989/09 - 1989/09)
Conference (Member of the Organising Committee)

Jury of academic degree

Topic
Role 		Candidate name (Type of degree)
Institution / Organization
2023/11 Hydrodynamic behavior of a degenerate microscopic dynamics with slow reservoirs
Thesis Member
 Gabriel Nahum (PhD)
Universidade de Lisboa Instituto Superior Técnico, Portugal
2023/05 Topics in elliptic problems: from semilinear equations to shape optimization
Thesis Member
 Hugo Tavares (Aggregation)
Universidade de Lisboa Instituto Superior Técnico, Portugal
2023/04 Dynamical Universality Classes in Driven Diffusive Systems
Thesis Member
 Gunter Schutz (Aggregation)
Universidade de Lisboa Instituto Superior Técnico, Portugal
2022/07 Sharp Restriction Theory
Thesis Member
 Diogo Oliveira e Silva (Aggregation)
Universidade de Lisboa Instituto Superior Técnico, Portugal
2021/12 Symétries des modèles stochastiques en mathématiques financières, en physique et en neurosciences
Thesis Member
 Laurène Valade (PhD)
Université de Rouen UFR des Sciences et Techniques, France
2021/11 Problème de Schroedinger, in égalit és fonctionnelles et transport optimal
Thesis Member
 Giovanni Conforti (Aggregation)
École Polytechnique, France
2021/11 Jump-diffusion processes in optimal stopping. Applications in real options
Thesis Member
 Claudia Philippart (Aggregation)
Universidade de Lisboa Instituto Superior Técnico, Portugal
2021/07 Hydrodynamic behavior of a degenerate microscopic dynamics with slow reservoirs
Thesis Member
 Renato de Paula (PhD)
Universidade de Lisboa Instituto Superior Técnico, Portugal
2021/04 On the effect of stochastic Lie transport noise on fluid dynamic equations
(Thesis) Arguer
 Aythami Bettencourt de Léon (PhD)
Imperial College London, United Kingdom
2021/04 Convolution-like structures, differential operators and diffusion processes
Thesis Member
 Rúben Sousa (PhD)
Universidade do Porto, Portugal
2020/12 Stochastic calculus on manifold and application to functional inequalities
Thesis Member
 Baptiste Huguet (PhD)
Université de Bordeaux, France
2020/07 Stochastic Geometric Mechanics for Fluid modelling and MCMC
(Thesis) Arguer
 So Takao (PhD)
Imperial College London, United Kingdom
2020/06 Viscous and incompressible fluids: asymptotic behavour and optimal control
(Thesis) Arguer
 Fernanda Cipriano (Aggregation)
Universidade Nova de Lisboa Departamento de Matemática, Portugal
2019/10 Le mouvement brownien cinétique en dimension infinie
Thesis Member
 Pierre Perruchaud (PhD)
Université de Rennes, France
2018/12 Sur le comportement qualitatif des solutions de certaines ´equations aux d ´eriv ´ees partielles stochastiques de type parabolique
(Thesis) Arguer
 Rim Toubi (PhD)
Institut de Mathématiques Élie Cartan, France
2018/09 A Thermodinamical formalism for free semigroup actions
Thesis Member
 Maria Carvalho (Aggregation)
Universidade do Porto, Portugal
2018/06 Universality from microscopic stochastic dynamics
Thesis Member
 Patrícia Gonçalves (Aggregation)
Universidade de Lisboa Instituto Superior Técnico Departamento de Matemática, Portugal
2015/06 Symétries d'équations aux dérivées partielles, calcul stochastique, applications à la physique mathématique et à la finance
(Thesis) Arguer
 Helene Quintard (PhD)
Université de Rouen Normandie, France
2012/06 Inversibilité stochastique et thèmes afférents
Thesis Member
 Rémi Lassalle (PhD)
Télécom Paris Laboratoire de Traitement et Communication de l¿Information, France
1993 Topics in dynamical systems on Wiener space
(Thesis) Main arguer
 Gunnar Peters (PhD)
Kungliga Tekniska Högskolan, Sweden

Association member

Society Organization name Role
2000 - 2004 Sociedade Portuguesa de Matemática Presidente

