Marc Christian Zimmermann
Universität zu Köln
Marc Christian Zimmermann
Universität zu Köln
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Universität zu Köln
I am a postdoctoral researcher in mathematics, currently affiliated with the Universität zu Köln.
I am a member of the group on "Optimierung, Geometrie und diskrete Mathematik" and you can find my university homepage here.
I am a postdoctoral researcher in mathematics, currently affiliated with the Universität zu Köln.
I am a member of the group on "Optimierung, Geometrie und diskrete Mathematik" and you can find my university homepage here.
Research
Research
My research concerns extremal problems in discrete geometry, lattices, and quadratic forms. My current focus is on energy related problems for Euclidean lattices, which are modern variants of the classical sphere packing and sphere covering problems.
I am particularly excited by the problems of energy minimization and the problem of lattice polarization.
I have worked on the problems of least distortion embeddings of flat tori into Hilbert spaces and problems related to the Voronoi tesselation of a lattice, such as the lattice quantizer problem and the chromatic number of lattices.
I am also interested in enumerative problems related to quadratic forms, quite recently with a focus on representation graphs associated to quadratic forms over (finite) fields and rings.
Preprints & Publications
Preprints & Publications
Critical modular lattices in the Gaussian core model, with A. Joharian and F. Vallentin, arXiv preprint (2025).
Diameter and girth of representation graphs of quadratic forms, with N. Lorenz, arXiv preprint (2025).
Polarization of lattices: Stable cold spots and spherical designs, with C. Bachoc, P. Moustrou, and F. Vallentin, arXiv preprint (2025).
The chromatic number of 4-dimensional lattices, with F. Vallentin and S. Weißbach, Indagationes Mathematicae (2024)
Bounds on polarization problems on compact sets via mixed integer programming, with J.H. Rolfes and R. Schüler, Discrete & Computational Geometry (2024)
Critical even unimodular lattices in the Gaussian core model, with A. Heimendahl, A. Marafioti, A. Thiemeyer, and F. Vallentin, International Mathematics Research Notices (2023)
Cliques in representation graphs of quadratic forms, with N. Lorenz, arXiv preprint (2023)
A semidefinite program for least distortion embeddings of flat tori into Hilbert spaces, with A. Heimendahl, M. Lücke, and F. Vallentin, arXiv preprint (2022)
Steinitz classes and partial genera of unimodular lattices over imagninary-quadratic fields, with M. Jürgens, Journal of Number Theory (2017)
Theses
Theses
Configurations of sublattices and Dirichlet-Voronoi cells of periodic point sets, Dissertation, Technische Universität Dortmund (2017)
Räume von Modulformen und ihre Anwendungen auf dual-extremale Gitter, Diploma thesis, Technische Universität Dortmund (2012)
Miscellaneous
Miscellaneous
Classification of dual-extremal lattices in low dimensions, preprint containing a short summary of results of my diploma thesis (2012)
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