--- _id: '66309' abstract: - lang: eng text: "Abstract\r\n \r\n Let\r\n \ \r\n \r\n \ \r\n $A$\r\n \ \r\n \r\n \ be an abelian variety with totally degenerate reduction over a non-Archimedean field. We describe the moduli space of semi-homogeneous vector bundles on\r\n \r\n \r\n \ \r\n $A$\r\n \ \r\n \r\n \ from the perspective of non-Archimedean uniformization and show that the essential skeleton may be identified with a tropical analogue of this moduli space. For\r\n \r\n \r\n \ \r\n $H=0$\r\n \ \r\n \r\n \ our moduli space may be identified with the moduli space\r\n \ \r\n \r\n \ \r\n $M_{0,r}(A)$\r\n \ \r\n \r\n \ of semi-stable vector bundles with vanishing Chern classes on\r\n \r\n \r\n \ \r\n $A$\r\n \ \r\n \r\n \ . In this case we construct a surjective analytic morphism from the character variety of the analytic fundamental group of\r\n \r\n \ \r\n \r\n \ $A$\r\n \r\n \ \r\n onto\r\n \r\n \ \r\n \r\n \ $M_{0,r}(A)$\r\n \r\n \ \r\n , which naturally tropicalizes. One may view this construction as a non-Archimedean uniformization of\r\n \r\n \r\n \ \r\n $M_{0,r}(A)$\r\n \ \r\n \r\n \ .\r\n " article_number: e8 author: - first_name: Andreas full_name: Gross, Andreas last_name: Gross - first_name: Inder full_name: Kaur, Inder last_name: Kaur - first_name: Martin full_name: Ulirsch, Martin id: '114697' last_name: Ulirsch - first_name: Annette full_name: Werner, Annette last_name: Werner citation: ama: 'Gross A, Kaur I, Ulirsch M, Werner A. Semi-homogeneous vector bundles on abelian varieties: moduli spaces and their tropicalization. Moduli. 2026;3. doi:10.1017/S2949764726100228' apa: 'Gross, A., Kaur, I., Ulirsch, M., & Werner, A. (2026). Semi-homogeneous vector bundles on abelian varieties: moduli spaces and their tropicalization. Moduli, 3, Article e8. https://doi.org/10.1017/S2949764726100228' bibtex: '@article{Gross_Kaur_Ulirsch_Werner_2026, title={Semi-homogeneous vector bundles on abelian varieties: moduli spaces and their tropicalization}, volume={3}, DOI={10.1017/S2949764726100228}, number={e8}, journal={Moduli}, publisher={Cambridge University Press (CUP)}, author={Gross, Andreas and Kaur, Inder and Ulirsch, Martin and Werner, Annette}, year={2026} }' chicago: 'Gross, Andreas, Inder Kaur, Martin Ulirsch, and Annette Werner. “Semi-Homogeneous Vector Bundles on Abelian Varieties: Moduli Spaces and Their Tropicalization.” Moduli 3 (2026). https://doi.org/10.1017/S2949764726100228.' ieee: 'A. Gross, I. Kaur, M. Ulirsch, and A. Werner, “Semi-homogeneous vector bundles on abelian varieties: moduli spaces and their tropicalization,” Moduli, vol. 3, Art. no. e8, 2026, doi: 10.1017/S2949764726100228.' mla: 'Gross, Andreas, et al. “Semi-Homogeneous Vector Bundles on Abelian Varieties: Moduli Spaces and Their Tropicalization.” Moduli, vol. 3, e8, Cambridge University Press (CUP), 2026, doi:10.1017/S2949764726100228.' short: A. Gross, I. Kaur, M. Ulirsch, A. Werner, Moduli 3 (2026). date_created: 2026-07-08T06:24:15Z date_updated: 2026-07-09T07:05:30Z doi: 10.1017/S2949764726100228 intvolume: ' 3' language: - iso: eng publication: Moduli publication_identifier: issn: - 2949-7647 - 2977-1382 publication_status: published publisher: Cambridge University Press (CUP) status: public title: 'Semi-homogeneous vector bundles on abelian varieties: moduli spaces and their tropicalization' type: journal_article user_id: '82981' volume: 3 year: '2026' ... --- _id: '66304' abstract: - lang: eng text: "Let $G$ be a connected reductive algebraic group over an algebraically closed field of characteristic zero carrying the trivial valuation. In this article we discuss two candidates for what could be the tropicalization of $G$.\r\n Our first suggestion is the extended affine building associated to $G$. This perspective makes makes use of Berkovich's embedding of the extended affine building into the Berkovich analytic space $G^{\\textrm{an}}$ and expands on work of Mumford by associating a toroidal bordification of $G$ to the choice of stacky fan in the building. We show that the natural retraction onto the building is compatible with the tropicalization map associated to a toroidal bordification.\r\n Our second suggestion is a Weyl chamber of $G$, a special instance of spherical tropicalization, where we think of $G$ as a spherical $G\\times G$-variety with respect to left-right-multiplication. We show that the spherical tropicalization map may be identified with the toroidal tropicalization map associated to a wonderful compactification of $G$. This map also has a moduli-theoretic interpretation expanding on the compactifications of $G$ as moduli spaces of framed $\\mathbb{G}_m$-equivariant principal bundles on chains of projective lines introduced by Martens and Thaddeus." author: - first_name: Desmond full_name: Coles, Desmond last_name: Coles - first_name: Martin full_name: Ulirsch, Martin id: '114697' last_name: Ulirsch citation: ama: Coles D, Ulirsch M. Towards the tropicalization of reductive groups. arXiv:250321654. Published online 2025. apa: Coles, D., & Ulirsch, M. (2025). Towards the tropicalization of reductive groups. In arXiv:2503.21654. bibtex: '@article{Coles_Ulirsch_2025, title={Towards the tropicalization of reductive groups}, journal={arXiv:2503.21654}, author={Coles, Desmond and Ulirsch, Martin}, year={2025} }' chicago: Coles, Desmond, and Martin Ulirsch. “Towards the Tropicalization of Reductive Groups.” ArXiv:2503.21654, 2025. ieee: D. Coles and M. Ulirsch, “Towards the tropicalization of reductive groups,” arXiv:2503.21654. 