Telmo Peixe

I am a Portuguese mathematician interested in Dynamical Systems and Evolutionary Game Theory. As an Assistant Professor in the Mathematics Department of ISEG - Lisbon School of Economics & Management, Universidade de Lisboa, Portugal, I teach graduate, master and PhD courses in Mathematics. I am an Integrated researcher at CEMAPRE - Centro de Matemática Aplicada à Previsão e Decisão Económica, one of the members of the research consortium REM - Research in Economics and Mathematics, based at ISEG. I am also member of the LxDS - Lisbon Dynamical Systems Group.

“Imagine, Share, Explore, and Give It All (I.S.E.G). We aim to inspire, innovate, and educate to shape a future that transcends expectations and transforms lives.”

Education

BSc in Psychology, Universidade de Lisboa, 1999.
BSc in Mathematics, Universidade de Lisboa, 2008.
MSc in Mathematics (supervisor: Pedro Miguel Duarte), Universidade de Lisboa, 2010.
PhD in Mathematics (supervisor: Pedro Miguel Duarte), Universidade de Lisboa, 2015.

Research interests

- Dynamical Systems,

- Hamiltonian dynamics,

- Evolutionary Game Theory/Dynamic games,

- Lotka-Volterra systems and replicator equation,

- Applications to economics and biology.

Research IDs

- ORCID: 0000-0002-0344-5959

- ResearcherID: F-8725-2018

- Scopus Author ID: 55308107200

- Google Scholar

- ResearchGate

- Ciência ID 0B15-D219-AF59

Research projects

Member of the research projects

- CEMAPRE/REM UIDB/05069/2020

- New Trens in Lyapunov Exponents FCT PTDC/MAT-PUR/29126/2017

Research

Dynamics of a dissipative polymatrix replicator

Basins of attraction of the discretized BR dynamics of the RPS game

Strange attractor in a polymatrix replicator

Flows on Polytopes - Mathematica code

(with P. Duarte)

We provide here the Mathematica code we had developed to explore the dynamics of polymatrix replicators for lower dimensional polytopes.

Publications

Recorrências, Progressões Aritméticas; e Teoria Ergódica: Teoremas de van der Warden e de Green-Tao
(with J. Buescu)
Revista Matemática Universitária, 48/49, 39-51, 2010.
Rank of stably dissipative graphs
i (with P. Duarte)
Linear Algebra and Its Applications, 437, 2537-2586, 2012.
Conservative and Dissipative Polymatrix Replicators
(with H. N. Alishah, P. Duarte)
Journal of Dynamics and Games, 2(2), 157-185, 2015.
Asymptotic Poincaré Maps along the edges of Polytopes
(with H. N. Alishah, P. Duarte)
Nonlinearity, 33(1), 469-510, 2020.
Permanence in Polymatrix Replicators
Journal of Dynamics and Games, 8(1), 21-34, 2021.
Periodic attractor in the discrete time best-response dynamics of the Rock-Paper-Scissors game
(with J. P. Gaivão)
Dynamic Games and Applications, 11(3), 491-511, 2021.
Persistent strange attractors in 3D Polymatrix Replicators
(with A. A. Rodrigues)
Physica D: Nonlinear Phenomena, 438, 2022.
Asymptotic Dynamics of Hamiltonian Polymatrix Replicators
(with H. Alishah and P. Duarte)
Nonlinearity, 36 (6), 2023.
Stability of heteroclinic cycles: a new approach based on a Replicator equation
(with A. A. Rodrigues)
Journal of Nonlinear Science, 33, 99, 2023.

Book editor

New Trends in Lyapunov Exponents NTLE, Lisbon, Portugal, February 7–11, 2022

(with João Lopes Dias, Pedro Duarte, José Pedro Gaivão, Silvius Klein, Jaqueline Siqueira, Maria Joana Torres)

in CIM Series in Mathematical Sciences, VII 179, Springer, 2023

Chapter in book

On the Roots of Underdevelopment: "Wrong; Equilibrium" or "Miscoordination;"?

