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James Kennedy. Completed the Título de Agregado in N/A in 2023/07/12 by Universidade de Lisboa Instituto Superior Técnico and Doctor of Philosophy in Doctor of Philosophy in 2010/04/09 by The University of Sydney - Camperdown and Darlington Campus. Is Assistant Professor in Universidade de Lisboa Faculdade de Ciências. Published 37 articles in journals. Has 2 section(s) of books. Organized 3 event(s). Supervised 1 PhD thesis(es). Co-supervised 1 MSc dissertation(s). Participates and/or participated as Post-doc Fellow in 1 project(s), Research Fellow in 1 project(s) and Researcher in 2 project(s). Works in the area(s) of Exact Sciences with emphasis on Mathematics. In his curriculum Ciência Vitae the most frequent terms in the context of scientific, technological and artistic-cultural output are: Operator theory; Spectral theory; Quantum graphs; Mathematics; .
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Identification

Personal identification

Full name
James Kennedy

Citation names

  • Kennedy, James
  • Kennedy, James B.
  • Kennedy, James Bernard
  • Kennedy, J. B.

Author identifiers

Ciência ID
EC11-C380-51A5
ORCID iD
0000-0001-5634-0301
Google Scholar ID
https://scholar.google.com/citations?hl=de&user=rm9fSMIAAAAJ

Addresses

  • Departamento de Matemática, Faculdade de Ciências da Universidade de Lisboa. Campo Grande, Edifício C6, 1749-016, Lisboa, Lisboa, Portugal (Professional)

Websites

Knowledge fields

  • Exact Sciences - Mathematics

Languages

Language Speaking Reading Writing Listening Peer-review
English (Mother tongue)
German Proficiency (C2) Proficiency (C2) Proficiency (C2) Proficiency (C2) Proficiency (C2)
Portuguese Upper intermediate (B2) Upper intermediate (B2) Upper intermediate (B2) Upper intermediate (B2) Upper intermediate (B2)
Education
Degree Classification
2023/07/11 - 2023/07/12
Concluded
 N/A (Título de Agregado)
Major in Matemática
Universidade de Lisboa Instituto Superior Técnico, Portugal
"Geometric Spectral Theory of Quantum Graphs" (THESIS/DISSERTATION)
 N/A
2010/04/09
Concluded
 Doctor of Philosophy (Doctor of Philosophy)
Major in Mathematics
The University of Sydney - Camperdown and Darlington Campus, Australia
"On the isoperimetric problem for the Laplacian with Robin and Wentzell boundary conditions" (THESIS/DISSERTATION)
Affiliation

Science

Category
Host institution 		Employer
2016/12/29 - 2020/04/30 Auxiliary Researcher (Research) Universidade de Lisboa Faculdade de Ciências, Portugal
Universidade de Lisboa Grupo de Física Matemática, Portugal
2011/09/01 - 2013/09/30 Researcher (Research) Alexander von Humboldt-Stiftung, Germany
Universität Ulm Fakultät für Mathematik und Wirtschaftswissenschaften, Germany
2010/05/17 - 2011/08/31 Postdoc (Research) Universidade de Lisboa Grupo de Física Matemática, Portugal

Teaching in Higher Education

Category
Host institution 		Employer
2020/05/01 - Current Assistant Professor (University Teacher) Universidade de Lisboa Faculdade de Ciências, Portugal
Universidade de Lisboa Faculdade de Ciências, Portugal
2013/10/01 - 2017/03/31 Assistant (University Teacher) Universität Stuttgart, Germany
Universität Stuttgart Fakultät 8 für Mathematik und Physik, Germany
2016/04/01 - 2016/09/30 Invited Associate Professor (University Teacher) Universität Ulm, Germany
Universität Ulm Fakultät für Mathematik und Wirtschaftswissenschaften, Germany
Projects

Grant

Designation Funders
2016/12/29 - 2020/04/30 Spectral geometry of quantum graphs
IF/01461/2015
Research Fellow
Universidade de Lisboa Grupo de Física Matemática, Portugal
 Fundação para a Ciência e a Tecnologia
Ongoing
2011/09/01 - 2013/09/30 The location of the spectrum and generation properties of elliptic partial differential equations
N/A
Post-doc Fellow
Universität Ulm Fakultät für Mathematik und Wirtschaftswissenschaften, Germany
 Alexander von Humboldt-Stiftung
Concluded