2025. mla: Coles, Desmond, and Martin Ulirsch. “Towards the Tropicalization of Reductive Groups.” ArXiv:2503.21654, 2025. short: D. Coles, M. Ulirsch, ArXiv:2503.21654 (2025). date_created: 2026-07-08T06:19:22Z date_updated: 2026-07-08T06:19:31Z external_id: arxiv: - '2503.21654' language: - iso: eng publication: arXiv:2503.21654 status: public title: Towards the tropicalization of reductive groups type: preprint user_id: '82981' year: '2025' ... --- _id: '66303' abstract: - lang: eng text: We propose an elementary tropical analogue of a reductive group that combines the datum of a Weyl group and the tropicalization of a fixed maximal torus. For the classical groups, as well as $G_2$, these tropical reductive groups admit descriptions as tropical matrix groups that resemble their classical counterparts. Employing this perspective, we introduce tropical principal bundles on metric graphs and study their explicit presentations as pushforwards of line bundles along covers with symmetries and extra data. Our main result identifies the essential skeleton of the moduli space of semistable principal bundles on a Tate curve with its tropical analogue. author: - first_name: Andreas full_name: Gross, Andreas last_name: Gross - first_name: Arne full_name: Kuhrs, Arne last_name: Kuhrs - first_name: Martin full_name: Ulirsch, Martin id: '114697' last_name: Ulirsch - first_name: Dmitry full_name: Zakharov, Dmitry last_name: Zakharov citation: ama: Gross A, Kuhrs A, Ulirsch M, Zakharov D. Tropical reductive groups and principal bundles on metric graphs. arXiv:251105422. Published online 2025. apa: Gross, A., Kuhrs, A., Ulirsch, M., & Zakharov, D. (2025). Tropical reductive groups and principal bundles on metric graphs. In arXiv:2511.05422. bibtex: '@article{Gross_Kuhrs_Ulirsch_Zakharov_2025, title={Tropical reductive groups and principal bundles on metric graphs}, journal={arXiv:2511.05422}, author={Gross, Andreas and Kuhrs, Arne and Ulirsch, Martin and Zakharov, Dmitry}, year={2025} }' chicago: Gross, Andreas, Arne Kuhrs, Martin Ulirsch, and Dmitry Zakharov. “Tropical Reductive Groups and Principal Bundles on Metric Graphs.” ArXiv:2511.05422, 2025. ieee: A. Gross, A. Kuhrs, M. Ulirsch, and D. Zakharov, “Tropical reductive groups and principal bundles on metric graphs,” arXiv:2511.05422. 2025. mla: Gross, Andreas, et al. “Tropical Reductive Groups and Principal Bundles on Metric Graphs.” ArXiv:2511.05422, 2025. short: A. Gross, A. Kuhrs, M. Ulirsch, D. Zakharov, ArXiv:2511.05422 (2025). date_created: 2026-07-08T06:18:46Z date_updated: 2026-07-08T06:19:02Z external_id: arxiv: - '2511.05422' language: - iso: eng publication: arXiv:2511.05422 status: public title: Tropical reductive groups and principal bundles on metric graphs type: preprint user_id: '82981' year: '2025' ... --- _id: '66308' abstract: - lang: eng text: "Abstract\r\n \r\n A bimatroid is a matroid-like generalization of the collection of regular minors of a matrix. In this article, we use the theory of Lorentzian polynomials to study the logarithmic concavity of natural sequences associated with bimatroids. Bimatroids can be used to characterize morphisms of matroids and this observation (originally due to Kung) allows us to prove a weak version of logarithmic concavity of the number of bases of a morphism of matroids. This is weaker than the original result by Eur and Huh; it nevertheless provides us with a new perspective on Mason’s log-concavity conjecture for independent sets of matroids. We finally show that for realizable bimatroids, the regular minor polynomial is a volume polynomial. Applied to morphisms of matroids, this shows that the weak basis generating polynomial of a morphism is a volume polynomial; this confirms a conjecture of Eur–Huh for morphisms of nullity\r\n \r\n \r\n \ $$\\le 1$$\r\n \r\n \r\n \ ≤\r\n 1\r\n \ \r\n \r\n \ \r\n \r\n \ and gives an algebro-geometric explanation for Mason’s log-concavity conjecture in the realizable case.\r\n " author: - first_name: Felix full_name: Röhrle, Felix last_name: Röhrle - first_name: Martin full_name: Ulirsch, Martin id: '114697' last_name: Ulirsch citation: ama: Röhrle F, Ulirsch M. Logarithmic concavity of bimatroids. Annals of Combinatorics. 