Committee member

Activity description
Role 		Institution / Organization
2017 - Current Membro do Conselho científico das Ciências Exatas e Engenharia da FCT
Member
 Fundação para a Ciência e a Tecnologia, Portugal
2017 - 2023 Scientific Council for Exact Sciences and Engineering
Member
 Fundação para a Ciência e a Tecnologia, Portugal
2010 - 2017 Committee for Conferences on Stochastic Processes (CCSP) of the Bernoulli Society for Mathematical Statistics and Probability
Member
 Bernoulli Enterprise Inc, United States
2010 - 2013 Membro do Committee for Conferences on Stochastic Processes and Their Applications da Bernoulli Society
Advisor / Consultant
2006 - 2011 Comission for Mathematical Physics (C18)
Member
 International Union of Pure and Applied Physics, Singapore
2006 - 2011 Member, then Secretary
Other
 International Union of Pure and Applied Physics, Singapore
2004 - 2008 Comissão para Encontros da European Mathematical Society
Member
 European Mathematical Society, Finland
2000 - 2004 President
President / Vice-president
 Sociedade Portuguesa de Matemática, Portugal

Conference scientific committee

Conference name Conference host
2023/08/30 - 2023/09/01 GSI 2023 Geometric Science of Information
2023/07/21 - 2023/07/28 SPA 2023 - Bernoulli Society
2021/11 - 2021/11 CIRM, Luminy
2018 - 2020 Geometric Science of Information Paris

Course / Discipline taught

Academic session Degree Subject (Type) Institution / Organization
2024/01/08 - 2024/01/12 Mini-course "Stochastic Lagrangian flows in Hydrodynamics" Centre International de Rencontres Mathématiques, France
2014/02 - 2014/02 Mini-course “Stochastic Lagrangian flows and the Navier- Stokes equation" Mathematics Institut de Mathématiques de Toulouse, France
2012/03 - 2012/03 Mini-course "Stochastic Lagrangian flows" École Polytechnique Fédérale de Lausanne, Switzerland

Evaluation committee

Activity description
Role 		Institution / Organization Funding entity
2023 - 2023 La Caixa projects
Evaluator
 Fundação 'la Caixa', Portugal Fundação 'la Caixa'
2021 - 2023 Projects
Evaluator
 Unitatea Executiva pentru Finantarea Invatamantului Superior a Cercetarii Dezvoltarii si Inovarii, Romania Unitatea Executiva pentru Finantarea Invatamantului Superior a Cercetarii Dezvoltarii si Inovarii
2016 - 2023 Avaliador de bolsas individuais Marie Sklodowska-Curie
Evaluator
 European Science Foundation
2022 - 2022 Projects
Evaluator
 Vetenskapsradet, Sweden Vetenskapsradet
2020 - 2020 IUF junior jury member
Evaluator
 Institut Universitaire de France, France
2019 - 2019 IUF Senior jury member
Evaluator
 Institut Universitaire de France, France
2016 - 2019 Projects
Evaluator
 European Science Foundation, France European Science Foundation
2016 - 2017 Avaliador de projectos
Evaluator
 Rossijskij naucnyj fond, Russia
2010 - 2013 Projects
Evaluator
 Irish Research Council, Ireland Irish Research Council
2012 - 2012 European Latsis Prize
Evaluator
 European Science Foundation, France European Science Foundation
2007 - 2010 Membro dos painéis de avaliação do ERC (European Research Council)
Evaluator
 European Research Council, Belgium
2008 - 2009 IUF senior members jury
Evaluator
 Institut Universitaire de France, France
2003 - 2003 Ramon y Cajal grants
Evaluator
 España Ministerio de Ciencia e Innovación, Spain España Ministerio de Ciencia e Innovación

Journal scientific committee

Journal title (ISSN) Publisher
2023 - Current Geometric Mechanics
2023 - Current Electronic Communications in Probability
2023 - Current Electronic Journal of Probability
2022 - Current Journal of Mathematical Analysis and Applications
2019 - Current Stochastic Analysis and Applications
2018 - Current Bollettino dell'Unione Matematica Italiana

Title

2020 Membro correspondente
Academia das Ciências de Lisboa, Portugal