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I am a postdoctoral researcher in the Logic group of the Technische Universität Darmstadt, Germany, and my postdoc advisor is Ulrich Kohlenbach. I am also an Associated researcher at the Institute for Logic and Data Science (ILDS) and at the Logic, Optimization & Security Center (LOS), and a Research Collaborator of the Center for Mathematical Studies (CEMS.UL). My current research is in Mathematical Logic, namely in applied Proof Theory focusing on proof interpretations and their use in mathematics (Proof Mining). In this research program, one employs proof-theoretical techniques to analyse prima facie noneffective mathematical proofs with the goal of uncovering new information, usually in the form of rates, bounds or even qualitative improvements. My areas of application include Convex Optimization, Fixed Point Theory, Operator Theory, and Partial Differential Equations. I got my PhD in Mathematics in 2019 from the Faculty of Sciences of the University of Lisbon under the supervision of Fernando Ferreira, for the first studies on concrete applications of the bounded functional interpretation in the context proof mining research. After my PhD, I moved to TU Darmstadt to work under the guidance of Ulrich Kohlenbach. In 2024, I was awarded a Leibniz Fellowship by the prestigious Oberwolfach Research Institute for Mathematics (MFO). I was also appointed member of the European Mathematical Society Young Academy (EMYA) for the period 2004-2027. I am currently the principal investigator of the DFG project PI 2070/1-1, "Proof Mining in Nonlinear Functional Analysis." My research focuses on exploring innovative applications of proof mining, particularly in extending techniques and results from linear to nonlinear contexts. Recently, I was awarded research funding by FCT through a CEEC at CEMS-UL, which will begin in July 2026 and will enable me to continue my research in Lisbon.
Identificação

Identificação pessoal

Nome completo
Pedro Miguel Santos Pinto

Nomes de citação

  • Pinto, Pedro

Identificadores de autor

Ciência ID
3C1B-7DBC-B7A4
ORCID iD
0000-0002-8761-523X
Google Scholar ID
7KRPsK8AAAAJ&hl
Researcher Id
JCE-4948-2023
Scopus Author Id
57210157226

Endereços de correio eletrónico

  • pinto@mathematik.tu-darmstadt.de (Profissional)

Moradas

  • Schlossgartenstrasse 7, 64289, Darmstadt, Darmstadt, Alemanha (Profissional)

Websites

  • https://pinto-pedro.github.io/ (Pessoal)

Domínios de atuação

  • Ciências Exatas - Matemática

Idiomas

Idioma Conversação Leitura Escrita Compreensão Peer-review
Português (Idioma materno)
Inglês Utilizador proficiente (C1) Utilizador proficiente (C1) Utilizador proficiente (C1) Utilizador proficiente (C1)
Alemão Utilizador elementar (A2) Utilizador elementar (A2) Utilizador elementar (A2) Utilizador elementar (A2) Utilizador elementar (A2)
Formação
Grau Classificação
2019/09/24
Concluído
Matemática (Doutoramento)
Especialização em Especialidade: Álgebra, Lógica e Fundamentos
Universidade de Lisboa Faculdade de Ciências, Portugal
"Proof mining with the bounded functional interpretation " (TESE/DISSERTAÇÃO)
Percurso profissional

Ciência

Categoria Profissional
Instituição de acolhimento
Empregador
2024/07/01 - 2026/06/30 Investigador principal (carreira) (Investigação) Deutsche Forschungsgemeinschaft, Alemanha
Technische Universitat Darmstadt, Alemanha

Cargos e Funções

Categoria Profissional
Instituição de acolhimento
Empregador
2024/03/17 - 2024/06/07 Leibniz Fellow Mathematisches Forschungsinstitut Oberwolfach gGmbH, Alemanha

Outros

Categoria Profissional
Instituição de acolhimento
Empregador
2019/10/01 - 2024/06/30 Postdoc Technische Universitat Darmstadt, Alemanha
Technische Universitat Darmstadt, Alemanha
Projetos

Projeto

Designação Financiadores
2024/07/01 - 2026/06/30 Proof Mining in Nonlinear Functional Analysis
PI 2070/1-1
Investigador responsável
Deutsche Forschungsgemeinschaft
2021/09/01 - 2023/08/31 Proof mining in Convex Optimization and Related Areas
KO 1737/6-2
Investigador
Technische Universitat Darmstadt, Alemanha
Deutsche Forschungsgemeinschaft
2020/10/01 - 2021/08/31 Proof mining in Convex Optimization and Related Areas
KO 1737/6-1
Investigador
Technische Universitat Darmstadt, Alemanha
Deutsche Forschungsgemeinschaft
Produções