2025;30(2):501-523. doi:10.1007/s00026-025-00780-z apa: Röhrle, F., & Ulirsch, M. (2025). Logarithmic concavity of bimatroids. Annals of Combinatorics, 30(2), 501–523. https://doi.org/10.1007/s00026-025-00780-z bibtex: '@article{Röhrle_Ulirsch_2025, title={Logarithmic concavity of bimatroids}, volume={30}, DOI={10.1007/s00026-025-00780-z}, number={2}, journal={Annals of Combinatorics}, publisher={Springer Science and Business Media LLC}, author={Röhrle, Felix and Ulirsch, Martin}, year={2025}, pages={501–523} }' chicago: 'Röhrle, Felix, and Martin Ulirsch. “Logarithmic Concavity of Bimatroids.” Annals of Combinatorics 30, no. 2 (2025): 501–23. https://doi.org/10.1007/s00026-025-00780-z.' ieee: 'F. Röhrle and M. Ulirsch, “Logarithmic concavity of bimatroids,” Annals of Combinatorics, vol. 30, no. 2, pp. 501–523, 2025, doi: 10.1007/s00026-025-00780-z.' mla: Röhrle, Felix, and Martin Ulirsch. “Logarithmic Concavity of Bimatroids.” Annals of Combinatorics, vol. 30, no. 2, Springer Science and Business Media LLC, 2025, pp. 501–23, doi:10.1007/s00026-025-00780-z. short: F. Röhrle, M. Ulirsch, Annals of Combinatorics 30 (2025) 501–523. date_created: 2026-07-08T06:23:01Z date_updated: 2026-07-09T06:42:56Z doi: 10.1007/s00026-025-00780-z intvolume: ' 30' issue: '2' language: - iso: eng page: 501-523 publication: Annals of Combinatorics publication_identifier: unknown: - 0218-0006 - 0219-3094 publication_status: published publisher: Springer Science and Business Media LLC status: public title: Logarithmic concavity of bimatroids type: journal_article user_id: '82981' volume: 30 year: '2025' ... --- _id: '66315' abstract: - lang: eng text: "Abstract\r\n Motivated by the recent surge of interest in the geometry of hybrid spaces, we prove an Abel–Jacobi theorem for a metrized complex of Riemann surfaces, generalizing both the classical Abel–Jacobi theorem and its tropical analogue." author: - first_name: Maximilian C. E. full_name: Hofmann, Maximilian C. E. last_name: Hofmann - first_name: Martin full_name: Ulirsch, Martin id: '114697' last_name: Ulirsch citation: ama: Hofmann MCE, Ulirsch M. An Abel-Jacobi theorem for metrized complexes of Riemann surfaces. Advances in Geometry. 2025;25(2):263-278. doi:10.1515/advgeom-2025-0010 apa: Hofmann, M. C. E., & Ulirsch, M. (2025). An Abel-Jacobi theorem for metrized complexes of Riemann surfaces. Advances in Geometry, 25(2), 263–278. https://doi.org/10.1515/advgeom-2025-0010 bibtex: '@article{Hofmann_Ulirsch_2025, title={An Abel-Jacobi theorem for metrized complexes of Riemann surfaces}, volume={25}, DOI={10.1515/advgeom-2025-0010}, number={2}, journal={Advances in Geometry}, publisher={Walter de Gruyter GmbH}, author={Hofmann, Maximilian C. E. and Ulirsch, Martin}, year={2025}, pages={263–278} }' chicago: 'Hofmann, Maximilian C. E., and Martin Ulirsch. “An Abel-Jacobi Theorem for Metrized Complexes of Riemann Surfaces.” Advances in Geometry 25, no. 2 (2025): 263–78. https://doi.org/10.1515/advgeom-2025-0010.' ieee: 'M. C. E. Hofmann and M. Ulirsch, “An Abel-Jacobi theorem for metrized complexes of Riemann surfaces,” Advances in Geometry, vol. 25, no. 2, pp. 263–278, 2025, doi: 10.1515/advgeom-2025-0010.' mla: Hofmann, Maximilian C. E., and Martin Ulirsch. “An Abel-Jacobi Theorem for Metrized Complexes of Riemann Surfaces.” Advances in Geometry, vol. 25, no. 2, Walter de Gruyter GmbH, 2025, pp. 263–78, doi:10.1515/advgeom-2025-0010. short: M.C.E. Hofmann, M. Ulirsch, Advances in Geometry 25 (2025) 263–278. date_created: 2026-07-08T06:41:22Z date_updated: 2026-07-09T06:42:28Z doi: 10.1515/advgeom-2025-0010 intvolume: ' 25' issue: '2' language: - iso: eng page: 263-278 publication: Advances in Geometry publication_identifier: issn: - 1615-7168 - 1615-715X publication_status: published publisher: Walter de Gruyter GmbH status: public title: An Abel-Jacobi theorem for metrized complexes of Riemann surfaces type: journal_article user_id: '82981' volume: 25 year: '2025' ... --- _id: '66318' author: - first_name: Alex full_name: Küronya, Alex last_name: Küronya - first_name: Pedro full_name: Souza, Pedro last_name: Souza - first_name: Martin full_name: Ulirsch, Martin id: '114697' last_name: Ulirsch citation: ama: 'Küronya A, Souza P, Ulirsch M. Tropicalization of toric prevarieties. In: EMS Series of Congress Reports. EMS Press; 2025. doi:10.4171/ECR/22/16' apa: Küronya, A., Souza, P., & Ulirsch, M. (2025). Tropicalization of toric prevarieties. In EMS Series of Congress Reports. EMS Press. https://doi.org/10.4171/ECR/22/16 bibtex: '@inbook{Küronya_Souza_Ulirsch_2025, title={Tropicalization of toric prevarieties}, DOI={10.4171/ECR/22/16}, booktitle={EMS Series of Congress Reports}, publisher={EMS Press}, author={Küronya, Alex and Souza, Pedro and Ulirsch, Martin}, year={2025} }' chicago: Küronya, Alex, Pedro Souza, and Martin Ulirsch. “Tropicalization of Toric Prevarieties.” In EMS Series of Congress Reports. EMS Press, 2025. https://doi.org/10.4171/ECR/22/16. ieee: A. Küronya, P. Souza, and M. Ulirsch, “Tropicalization of toric prevarieties,” in EMS Series of Congress Reports, EMS Press, 2025. mla: Küronya, Alex, et al. “Tropicalization of Toric Prevarieties.” EMS Series of Congress Reports, EMS Press, 2025, doi:10.4171/ECR/22/16. short: 'A. Küronya, P. Souza, M. Ulirsch, in: EMS Series of Congress Reports, EMS Press, 2025.' date_created: 2026-07-08T06:45:28Z date_updated: 2026-07-09T06:45:31Z doi: 10.4171/ECR/22/16 language: - iso: eng publication: EMS Series of Congress Reports publication_identifier: isbn: - '9783985470969' - '9783985475964' issn: - 2523-515X - 2523-5168 publication_status: published