Thomas Markwig Publications
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Research Interests
Curriculum Vitae
Publications
Teaching
Tropical Geometry Software
SFB-TRR 195
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Master Dissertation

• Thomas Keilen: A Claim on the Rank of an Injective Map. Dissertation submitted for the degree of Master of Science. University of Warwick (1993).

PhD Thesis

• Thomas Keilen: Families of Curves with Prescribed Singularities. PhD-Thesis (Extended Version). Universität Kaiserslautern (2001).

Habilitation Thesis

• Thomas Markwig: Families of Curves and a Lifting Problem for Tropical Varieties. Habilitationsschrift. Technische Universität Kaiserslautern (2007).

Scientific Papers

1 Thomas Keilen, Ilya Tyomkin: Existence of Curves with Prescribed Topological Singularities. Trans. Amer. Math. Soc. 354,5 (2002), 1837-1860, e-print arXiv:math/0104062.
2 Thomas Keilen: Irreducibility of Equisingular Families of Curves. Trans. Amer. Math. Soc. 355,9 (2003), 3485-3512, e-print arXiv:math/0108089.
3 Thomas Keilen, David Mond: Injective Analytic Maps - A Counterexample to the Proof. Preprint (2003), e-print arXiv:math/0409426.
4 Thomas Keilen: Irreducibility of Equisingular Families of Curves - Improved Conditions. Comm. in Algebra 33,2 (2005), 455-466, e-print arXiv:math/0212090.
5 Thomas Keilen: Smoothness of Equisingular Families of Curves. Trans. Amer. Math. Soc. 357,6 (2005), 2467-2481, e-print arXiv:math/0308247.
6 Thomas Keilen, Christoph Lossen: A new Invariant for Plane Curve Singularities. Rend. Semin. Mat. Torino 63,1 (2005), 15-42, e-print arXiv:math/0409404.
7 Thomas Keilen: Equisingular Families of Curves. Rend. Semin. Mat. Torino 63,1 (2005), 103-106.
8 Thomas Keilen: Reducible Families of Curves with Ordinary Multiple Points on Surfaces in P3. Comm. in Algebra 34,5 (2006), 1921-1926, e-print arXiv:0706.2440.
9 Thomas Markwig: Some Obstructed Equisingular Families of Curves on Surfaces in P3. In: Singularity theory, World Sci. Publ., Hackensack, NJ (2007), 715--723, e-print arXiv:0706.2441.
10 Thomas Markwig: A Note on Equimultiple Deformations. Preprint (2006), e-print arXiv:0705.3911.
11 Luca Chiantini, Thomas Markwig: Triple-Point Defective Regular Surfaces. Preprint (2006), e-print arXiv:0705.3912.
12 Luca Chiantini, Thomas Markwig: Triple-Point Defective Ruled Surfaces. J. Pure Appl. Alg. 212,6 (2008), 1337-1346, e-print arXiv:0705.3913.
13 Thomas Markwig: Standard Bases in K[[t1,...,tm]][x1,...,xn]s. J. Symbolic Computation 43 (2008), 765-786, e-print arXiv:0705.2436. (longer version)
14 Anders Nedergaard Jensen, Hannah Markwig, Thomas Markwig: An Algorithm for Lifting Points in a Tropical Variety. Collect. Math. 59,2 (2008), 129-165, e-print arXiv:0705.2441. (longer version)
15 Thomas Markwig: A Field of Generalised Puiseux Series for Tropical Geometry. Rend. Semin. Mat. Torino 68,1 (2010), 79-92, e-print arXiv:0709.3784.
16 Eric Katz, Hannah Markwig, Thomas Markwig: The j-Invariant of a Plane Tropical Cubic. Journal of Algebra 320 (2008), 3832-3848, e-print arXiv:0709.3785.
17 Eric Katz, Hannah Markwig, Thomas Markwig: The Tropical j-Invariant. LMS J. Comput. Math. 12 (2009), 275-294, e-print arXiv:0803.4021.
18 Thomas Markwig: Tropical Geometry. Computeralgebrarundbrief 44 (März 2009). (German version)
19 Hannah Markwig, Thomas Markwig, Eugenii Shustin: Tropical Curves with a Singularity in a Fixed Point. Man. Math. 137,3-4 (2011), 383-418, e-print arXiv:0909.1827.
20 Luca Chiantini, Thomas Markwig: Triple-Point Defective Surfaces. Adv. Geom. 10,3 (2010), 527-547, e-print arXiv:0911.1222.
21 Yousra Boubakri, Gert-Martin Greuel, Thomas Markwig: Invariants of Hypersurface Singularities in Positive Characteristic. Rev. Mat. Comp. 25,1 (2011), 61-85, e-print arXiv:1005.4503.
22 Yousra Boubakri, Gert-Martin Greuel, Thomas Markwig: Normal Forms of Hypersurface Singularities in Positive Characteristic. Moscow Math. J. 11,4 (2011), 657-683, e-print arXiv:1007.0170.
23 Hannah Markwig, Thomas Markwig, Eugenii Shustin: Tropical Surface Singularities. Discrete Comput. Geom. 48,4 (2012), 879-914, e-print arXiv:1106.2676.
24 Hannah Markwig, Thomas Markwig, Eugenii Shustin: Enumeration of complex and real surfaces via tropical geometry. Adv. Geom. 18,1 (2018), 69-100, e-print arXiv:1503.08593.
25 Thomas Markwig, Yue Ren, Oliver Wienand: Standard Bases in mixed Power Series and Polynomial Rings over Rings. J. Symbolic Computation 79 (2017), 119-139.
26 Thomas Markwig, Yue Ren: Gröbner Fans of x-homogeneous ideals in R[[t]][x]. J. Symbolic Computation 83 (2017), 315-341.
27 Thomas Markwig, Yue Ren: Computing Tropical Varieties over Fields with Valuation. Found. Comp. Math. 20,4 (2020), 783-800.
28 Hannah Markwig, Thomas Markwig, Kristin Shaw, Eugenii Shustin: Tropical Floor Plans and Enumeration of Complex and Real Multi-Nodal Surfaces. (2019), e-print arXiv:1910.08585.