(with J. P. Pontes)

in Estudos de Homenagem a José da Costa Silva, Coleção Transversal, U.Porto Press, 2023

Monographs and other works

Sistemas Lotka-Volterra dissipativos (in portuguese)
MSc thesis, University of Lisboa, 2010.
Lotka-Volterra systems and Polymatrix Replicators
PhD thesis, University of Lisboa, 2015.
Observar Golfinhos... Com Trigonometria
(with P. Duarte, T. Caissotti)
Gazeta de Matemática;, 169, 16-22, 2013.
Evaluating the effect of measurement error in pairs of 3D bearings in point transect sampling estimates of density
(with T. A. Marques, P. Duarte, D. Moretti, L. Thomas)
CREEM Technical Report, no.1, University of St Andrews, 2018.
Lecture notes of Matemática I (in portuguese) for the undergraduates in Economics, in Management, and in Finance, 2017 (1ed), 2023 (2ed), with Filipa de Carvalho.
Lecture notes of Mathematics I (in english) for the undergraduates in Economics, in Management, and in Finance, 2025.

Jury member

The Lotka-Volterra equations in Finance and Economics, Mafalda Oliveira Martins Bastos de Almeida, MSc in Mathematical Finance, ISEG, University of Lisboa, 2017.
Classification of 2x2 Fictitious Play, Maria Ferreira Vila Luz, MSc in Mathematical Finance, ISEG, University of Lisboa, 2017.
Balanceamento automático de linhas de produção: Bucket Brigade, Adriana Maria Soares, MSc in Quantitative Methods for Decision-making in Economics and Business, ISEG, University of Lisboa, 2021.

Teaching

2009-2012, Faculdade de Ciências, Universidade de Lisboa
- Numbers and Functions
- Matemathics I and Mathematics II (Bachelor in Geology)
- Analysis II (Bachelor in Biochemistry, in Chemistry, and in Techonological Chemistry)
- Algebra II (Bachelor in Mathematics)
2014-now, ISEG, Universidade de Lisboa
- Mathematics I (differential and integral calculus in R, for the Bachelor in Economics, in Management, in Finance, and in Sports Management)

- Mathematics II (differential and integral calculus in Rn, for the Bachelor in Economics, in Management, in Finance, and in Sports Management)
- Discrete Mathematics (Bachelor in Economics, in Management, in Finance, and in Applied Mathematics for Economics and Management)
- Stochastic Processes and Applications (Bachelor in Applied Mathematics for Economics and Managemet)
- Probability Theory and Stochastic Processes (MsC in Mathematical Finance, and PhD in Applied Mathematics for Economics and Management)

- Numerical Analysis (Bachelor in Applied Mathematics for Economics and Management)

- Linear Algebra (Bachelor in Applied Mathematics for Economics and Management)

Supervision

PhD
Joana Luzia Monteiro Passinhas, Essays on Macroprudential Policy, co-supervision with Isabel Proença, PhD in Economics – ISEG, Universidade de Lisboa, April 2025.
MsC
Bernardo Amaral Sardinha Ferreira da Silva, Two player game with two strategies: regulation and innovation in finance, MsC in Mathematical Finance – ISEG, Universidade de Lisboa, November 2023.

Faysel Kharab, Rough Marked Heston-Hawkes Model: Simulation and Analysis, MsC in Mathematical Finance – ISEG, Universidade de Lisboa, July 2025.

Communications in Conferences

Estabilidade e Inércia; de Matrizes, national meeting of the Novos Talentos em Matemática program by Fundação Calouste Gulbenkian, Lisboa, 2007.
The Rank of Stably Dissipative Graphs (poster), Dynamical Models in Life Sciences, University of Évora, 2011.
Polymatrix Games and Replicators, Seventh Workshop Dynamical Systems Applied to Biology and Natural Sciences, University of Évora, 2016.
Games and Polymatrix Replicators, National Meeting of the SPM - Sociedade Portuguesa de Matemática, Escola Superior de Tecnologia do Barreiro Instituto Politécnico de Setúbal, 2016.
From Lotka-Volterra systems to Polymatrix Replicators, 12th International ISAAC Congress, University of Aveiro, 2019.
Periodic attractor in the discrete time best-response dynamics of the Rock-Paper-Scissors game, The Lisbon Meetings in Game Theory and Applications #11, ISEG, Universidade de Lisboa, 2019.
Can Strange Attractors Occur in 3D Polymatrix Replicators?, SIAM Conference on Applications of Dynamical Systems (DS21), 2021, Virtual Conference | Originally scheduled in Portland, Oregon, U.S.
Permanence in Polymatrix Replicators, 13th International ISAAC Congress, Ghent University, Belgium, @Zoom, 2021.
Stability of heteroclinic cycles based on a projective map, National Meeting of the SPM - Sociedade Portuguesa de Matemática, Universidade do Minho, Braga, 10-12 Julho, 2024.

