@unpublished{66322,
  abstract     = {{Motivated by the realizability problem for principal tropical divisors with a fixed ramification profile, we explore the tropical geometry of the double ramification locus in $\mathcal{M}_{g,n}$.There are two ways to define a tropical analogue of the double ramification locus: one as a locus of principal divisors, the other as a locus of finite effective ramified covers of a tree. We show that both loci admit a structure of a generalized cone complex in $M_{g,n}^{trop}$, with the latter contained in the former. We prove that the locus of principal divisors has cones of codimension zero in $M_{g,n}^{trop}$, while the locus of ramified covers has the expected codimension $g$. This solves the deformation-theoretic part of the realizability problem for principal divisors, reducing it to the so-called Hurwitz existence problem for covers of a fixed ramification type.}},
  author       = {{Ulirsch, Martin and Zakharov, Dmitry}},
  booktitle    = {{arXiv:1910.01499}},
  title        = {{{Tropical double ramification loci}}},
  year         = {{2019}},
}

@article{66338,
  author       = {{Foster, Tyler and Ranganathan, Dhruv and Talpo, Mattia and Ulirsch, Martin}},
  issn         = {{0025-5874}},
  journal      = {{Mathematische Zeitschrift}},
  number       = {{1-2}},
  pages        = {{313--327}},
  publisher    = {{Springer Science and Business Media LLC}},
  title        = {{{Logarithmic Picard groups, chip firing, and the combinatorial rank}}},
  doi          = {{10.1007/s00209-018-2085-2}},
  volume       = {{291}},
  year         = {{2018}},
}

@article{66334,
  author       = {{Huszar, Alana and Marcus, Steffen and Ulirsch, Martin}},
  issn         = {{0022-4049}},
  journal      = {{Journal of Pure and Applied Algebra}},
  number       = {{5}},
  pages        = {{2036--2061}},
  publisher    = {{Elsevier BV}},
  title        = {{{Clutching and gluing in tropical and logarithmic geometry}}},
  doi          = {{10.1016/j.jpaa.2018.08.014}},
  volume       = {{223}},
  year         = {{2018}},
}

@article{66354,
  author       = {{Ulirsch, Martin}},
  issn         = {{0024-6115}},
  journal      = {{Proceedings of the London Mathematical Society}},
  number       = {{6}},
  pages        = {{1081--1113}},
  publisher    = {{Wiley}},
  title        = {{{Functorial tropicalization of logarithmic schemes: the case of constant coefficients}}},
  doi          = {{10.1112/plms.12031}},
  volume       = {{114}},
  year         = {{2017}},
}

@inbook{66337,
  author       = {{Lin, Bo and Ulirsch, Martin}},
  booktitle    = {{Fields Institute Communications}},
  isbn         = {{9781493974856}},
  issn         = {{1069-5265}},
  publisher    = {{Springer New York}},
  title        = {{{Towards a tropical Hodge bundle}}},
  doi          = {{10.1007/978-1-4939-7486-3_16}},
  year         = {{2017}},
}

@inbook{66349,
  author       = {{Abramovich, Dan and Chen, Qile and Marcus, Steffen and Ulirsch, Martin and Wise, Jonathan}},
  booktitle    = {{Simons Symposia}},
  isbn         = {{9783319309446}},
  issn         = {{2365-9564}},
  publisher    = {{Springer International Publishing}},
  title        = {{{Skeletons and fans of logarithmic structures}}},
  doi          = {{10.1007/978-3-319-30945-3_9}},
  year         = {{2016}},
}

@article{66362,
  author       = {{Cheung, Man-Wai and Fantini, Lorenzo and Park, Jennifer and Ulirsch, Martin}},
  issn         = {{1073-7928}},
  journal      = {{International Mathematics Research Notices}},
  number       = {{15}},
  pages        = {{4706--4727}},
  publisher    = {{Oxford University Press (OUP)}},
  title        = {{{Faithful Realizability of Tropical Curves}}},
  doi          = {{10.1093/imrn/rnv269}},
  volume       = {{2016}},
  year         = {{2015}},
}

@article{66355,
  author       = {{Ulirsch, Martin}},
  issn         = {{0025-5874}},
  journal      = {{Mathematische Zeitschrift}},
  number       = {{1-2}},
  pages        = {{195--210}},
  publisher    = {{Springer Science and Business Media LLC}},
  title        = {{{Tropical compactification in log-regular varieties}}},
  doi          = {{10.1007/s00209-015-1418-7}},
  volume       = {{280}},
  year         = {{2015}},
}

@article{66352,
  author       = {{Ulirsch, Martin}},
  issn         = {{0024-6107}},
  journal      = {{Journal of the London Mathematical Society}},
  number       = {{2}},
  pages        = {{427--450}},
  publisher    = {{Wiley}},
  title        = {{{Tropical geometry of moduli spaces of weighted stable curves}}},
  doi          = {{10.1112/jlms/jdv032}},
  volume       = {{92}},
  year         = {{2015}},
}