publisher: EMS Press status: public title: Tropicalization of toric prevarieties type: book_chapter user_id: '82981' year: '2025' ... --- _id: '66306' abstract: - lang: eng text: Recently, several proofs of the Mason--Welsh conjecture for matroids have been found, which asserts the log-concavity of the sequence that counts independent sets of a given size. In this article we use the theory of Lorentzian polynomials, developed by Brändén and Huh, to prove a generalization of the Mason-Welsh conjecture to the context of valuated matroids. In fact, we provide a log-concavity result in the more general setting of valuated discrete polymatroids, or equivalently, M-convex functions. Our approach is via the construction of a generic extension of a valuated matroid or M-convex function, so that the bases of the extension are related to the independent sets of the original matroid. We also provide a similar log-concavity result for valuated bimatroids, which, we believe, might be of independent interest. author: - first_name: Jeffrey full_name: Giansiracusa, Jeffrey last_name: Giansiracusa - first_name: Felipe full_name: Rincón, Felipe last_name: Rincón - first_name: Victoria full_name: Schleis, Victoria last_name: Schleis - first_name: Martin full_name: Ulirsch, Martin id: '114697' last_name: Ulirsch citation: ama: Giansiracusa J, Rincón F, Schleis V, Ulirsch M. Log-concavity for independent sets of valuated matroids. arXiv:240705808. Published online 2024. apa: Giansiracusa, J., Rincón, F., Schleis, V., & Ulirsch, M. (2024). Log-concavity for independent sets of valuated matroids. In arXiv:2407.05808. bibtex: '@article{Giansiracusa_Rincón_Schleis_Ulirsch_2024, title={Log-concavity for independent sets of valuated matroids}, journal={arXiv:2407.05808}, author={Giansiracusa, Jeffrey and Rincón, Felipe and Schleis, Victoria and Ulirsch, Martin}, year={2024} }' chicago: Giansiracusa, Jeffrey, Felipe Rincón, Victoria Schleis, and Martin Ulirsch. “Log-Concavity for Independent Sets of Valuated Matroids.” ArXiv:2407.05808, 2024. ieee: J. Giansiracusa, F. Rincón, V. Schleis, and M. Ulirsch, “Log-concavity for independent sets of valuated matroids,” arXiv:2407.05808. 2024. mla: Giansiracusa, Jeffrey, et al. “Log-Concavity for Independent Sets of Valuated Matroids.” ArXiv:2407.05808, 2024. short: J. Giansiracusa, F. Rincón, V. Schleis, M. Ulirsch, ArXiv:2407.05808 (2024). date_created: 2026-07-08T06:22:23Z date_updated: 2026-07-08T06:22:38Z external_id: arxiv: - '2407.05808' language: - iso: eng publication: arXiv:2407.05808 status: public title: Log-concavity for independent sets of valuated matroids type: preprint user_id: '82981' year: '2024' ... --- _id: '66312' abstract: - lang: eng text: Let $X$ be a complex abelian variety. We prove an analogue of both the (cohomological) $P=W$ conjecture and the geometric $P=W$ conjecture connecting the finer topological structure of the Dolbeault moduli space of topologically trivial semistable Higgs bundles on $X$ and the Betti moduli space of characters of the fundamental group of $X$. The geometric heart of our approach is the spectral data morphism for Dolbeault moduli spaces on abelian varieties that naturally factors the Hitchin morphism and whose target is not an affine space of pluricanonical sections, but a suitable symmetric product. author: - first_name: Barbara full_name: Bolognese, Barbara last_name: Bolognese - first_name: Alex full_name: Küronya, Alex last_name: Küronya - first_name: Martin full_name: Ulirsch, Martin id: '114697' last_name: Ulirsch citation: ama: Bolognese B, Küronya A, Ulirsch M. $P=W$ phenomena on abelian varieties. arXiv:230303734. Published online 2023. apa: Bolognese, B., Küronya, A., & Ulirsch, M. (2023). $P=W$ phenomena on abelian varieties. In arXiv:2303.03734. bibtex: '@article{Bolognese_Küronya_Ulirsch_2023, title={$P=W$ phenomena on abelian varieties}, journal={arXiv:2303.03734}, author={Bolognese, Barbara and Küronya, Alex and Ulirsch, Martin}, year={2023} }' chicago: Bolognese, Barbara, Alex Küronya, and Martin Ulirsch. “$P=W$ Phenomena on Abelian Varieties.” ArXiv:2303.03734, 2023. ieee: B. Bolognese, A. Küronya, and M. Ulirsch, “$P=W$ phenomena on abelian varieties,” arXiv:2303.03734. 2023. mla: Bolognese, Barbara, et al. “$P=W$ Phenomena on Abelian Varieties.” ArXiv:2303.03734, 2023. short: B. Bolognese, A. Küronya, M. Ulirsch, ArXiv:2303.03734 (2023). date_created: 2026-07-08T06:32:00Z date_updated: 2026-07-08T06:32:25Z external_id: arxiv: - '2303.03734' language: - iso: eng publication: arXiv:2303.03734 status: public title: $P=W$ phenomena on abelian varieties type: preprint user_id: '82981' year: '2023' ... --- _id: '66325' abstract: - lang: eng text: AbstractLet$\mathfrak{A}$be a finite abelian group. In this paper, we classify harmonic$\mathfrak{A}$-covers of a tropical curve$\Gamma$(which allow dilation along edges and at vertices) in terms of the cohomology group of a suitably defined sheaf on$\Gamma$. We give a realisability criterion for harmonic$\mathfrak{A}$-covers by patching local monodromy data in an extended homology group on$\Gamma$. As an explicit example, we work out the case$\mathfrak{A}=\mathbb{Z}/p\mathbb{Z}$and explain how realisability for such covers is related to the nowhere-zero flow problem from graph theory. author: - first_name: Yoav full_name: Len, Yoav last_name: Len - first_name: Martin full_name: Ulirsch, Martin id: '114697' last_name: Ulirsch - first_name: Dmitry full_name: Zakharov, Dmitry last_name: Zakharov citation: ama: Len Y, Ulirsch M, Zakharov D. Abelian tropical covers. Mathematical Proceedings of the Cambridge Philosophical Society. 