SINGULAR -Libraries

1 Thomas Keilen: paramet.lib. A SINGULAR 2.0 library for computing parametrizations of algebraic varieties or of plane curve singularities (2001).
2 Fernando Hernando Carillo, Thomas Keilen: alexpoly.lib. A SINGULAR 2.0 library for computing the resolution graph, the semigroup and the Alexander polynomial of plane curve singularities (2003).
3 Anders Nedergaard Jensen, Hannah Markwig, Thomas Markwig: tropical.lib. A SINGULAR 3.0 library for computations in tropical geometry (2007).
4 Thomas Markwig: polymake.lib. A SINGULAR 3.0 library for polyhedral computations invoking polymake (2007).
5 Eric Katz, Hannah Markwig, Thomas Markwig: jinvariant.lib. A SINGULAR 3.0 library for proving statements about the tropical j-invariant (2007).

Lecture Notes

1 Thomas Keilen: Kurzeinführung in Singular. Skript für die Teilnehmer der Übungen zur Linearen Algebra (1999).
2 Gert-Martin Greuel, Thomas Keilen: Lineare Algebra I und II. Vorlesungsskript (2000).
3 Thomas Keilen: Endliche Gruppen. Eine Einführung mit dem Ziel der Klassifikation von Gruppen kleiner Ordnung (2001).
4 Thomas Keilen: Algebra I. Lecture Notes (2002).
5 Thomas Keilen: A Short Introduction to Singular. Lecture Notes (2003).
6 Thomas Markwig: Algebraische Strukturen. Vorlesungsskript (2008).
7 Thomas Markwig: Elementare Zahlentheorie. Vorlesungsskript (2008).
8 Thomas Markwig: Euro-Münzen zum 732. Jahrestag?. Lösung zum Mathematikwettbewerb 'Mathematik bewegt - steig ein' (2008).
9 Thomas Markwig: Algebraic Structures. Lecture Notes (2009).
10 Stephan Klaus, Oliver Labs, Thomas Markwig: Theorie und Visualisierung algebraischer Kurven und Flächen. Fortbildung für Mathematiklehrer (2009).
11 Thomas Markwig: Computational Algebraic Geometry. Lecture Notes for the EMALCA 2010 in Villahermosa, Mexico (2010).
12 Thomas Markwig: Grundlagen der Mathematik. Vorlesungsskript zum Jahrgang 2009/10 (2010).
13 Thomas Markwig: Vorkurs Mathematik für Ingenieursstudiengänge. Vorlesungsskript zum SS 2013 (2013).
14 Thomas Markwig: Vorkurs Mathematik für Mathematiker und Informatiker. Vorlesungsskript zum WS 2013/14 (2013).
15 Thomas Markwig: Höhere Mathematik Funktionentheorie. Vorlesungsskript zum SS 2014 (2015).
16 Thomas Markwig: Einführung in die Algebra. Vorlesungsskript zum WS 2014/15 (2015).
17 Thomas Markwig: Algebra. Vorlesungsskript zum SS 2019 (2019).
Universität Tübingen • Dept. of Mathematics • Section Algebra • CAS SINGULAR • SFB-TRR 195 • Alma