Seminars

Stable Dissipativity in the Replicator Equation, Differential Equations and Numerical Analysis Seminar, Faculdade de Ciências; e Tecnologia, Universidade Nova de Lisboa, 2012.
Polymatrix Replicators and Lotka-Volterra Systems, CMUP Seminar, Faculdade de Ciências;, Universidade do Porto, 2015.
Polymatrix Replicators and Lotka-Volterra Systems, LxDS Seminar, Faculdade de Ciências;, Universidade de Lisboa, 2015.
The maximum principle of Pontryagin, Dynamical Systems Seminar, ISEG, Universidade de Lisboa, 2016.
From Lotka-Volterra systems to Polymatrix Replicators, PhD program in Matemática; Aplicada à Economia e à Gestão; of ISEG, Universidade de Lisboa, 2018.
Periodic attractor in the discrete time best-response dynamics of the Rock-Paper-Scissors game, Dia das Equações;, Center of Mathematics, Universidade do Minho, 2019.
Open problems in fictitious play dynamics for bimatrix games, Dynamical Systems Seminar, Faculdade de Ciências;, Universidade de Lisboa, 2019.
Persistent strange attractors in 3D Polymatrix Replicators, Dynamical Systems Seminar, Faculdade de Ciências;, Universidade de Lisboa, 2021.
Dynamics along the heteroclinic network of polymatrix replicators, Dynamical Systems in Porto, Dynamics of singularities and networks, Faculdade de Ciências, Universidade do Porto, 2023.
Stability of heteroclinic cycles: a new approach, Differential Equations and Numerical Analysis Seminar, Faculdade de Ciências; e Tecnologia, Universidade Nova de Lisboa, 2024.

Events organization

LxDS Spring School 2018, May 28-30, 2018, ISEG, University of Lisboa, Portugal.
LxDS Spring School 2019, May 29-31, 2019, FCUL, University of Lisboa, Portugal.
Evolutionary Game Theory session in the conference The Lisbon Meetings in Game Theory and Applications #11, November 7-9, 2019, ISEG, University of Lisboa, Portugal.
LxDS Spring School 2020, May 27-29, 2020, ISEG, University of Lisboa, Portugal.
New Trends in Lyapunov Exponents, July 6-10, 2020, ISEG & FCUL, University of Lisboa, Portugal.
9th One Day Meeting on Dynamical Systems, dedicated to New Trends in Lyapunov Exponents, 7th July, @Zoom, 2020.
Heteroclinic dynamics and beyond session in the conference Encontro Nacional SPM2021, @Zoom, July 12-16, 2021 (with A. A. Rodrigues).
LxDS mini-course on Determinantal Point Processes, FCUL, University of Lisboa, 18th-22nd October, 2021.
LxDS workshop on New Trends in Lyapunov Exponents, February 7-11, 2022, ISEG, University of Lisboa, Portugal.
From elliptic islands to hyperbolic waves - Celebrating Pedro Duarte's 60th birthday, August 29-30 (PUC-Rio) and September 2 (UFRJ), 2022, Rio de Janeiro, Brasil.
LxDS Spring School 2023, May 24-26, 2023, ISEG, Universidade de Lisboa, Portugal.
LxDS Spring School 2024, May 27-29, 2024, Faculdade de Ciências, Universidade de Lisboa, Portugal.
LxDS Spring School 2025, May 28-30, 2025, ISEG, Universidade de Lisboa, Portugal.