Contract

Designation Funders
2019/10/04 - Current COST Action CA18232: Mathematical models for interacting dynamics on networks
CA18232
 European Cooperation in Science and Technology
2021/03/01 - 2024/02/29 Nonlinear Dispersive and Elliptic Systems - new horizons in regularity, dynamics and asymptotic analysis
PTDC/MAT-PUR/1788/2020
Researcher
Fundação para a Ciência e a Tecnologia, Portugal
Ongoing
2019/01/01 - 2019/12/31 Grupo de Física-Matemática da Universidade de Lisboa
UID/MAT/00208/2019
Fundação da Faculdade de Ciências da Universidade de Lisboa, Portugal

Universidade de Lisboa Grupo de Física Matemática, Portugal

FCiênciasID Associação para a Investigação e Desenvolvimento de Ciências, Portugal

Universidade de Lisboa Faculdade de Ciências, Portugal
Fundação para a Ciência e a Tecnologia
Concluded
2017/04/01 - 2019/09/14 Extremal spectral quantities and related problems
ptdc/mat-cal/4334/2014
Researcher
Universidade de Lisboa Grupo de Física Matemática, Portugal
 Fundação para a Ciência e a Tecnologia
Concluded
2010/01/18 - 2011/08 Eigenvalues of the Laplacian: analytic, geometric and computational aspects
ptdc/mat/101007/2008
 Fundação para a Ciência e a Tecnologia
Concluded
Outputs