2023;176(2):395-416. doi:10.1017/S0305004123000518 apa: Len, Y., Ulirsch, M., & Zakharov, D. (2023). Abelian tropical covers. Mathematical Proceedings of the Cambridge Philosophical Society, 176(2), 395–416. https://doi.org/10.1017/S0305004123000518 bibtex: '@article{Len_Ulirsch_Zakharov_2023, title={Abelian tropical covers}, volume={176}, DOI={10.1017/S0305004123000518}, number={2}, journal={Mathematical Proceedings of the Cambridge Philosophical Society}, publisher={Cambridge University Press (CUP)}, author={Len, Yoav and Ulirsch, Martin and Zakharov, Dmitry}, year={2023}, pages={395–416} }' chicago: 'Len, Yoav, Martin Ulirsch, and Dmitry Zakharov. “Abelian Tropical Covers.” Mathematical Proceedings of the Cambridge Philosophical Society 176, no. 2 (2023): 395–416. https://doi.org/10.1017/S0305004123000518.' ieee: 'Y. Len, M. Ulirsch, and D. Zakharov, “Abelian tropical covers,” Mathematical Proceedings of the Cambridge Philosophical Society, vol. 176, no. 2, pp. 395–416, 2023, doi: 10.1017/S0305004123000518.' mla: Len, Yoav, et al. “Abelian Tropical Covers.” Mathematical Proceedings of the Cambridge Philosophical Society, vol. 176, no. 2, Cambridge University Press (CUP), 2023, pp. 395–416, doi:10.1017/S0305004123000518. short: Y. Len, M. Ulirsch, D. Zakharov, Mathematical Proceedings of the Cambridge Philosophical Society 176 (2023) 395–416. date_created: 2026-07-08T06:50:59Z date_updated: 2026-07-09T07:11:55Z doi: 10.1017/S0305004123000518 intvolume: ' 176' issue: '2' language: - iso: eng page: 395-416 publication: Mathematical Proceedings of the Cambridge Philosophical Society publication_identifier: issn: - 0305-0041 - 1469-8064 publication_status: published publisher: Cambridge University Press (CUP) status: public title: Abelian tropical covers type: journal_article user_id: '82981' volume: 176 year: '2023' ... --- _id: '66358' abstract: - lang: eng text: AbstractAffine Bruhat–Tits buildings are geometric spaces extracting the combinatorics of algebraic groups. The building of parameterizes flags of subspaces/lattices in or, equivalently, norms on a fixed finite‐dimensional vector space, up to homothety. It has first been studied by Goldman and Iwahori as a piecewise‐linear analogue of symmetric spaces. The space of seminorms compactifies the space of norms and admits a natural surjective restriction map from the Berkovich analytification of projective space that factors the natural tropicalization map. Inspired by Payne's result that the analytification is the limit of all tropicalizations, we show that the space of seminorms is the limit of all tropicalized linear embeddings and prove a faithful tropicalization result for compactified linear spaces. The space of seminorms is in fact the tropical linear space associated to the universal realizable valuated matroid. article_number: e12850 author: - first_name: Luca full_name: Battistella, Luca last_name: Battistella - first_name: Kevin full_name: Kühn, Kevin last_name: Kühn - first_name: Arne full_name: Kuhrs, Arne last_name: Kuhrs - first_name: Martin full_name: Ulirsch, Martin id: '114697' last_name: Ulirsch - first_name: Alejandro full_name: Vargas, Alejandro last_name: Vargas citation: ama: Battistella L, Kühn K, Kuhrs A, Ulirsch M, Vargas A. Buildings, valuated matroids, and tropical linear spaces. Journal of the London Mathematical Society. 2023;109(1). doi:10.1112/jlms.12850 apa: Battistella, L., Kühn, K., Kuhrs, A., Ulirsch, M., & Vargas, A. (2023). Buildings, valuated matroids, and tropical linear spaces. Journal of the London Mathematical Society, 109(1), Article e12850. https://doi.org/10.1112/jlms.12850 bibtex: '@article{Battistella_Kühn_Kuhrs_Ulirsch_Vargas_2023, title={Buildings, valuated matroids, and tropical linear spaces}, volume={109}, DOI={10.1112/jlms.12850}, number={1e12850}, journal={Journal of the London Mathematical Society}, publisher={Wiley}, author={Battistella, Luca and Kühn, Kevin and Kuhrs, Arne and Ulirsch, Martin and Vargas, Alejandro}, year={2023} }' chicago: Battistella, Luca, Kevin Kühn, Arne Kuhrs, Martin Ulirsch, and Alejandro Vargas. “Buildings, Valuated Matroids, and Tropical Linear Spaces.” Journal of the London Mathematical Society 109, no. 1 (2023). https://doi.org/10.1112/jlms.12850. ieee: 'L. Battistella, K. Kühn, A. Kuhrs, M. Ulirsch, and A. Vargas, “Buildings, valuated matroids, and tropical linear spaces,” Journal of the London Mathematical Society, vol. 109, no. 1, Art. no. e12850, 2023, doi: 10.1112/jlms.12850.' mla: Battistella, Luca, et al. “Buildings, Valuated Matroids, and Tropical Linear Spaces.” Journal of the London