Matthias Zach - Mathematical Researcher and Software Engineer

I graduated in 2017 from the Leibniz Universitaet Hannover with a Dr. rer. nat. in Mathematics with a thesis on Topological Invariants of Isolated Determinantal Singularities.

I am currently employed at the RPTU Kaiserslautern as part of the SFB-TRR 195 on Symbolic Tools in Mathematics and their Application where I am one of the core developers for the OSCAR software package for Algebraic schemes; see also our chapter on Elliptic fibrations on Vinberg's most algebraic K3-surface (joint with Simon Brandhorst) for the OSCAR book or my talk at BIRS in 2024 about our joint work in progress.

See here for my GitHub page. You can reach me under lastname at rptu dot de.

Research interests

Complex analytic singularities: Deformations and their topology, computation of (topological) invariants, characteristic classes.
Singularities of mappings: Disentanglements, alternating homology, perverse sheaves.
Algorithmic commutative algebra: applications to Algebraic Geometry at scale, computation of global geometric invariants, (sheaf) cohomology.

Upcoming conferences and workshops

I have been invited to participate in the following upcoming conferences:

Characteristic classes of Singular Varieties and Their Applications Miami, USA from November 3-9, 2024
Computational Algebraic Geometry workshop Durham, UK from November 18-22, 2024

Scientific publications

On the topology of determinantal links To appear in the Journal of the LMS
Cohomological connectivity of perturbations of map-germs: joint with Guillermo Penafort and Yongqiang Liu, Math. Nachrichten, vol. 297, issue 5 (2024), pp. 1601-1631
On the topology of complex univariate polynomials: Matematica Contemporanea, vol. 53, pp. 75-119
A generalization of Milnor's formula: Math. Annalen, Volume 382, pp. 901-942 (2022)
On the vanishing topology of isolated Cohen-Macaulay codimension 2 singularities: joint with Anne Fruehbis-Krueger, Geometry & Topology, vol. 25 (2021), pp. 2167-2197
Kato-Matsumoto-type results for disentanglements: joint with Guillermo Penafort, Proceedings of the Royal Society of Edinburgh, Section A: Mathematics, vol. 151, n. 1 (2021), pp. 1-27
Bouquet decomposition for Determinantal Milnor fibers: Journal of Singularities, vol. 22 (2020), pp. 190-204
An observation concerning the vanishing topology of certain isolated determinantal singularities: Math. Zeitschrift, vol. 291 (2019), pp. 1263-1293

Book chapters

Elliptic fibrations on Vinberg's most algebraic K3 surface: joint with Simon Brandhorst, to appear as a chapter of the OSCAR book
Determinantal Singularities: joint with Anne Fruehbis-Krueger, Handbook of Geometry and Topology of Singularities IV, Springer (2023)

Software

OSCAR Computer algebra system: together with Simon Brandhorst, Anne Fruehbis-Krueger, Wolfram Decker, and Janko Boehm we develop a framework for algebraic schemes in the computer algebra system OSCAR.
The Poleidoscope: a smartphone application that allows you to look through a meromorphic function. The image above was taken with that app! See also its GitLab page

Impressum: Matthias Zach, Fachbereich Mathematik, RPTU Kaiserslautern, Gottlieb Daimler Str., Gebaeude 48, 67663 Kaiserslautern. Tel: +49 631 205 2850, Email: zach at rptu dot de.

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