Grant CNCS IDEI Nr. PN-II-ID-PCE-2011-3-0383 (2011-2014)
Proof mining in
metric analysis, geometric group theory and ergodic theory
Members
1.
Laurentiu Leustean - Project Director
2.
Marius Buliga - Senior Researcher
3. Emanuel Vlad - Master Student
Abstract
We shall use proof mining techniques in order to obtain finitary versions with effective bounds of some important results in metric analysis, geometric group theory (Gromov's theorem on groups with polynomial growth, approximate groups) and ergodic Ramsey theory. Proof mining is a new paradigm of research, with researchers working at different universities in Europe and USA. The program of proof mining is concerned with the extraction of hidden finitary and combinatorial content, such as algorithms and effective bounds, from proofs that make use of highly infinitary principles. This research direction can be related to Terence Tao's proposal of "hard analysis", based on finitary arguments, instead of the infinitary ones from "soft analysis".
Scientific Seminar Effective methods in metric analysis
Publications produced as a result of this research
- David Ariza-Ruiz, Laurentiu Leustean, Genaro Lopez-Acedo, Firmly nonexpansive mappings in classes of geodesic spaces, arXiv:1203.1432v1 [math.FA], 2012.
- Ulrich Kohlenbach, Laurentiu Leustean,
On the computational content of convergence proofs via Banach limits,
to appear in Philosophical Transactions of the Royal Society A.
- Ulrich Kohlenbach,
Laurentiu Leustean
Effective metastability of Halpern iterates in CAT(0) spaces, arXiv:1107.3215v3, 2011.
- Marius Buliga,
Emergent algebras, arXiv:0907.1520v3, 2011.
- Laurentiu Leustean (joint work with Ulrich Kohlenbach), Recent developments in proof mining,
Mathematisches Forschungsinstitut Oberwolfach,
Report No. 52/2011, 20-22.
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