Mathematical Society, vol. 109, no. 1, e12850, Wiley, 2023, doi:10.1112/jlms.12850. short: L. Battistella, K. Kühn, A. Kuhrs, M. Ulirsch, A. Vargas, Journal of the London Mathematical Society 109 (2023). date_created: 2026-07-08T08:04:28Z date_updated: 2026-07-08T08:04:43Z doi: 10.1112/jlms.12850 intvolume: ' 109' issue: '1' language: - iso: eng publication: Journal of the London Mathematical Society publication_identifier: issn: - 0024-6107 - 1469-7750 publication_status: published publisher: Wiley status: public title: Buildings, valuated matroids, and tropical linear spaces type: journal_article user_id: '82981' volume: 109 year: '2023' ... --- _id: '66316' article_number: '108775' author: - first_name: Andreas full_name: Gross, Andreas last_name: Gross - first_name: Martin full_name: Ulirsch, Martin id: '114697' last_name: Ulirsch - first_name: Dmitry full_name: Zakharov, Dmitry last_name: Zakharov citation: ama: 'Gross A, Ulirsch M, Zakharov D. Principal bundles on metric graphs: the $\mathrm{GL}_n$ case. Advances in Mathematics. 2022;411. doi:10.1016/j.aim.2022.108775' apa: 'Gross, A., Ulirsch, M., & Zakharov, D. (2022). Principal bundles on metric graphs: the $\mathrm{GL}_n$ case. Advances in Mathematics, 411, Article 108775. https://doi.org/10.1016/j.aim.2022.108775' bibtex: '@article{Gross_Ulirsch_Zakharov_2022, title={Principal bundles on metric graphs: the $\mathrm{GL}_n$ case}, volume={411}, DOI={10.1016/j.aim.2022.108775}, number={108775}, journal={Advances in Mathematics}, publisher={Elsevier BV}, author={Gross, Andreas and Ulirsch, Martin and Zakharov, Dmitry}, year={2022} }' chicago: 'Gross, Andreas, Martin Ulirsch, and Dmitry Zakharov. “Principal Bundles on Metric Graphs: The $\mathrm{GL}_n$ Case.” Advances in Mathematics 411 (2022). https://doi.org/10.1016/j.aim.2022.108775.' ieee: 'A. Gross, M. Ulirsch, and D. Zakharov, “Principal bundles on metric graphs: the $\mathrm{GL}_n$ case,” Advances in Mathematics, vol. 411, Art. no. 108775, 2022, doi: 10.1016/j.aim.2022.108775.' mla: 'Gross, Andreas, et al. “Principal Bundles on Metric Graphs: The $\mathrm{GL}_n$ Case.” Advances in Mathematics, vol. 411, 108775, Elsevier BV, 2022, doi:10.1016/j.aim.2022.108775.' short: A. Gross, M. Ulirsch, D. Zakharov, Advances in Mathematics 411 (2022). date_created: 2026-07-08T06:42:43Z date_updated: 2026-07-09T06:57:16Z doi: 10.1016/j.aim.2022.108775 intvolume: ' 411' language: - iso: eng publication: Advances in Mathematics publication_identifier: issn: - 0001-8708 publication_status: published publisher: Elsevier BV status: public title: 'Principal bundles on metric graphs: the $\mathrm{GL}_n$ case' type: journal_article user_id: '82981' volume: 411 year: '2022' ... --- _id: '66329' abstract: - lang: eng text: "

\r\n We show that the non-Archimedean skeleton of the\r\n \ \r\n \r\n \r\n \ d\r\n d\r\n \r\n \ \r\n \r\n \ -th symmetric power of a smooth projective algebraic curve\r\n \ \r\n \r\n \r\n \ X\r\n X\r\n \r\n \ \r\n \r\n \ is naturally isomorphic to the\r\n \r\n \r\n \r\n d\r\n \ d\r\n \ \r\n \r\n \ \r\n -th symmetric power of the tropical curve that arises as the non-Archimedean skeleton of\r\n \r\n \r\n \r\n X\r\n \ X\r\n \ \r\n \r\n \ \r\n . The retraction to the skeleton is precisely the specialization map for divisors. Moreover, we show that the process of tropicalization naturally commutes with the diagonal morphisms and the Abel-Jacobi map and we exhibit a faithful tropicalization for symmetric powers of curves. Finally, we prove a version of the Bieri-Groves Theorem that allows us, under certain tropical genericity assumptions, to deduce a new tropical Riemann-Roch-Theorem for the tropicalization of linear systems.\r\n

" author: - first_name: Madeline full_name: Brandt, Madeline last_name: Brandt - first_name: Martin full_name: Ulirsch, Martin id: '114697' last_name: Ulirsch citation: ama: 'Brandt M, Ulirsch M. Symmetric powers of algebraic and tropical curves: a non-Archimedean perspective. Transactions of the American Mathematical Society, Series B. 2022;9(20):586-618. doi:10.1090/btran/113' apa: 'Brandt, M., & Ulirsch, M. (2022). Symmetric powers of algebraic and tropical curves: a non-Archimedean perspective. Transactions of the American Mathematical Society, Series B, 9(20), 586–618. https://doi.org/10.1090/btran/113' bibtex: '@article{Brandt_Ulirsch_2022, title={Symmetric powers of algebraic and tropical curves: a non-Archimedean perspective}, volume={9}, DOI={10.1090/btran/113}, number={20}, journal={Transactions of the American Mathematical Society, Series B}, publisher={American Mathematical Society (AMS)}, author={Brandt, Madeline and Ulirsch, Martin}, year={2022}, pages={586–618} }' chicago: 'Brandt, Madeline, and Martin Ulirsch. “Symmetric Powers of Algebraic and Tropical Curves: A Non-Archimedean Perspective.” Transactions of the American Mathematical Society, Series B 9, no. 20 (2022): 586–618. https://doi.org/10.1090/btran/113.' ieee: 'M. Brandt and M. Ulirsch, “Symmetric powers of algebraic and tropical curves: a non-Archimedean perspective,” Transactions of the American Mathematical Society, Series B, vol. 9, no. 