Publicações

Artigo em revista
  1. Firmino, Paulo; Pinto, Pedro. "The alternating Halpern-Mann iteration for families of maps". Journal of Computational and Applied Mathematics 485 (2026): 117514. https://doi.org/10.1016/j.cam.2026.117514.
    10.1016/j.cam.2026.117514
  2. Pinto, Pedro; Pischke, Nicholas. "On the Halpern method with adaptive anchoring parameters". Mathematics of Computation (2026): https://doi.org/10.1090/mcom/4182.
    10.1090/mcom/4182
  3. PINTO, PEDRO. "PROOF MINING AND THE CONVEX FEASIBILITY PROBLEM: THE CURIOUS CASE OF DYKSTRA’S ALGORITHM". The Review of Symbolic Logic 18 3 (2025): 775-811. https://doi.org/10.1017/s1755020325100695.
    10.1017/s1755020325100695
  4. Pinto, Pedro. "Nonexpansive maps in nonlinear smooth spaces". Transactions of the American Mathematical Society 377 9 (2024): 6379-6426. https://doi.org/10.1090/tran/9166.
    Publicado
  5. Pedro Pinto; Pinto, Pedro. "On the finitary content of Dykstra’s cyclic projections algorithm". Zeitschrift für Analysis und ihre Anwendungen (2024): https://doi.org/10.4171/zaa/1768.
    Aceite para publicação • 10.4171/zaa/1768
  6. Bruno Dinis; Pinto, Pedro. "Effective metastability for a method of alternating resolvents". Fixed Point Theory (2024): https://doi.org/10.24193/fpt-ro.2024.1.05.
    Publicado • 10.48550/ARXIV.2101.12675
  7. Kohlenbach, Ulrich; Pinto, Pedro. "Fejér monotone sequences revisited". Journal of Convex Analysis (2024):
    Aceite para publicação
  8. Pinto, Pedro; Pischke, Nicholas. "On computational properties of Cauchy problems generated by accretive operators". Documenta Mathematica 28 5 (2023): 1235-1274. http://dx.doi.org/10.4171/dm/924.
    Publicado • 10.4171/dm/924
  9. Dinis, Bruno; Pinto, Pedro. "Strong Convergence for the Alternating Halpern–Mann Iteration in CAT(0) Spaces". SIAM Journal on Optimization 33 2 (2023): 785-815. http://dx.doi.org/10.1137/22m1511199.
    Publicado • 10.1137/22m1511199
  10. Leustean, Laurentiu; Pinto, Pedro. "Rates of asymptotic regularity for the alternating Halpern–Mann iteration". Optimization Letters (2023): http://dx.doi.org/10.1007/s11590-023-02002-y.
    10.1007/s11590-023-02002-y
  11. Kohlenbach, Ulrich; Pinto, Pedro. "Quantitative translations for viscosity approximation methods in hyperbolic spaces". Journal of Mathematical Analysis and Applications 507 2 (2022): http://dx.doi.org/10.1016/j.jmaa.2021.125823.
    Publicado • 10.1016/j.jmaa.2021.125823
  12. Leustean, Laurentiu; Pinto, Pedro. "Quantitative results on a Halpern-type proximal point algorithm". Computational Optimization and Applications 79 1 (2021): 101-125. http://dx.doi.org/10.1007/s10589-021-00263-w.
    Publicado • 10.1007/s10589-021-00263-w
  13. Pinto, Pedro. "A Rate of Metastability for the Halpern Type Proximal Point Algorithm". Numerical Functional Analysis and Optimization 42 3 (2021): 320-343. http://dx.doi.org/10.1080/01630563.2021.1876726.
    Publicado • 10.1080/01630563.2021.1876726
  14. Pinto, Pedro; Dinis, Bruno. "Quantitative results on the multi-parameters Proximal Point Algorithm". Journal of Convex Analysis 28 3 (2021): 729-750. https://www.heldermann.de/JCA/JCA28/JCA283/jca28041.htm.
    Publicado
  15. Dinis, Bruno; Pinto, Pedro. "Metastability of the proximal point algorithm with multi-parameters". Portugaliae Mathematica 77 3 (2020): 345-381. http://dx.doi.org/10.4171/pm/2054.
    Publicado • 10.4171/pm/2054
  16. Dinis, Bruno; Pinto, Pedro. "On the convergence of algorithms with Tikhonov regularization terms". Optimization Letters 15 4 (2020): 1263-1276. http://dx.doi.org/10.1007/s11590-020-01635-7.
    Publicado • 10.1007/s11590-020-01635-7
  17. Ferreira, Fernando; Leustean, Laurentiu; Pinto, Pedro. "On the removal of weak compactness arguments in proof mining". Advances in Mathematics 354 (2019): http://dx.doi.org/10.1016/j.aim.2019.106728.
    Publicado • 10.1016/j.aim.2019.106728
Pré-impressão
  1. Pinto, Pedro; Pischke, Nicholas. "On Dykstra's algorithm with Bregman projections". 2024.
  2. Pinto, Pedro; Sipos, Andrei. "Products of hyperbolic spaces". 2024.
Recurso online
  1. Pinto, Pedro. On quantitative versions of Xu’s Lemma. 2023. https://www2.mathematik.tu-darmstadt.de/~pinto/.
Tese / Dissertação
  1. Pinto, Pedro Miguel dos Santos. "Proof mining with the bounded functional interpretation". Doutoramento, Universidade de Lisboa Faculdade de Ciências, 2019. http://hdl.handle.net/10451/42661.
  2. Pinto, Pedro Miguel dos Santos. "Teorema da estrutura de Furstenberg: demonstração e redução ao nível Www". Mestrado, Universidade de Lisboa Faculdade de Ciências, 2013. http://hdl.handle.net/10451/10364.
Atividades

