Research

Preprints

• M. Dymond, O. Maleva, Typical Lipschitz mappings are typically non-differentiable, arXiv Preprint (2021), arXiv:2111.09644

• M. Dymond, Lipschitz constant $\log n$ almost surely suffices for mapping $n$ grid points onto a cube, arXiv Preprint (2020), arXiv:2010.15073 

Publications

• M. Dymond, V. Kaluža, Divergence of separated nets with respect to displacement equivalence. Geom Dedicata 218, 15 (2024). https://doi.org/10.1007/s10711-023-00862-3, arXiv:2102.13046 

• M. Dymond, Porosity phenomena of non-expansive, Banach space mappings. Isr. J. Math. (2022). https://doi.org/10.1007/s11856-022-2461-9 

• M. Dymond, V. Kaluža, Highly irregular separated nets. Isr. J. Math. (2022). https://doi.org/10.1007/s11856-022-2448-6 

• M. Dymond, O. Maleva, A dichotomy of sets via typical differentiability. Forum of Mathematics, Sigma, 8, E41., (2020). https://doi.org/10.1017/fms.2020.45, arXiv:1909.03487

• M. Dymond, Typical differentiability within an exceptionally small set, Journal of Mathematical Analysis and Applications, Volume 490, Issue 2, (2020). https://doi.org/10.1016/j.jmaa.2020.124317, arXiv:1901.03133

• C. Bargetz, M. Dymond, E. Medjic, S. Reich, On the existence of fixed points for typical nonexpansive mappings on spaces with positive curvature, Topological Methods in Nonlinear Analysis, p. 1 - 14, (2020). https://doi.org/10.12775/TMNA.2020.040, arXiv:2004.02567

• M. Dymond, V. Kaluža, E. Kopecká, Mapping n Grid Points Onto a Square Forces an Arbitrarily Large Lipschitz Constant, Geom. Funct. Anal. 28, 589–644 (2018). https://doi.org/10.1007/s00039-018-0445-z, arXiv:1704.01940

•  C. Bargetz. M. Dymond. S. Reich, Porosity results for sets of strict contractions on geodesic metric spaces, Topol. Methods Nonlinear Anal. 50 (1) 89 - 124, (2017). https://doi.org/10.12775/TMNA.2017.013, arXiv:1602.05230

• M. Dymond, B. Randrianantoanina, H. Xu, On Interval Based Generalizations of Absolute Continuity for Functions on Rn, Real Anal. Exchange 42 (1) 49 - 78, (2017). https://projecteuclid.org/journals/real-analysis-exchange/volume-42/issue-1/On-Interval-Based-Generalizations-of-Absolute-Continuity-for-Functions-on/rae/1490580012.short, arXiv:1306.4291

• M. Dymond, On the structure of universal differentiability sets. Commentationes Mathematicae Universitatis Carolinae. 58. (2016). https://doi.org/10.14712/1213-7243.2015.218, arXiv:1607.05933

• M. Dymond, O. Maleva, Differentiability inside sets with Minkowski dimension one, Michigan Math. J. 65 (3) 613 - 636, (2016). https://doi.org/10.1307/mmj/1472066151, arXiv:1305.3154 

• C. Bargetz, M. Dymond, σ-porosity of the set of strict contractions in a space of non-expansive mappings. Isr. J. Math. 214, 235–244 (2016). https://doi.org/10.1007/s11856-016-1372-z, arXiv:1505.07656  

• M. Dymond, Avoiding σ-porous sets in Hilbert spaces, Journal of Mathematical Analysis and Applications, Volume 413, Issue 2, p. 668-684, (2014) https://doi.org/10.1016/j.jmaa.2013.12.027.

Completed Research Project

FWF Projekt 30902-N35, Lipschitz Mappings, Differentiability and Exceptional Sets, https://www.uibk.ac.at/mathematik/personal/dymond/projekt

Academic Thesis

• M. Dymond, Differentiability and negligible sets in Banach spaces, PhD Thesis, (2014). http://etheses.bham.ac.uk/5158/