20, pp. 586–618, 2022, doi: 10.1090/btran/113.' mla: 'Brandt, Madeline, and Martin Ulirsch. “Symmetric Powers of Algebraic and Tropical Curves: A Non-Archimedean Perspective.” Transactions of the American Mathematical Society, Series B, vol. 9, no. 20, American Mathematical Society (AMS), 2022, pp. 586–618, doi:10.1090/btran/113.' short: M. Brandt, M. Ulirsch, Transactions of the American Mathematical Society, Series B 9 (2022) 586–618. date_created: 2026-07-08T06:52:13Z date_updated: 2026-07-09T06:54:02Z doi: 10.1090/btran/113 intvolume: ' 9' issue: '20' language: - iso: eng page: 586-618 publication: Transactions of the American Mathematical Society, Series B publication_identifier: issn: - 2330-0000 publication_status: published publisher: American Mathematical Society (AMS) status: public title: 'Symmetric powers of algebraic and tropical curves: a non-Archimedean perspective' type: journal_article user_id: '82981' volume: 9 year: '2022' ... --- _id: '66317' abstract: - lang: eng text: 'In this article we provide a stack-theoretic framework to study the universal tropical Jacobian over the moduli space of tropical curves. We develop two approaches to the process of tropicalization of the universal compactified Jacobian over the moduli space of curves -- one from a logarithmic and the other from a non-Archimedean analytic point of view. The central result from both points of view is that the tropicalization of the universal compactified Jacobian is the universal tropical Jacobian and that the tropicalization maps in each of the two contexts are compatible with the tautological morphisms. In a sequel we will use the techniques developed here to provide explicit polyhedral models for the logarithmic Picard variety.Comment: 51 pages, 2 figures, v3: published version' article_number: '8352' author: - first_name: Margarida full_name: Melo, Margarida last_name: Melo - first_name: Samouil full_name: Molcho, Samouil last_name: Molcho - first_name: Martin full_name: Ulirsch, Martin id: '114697' last_name: Ulirsch - first_name: Filippo full_name: Viviani, Filippo last_name: Viviani citation: ama: Melo M, Molcho S, Ulirsch M, Viviani F. Tropicalization of the universal Jacobian. Épijournal de Géométrie Algébrique. 2022;Volume 6. doi:doi.org/10.46298/epiga.2022.8352 apa: Melo, M., Molcho, S., Ulirsch, M., & Viviani, F. (2022). Tropicalization of the universal Jacobian. Épijournal de Géométrie Algébrique, Volume 6, Article 8352. https://doi.org/doi.org/10.46298/epiga.2022.8352 bibtex: '@article{Melo_Molcho_Ulirsch_Viviani_2022, title={Tropicalization of the universal Jacobian}, volume={Volume 6}, DOI={doi.org/10.46298/epiga.2022.8352}, number={8352}, journal={Épijournal de Géométrie Algébrique}, publisher={Centre pour la Communication Scientifique Directe (CCSD)}, author={Melo, Margarida and Molcho, Samouil and Ulirsch, Martin and Viviani, Filippo}, year={2022} }' chicago: Melo, Margarida, Samouil Molcho, Martin Ulirsch, and Filippo Viviani. “Tropicalization of the Universal Jacobian.” Épijournal de Géométrie Algébrique Volume 6 (2022). https://doi.org/doi.org/10.46298/epiga.2022.8352. ieee: 'M. Melo, S. Molcho, M. Ulirsch, and F. Viviani, “Tropicalization of the universal Jacobian,” Épijournal de Géométrie Algébrique, vol. Volume 6, Art. no. 8352, 2022, doi: doi.org/10.46298/epiga.2022.8352.' mla: Melo, Margarida, et al. “Tropicalization of the Universal Jacobian.” Épijournal de Géométrie Algébrique, vol. Volume 6, 8352, Centre pour la Communication Scientifique Directe (CCSD), 2022, doi:doi.org/10.46298/epiga.2022.8352. short: M. Melo, S. Molcho, M. Ulirsch, F. Viviani, Épijournal de Géométrie Algébrique Volume 6 (2022). date_created: 2026-07-08T06:44:47Z date_updated: 2026-07-09T07:08:32Z doi: doi.org/10.46298/epiga.2022.8352 language: - iso: eng publication: Épijournal de Géométrie Algébrique publication_identifier: issn: - 2491-6765 publication_status: published publisher: Centre pour la Communication Scientifique Directe (CCSD) status: public title: Tropicalization of the universal Jacobian type: journal_article user_id: '82981' volume: Volume 6 year: '2022' ... --- _id: '66326' author: - first_name: Yoav full_name: Len, Yoav last_name: Len - first_name: Martin full_name: Ulirsch, Martin id: '114697' last_name: Ulirsch citation: ama: Len Y, Ulirsch M. Skeletons of Prym varieties and Brill--Noether theory. Algebra & Number Theory. 