Mathematisches Kolloquium

Zusammenfassung: In this talk we will give an account of the applied re-orientation of proof theory towards the analysis of concrete proofs in mathematics which was prompted by Georg Kreisel's pioneering ideas in the 50's and systematically developed during the last 10-20 years. We will give a survey of uses of proof theoretic transformations to extract explicit effective bounds in nonlinear analysis, fixed point theory and ergodic theory. Most recently, even proofs in nonlinear analysis that use a substantial amount of the axiom of choice in the form of Banach limits could be given a quantitative finitary re-interpretation. The success of this program (sometimes called `proof mining') largely vindicates David Hilbert's original proposal to show that the use of `ideal elements' in the course of proving `real statements' can, in principle, be replaced by an effective finitary reasoning. Surprisingly, this proof-theoretic approach has close connections to the concept of `finitary analysis' as proposed recently by Terence Tao.

Alle Interessierten sind hiermit herzlich eingeladen. Eine halbe Stunde vor dem Vortrag gibt es Kaffee und Tee im Sozialraum (Raum 448) im 4. Stock.

Treffpunkt zum Abendessen um 18.00 Uhr wird noch bekannt gegeben.