Publications

Preprints

k-leaky double Hurwitz descendants (with Renzo Cavalieri and Johannes Schmitt)
Tropical twisted Hurwitz numbers of elliptic curves (with Marvin Anas Hahn)
Arithmetic counts of tropical plane curves and their properties (with Andrés Jaramillo Puentes, Sabrina Pauli and Felix Röhrle)
Counting tropical curves in P^1xP^1: computation and polynomiality properties (with Dan Corey and Dhruv Ranganathan)
Pluricanonical cycles and tropical covers (with Renzo Cavalieri and Dhruv Ranganathan)

To appear

Twisted Hurwitz numbers: tropical and polynomial structures (with Marvin Anas Hahn), Algebraic Combinatorics (to appear)
Avoidance loci and tropicalizations of real bitangents to plane quartics (with Sam Payne and Kris Shaw), Proc. Edinb. Math. Soc. A (to appear)

Published Papers

Tropical descendant invariants with line constraints (with Thomas Blomme), J. Lond. Math. Soc. (2) 108 (2023). no. 6, 2248-2296.
Recovery of plane curves from branch points (with Daniele Agostini, Clemens Nollau, Victoria Schleis, Javier Sendra-Arranz and Bernd Sturmfels), Discrete Comput. Geom. (2023), doi:10.1007/s00454-023-00538-5.
Combinatorics and real lifting of bitangents to tropical quartic curves (with Maria Angelica Cueto),
Discrete Comput, Geom. 69 (2023), no. 3, 597-658.
Bitangents to plane quartics via tropical geometry: rationality, A^1-enumeration and real signed count (with Sam Payne and Kris Shaw), Res. Math. Sci. (2023). 10:21, doi:0.1007/s40687-023-00383-1.
Tropical Psi-classes (with Renzo Cavalieri and Andreas Gross),Geom. Topol. 26 (2022), no. 8, 3421-3524.
Counting curves on toric surfaces: tropical geometry and the Fock space (with Renzo Cavalieri, Paul Johnson and Dhruv Ranganathan), Math. Proc. Cambridge Philos. Soc. 171 (2021), no. 1, 165–205.
Tropical lines in planes and beyond (with Philipp Jell, Felipe Rincon and Benjamin Schroeter) Electron. J. Combin. 29 (2022), no. 2, Paper No. 2.31, 33 pp.
Tropical floor plans and enumeration of complex and real multi-nodal surfaces (with Thomas Markwig, Kris Shaw and Eugenii Shustin), J. Algebraic Geom. 31 (2022), no. 2, 261–301.
Tropical mirror symmetry in dimension one (with Janko Boehm and Christoph Goldner), SIGMA 18 (2022), 046.
Counts of (tropical) curves in ExP^1 and Feynman integrals (with Janko Boehm and Christoph Goldner), Ann. Inst. Henri Poincaré D 9 (2022), no. 1, 121-158.
Tropicalized quartics and canonical embeddings for tropical curves of genus 3 (with Marvin Hahn, Yue Ren and Ilya Tyomkin), IMRN (2019), doi:10.1093/imrn/rnz084.
Lifting tropical bitangents (with Yoav Len), J. Symbolic Comput. (2019), doi:10.1016/j.jsc.2019.02.015.
Tropical geometry of genus two curves (with Maria Angelica Cueto), J. Algebra (2018), doi: 10.1016/j.jalgebra.2018.08.034.
T ropical moduli spaces of stable maps to a curve (with Andreas Gathmann and Dennis Ochse), in Algorithmic and experimental methods in algebra, geometry, and number theory, ed. by G. Böckle, W. Decker, G. Malle, 287-309, Springer, Cham, 2017.
A graphical interface for the Gromov-Witten theory of curves (with Renzo Cavalieri, Paul Johnson and Dhruv Ranganathan), Algebraic geometry: Salt Lake City 2015, 139-167, Proc. Sympos. Pure Math., 97.2, Amer. Math. Soc., Providence, RI, 2018.
Enumeration of complex and real surfaces via tropical geometry (with Thomas Markwig and Eugenii Shustin), Adv. Geom. 18 (2018), no. 1, 69-100.
Deformation of tropical Hirzebruch surfaces and enumerative geometry (with Erwan Brugallé), J. Algebraic Geom. 25 (2016), no. 4, 633-702.
Moduli spaces of rational weighted stable curves and tropical geometry (with Renzo Cavalieri, Simon Hampe and Dhruv Ranganathan), Forum Math. Sigma 4 (2016), e9, 35pp.
