I am currently employed as senior lecturer at the University of Pretoria. My current research centers around computational geometry and functional analysis.
Previously I held a Claude Leon postdoctoral fellowship at the University of Pretoria (2016-2017) and a postdoctoral fellowship at the North-west University (2014-2016).
I completed my PhD at Leiden University in November of 2013 under supervision of Marcel de Jeu, with thesis titled Positive representations on ordered Banach spaces.
Email: miek(dot)messerschmidt(at)up(dot)ac(anotherdot)za
Office: University of Pretoria (Hatfield); Botany Building; Room 2-7.
[github] [ResearchGate] [arXiv] [MathOverflow] [linkedin] [orcid]
Eder Kikianty, Miek Messerschmidt, Luan Naude, Mark Roelands, Christopher Schwanke, Walt van Amstel, Jan Harm van der Walt, Marten Wortel. L-functional analysis
https://arxiv.org/abs/2403.10222
Messerschmidt, M., Kikianty, E. On Compact Packings of Euclidean Space with Spheres of Finitely Many Sizes. Discrete Comput Geom (2024).
https://doi.org/10.1007/s00454-024-00628-y
http://arxiv.org/abs/2305.00758
N.J. Laustsen, M. Messerschmidt, M. Wortel. A surjective summation operator with no Lipschitz right inverse. Proc. Amer. Math. Soc. 152 (2024), 253-266
https://doi.org/10.1090/proc/16496
M. Messerschmidt. The number of configurations of radii that can occur in compact packings of the plane with discs of n sizes is finite. Discrete Comput Geom 71, 667–682 (2024).
https://doi.org/10.1007/s00454-022-00471-z
https://arxiv.org/abs/2110.15831
S. ter Horst, M. Messerschmidt, A.C.M. Ran. Equivalence After Extension and Schur Coupling for Relatively Regular Operators. Integral Equations and Operator Theory 92, 40 (2020).
https://arxiv.org/abs/2005.14563
https://doi.org/10.1007/s00020-020-02597-2
M. Messerschmidt. On compact packings of the plane with circles of three radii. Computational Geometry. Volume 86, January 2020, 101564.
https://doi.org/10.1016/j.comgeo.2019.05.002
https://arxiv.org/abs/1709.03487
M. Messerschmidt. A family of quotient maps of $\ell^\infty$ that do not admit uniformly continuous right inverses (2019)
arxiv.org/abs/1909.10417
M. Messerschmidt. A Pointwise Lipschitz Selection Theorem. Set-Valued and Variational Analysis. Volume 27, pp. 223-240(2019)
10.1007/s11228-017-0455-2
arxiv.org/abs/1611.08435
S. ter Horst, M. Messerschmidt, A.C.M. Ran, M. Roelands. Equivalence after extension and Schur coupling do not coincide on essentially incomparable Banach spaces. Bulletin London Mathematical Society Volume 51 (2019) 1005-1014
10.1112/blms.12292
arxiv.org/abs/1901.09254
M. Messerschmidt. On the Lipschitz decomposition problem in ordered Banach spaces and its connections to other branches of mathematics. Positivity and Noncommutative Analysis (2019) Birkhauser. pp 405-423. Festschrift in honour of Ben de Pagter on the occasion of his 65th birthday.
https://doi.org/10.1007/978-3-030-10850-2 22
M. Messerschmidt. Strong Klee-Andô Theorems through an Open Mapping Theorem for cone-valued multi-functions. Journal of Functional Analysis. Volume 275, Issue 12, 15 December 2018, Pages 3325-3337.
10.1016/j.jfa.2018.02.008
arxiv.org/abs/1606.00249
S. ter Horst, M. Messerschmidt, A.C.M. Ran, M. Roelands, M. Wortel. Equivalence after extension and Schur coupling coincide for inessential operators. Indagationes Mathematicae (N.S.) 29 (2018), no. 5, 1350--1361.
10.1016/j.indag.2018.07.001
arxiv.org/abs/1706.09177
M. Messerschmidt and M. Wortel. The intrinsic metric on the unit sphere of a normed space. 2015
arxiv.org/abs/1510.07442
S. ter Horst, M. Messerschmidt, A. Ran. Equivalence after extension for compact operators on Banach spaces Journal of Mathematical Analysis and Applications. 431 (2015), pp. 136–149
doi:10.1016/j.jmaa.2015.05.059
arxiv.org/abs/1503.07350
M. Messerschmidt. Geometric duality theory for cones in dual pairs of vector spaces. Journal of Functional Analysis. 269 (2015), pp. 2018-2044
doi:10.1016/j.jfa.2015.04.022
arxiv.org/abs/1407.2434
M. Messerschmidt. Normality of spaces of operators and quasi-lattices. Positivity. 19 (2015), pp. 695-724
doi:10.1007/s11117-015-0323-y
arxiv.org/abs/1307.1415
M. de Jeu, and M. Messerschmidt. A strong open mapping theorem for surjections from cones onto Banach spaces. Advances in Mathematics. 259 (2014) p.43-66
doi:10.1016/j.aim.2014.03.008
arxiv.org/abs/1302.2822
M. de Jeu, M. Messerschmidt, and M. Wortel. Crossed products of Banach algebras. II.
arxiv.org/abs/1305.2304
M. de Jeu, and M. Messerschmidt. Crossed products of Banach algebras. III.
arxiv.org/abs/1306.6290