Management

2017 - 2019, Managing board of CEMAPRE - Centro de Matemática Aplicada à Previsão e Decisão Económica, and its representative at
CIM - Centro Internacional de Matemática and
CNM - Comissão Nacional de Matemática
2019 - 2021, Managing board of CEMAPRE - Centro de Matemática Aplicada à Previsão e Decisão Económica, and its representative at
CIM - Centro Internacional de Matemática and
CNM - Comissão; Nacional de Matemática
2023 - 2025, Secretary of the General Assembly of CEMAPRE - Centro de Matemática Aplicada à Previsão e Decisão Económica
2024 - current, Secretary of the General Assembly of CIM - Centro Internacional de Matemática
2024 - current, Coordinator of the ISEG Tutoring and Mentoring program
2025 - current, Member of the Monitoring and Evaluation Committee of the Different Minds Inclusive Academy program at ISEG

Scholarships and awards

2006/2007 - Novos Talentos em Matemática; program by Fundação; Calouste Gulbenkian.
2007/2008 - BES-FCUL award for the best ranked graduate student.
2008 Scholarship by the Portugal|UT-Austin Colab to attend the "Summer; School on Multiscale Modeling and Analysis" at the University of Austin-Texas.
2008/2009 - Scientific initiation scholarship in Dynamical Systems by CMAF - Centro de Matemática; e Aplicações; Fundamentais and FCT - Fundação; para a Ciência; e a Tecnologia.
2011 - 2015 - PhD scholarship SFRH/BD/72755/2010 by FCT - Fundação; para a Ciência; e a Tecnologia.

Pedagogical Training

Formação Pedagógica para Docentes ULisboa, Pedagogical Training for faculty at the start of their careers, 4-6 September, 2023, Universidade de Lisboa.
Jornadas Pedagógicas da ULisboa 2023, Os desafios da docência no Ensino Superior – a importância da relação pedagógica no processo de ensino-aprendizagem, 28 November, 2023, Universidade de Lisboa.
Formação Pedagógica para Docentes ULisboa, ChatGPT & Active Learning: Uma Parceria de Sucesso, January, 2024, Universidade de Lisboa.
Formação Pedagógica para Docentes ULisboa, Ensinar e Aprender com o Digital, January, 2024, Universidade de Lisboa.
Formação Pedagógica para Docentes ULisboa, Metodologias Ativas, Relação Pedagógica e Introversão: Uma Tríade Inesperada, January, 2024, Universidade de Lisboa.
Seminário - Como envolver ativamente os alunos, mesmo em salas com audiências numerosas?, promovido no âmbito do Projeto de Promoção de Sucesso e de Redução de Abandono no Ensino Superior da ULisboa, January, 2024, Universidade de Lisboa.
Formação Pedagógica para Docentes ULisboa, Flash Active Learning, July, 2024, Universidade de Lisboa.
Formação de Mentores, 15th July, 2024, Faculdade de Psicologia e Instituto de Educação, Universidade de Lisboa.
Jornadas Pedagógicas da ULisboa 2024, Metodologias Ativas no Processo de Ensino-Aprendizagem, 18 September, 2024, Universidade de Lisboa.
Formação de Docentes ULisboa, Perturbação de Hiperatividade e Défice de Atenção no Jovem Adulto – Intervenção Psicossocial no Ensino Universitário, 12th november, 2024, Universidade de Lisboa.
Formação de Docentes ULisboa, Welcome Mentimeter, 20th november, 2024, Universidade de Lisboa.
Formação de Docentes ULisboa, Quando o autismo vai para a Universidade, 22nd november, 2024, Universidade de Lisboa.
Formação de Docentes ULisboa, Effective Personal Tutoring in Higher Education, 29th january, 2025, Universidade de Lisboa.
Formação de Docentes ULisboa, Geração de Imagens com IA para Fins Pedagógicos, 12th february, 2025, Universidade de Lisboa.

Contacts

Rua do Quelhas 6, 1200-781 Lisboa, Portugal
Email: telmop at iseg.ulisboa.pt
Phone: (+351) 213 925 831
Office: 505, Quelhas 6 Building

You can visit my older Homepage!

Last update: 23-07-2025

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