Dr Michael Dymond MMath PhD

Dr Michael Dymond

School of Mathematics
Assistant Professor

Contact details

Address
School of Mathematics
Watson Building
University of Birmingham
Edgbaston
Birmingham
B15 2TT
UK

Dr Michael Dymond is an Assistant Professor in the Analysis group. Michael's research interests lie in the intersection of functional analysis, geometric measure theory and discrete mathematics. Michael studies Lipschitz mappings in a range of different settings and their relation to exceptional sets, such as porous and sigma porous sets. An example of a project that Michael is currently working on is the problem of determining the best possible Lipschitz constant (or stretch factor) with which n grid points can rearranged into a square formation. This is connected to the bandwidth problem in computer science.

Personal website

Qualifications

  • PhD in Pure Mathematics, University of Birmingham, 2014
  • MMath in Mathematics, University of Warwick, 2011

Biography

Michael obtained a master's degree in Mathematics (MMath) from the University of Warwick in 2011 and his 4th Year research project "Avoiding sigma porous sets in Hilbert spaces", supervised by Professor David Preiss, earnt him the Warwick MMath Prize. Michael then went on to study for a PhD in Pure Mathematics, supervised by Professor Olga Maleva, at the University of Birmingham between 2011 and 2014. In his PhD thesis "Differentiability and negligible sets in Banach spaces", Michael, among other things, investigated the Minkowski dimension of sets capturing points of differentiability of every Lipschitz function. After obtaining his PhD, Michael held positions as a postdoc for a total of 6 years at University of Innsbruck in Austria, during which time he obtained an Austrian Science Fund grant for his research project "Lipschitz mappings, differentiability and exceptional sets". Michael held a further postdoc position at the University of Leipzig, starting in 2020, before arriving in Birmingham in 2022.

Teaching

Semester 2

LM Advanced Topics in Analysis

Postgraduate supervision

Michael is offering projects suitable for PhD studies in pure mathematics and invites enquires from prospective postgraduate students.

Publications

Recent publications

Article

Dymond, M & Maleva, O 2020, 'A dichotomy of sets via typical differentiability', Forum of Mathematics, Sigma, vol. 8, e41. https://doi.org/10.1017/fms.2020.45

Bargetz, C, Dymond, M, Medjic, E & Reich, S 2020, 'On the existence of fixed points for typical nonexpansive mappings on spaces with positive curvature', Topological Methods in Nonlinear Analysis. https://doi.org/10.12775/tmna.2020.040

Dymond, M 2020, 'Typical differentiability within an exceptionally small set', Journal of Mathematical Analysis and Applications. https://doi.org/10.1016/j.jmaa.2020.124317

Dymond, M, Kaluža, V & Kopecká, E 2018, 'Mapping n Grid Points Onto a Square Forces an Arbitrarily Large Lipschitz Constant', Geometric and Functional Analysis. https://doi.org/10.1007/s00039-018-0445-z

Dymond, M 2017, 'On the structure of universal differentiability sets', Commentationes Mathematicae Universitatis Carolinae. https://doi.org/10.14712/1213-7243.2015.218

Maleva, O & Dymond, M 2016, 'Differentiability inside sets with Minkowski dimension one', Michigan Mathematical Journal, vol. 65, no. 3, pp. 613-636. https://doi.org/10.1307/mmj/1472066151

Dymond, M 2016, 'σ-porosity of the set of strict contractions in a space of non-expansive mappings', Israel Journal of Mathematics. https://doi.org/10.1007/s11856-016-1372-z

Dymond, M 2014, 'Avoiding σ -porous sets in Hilbert spaces', Journal of Mathematical Analysis and Applications. https://doi.org/10.1016/j.jmaa.2013.12.027

Preprint

Dymond, M & Kaluža, V 2021 'Divergence of separated nets with respect to displacement equivalence'. https://doi.org/10.48550/arXiv.2102.13046

Dymond, M 2021 'Porosity phenomena of non-expansive, Banach space mappings'. https://doi.org/10.48550/arXiv.2110.13722

Dymond, M & Maleva, O 2021 'Typical Lipschitz mappings are typically non-differentiable' arXiv. <https://arxiv.org/pdf/2111.09644.pdf>

Dymond, M 2020 'Lipschitz constant $\log{n}$ almost surely suffices for mapping $n$ grid points onto a cube'.

Dymond, M & Kaluža, V 2019 'Highly irregular separated nets'.

View all publications in research portal