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.
- (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.
- Diener H. (2018) Constructive Reverse Mathematics (Habilitationsschrift). Siegen, Germany: Universität Siegen.
- 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.
- 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.
- 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.