Grant CNCS-UEFISCDI

Proof mining in metric analysis, geometric group theory and ergodic theory

Project Code: PN-II-ID-PCE-2011-3-0383

Contract no. 24/2011 financed by the Romanian National Authority for Scientific Research, CNCS - UEFISCDI

Period: October 2011 - October 2016

Host: "Simion Stoilow" Institute of Mathematics of the Romanian Academy

Team

• Laurențiu Leuștean (Project Director)
• Marius Buliga
• Andrei Sipoș

Abstract and expected results

Scientific reports

Publications produced as a result of this research

Published

• Laurențiu Leuștean, Adriana Nicolae, A note on an alternative iterative method for nonexpansive mappings,
  Journal of Convex Analysis 24 (2017), No.2.
• Andrei Sipoș, A note on the Mann iteration for k-strict pseudocontractions in Banach spaces,
  Numerical Functional Analysis and Optimization 38 (2017), No. 1, 80-90.
• Andrei Sipoș, Effective results on a fixed point algorithm for families of nonlinear mappings,
  Annals of Pure and Applied Logic 168 (2017), 112-128.
• Laurențiu Leuștean, Vlad Radu, Andrei Sipoș, Quantitative results on the Ishikawa iteration of Lipschitz pseudo-contractions,
  Journal of Nonlinear and Convex Analysis 17 (2016), No. 11, 2277-2292.
• Laurențiu Leuștean, Adriana Nicolae, Effective results on nonlinear ergodic averages in CAT(k) spaces,
  Ergodic Theory and Dynamical Systems 36 (2016), 2580-2601.
• Laurențiu Leuștean, Adriana Nicolae, A note on an ergodic theorem in weakly uniformly convex geodesic spaces,
  Archiv der Mathematik 105 (2015), 467-477.
• Daniel Ivan, Laurențiu Leuștean, A rate of asymptotic regularity for the Mann iteration of k-strict pseudo-contractions,
  Numerical Functional Analysis and Optimization 36 (2015), 792-798.
• Laurențiu Leuștean (joint with Ulrich Kohlenbach and Adriana Nicolae), Proof-theoretic methods in nonlinear analysis III: Quantitative results on Fejer monotone sequences,
  Mathematisches Forschungsinstitut Oberwolfach, Report No. 52/2014, 2960-2961.
• David Ariza-Ruiz, Laurențiu Leuștean, Genaro Lopez-Acedo, Firmly nonexpansive mappings in classes of geodesic spaces,
  Transactions of the American Mathematical Society 366 (2014), 4299-4322.
• Ulrich Kohlenbach,
Addendum to "Effective metastability of Halpern iterates in CAT(0) spaces" [Adv.Math. 231 (5) (2012) 2526-2556],
Advances in Mathematics 250 (2014), 650-651.
• Laurențiu Leuștean, Adriana Nicolae, Effective results on compositions of nonexpansive mappings,
  Journal of Mathematical Analysis and Applications 410 (2014), 902-907.
• Aurora Fernandez Leon, Adriana Nicolae, Best proximity pair results for relatively nonexpansive mappings in geodesic spaces
  Numerical Functional Analysis and Optimization 35 (2014), 1399-1418.
• Marius Buliga, Graphic lambda calculus,
  Complex Systems 22 (2013), 311-360.
• Adriana Nicolae, Asymptotic behavior of averaged and firmly nonexpansive mappings in geodesic spaces,
  Nonlinear Analysis - Theory, Methods & Applications 87 (2013), 102-115.
• Aurora Fernandez-Leon, Adriana Nicolae, Averaged alternating reflections in geodesic spaces,
  Journal of Mathematical Analysis and Applications 402 (2013), 558-566.
• Ulrich Kohlenbach, Laurențiu Leuștean, On the computational content of convergence proofs via Banach limits,
  Philosophical Transactions of the Royal Society A 370 (2012), No. 1971, 3449-3463
  Theme Issue The foundations of computation, physics and mentality: the Turing legacy.
• Ulrich Kohlenbach, Laurențiu Leuștean, Effective metastability of Halpern iterates in CAT(0) spaces,
  Advances in Mathematics 231 (2012), 2526-2556.
• Laurențiu Leuștean (joint work with Ulrich Kohlenbach), Recent developments in proof mining,
  Mathematisches Forschungsinstitut Oberwolfach, Report No. 52/2011, 2982-2984.

Accepted for publication

• Ulrich Kohlenbach, Laurențiu Leuștean, Adriana Nicolae, Quantitative results on Fejer monotone sequences,
  to appear in Communications in Contemporary Mathematics.
• Andrei Sipoș, Codensity and Stone spaces,
  to appear in Mathematica Slovaca.

