Email: (lastname).math(at)gmail.com
CV (08/2024)
ORCID
Research topics: Algebraic geometry, arithmetic geometry and computational geometry; in particular: resolution of singularities; polyhedral and combinatorial methods; local uniformization; positive characteristic methods; cluster algebras; order zeta functions and p-adic integrals;
Mathematical publications
Classification of singularities of cluster algebras of finite type II: coefficients. Accepted for publication in J. Comb. Algebra (with Angélica Benito, Eleonore Faber, and Hussein Mourtada).
Teissier singularities. C. R. Math. Acad. Sci. Paris 363 (2025), 799-808 (with Hussein Mourtada).
Constancy of the Hilbert-Samuel function. Nagoya Math. J. 256 (2024), 938-952 (with Vincent Cossart and Olivier Piltant).
Desingularization of binomial varieties using toric Artin stacks. Math. Z. 306, 48 (2024). (with Dan Abramovich).
Desingularization of generic symmetric and generic skew-symmetric determinantal singularities. Manuscripta Math. 174 (2024), no. 3-4, 1113-1131 (with Sabrina Alexandra Gaube).
Algorithmic local monomialization of a binomial: a comparison of different approaches. Internat. J. Algebra Comput. 33 (2023), no. 1, 161-195 (with Sabrina Alexandra Gaube).
Classification of singularities of cluster algebras of finite type: the case of trivial coefficients. Glasg. Math. J. 65 (2023), no. 1, 170-204 (with Angélica Benito, Eleonore Faber, and Hussein Mourtada).
Embedded desingularization for arithmetic surfaces -- toward a parallel implementation. Math. Comp. 90 (2021), no. 330, 1957-1997 (with Anne Frühbis-Krüger and Lukas Ristau).
Idealistic exponents: Tangent cone, ridge, characteristic polyhedra. J. Algebra 565 (2021), 353-401.
Characteristic polyhedra of singularities without completion: Part II. Collect. Math. 72 (2021), no. 2, 351-392 (with Vincent Cossart).
Loose Edges and Factorization Theorems. Proc. of the AMS 149 (2021), no. 6, 2265-2278 (with Beata Gryszka and Janusz Gwoździewicz).
Hironaka's characteristic polyhedron. Notes for novices. Appendix to Vincent Cossart, Uwe Jannsen, Shuji Saito. Desingularization: Invariants and Strategy. Applications to Dimension 2. Lecture Notes in Math. 2270 (2020).
A strictly decreasing invariant for resolution of singularities in dimension two. Publ. Res. Inst. Math. Sci. 56 (2020), no. 2, 217-280 (with Vincent Cossart).
Invariance of Hironaka's characteristic polyhedron. Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Mat. RACSAM 113 (2019), no. 4, 4145-4169 (with Vincent Cossart and Uwe Jannsen).
A polyhedral characterization of quasi-ordinary singularities. Moscow Math. J. 18 (2018), no. 4, 755-785 (with Hussein Mourtada).
Partial local resolution by characteristic zero methods. Results Math. (2018) 73:48, 39pp.
An irreducibility criterion for power series. Proc. of the AMS 145 (2017), no. 11, 4731--4739 (with Guillaume Rond).
Faîte du cône tangent à une singularité: un théorème oublié. C. R. Math. Acad. Sci. Paris, Ser. I 355 (2017), no. 4, 455-459 (with Vincent Cossart and Olivier Piltant).
Preprints
Torus actions, weighted blow-ups, and desingularization of plane curves. (2025), 13 pages (with Dan Abramovich and Ming Hao Quek).
Resolving plane curves using stack-theoretic blow-ups. (2024), 23 pages (with Dan Abramovich and Ming Hao Quek).
Frieze patterns and combinatorics of curve singularities. (2024), 40 pages (with Eleonore Faber).
A polyhedral approach to the invariant of Bierstone and Milman. (2014), 28 pages.
Others
Resolution of singularities for Arithmetic Threefolds, Oberwolfach Report 57/2016 (Workshop "Asymptotic Phenomena in Local Algebra and Singularity Theory").
Characteristic polyhedra without completion, Oberwolfach Report 6/2019 (Workshop "Singularities and Homological Aspects of Commutative Algebra").
Generalized Loose Edge Factorization Theorems, preprint (2018), 10 pages. Replaced by "Loose Edges and Factorization Theorems".
Theses
Habilitation Thesis: Singularities and Polyhedra, Carl von Ossietzky University Oldenburg (2022), 48 pages.
Phd Thesis: Characteristic polyhedra for idealistic exponents with history, University of Regensburg (2013), 134 pages.
Diploma thesis: Starke Auflösung von Singularitäten für die dreidimensionale Narasimhan-Varietät (German), University of Regensburg (2010), 259 pages.