Tropical mirror symmetry for elliptic curves (with Janko Boehm, Kathrin Bringmann and Arne Buchholz), J. Reine Angew. Math. 732 (2017), 211-246, doi:10.1515/crelle-2014-0143.
Tropical compactifications and the Gromov-Witten theory of P^1 (with Renzo Cavalieri and Dhruv Ranganathan), D. Sel. Math. New Ser. (2017) 23: 1027-1060, doi:10.1007/s00029-016-0265-7.
How to repair tropicalizations of plane curves using modifications (with Maria Angelica Cueto), Exp. Math. 25,2 (2016), 130-164.
Tropical Real Hurwitz numbers (with Johannes Rau), Math. Z., 281 (1), 2015, 501-522.
Tropicalizing the Space of Admissible Covers (with Renzo Cavalieri and Dhruv Ranganathan), Math. Ann. (2015); doi:10.1007/s00208-015-1250-8.
The combinatorics of real double Hurwitz numbers with real positive branch points (with Mathieu Guay-Paquet and Johannes Rau). Int. Math. Res. Not. (2015); doi: 10.1093/imrn/rnv135.
Tropical covers of curves and their moduli spaces (with Arne Buchholz), Commun. Contemp. Math. DOI: 10.1142/S0219199713500454.
Polynomiality, Wall Crossings and Tropical Geometry of Rational Double Hurwitz Cycles (with Aaron Bertram and Renzo Cavalieri), JCTA 120,7 (2013), 1604-1631.
Broccoli curves and the tropical invariance of Welschinger numbers (with Andreas Gathmann and Franziska Schroeter). Adv. Math. 240 (2013), 520-574, doi:10.1016/j.aim.2013.03.004.
Tropical surface singularities (with Thomas Markwig and Eugenii Shustin), DCG 48,4 (2012), 879-914, DOI: 10.1007/s00454-012-9453-1. arXiv:1106.2676
Tropical curves with a singularity in a fixed point (with Thomas Markwig and Eugenii Shustin), Manuscripta Math 137 (2012), no. 3-4, 383–418, doi: 10.1007/s00229-011-0471-8.
Chamber Structure of Double Hurwitz numbers (with Renzo Cavalieri and Paul Johnson), Adv. Math. 228 (2011), no. 4, 1894–1937.
Psi-floor diagrams and a Caporaso-Harris type recursion (with Florian Block and Andreas Gathmann), Israel J. of Math. (2011), doi: 10.1007/s11856-011-0216-0.
Tropical enumerative invariants of F_0 and F_2 (with Marina Franz), Adv. Geom., 11, 1 (2011), 49-72.
Tropical Hurwitz numbers (with Renzo Cavalieri and Paul Johnson) J Algebr Comb (2010) 32,2: 241–265. arXiv:0804.0579.
The tropical j-invariant (with Eric Katz and Thomas Markwig), LMS J. Comput. Math. 12 (2009), 275-294.
Counting tropical elliptic plane curves with fixed j-invariant (with Michael Kerber), Comment. Math. Helv., 84, 2 (2009), 387–427.
Tropical fans and the moduli space of tropical curves (with Andreas Gathmann and Michael Kerber), Compos. Math. 145 (2009), no. 1, 173-195.
Tropical descendant Gromov-Witten invariants (with Johannes Rau), Manuscripta Mathematica, volume 129, issue 3 (2009), 293-335, doi: 10.1007/s00229-009-0256-5.
Intersecting Psi-classes on tropical M_0,n (with Michael Kerber), Int. Math. Res. Not. (2008); doi: 10.1093/imrn/rnn130.
The space of tropically collinear points is shellable (with Josephine Yu), Collect. Math. 60,1 (2009), 63-77.
The j-invariant of a plane tropical cubic (with Eric Katz and Thomas Markwig), Journal of Algebra 320 (2008), 3832-3848.
Kontsevich's formula and the WDVV equations in tropical geometry (with Andreas Gathmann), Adv. Math. 217 (2008), 537-560.
An algorithm for lifting points in a tropical variety (with Anders Jensen and Thomas Markwig), Collect. Math. 59 (2008), 129-165.
The Caporaso-Harris formula and plane relative Gromov-Witten invariants in tropical geometry (with Andreas Gathmann), Math. Ann. 338 (2007), 845-868.
The numbers of tropical plane curves through points in general position (with Andreas Gathmann), J. Reine Angew. Math. 602 (2007), 155-177.
Free resolutions of fat points on a conic in the projective plane. Rend. Semin. Mat. Torino 63,1 (2005), 63-80.