Publications

Book
  1. Arendt, Wolfgang; Urban, Karsten. Partial Differential Equations. Springer International Publishing. 2023.
    10.1007/978-3-031-13379-4 • Translator
Book chapter
  1. "A Family of Diameter-Based Eigenvalue Bounds for Quantum Graphs". 213-239. Springer International Publishing, 2020.
    10.1007/978-3-030-44097-8_11
  2. Bucur, D.; Freitas, P.; Kennedy, J.. "The robin problem". 78-119. 2017.
Journal article
  1. Ahrami, Mohammed; El Allali, Zakaria; Harrell II, Evans M; Kennedy, James B. "Optimizing the fundamental eigenvalue gap of quantum graphs". Journal of Physics A: Mathematical and Theoretical 57 38 (2024): 385205. http://dx.doi.org/10.1088/1751-8121/ad6410.
    10.1088/1751-8121/ad6410
  2. Kennedy, James. "Geometric spectral theory of quantum graphs". Communications in Mathematics Volume 32 (2024): http://dx.doi.org/10.46298/cm.12380.
    10.46298/cm.12380
  3. Baptista, Luís N.; Kennedy, James B.; Mugnolo, Delio. "Mean Distance on Metric Graphs". The Journal of Geometric Analysis 34 5 (2024): http://dx.doi.org/10.1007/s12220-024-01574-0.
    10.1007/s12220-024-01574-0
  4. Berkolaiko, G.; Kennedy, J.B.; Kurasov, P.; Mugnolo, D.. "IMPEDIMENTS TO DIFFUSION IN QUANTUM GRAPHS: GEOMETRY-BASED UPPER BOUNDS ON THE SPECTRAL GAP". Proceedings of the American Mathematical Society 151 8 (2023): 3439-3455. http://www.scopus.com/inward/record.url?eid=2-s2.0-85162213019&partnerID=MN8TOARS.
    10.1090/proc/16322
  5. Hofmann, M.; Kennedy, J.B.; Serio, A.. "Spectral minimal partitions of unbounded metric graphs". Journal of Spectral Theory 13 2 (2023): 593-622. http://www.scopus.com/inward/record.url?eid=2-s2.0-85174716810&partnerID=MN8TOARS.
    10.4171/JST/462
  6. Sabine Bögli; James B. Kennedy; Robin Lang. "On the eigenvalues of the Robin Laplacian with a complex parameter". Analysis and Mathematical Physics (2022): https://doi.org/10.1007/s13324-022-00646-0.
    10.1007/s13324-022-00646-0
  7. Buoso, D.; Kennedy, J.B.. "THE BILAPLACIAN WITH ROBIN BOUNDARY CONDITIONS". SIAM Journal on Mathematical Analysis 54 1 (2022): 36-78. http://www.scopus.com/inward/record.url?eid=2-s2.0-85121624866&partnerID=MN8TOARS.
    10.1137/20M1363984
  8. Matthias Hofmann; James B. Kennedy. "Interlacing and Friedlander-type inequalities for spectral minimal partitions of metric graphs". Letters in Mathematical Physics 111 4 (2021): https://doi.org/10.1007/s11005-021-01438-6.
    10.1007/s11005-021-01438-6
  9. "On Pleijel’s Nodal Domain Theorem for Quantum Graphs". Annales Henri Poincaré (2021): http://dx.doi.org/10.1007/s00023-021-01077-6.
    10.1007/s00023-021-01077-6
  10. "Asymptotics and Estimates for Spectral Minimal Partitions of Metric Graphs". Integral Equations and Operator Theory 93 3 (2021): http://dx.doi.org/10.1007/s00020-021-02635-7.
    10.1007/s00020-021-02635-7
  11. "A theory of spectral partitions of metric graphs". Calculus of Variations and Partial Differential Equations 60 2 (2021): http://dx.doi.org/10.1007/s00526-021-01966-y.
    10.1007/s00526-021-01966-y
  12. "On the hot spots of quantum graphs". Communications on Pure & Applied Analysis 0 0 (2021): 0-0. http://dx.doi.org/10.3934/cpaa.2021095.
    10.3934/cpaa.2021095
  13. Arendt, W.; Kennedy, J.B.. "Disjointness-preserving operators and isospectral Laplacians". Journal of Spectral Theory 11 4 (2021): 1471-1510. http://www.scopus.com/inward/record.url?eid=2-s2.0-85122134268&partnerID=MN8TOARS.
    10.4171/JST/379
  14. "On the eigenvalues of quantum graph Laplacians with large complex $\delta$ couplings". Portugaliae Mathematica 77 2 (2020): 133-161. http://dx.doi.org/10.4171/pm/2047.
    10.4171/pm/2047
  15. Kennedy, James B.; Lang, Robin. "On the eigenvalues of quantum graph Laplacians with large complex $\delta$ couplings". arXiv preprints (2020): https://arxiv.org/abs/2001.10244.
    Submitted
  16. Arendt, Wolfgang; Kennedy, James B.. "Disjointness-preserving operators and isospectral Laplacians". arXiv preprints (2020): https://arxiv.org/abs/2002.09207.
    Submitted
  17. Kennedy, James B.; Rohleder, Jonathan. "On the hot spots of quantum graphs". arXiv preprints (2020): https://arxiv.org/abs/2003.14335.
    Submitted
  18. Freitas, Pedro; Kennedy, James B. "Extremal Domains and Pólya-type Inequalities for the Robin Laplacian on Rectangles and Unions of Rectangles". International Mathematics Research Notices (2019): http://dx.doi.org/10.1093/imrn/rnz204.
    10.1093/imrn/rnz204
  19. Gregory Berkolaiko; James B. Kennedy; Pavel Kurasov; Delio Mugnolo. "Surgery principles for the spectral analysis of quantum graphs". Transactions of the American Mathematical Society 372 7 (2019): 5153-5197. https://doi.org/10.1090%2Ftran%2F7864.