Apresentação oral de trabalho

Título da apresentação Nome do evento
Anfitrião (Local do evento)
2026/01 Moduli and quantitative aspects of hyperbolic spaces via proof mining Days in Logic 2026
University of Minho (Portugal)
2026/01 Proof-theoretical unwinding of mathematics CEMS Day
University of Lisbon (Portugal)
2025/06 Proof mining in nonlinear convex analysis Workshop on Optimization, Dynamics and Convex Analysis
University of Aveiro (Portugal)
2025/01/15 On the Halpern method with adaptive anchoring parameters LOS-ILDS Proof Mining Seminar
University of Bucharest
2024/07/12 Proof-theoretical unwinding of mathematics Encontro Nacional da SPM 2024 (Invited for parallel session: ‘Logic and Theory of Computation')
2023/11/12 Sunny nonexpansive retractions in nonlinear spaces Oberwolfach Workshop on Mathematical Logic: Proof Theory, Constructive Mathematics
MFO, Oberwolfach Research Institute for Mathematics (Oberwolfach, Alemanha)
2022/09/02 Proof mining on PDE theory International Conference on Applied Proof Theory 2022 (APT22)
University of Chieti (Pescara, Itália)
2020/11/08 Quantitative translations for viscosity approximation methods Oberwolfach Workshop on Mathematical Logic: Proof Theory, Constructive Mathematics
MFO, Oberwolfach Research Institute for Mathematics (Oberwolfach, Alemanha)
2019/08/11 Proof mining with the bounded functional interpretation Logic Colloquium 2019 - Special Session: Proof Theory and Proof Complexity
Faculty of Architecture, Czech Technical University (Praga, República Checa)
2018/04/26 The bounded functional interpretation and the elimination of weak compactness FMI/IMAR Logic Seminar
Faculty of Mathematics and Computer Science, University of Bucharest (Bucareste, Roménia)

Orientação

Título / Tema
Papel desempenhado
Curso (Tipo)
Instituição / Organização
2022/05/17 - 2023/10/10 Proof Mining: análise quantitative de demonstrações matemáticas
Coorientador
Estatística, Matemática e Computação (Mestrado)
Universidade Aberta, Portugal

Organização de evento

Nome do evento
Tipo de evento (Tipo de participação)
Instituição / Organização
2024/09/04 - 2024/09/06 Workshop on Proof Mining (2024/09/04 - 2024/09/06)
Oficina (workshop) (Coorganizador)
Technische Universitat Darmstadt, Alemanha

Membro de associação

Nome da associação Tipo de participação
2024/01/01 - Atual AMS – American Mathematical Society
2024/01/01 - Atual EMS – European Mathematical Society
2023/01/01 - Atual SPM – Sociedade Portuguesa de Matemática
2022/01/01 - Atual SPL – Sociedade Portuguesa de Lógica
2021/01/01 - Atual ASL – Association for Symbolic Logic
2021/01/01 - Atual Proof Society
2024 - 2027 EMYA – European Mathematical Society Young Academy Appointed member
Distinções

Prémio

2024 Oberwolfach Leibniz Fellowship
Mathematisches Forschungsinstitut Oberwolfach gGmbH, Alemanha

Outra distinção

2024 Appointed as a member of EMS Young Academy (EMYA) for the period 2024–2027
European Mathematical Society, Finlândia