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Dr Hannes Diener

Contact

Department: Mathematics and Statistics

Email: hannes.diener@canterbury.ac.nz

Office: Jack Erskine Rm 622

Languages: English, German

About
Research / Creative works
Networks

Researcher Summary

My main research interests are algorithmic aspects of analysis and topology. Even though classical existence results are often reasonably simple to prove, their proofs mostly do not contain any information of how to actually find these objects. The subtleties and intricacies of giving constructive content in analytical and topological theorems is therefore a valuable task, especially if one is interested in the implementation of those results.

Subject Area: Disciplines

  • Mathematics: Computable Mathematics; Constructive Mathematics; Foundations of Mathematics; Pure Mathematics

Resources

  • Staff webpage

Research/Scholarly/Creative Works

  • Diener H. and Hendtlass M. (2019) (Seemingly) Impossible Theorems in Constructive Mathematics. arXiv. (Journal Articles)
  • Diener H. and Lubarsky RS.. (2019) Weakenings of Cauchy convergence. In 12th International Conference on Computability and Complexity in Analysis, CCA 2015 - Proceedings: 16-17. (Conference Contributions - Published)
  • Diener H. (2018) Constructive Reverse Mathematics (Habilitationsschrift). Siegen, Germany: Universität Siegen. (Other)
  • Diener H. and Hendtlass M. (2018) Bishop’s Lemma. Mathematical Logic Quarterly 64 1-2: 49-54. http://dx.doi.org/10.1002/malq.201600041. (Journal Articles)
  • Diener H. and Hendtlass M. (2018) The Third Trick. arXiv. (Journal Articles)
  • Diener H. and Lubarsky R.. (2018) Notions of cauchyness and metastability. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 10703 LNCS: 140-153. http://dx.doi.org/10.1007/978-3-319-72056-2_9. (Conference Contributions - Published)
  • Warren L., Diener H. and McKubre-Jordens M. (2018) The Drinker Paradox and its Dual. arXiv. (Journal Articles)
  • Diener H. and McKubre Jordens M. (2017) Paradoxes of material implication in minimal logic. In Christiansen H; Jiménez-López MD; Loukanova R; Moss LS (Ed.), Partiality and Underspecification in Information, Languages, and Knowledge: 27-64.Cambridge Scholars Publishing. (Chapters)
  • Diener H. and McKubre-Jordens M. (2016) Classifying Material Implications over Minimal Logic. arXiv. (Journal Articles)
  • Diener H. (2015) Variations on a theme by Ishihara. Mathematical Structures in Computer Science 25(7): 1569-1577. http://dx.doi.org/10.1017/S0960129513000261. (Journal Articles)
  • Brattka V., Diener H. and Spreen D. (2014) Logic, Computation, Hierarchies. Berlin, Boston: De Gruyter. 414pp. (Edited Volumes)
  • Lubarsky B. and Diener H. (2014) Separating the Fan Theorem and Its Weakenings. Journal of Symbolic Logic 79(3): 792-813. http://dx.doi.org/10.1017/jsl.2014.9. (Journal Articles)
  • Berger J., Bridges D., Diener H. and Schwichtenberg H. (2013) Constructive aspects of Riemann's permutation theorem for series. . (Journal Articles)
  • Diener H. (2013) Weak Königs Lemma implies the Uniform Continuity Theorem. Computability Volume 2(Number 1): 9-13. http://dx.doi.org/10.3233/COM-13009. (Journal Articles)
  • Lubarsky R. and Diener H.. (2013) Separating the fan theorem and its weakenings. In Artemov S; Nerode A (Eds). : 280-295. Berlin Heidelberg: Springer. (Conference Contributions - Published)
  • Lubarsky RS. and Diener H. (2013) Principles Weaker than BD-N. Journal of Symbolic Logic 78(3): 873-885. http://dx.doi.org/10.2178/jsl.7803090. (Journal Articles)
  • Berger U., Diener H., Schuster P. and Seisenberger M. (2012) Logic, Construction, Computation. Frankfurt: Ontos Verlag. 540. (Edited Volumes)
  • Diener H. (2012) Re-Classifying the anti-Specker property. Archive for Mathematical Logic Vol. 51: 687-693. http://dx.doi.org/10.1007/s00153-012-0292-9. (Journal Articles)
  • Diener H. (2012) Reclassifying the antithesis of Specker’s theorem. Archive for Mathematical Logic 51(7-8): 687-693. (Journal Articles)
  • Diener H. and Hedin A. (2012) The Vitali covering theorem in constructive mathematics. Journal of Logic and Analysis 4(7): 1-22. http://dx.doi.org/10.4115/jla.2012.4.7. (Journal Articles)
  • Diener H. and Schuster P. (2011) Uniqueness, continuity and the existence of implicit functions in constructive analysis. LMS Journal of Computation and Mathematics 14(1): 127-136. http://dx.doi.org/10.1112/S1461157010000057. (Journal Articles)
  • Bridges DS. and Diener H. (2010) The anti-Specker property, positivity, and total boundedness. Mathematical Logic Quarterly 56(4): 434-441. http://dx.doi.org/10.1002/malq.200910017. (Journal Articles)
  • Diener H. and Schuster P. (2010) On choice principles and fan theorems. Journal of Universal Computer Science 16(18): 2556-2562. (Journal Articles)
  • Diener H. and Loeb I. (2009) Sequences of Real Functions on [0,1] in Constructive Reverse Mathematics. Annals of Pure and Applied Logic 157(1): 50-61. http://dx.doi.org/10.1016/j.apal.2008.09.018. (Journal Articles)
  • Diener H. and Schuster P.. (2009) Uniqueness, continuity, and existence of implicit functions in constructive analysis. In OpenAccess Series in Informatics 11: 131-140. (Conference Contributions - Published)
  • Bridges DS. and Diener H. (2008) The pseudocompactness of [0,1] is equivalent to the uniform continuity theorem. Journal of Symbolic Logic 72(4): 1379-1384. http://dx.doi.org/10.2178/jsl/1203350793. (Journal Articles)
  • Diener H. (2008) Compactness Under Constructive Scrutiny. Christchurch, New Zealand. University of Canterbury. (Theses / Dissertations)
  • Diener H. (2008) Generalising compactness. Mathematical Logic Quarterly 54(1): 49-57. http://dx.doi.org/10.1002/malq.200710041. (Journal Articles)
  • Bridges D. and Diener H. (2006) A constructive treatment of Urysohn's lemma in an apartness space. Mathematical Logic Quarterly 52(5): 464-469. http://dx.doi.org/10.1002/malq.200610006. (Journal Articles)

Review and Refereeing

  • International workshop Mathematics for Computation ( 2016 )
  • Tenth International Conference on Computability and Complexity in Analysis ( 2013 - 2021)
  • Journal of Symbolic Logic; Annals of Pure and Applied Logic; Journal of Universal Computer Science; Logical Methods in Computer Science; Logic Journal of the IGPL; Research Foundation Flanders (FWO) ( 2009 - 2021)

Research Groups

  • Centre for Computable and Constructive Mathematics (CCCM)
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