Kohlenbach, Ulrich Proof-theoretic methods in nonlinear analysis. (English) Zbl 1445.03062 Sirakov, Boyan (ed.) et al., Proceedings of the international congress of mathematicians, ICM 2018, Rio de Janeiro, Brazil, August 1–9, 2018. Volume II. Invited lectures. Hackensack, NJ: World Scientific; Rio de Janeiro: Sociedade Brasileira de Matemática (SBM). 61-82 (2018). Summary: We discuss applications of methods from proof theory, so-called proof interpretations, for the extraction of explicit bounds in convex optimization, fixed point theory, ergodic theory and nonlinear semigroup theory.For the entire collection see [Zbl 1437.00044]. Cited in 27 Documents MSC: 03F10 Functionals in proof theory 03F35 Second- and higher-order arithmetic and fragments 47H10 Fixed-point theorems 47H20 Semigroups of nonlinear operators 47H25 Nonlinear ergodic theorems Keywords:proof mining; effective bounds; convex optimization; fixed points; ergodic theory; nonlinear semigroups PDFBibTeX XMLCite \textit{U. Kohlenbach}, in: Proceedings of the international congress of mathematicians, ICM 2018, Rio de Janeiro, Brazil, August 1--9, 2018. Volume II. Invited lectures. Hackensack, NJ: World Scientific; Rio de Janeiro: Sociedade Brasileira de Matemática (SBM). 61--82 (2018; Zbl 1445.03062) Full Text: DOI Link