    10.1090/tran/7864
  20. Bögli, Sabine; Kennedy, James B.; Lang, Robin. "On the eigenvalues of the Robin Laplacian with a complex parameter". arXiv preprints (2019): https://arxiv.org/abs/1908.06041.
    Submitted
  21. Gregory Berkolaiko; James B Kennedy; Pavel Kurasov; Delio Mugnolo. "Edge connectivity and the spectral gap of combinatorial and quantum graphs". Journal of Physics A: Mathematical and Theoretical 50 36 (2017): 365201-365201. https://doi.org/10.1088%2F1751-8121%2Faa8125.
    10.1088/1751-8121/aa8125
  22. J. B. Kennedy. "A toy Neumann analogue of the nodal line conjecture". Archiv der Mathematik (2017): https://doi.org/10.1007%2Fs00013-017-1117-1.
    10.1007/s00013-017-1117-1
  23. James B. Kennedy; Delio Mugnolo. "The Cheeger constant of a quantum graph". PAMM 16 1 (2016): 875-876. https://doi.org/10.1002%2Fpamm.201610426.
    10.1002/pamm.201610426
  24. Daniel Daners; Jochen Glück; James B. Kennedy. "Eventually and asymptotically positive semigroups on Banach lattices". Journal of Differential Equations 261 5 (2016): 2607-2649. https://doi.org/10.1016%2Fj.jde.2016.05.007.
    10.1016/j.jde.2016.05.007
  25. Kennedy, James. "Summation formula inequalities for eigenvalues of the perturbed harmonic oscillator". Osaka Journal of Mathematics (2016): http://projecteuclid.org/euclid.ojm/1461781794.
  26. James B. Kennedy; Pavel Kurasov; Gabriela Malenová; Delio Mugnolo. "On the Spectral Gap of a Quantum Graph". Ann. Henri Poincaré (2016): http://dx.doi.org/10.1007/s00023-016-0460-2.
    10.1007/s00023-016-0460-2
  27. Pedro Freitas; James Kennedy. "Summation formula inequalities for eigenvalues of Schrödinger operators". Journal of Spectral Theory 6 3 (2016): 483-503. https://doi.org/10.4171%2Fjst%2F130.
    10.4171/jst/130
  28. Ralph Chill; Daniel Hauer; James Kennedy. "Nonlinear semigroups generated by j-elliptic functionals". Journal de Mathématiques Pures et Appliquées (2015): http://dx.doi.org/10.1016/j.matpur.2015.11.005.
    10.1016/j.matpur.2015.11.005
  29. Daniel Daners; Jochen Glück; James B. Kennedy. "Eventually positive semigroups of linear operators". Journal of Mathematical Analysis and Applications (2015): http://dx.doi.org/10.1016/j.jmaa.2015.08.050.
    10.1016/j.jmaa.2015.08.050
  30. W. Arendt; A.F.M. ter Elst; J.B. Kennedy; M. Sauter. "The Dirichlet-to-Neumann operator via hidden compactness". Journal of Functional Analysis 266 3 (2014): 1757-1786. http://dx.doi.org/10.1016/j.jfa.2013.09.012.
    10.1016/j.jfa.2013.09.012
  31. Kennedy, James. "Analytical aspects of isospectral drums". Operators and Matrices 1 (2014): 255-277. http://dx.doi.org/10.7153/oam-08-14.
    10.7153/oam-08-14
  32. Pedro Ricardo Simão Antunes; Pedro Freitas; James Bernard Kennedy. "Asymptotic behaviour and numerical approximation of optimal eigenvalues of the Robin Laplacian". ESAIM: COCV 19 2 (2013): 438-459. http://dx.doi.org/10.1051/cocv/2012016.
    10.1051/cocv/2012016
  33. James Kennedy. "Closed nodal surfaces for simply connected domains in higher dimensions". Indiana Univ. Math. J. 62 3 (2013): 785-798. http://dx.doi.org/10.1512/iumj.2013.62.4975.
    10.1512/iumj.2013.62.4975
  34. J.B. Kennedy. "The nodal line of the second eigenfunction of the Robin Laplacian in can be closed". Journal of Differential Equations 251 12 (2011): 3606-3624. http://dx.doi.org/10.1016/j.jde.2011.08.012.
    10.1016/j.jde.2011.08.012
  35. JAMES B. KENNEDY. "ON THE ISOPERIMETRIC PROBLEM FOR THE LAPLACIAN WITH ROBIN AND WENTZELL BOUNDARY CONDITIONS". Bull. Aust. Math. Soc. 82 02 (2010): 348-350. http://dx.doi.org/10.1017/s0004972710000456.
    10.1017/s0004972710000456
  36. J. B. Kennedy. "On the isoperimetric problem for the higher eigenvalues of the Robin and Wentzell Laplacians". Z. Angew. Math. Phys. 61 5 (2010): 781-792. http://dx.doi.org/10.1007/s00033-009-0052-9.
    10.1007/s00033-009-0052-9
  37. Kennedy, James. "On the asymptotic behaviour of the eigenvalues of a Robin problem". Differential Integral Equations (2010):
  38. James Kennedy. "An isoperimetric inequality for the second eigenvalue of the Laplacian with Robin boundary conditions". Proc. Amer. Math. Soc. 137 02 (2008): 627-633. http://dx.doi.org/10.1090/s0002-9939-08-09704-9.
    10.1090/s0002-9939-08-09704-9
  39. James Kennedy. "A Faber-Krahn inequality for the Laplacian with Generalised Wentzell boundary conditions". J. evol. equ. 8 3 (2008): 557-582. http://dx.doi.org/10.1007/s00028-008-0393-4.
    10.1007/s00028-008-0393-4
  40. Daniel Daners; James Kennedy. "Uniqueness in the Faber–Krahn Inequality for Robin Problems". SIAM J. Math. Anal. 39 4 (2008): 1191-1207. http://dx.doi.org/10.1137/060675629.
    10.1137/060675629