Preprints

• Andrei Sipoș, Proof mining in L^p spaces,
  arXiv:1609.02080 [math.LO], 2016.
• Laurențiu Leuștean, Adriana Nicolae, Alexandru Zaharescu, Barycenters in uniformly convex geodesic spaces,
  arXiv:1609.02589 [math.MG], 2016.
• Marius Buliga, Geometric Ruzsa triangle inequality in metric spaces with dilations,
  arXiv:1304.3358 [math.CO], 2016.
• Andrei Sipoș, Ultraproducts and uniform rates of asymptotic regularity and metastability, 2015.
• Marius Buliga, Sub-riemannian geometry from intrinsic viewpoint,
  arXiv:1206.3093v1 [math.MG], 2012.

Workshops/Conferences/Scientific seminars organized

• Special Session Logic in Computer Science at The Eighth Congress of Romanian Mathematicians, 26.06 - 01.07 2015, Alexandru Ioan Cuza University of Iasi.
• Logic Seminar (2012 - present).
• Scientific Seminar Effective methods in metric analysis (2011 - 2013).

Conference and Seminar Talks

• Laurențiu Leuștean, Proof mining and applications,
  Middlesex University London, 19.09.2016.
• Andrei Sipoș, Proof mining and positive-bounded logic,
  Colloquium Logicum 2016, Hamburg, 10 - 12.09.2016.
• Andrei Sipoș, Proof mining and positive-bounded logic,
  Logic Colloquium 2016, Leeds, 31.07. - 06.08.2016.
• Andrei Sipoș, Effective results on algorithms using strict pseudocontractions,
  IMUS Analysis Seminar, University of Seville, 30.06.2016.
• Andrei Sipoș, Proof mining and families of mappings,
  PhDs in Logic VIII, Darmstadt, 09 - 11.05.2016.
• Andrei Sipoș, Codensity and Stone spaces,
  Logic Colloquium 2015, Helsinki, 03 - 08.08 2015.
• Andrei Sipoș, Codensity and Stone spaces,
  Special Session Logic in Computer Science,
  The Eighth Congress of Romanian Mathematicians, Iași, 26.06 - 01.07 2015.
• Laurențiu Leuștean, Proof theoretic methods in nonlinear analysys III. Quantitative results on Fejer monotone sequences,
  Oberwolfach Workshop 1147: Mathematical Logic: Proof Theory, Type Theory and Constructive Mathematics,
  Mathematisches Forschungsinstitut Oberwolfach, 16 - 22.11.2014.
• Laurențiu Leuștean, An invitation to proof mining,
  Topics in Geometric Group Theory, Bucharest, 29.09 - 05.10 2014.
• Laurențiu Leuștean, Effective results on the asymptotic behavior of nonexpansive iterations,
  Logic Colloquium 2014, Vienna, 14.07 - 19.07.2014.
  Abstract appeared in Bulletin of Symbolic Logic 21 (2015), No. 1, p. 79.
• Laurențiu Leuștean, An invitation to proof mining II (Effective results on the mean ergodic theorem),
  Logic in Computer Science Seminar, University of Bucharest, 22.05.2014.
• Laurențiu Leuștean, An invitation to proof mining I,
  Logic in Computer Science Seminar, University of Bucharest, 16.05.2014.
• Laurențiu Leuștean, Effective methods in geodesic spaces,
  IRTG 1529 Research Seminar "Proof Mining and Nonlinear Analysis", Technische Universität Darmstadt, 26.02 - 28.02.2014.
• Laurențiu Leuștean, Proof mining and applications in nonlinear ergodic theory,
  Anniversary Conference "Faculty of Sciences - 150 years", University of Bucharest, 29.08 - 01.09.2013.
• Laurențiu Leuștean, Effective methods in geodesic spaces,
  Workshop on Operator Theory in Metric Spaces, Sevilla, 03 - 04.04.2013.
• Adriana Nicolae, Asymptotic behavior of averaged and firmly nonexpansive mappings in geodesic spaces,
  Workshop on Operator Theory in Metric Spaces, Sevilla, 03 - 04.04.2013.
• Laurențiu Leuștean, Proof mining in nonlinear analysis,
  Logic Seminar, Technische Universität Darmstadt, 09.11.2012.
• Adriana Nicolae, Reflecting in classes of geodesic spaces,
  IMUS Analysis Seminar, University of Seville, 23.10.2012.
• Laurențiu Leuștean, Firmly nonexpansive mappings in classes of geodesic spaces,
  Invited Session: Variational inequalities and optimization problems on Riemannian manifolds,
  21st International Symposium on Mathematical Programming (ISMP 2012), Berlin, 19 - 24.08.2012.
• Laurențiu Leuștean, Recent developments in proof mining,
  Oberwolfach Workshop 1145: Mathematical Logic: Proof Theory, Type Theory and Constructive Mathematics,
  Mathematisches Forschungsinstitut Oberwolfach, 06 - 12.11.2011.

Participations in Summer Schools

• Andrei Sipoș, Scandinavian Logic Society Summer School in Logic, University of Helsinki, 27 - 31.07 2015.