Proof Mining in Nonlinear Functional Analysis

• Applicant: Dr. Pedro Pinto
• Subject Area: Mathematics
• Term: since 2024
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 549333475

This project is set within the context of Applied Proof Theory. In this particular line of research, one applies methods from proof theory (like Kurt Gödel’s functional interpretation and its variants) to study prima facie noneffective mathematical proofs in order to derive new results that exhibit the hidden information contained inside them. Such information then may in particular take the form of additional quantitative data on previous non-quantitative statements. In the concrete context of convergence statements in mathematical analysis, the desired information usually comes in the form of rates of convergence or rates of metastability (in the sense of Terence Tao), and frequently shines light on the crucial underlying hypotheses of the proof, thus allowing for generalizations of the results analyzed. The central goal of the project is to obtain novel applications to functional analysis with focus on the study of potential generalizations from linear to nonlinear settings.

• DFG Programme: Research Grants