Surveys et.al.

Tropical curves and covers and their moduli spaces. Jahresbericht der DMV 2020 122(3), 139-166.
Three tropical enumerative problems. Mathematisches Institut, Georg-August-Universität Göttingen: Seminars Winter Term 2007/2008. Lecture notes from the “Courant Colloquia” held at the University of Göttingen, Göttingen, 2004–2005. Edited by Yuri Tschinkel. Universitätsdrucke Göttingen, Göttingen.
The j-invariant of a plane tropical cubic. In Ina Kersten and Ralf Meyer (editors), Symmetries in Algebra and Number Theory, 65--68, Universitä tsverlag Gö ttingen, 2009. Proceedings of the Gö ttingen-Jerusalem Conference held October 27-30, 2008 in Göttingen.
Tropische Geometrie, Artikel in den Mitteilungen der Deutschen Mathematiker Vereinigung.
Tropische Geometrie, Kapitel im Buch Facettenreiche Mathematik, Katrin Wendland, Annette Werner (Hrsg.), Vieweg+Teubner 2011.
with Renzo Cavalieri and Paul Johnson: Chamber structure for double Hurwitz numbers. 22nd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2010), 227–238, Discrete Math. Theor. Comput. Sci. Proc., AN, Assoc. Discrete Math. Theor. Comput. Sci., Nancy, 2010.
with Dhruv Ranganathan: Appendix in the book "Riemann Surfaces and Algebraic Curves - a first course in Hurwitz theory" by Renzo Cavalieri and Eric Miles. London Math. Soc. 87 (2016).
with Lukas Ristau and Victoria Schleis: Faithful tropicalization of hyperelliptic curves. Submitted to OSCAR book.
with Renzo Cavalieri and Dhruv Ranganathan: Tropical and logarithmic methods in enumerative geometry. Oberwolfach Seminars 52. Birkhäuser Cham.

Theses

Free resolutions of fat points on a conic in the projective plane. Diplomarbeit an der Universität Kaiserslautern (2003).
The enumeration of plane tropical curves. PhD thesis. Technische Universität Kaiserslautern (2006).

SINGULAR-libraries

ellipticcovers.lib (with Janko Boehm, Kathrin Bringmann and Arne Buchholz). A Singular 4 library for Gromov-Witten invariants of elliptic curves (2013).
tropical.lib (with Anders Jensen and Thomas Markwig), A SINGULAR 3.0 library for computations in tropical geometry (2007).
jinvariant.lib (with Eric Katz and Thomas Markwig), A SINGULAR 3.0 library for proving statements about the tropical j-invariant (2007).