Other

Other output
  1. 4 The Robin problem. 2017. Dorin Bucur; Pedro Freitas; James Kennedy. https://doi.org/10.1515%2F9783110550887-004.
    10.1515/9783110550887-004
Activities

Oral presentation

Presentation title Event name
Host (Event location)
2023/04/18 Spectral geometry and surgery of quantum graphs: an overview Geometric Aspects of Evolution and Control
University of Hagen (Germany)
2022/09/21 The behaviour of the spectrum of the Robin Laplacian with a complex boundary parameter Shape Optimisation and Spectral Theory
ICMS, Edinburgh (United Kingdom)
2022/07/05 Unbounded spectral minimal partitions? PICNDEA 22
Universidade de Évora (Portugal)
2022/06/28 What geometric structures of a graph limit the speed of diffusion? OTAMP
Stockholm University (Sweden)
2021/08/13 Spectral minimal partitions of metric graphs IWOTA
Chapman University (United States)
2020/04/19 An introduction to quantum graphs Colóquio de Matemática
Departamento de Matemática, Faculdade de Ciências, Universidade de Lisboa (Lisbon, Portugal)
2019/12/06 The Shape of Sound Mathematisches Kolloquium
Ulm University (Ulm, Germany)
2019/09/02 On the eigenvalues of the Robin Laplacian with a complex parameter
The University of Sydney (Sydney, Australia)
2019/07/09 Spectral geometry of quantum graphs via surgery principles Equadiff 2019
Technical University Leiden (Leiden, Netherlands)
2019/06/17 Die Eigenwerte des Robin-Laplace-Operators mit komplexem Parameter
University of Hagen (Hagen, Germany)
2019/05/06 Disjointness-preserving operators and isospectral Laplacians Parabolic Evolution Equations, Harmonic Analysis and Spectral Theory
(Bad Herrenalb, Germany)
2019/04/15 An introduction to spectral geometry on quantum graphs
Faculdade de Ciências e Tecnologia, Universidade Nova de Lisboa (Lisbon, Portugal)
2018/12/14 Variational theory and spectral geometry of quantum graphs
Centro de Matemática da Universidade de Coimbra (Coimbra, Portugal)
2018/10/10 An introduction to variational methods on quantum graphs Topics in Nonlinear Analysis: Calculus of Variations and PDEs
(Lisbon, Portugal)
2018/10/02 Hot spots of quantum graphs Semigroups of Operators: Theory and Applications
(Kazimierz Dolny, Poland)
2018/05/15 Asymptotically optimal eigenvalues of the Robin Laplacian Eigenvalues and Inequalities
Institut Mittag-Leffler (Stockholm, Sweden)
2018/04/26 Asymptotically optimal eigenvalues and Pólya's conjecture
Czech Technical University in Prague (Prague, Czech Republic)
2018/04/17 Asymptotisch optimale Eigenwerte des Dirichlet-Laplaceoperators und die Vermutung von Pólya Hagen-Wuppertal Analysis-Treffen
University of Wuppertal (Wuppertal, Germany)
2018/04/12 (Nicht nur) Diffusion bestimmt die Form des Gebiets Evolutionsgleichungen in Ulm 2018
Ulm University (Ulm, Germany)
2018/03/26 The shape of sound ENEMath 2018
Universidade de Aveiro (Aveiro, Portugal)
2018/02/09 Asymptotically optimal eigenvalues and Pólya's conjecture
Texas A&M University (College Station, United States)
2018/01/18 Asymptotically optimal eigenvalues and Pólya's conjecture
The University of Auckland (Auckland, New Zealand)
2018/01/12 Asymptotically optimal eigenvalues and Pólya's conjecture
The University of Sydney (Sydney, Australia)
2017/11/28 Spectral geometry of quantum graphs via surgery principles Discrete and continuous models in the Theory of Networks
Center for Interdisciplinary Research (ZiF), University of Bielefeld (Bielefeld, Germany)
2017/11/21 Asymptotisch optimale Eigenwerte des Dirichlet-Laplace-Operators und die Vermutung von Pólya
DFG Research Training School 1838, University of Stuttgart (Stuttgart, Germany)
2017/07/03 Welche Eigenschaften einer Trommel kann man hören?
University of Stuttgart (Stuttgart, Germany)
2017/06/28 Shape optimisation for the Robin Laplacian: an overview
University of Hagen (Hagen, Germany)
2017/06/22 Shape optimisation for the Robin Laplacian: an overview Geometric Spectral Theory
Université de Neuchâtel (Neuchâtel, Switzerland)

