Pedro Pinto's Homepage

I am a postdoctoral researcher in the Logic group of the Technische Universität Darmstadt, Germany.
I am also a Research Collaborator of the Institute for Logic and Data Science (ILDS).

My current focus is in proof mining (in particular on the application of the bounded functional interpretation) and related topics.
I got my PhD in Mathematics in 2019 at the Faculdade de Ciências da Universidade de Lisboa, Portugal (PhD Thesis).
Here is my CV (last version: September/2022).

Research Interests: Logic (in particular proof theory), proof interpretations and their use in mathematics (namely proof mining), convex optimization, computability theory, approximation theory, nonlinear analysis and fixed point theory.

Teaching experience

• Research Assistant at Technische Universität Darmstadt, 2020-Present
• Teacher at Universidade Autónoma de Lisboa, 2018/2019
• Teaching assistant at Faculdade de Ciências da Universidade de Lisboa, 2012/2013

Articles

1. Rates of asymptotic regularity for the alternating Halpern-Mann iteration, with Laurenţiu Leuştean,
   submitted (2022)
2. Strong convergence for the alternating Halpern-Mann iteration in CAT(0) spaces, with Bruno Dinis,
   submitted (2021)
3. Quantitative translations for viscosity approximation methods in hyperbolic spaces, with Ulrich Kohlenbach,
   Journal of Mathematical Analysis and Applications, 507: 125823, 33 pp (2022), DOI
4. Effective metastability for a method of alternating resolvents, with Bruno Dinis,
   Final version to appear in: Fixed Point Theory
5. On the convergence of algorithms with Tikhonov regularization terms, with Bruno Dinis,
   Optimization Letters, 15(4), 1263-1276, (2021), DOI
6. Quantitative results on a Halpern-type proximal point algorithm, with Laurenţiu Leuştean,
   Computational Optimization and Applications, 79(1), 101-125, (2021), DOI
7. Quantitative Results on the Multi-Parameters Proximal Point Algorithm, with Bruno Dinis,
   Journal of Convex Analysis, 28(3): 729-750, (2021)
8. A Rate of Metastability for the Halpern Type Proximal Point Algorithm,
   Numerical Functional Analysis and Optimization, 42(3): 320-343, (2021), DOI
9. Metastability of the multi-parameters proximal point algorithm, with Bruno Dinis,
   Portugaliae Mathematica 77(3/4): 345-381, (2020), DOI
10. On the removal of weak compactness arguments in proof mining, with Fernando Ferreira and Laurenţiu Leuştean,
    Advances in Mathematics 354: 106728, 55pp, (2019), DOI

Recent

• International Conference on Applied Proof Theory 2022 (APT22)
  Talk: "Proof mining on PDE theory"
  University of Chieti–Pescara, Pescara, Italy, 29 August-2 September, 2022
• LOS-ILDS Proof Mining Seminar
  Talk: "The alternating Halpern-Mann iteration"
  Faculty of Mathematics and Computer Science, University of Bucharest, (online) 6 July, 2022
• Days in Logic 2022
  Talk: "The Halpern-Mann iteration in UCW-hyperbolic spaces"
  University of Algarve, Faro, Portugal, 30 June-2 July, 2022
• LOS-IMAR Logic Seminar
  Talk: "Halpern and Mann iterative schemas: A path towards generalization"
  Faculty of Mathematics and Computer Science, University of Bucharest, (online) 27 January, 2022
• Logic Seminar at Universidade de Lisboa (SLM)
  Talk: "Halpern and Mann iterative schemas: A path towards generalization"
  Faculdade de Ciências, Universidade de Lisboa, 10 January, 2022
  
• New Frontiers in Proofs and Computations
  Talk: "Quantitative results on variants of the proximal point algorithm"
  Institute for Advanced Study in Mathematics, Hangzhou, China, (online) September 12-17, 2021.
• Eighteenth International Conference on Computability and Complexity in Analysis
  Contributed Talk: "Quantitative translations for viscosity approximation methods"
  Universität der Bundeswehr München, (online) 26-28 July, 2021.
• FMI/IMAR Logic Seminar
  Talk: "Unwinding of proofs"
  Faculty of Mathematics and Computer Science, University of Bucharest, (online) 4 March, 2021

Future events

• Colloquium Logicum 2022 (CL2022)
  Talk: "A generalization via proof mining methods"
  University of Konstanz , Konstanz, Germany, 26-28 September, 2022

Past Events

• Oberwolfach Workshop on Mathematical Logic: Proof Theory, Constructive Mathematics
  MFO, Oberwolfach, Germany (hybrid format), 8-14 November, 2020
• Logic Seminar at Universidade de Lisboa (SLM)
  Talk: "Quantitative translations for viscosity approximation methods"
  Faculdade de Ciências, Universidade de Lisboa, (online) 26 October 2020
  
• Logic Seminar at Universidade de Lisboa (SLM)
  Talk: "Commentaries on the application of the bounded functional interpretation"
  Faculdade de Ciências, Universidade de Lisboa, 3 February 2020
  
• Days in Logic 2020
  Talk: "Proof mining of a discussion by cases"
  Faculdade de Ciências da Universidade de Lisboa, Portugal, 30 January-1 February 2020
• Logic Colloquium 2019 Prague (invited special session speaker)
  Special Session on Proof Theory and Proof Complexity
  Talk: "Proof mining with the bounded functional interpretation"
  Faculty of Architecture, Czech Technical University, Prague, August 2019
• FMI/IMAR Logic Seminar
  Talk: "The bounded functional interpretation and the elimination of weak compactness"
  Faculty of Mathematics and Computer Science, University of Bucharest, 26 April, 2018
• Computational Approaches to the Foundations of Mathematics
  Talk: "Concrete Examples on the Elimination of Weak Compactness"
  Mathematisches Institut, LMU, Munich, 13 April, 2018

Links

ResearchGate      ArXiv      GoogleScholar      Logic group