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

1. A polyhedral approach to the invariant of Bierstone and Milman. Accepted for publication in J. Pure Appl. Algebra.  

2. 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).

3. Teissier singularities. C. R. Math. Acad. Sci. Paris 363 (2025), 799-808 (with Hussein Mourtada).

4. Constancy of the Hilbert-Samuel function. Nagoya Math. J. 256 (2024), 938-952 (with Vincent Cossart and Olivier Piltant).

5. Desingularization of binomial varieties using toric Artin stacks. Math. Z. 306, 48 (2024). (with Dan Abramovich).

6. Desingularization of generic symmetric and generic skew-symmetric determinantal singularities. Manuscripta Math. 174 (2024), no. 3-4, 1113-1131 (with Sabrina Alexandra Gaube).

7. 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).

8. 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).

9. Embedded desingularization for arithmetic surfaces -- toward a parallel implementation. Math. Comp. 90 (2021), no. 330, 1957-1997 (with Anne Frühbis-Krüger and Lukas Ristau).

10. Idealistic exponents: Tangent cone, ridge, characteristic polyhedra. J. Algebra 565 (2021), 353-401.

11. Characteristic polyhedra of singularities without completion: Part II. Collect. Math. 72 (2021), no. 2, 351-392 (with Vincent Cossart).

12. Loose Edges and Factorization Theorems. Proc. of the AMS 149 (2021), no. 6, 2265-2278 (with Beata Gryszka and Janusz Gwoździewicz).

13. 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).

14. 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).

15. 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).

16. A polyhedral characterization of quasi-ordinary singularities. Moscow Math. J. 18 (2018), no. 4, 755-785 (with Hussein Mourtada).

17. Partial local resolution by characteristic zero methods. Results Math. (2018) 73:48, 39pp.

18. An irreducibility criterion for power series. Proc. of the AMS 145 (2017), no. 11, 4731--4739 (with Guillaume Rond).

19. 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

1. Torus actions, weighted blow-ups, and desingularization of plane curves. (2025), 13 pages (with Dan Abramovich and Ming Hao Quek).

2. Resolving plane curves using stack-theoretic blow-ups. (2024), 23 pages (with Dan Abramovich and Ming Hao Quek).

3. Frieze patterns and combinatorics of curve singularities. (2024), 40 pages (with Eleonore Faber).
    

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.