Supervision

Thesis Title
Role 		Degree Subject (Type)
Institution / Organization
2023/04/01 - 2023/12/31 Mean distance in metric graphs [distância média em grafos métricos]
Supervisor
Universidade de Lisboa Faculdade de Ciências, Portugal
2023/04/01 - 2023/12/31 Partições de Robin para grafos métricos
Supervisor
Universidade de Lisboa Faculdade de Ciências, Portugal
2018/05 - 2021/07 Spectral theory, clustering problems and differential equations on metric graphs
Supervisor
Universidade de Lisboa Faculdade de Ciências, Portugal

Universidade de Lisboa Grupo de Física Matemática, Portugal
2019 - 2020 Existence and qualitative properties of solutions to nonlinear Schrödinger equations on metric graphs
Co-supervisor
Universidade de Lisboa Faculdade de Ciências, Portugal

Event organisation

Event name
Type of event (Role) 		Institution / Organization
2024/02/05 - 2024/02/09 Organisation of the final workshop of COST Action CA18232, MAT-DYN-NET 24, as member of the organising committee and local organiser. (2024/02/05 - 2024/02/09)
Conference (Member of the Organising Committee)
 Universidade do Minho Departamento de Matemática, Portugal
2023/10/30 - 2023/11/03 Atlantic Conference in Nonlinear PDEs, brought together ca. 80 mathematicians working in the parallel areas of elliptic and dispersive equations and systems for a week-long event in Lisbon, financed mostly via the project NoDES (PTDC/MAT-PUR/1788/2020). (2023/10/30 - 2023/11/03)
Conference (Co-organisor)
 Universidade de Lisboa Instituto Superior Técnico, Portugal
2019/07/29 - 2019/08/02 12th ISAAC Congress, on analysis, its applications and computations. Brought together ca. 500 mathematicians, the majority from abroad. (2019/07/29 - 2019/08/02)
Congress (Co-organisor)
 Universidade de Aveiro Centro de Investigação e Desenvolvimento em Matemática e Aplicações, Portugal

Course / Discipline taught

Academic session Degree Subject (Type) Institution / Organization
2024/02/01 - 2024/07/31 Métodos Matemáticos nas Ciências (Licenciatura) Universidade de Lisboa Faculdade de Ciências, Portugal
2024/02/01 - 2024/07/31 Semigrupos de Operadores e Equações de Evolução (Mestrado) Universidade de Lisboa Faculdade de Ciências, Portugal
2023/09/01 - 2024/01/31 Análise Matemática III (Licenciatura) Universidade de Lisboa Faculdade de Ciências, Portugal
2023/09/01 - 2024/01/31 Análise Funcional Aplicada (Mestrado) Universidade de Lisboa Faculdade de Ciências, Portugal
2023/02/01 - 2023/07/31 Métodos Matemáticos nas Ciências (Licenciatura) Universidade de Lisboa Faculdade de Ciências, Portugal
2022/09/01 - 2023/01/31 Tópicos de Matemática (Mestrado) Universidade de Lisboa Faculdade de Ciências, Portugal
2022/09/01 - 2023/01/31 Análise Matemática III (Licenciatura) Universidade de Lisboa Faculdade de Ciências, Portugal
2022/08/29 - 2022/09/02 Geometric Spectral Theory of Quantum Graphs Summer School "Heat kernels and spectral geometry: from graphs to manifolds", Bregenz, Austria FernUniversität in Hagen, Germany
2022/02/01 - 2022/07/31 Métodos Matemáticos nas Ciências (Licenciatura) Universidade de Lisboa Faculdade de Ciências, Portugal
2021/09/01 - 2022/01/31 Tópicos de Matemática (Mestrado) Universidade de Lisboa Faculdade de Ciências, Portugal
2021/02/01 - 2021/07/31 Métodos Matemáticos nas Ciências (Licenciatura) Universidade de Lisboa Faculdade de Ciências, Portugal
2020/09/01 - 2021/01/31 Tópicos de Matemática (Mestrado) Universidade de Lisboa Faculdade de Ciências, Portugal
2020/02 - 2020/06 Métodos Matemáticos nas Ciências (Licenciatura) Universidade de Lisboa Faculdade de Ciências, Portugal
2019/02 - 2019/06 Métodos Matemáticos nas Ciências (Licenciatura) Universidade de Lisboa Faculdade de Ciências, Portugal
2016/04 - 2016/09 Elemente der Variationsrechnung (Bachelor) Universität Ulm Fakultät für Mathematik und Wirtschaftswissenschaften, Germany
2016/04 - 2016/09 Nonlinear Partial Differential Equations (Master) Universität Ulm Fakultät für Mathematik und Wirtschaftswissenschaften, Germany