Speaker: Ulrich Kohlenbach (Department of Mathematics - Technische Universität Darmstadt).

Abstract: During the last two decades a systematic program of `proof mining' emerged as a new applied form of proof theory and has successfully been applied to a number of areas of core mathematics. We are primarily concerned with the extraction of hidden finitary and combinatorial content from proofs that make use of infinitary noneffective principles. The main logical tools for this are so-called interpretations. Logical metatheorems based on such interpretations have been applied with particular success in the context of nonlinear analysis including fixed point theory, ergodic theory, continuous optimization, game theory and abstract Cauchy problems. The combinatorial content can manifest itself both in explicit effective bounds as well as uniformity results.

In this talk we will outline some recent new developments in proof mining and focus on the following points:

• tameness of bounds extracted,
• new qualitative results obtained as a byproduct of proof mining,
• mathematically enriched metastability results as finitizations of theorems going beyond mere convergence.

Zoom |  ID da reunião: 890 8479 3299 - senha de acesso: 409604