2021;15(3):785-820. doi:10.2140/ant.2021.15.785 apa: Len, Y., & Ulirsch, M. (2021). Skeletons of Prym varieties and Brill--Noether theory. Algebra & Number Theory, 15(3), 785–820. https://doi.org/10.2140/ant.2021.15.785 bibtex: '@article{Len_Ulirsch_2021, title={Skeletons of Prym varieties and Brill--Noether theory}, volume={15}, DOI={10.2140/ant.2021.15.785}, number={3}, journal={Algebra & Number Theory}, publisher={Mathematical Sciences Publishers}, author={Len, Yoav and Ulirsch, Martin}, year={2021}, pages={785–820} }' chicago: 'Len, Yoav, and Martin Ulirsch. “Skeletons of Prym Varieties and Brill--Noether Theory.” Algebra & Number Theory 15, no. 3 (2021): 785–820. https://doi.org/10.2140/ant.2021.15.785.' ieee: 'Y. Len and M. Ulirsch, “Skeletons of Prym varieties and Brill--Noether theory,” Algebra & Number Theory, vol. 15, no. 3, pp. 785–820, 2021, doi: 10.2140/ant.2021.15.785.' mla: Len, Yoav, and Martin Ulirsch. “Skeletons of Prym Varieties and Brill--Noether Theory.” Algebra & Number Theory, vol. 15, no. 3, Mathematical Sciences Publishers, 2021, pp. 785–820, doi:10.2140/ant.2021.15.785. short: Y. Len, M. Ulirsch, Algebra & Number Theory 15 (2021) 785–820. date_created: 2026-07-08T06:51:20Z date_updated: 2026-07-09T07:36:46Z doi: 10.2140/ant.2021.15.785 intvolume: ' 15' issue: '3' language: - iso: eng page: 785-820 publication: Algebra & Number Theory publication_identifier: issn: - 1944-7833 - 1937-0652 publication_status: published publisher: Mathematical Sciences Publishers status: public title: Skeletons of Prym varieties and Brill--Noether theory type: journal_article user_id: '82981' volume: 15 year: '2021' ... --- _id: '66361' author: - first_name: Yoav full_name: Len, Yoav last_name: Len - first_name: Martin full_name: Ulirsch, Martin id: '114697' last_name: Ulirsch citation: ama: Len Y, Ulirsch M. Skeletons of Prym varieties and Brill–Noethertheory. Algebra & Number Theory. 2021;15(3):785-820. doi:10.2140/ant.2021.15.785 apa: Len, Y., & Ulirsch, M. (2021). Skeletons of Prym varieties and Brill–Noethertheory. Algebra & Number Theory, 15(3), 785–820. https://doi.org/10.2140/ant.2021.15.785 bibtex: '@article{Len_Ulirsch_2021, title={Skeletons of Prym varieties and Brill–Noethertheory}, volume={15}, DOI={10.2140/ant.2021.15.785}, number={3}, journal={Algebra & Number Theory}, publisher={Mathematical Sciences Publishers}, author={Len, Yoav and Ulirsch, Martin}, year={2021}, pages={785–820} }' chicago: 'Len, Yoav, and Martin Ulirsch. “Skeletons of Prym Varieties and Brill–Noethertheory.” Algebra & Number Theory 15, no. 3 (2021): 785–820. https://doi.org/10.2140/ant.2021.15.785.' ieee: 'Y. Len and M. Ulirsch, “Skeletons of Prym varieties and Brill–Noethertheory,” Algebra & Number Theory, vol. 15, no. 3, pp. 785–820, 2021, doi: 10.2140/ant.2021.15.785.' mla: Len, Yoav, and Martin Ulirsch. “Skeletons of Prym Varieties and Brill–Noethertheory.” Algebra & Number Theory, vol. 15, no. 3, Mathematical Sciences Publishers, 2021, pp. 785–820, doi:10.2140/ant.2021.15.785. short: Y. Len, M. Ulirsch, Algebra & Number Theory 15 (2021) 785–820. date_created: 2026-07-08T08:36:11Z date_updated: 2026-07-08T08:37:00Z doi: 10.2140/ant.2021.15.785 intvolume: ' 15' issue: '3' language: - iso: eng page: 785-820 publication: Algebra & Number Theory publication_identifier: issn: - 1944-7833 - 1937-0652 publication_status: published publisher: Mathematical Sciences Publishers status: public title: Skeletons of Prym varieties and Brill–Noethertheory type: journal_article user_id: '82981' volume: 15 year: '2021' ... --- _id: '66321' abstract: - lang: eng text: AbstractIn this article we use techniques from tropical and logarithmic geometry to construct a non-Archimedean analogue ofTeichmüller space$$\overline{{{\mathcal {T}}}}_g$$T¯gwhose points are pairs consisting of a stable projective curve over a non-Archimedean field and a Teichmüller marking of the topological fundamental group of its Berkovich analytification. This construction is closely related to and inspired by the classical construction of a non-Archimedean Schottky space for Mumford curves by Gerritzen and Herrlich. We argue that the skeleton of non-Archimedean Teichmüller space is precisely the tropical Teichmüller space introduced by Chan–Melo–Viviani as a simplicial completion of Culler–Vogtmann Outer space. As a consequence, Outer space turns out to be a strong deformation retract of the locus of smooth Mumford curves in$$\overline{{\mathcal {T}}}_g$$T¯g. author: - first_name: Martin full_name: Ulirsch, Martin id: '114697' last_name: Ulirsch citation: ama: Ulirsch M. A non-Archimedean analogue of Teichmüller space and its tropicalization. Selecta Mathematica. 2021;27(3):39. doi:10.1007/s00029-021-00651-4 apa: Ulirsch, M. (2021). A non-Archimedean analogue of Teichmüller space and its tropicalization. Selecta Mathematica, 27(3), 39. https://doi.org/10.1007/s00029-021-00651-4 bibtex: '@article{Ulirsch_2021, title={A non-Archimedean analogue of Teichmüller space and its tropicalization}, volume={27}, DOI={10.1007/s00029-021-00651-4}, number={3}, journal={Selecta Mathematica}, publisher={Springer Science and Business Media LLC}, author={Ulirsch, Martin}, year={2021}, pages={39} }' chicago: 'Ulirsch, Martin. “A Non-Archimedean Analogue of Teichmüller Space and Its Tropicalization.” Selecta Mathematica 27, no. 3 (2021): 39. https://doi.org/10.1007/s00029-021-00651-4.' ieee: 'M. Ulirsch, “A non-Archimedean analogue of Teichmüller space and its tropicalization,” Selecta Mathematica, vol. 27, no. 3, p. 39, 2021, doi: 10.1007/s00029-021-00651-4.' mla: Ulirsch, Martin. “A Non-Archimedean Analogue of Teichmüller Space and Its Tropicalization.” Selecta Mathematica, vol. 27, no. 3, Springer Science and Business Media LLC, 2021, p. 39, doi:10.1007/s00029-021-00651-4. short: M. Ulirsch, Selecta Mathematica 27 (2021) 39. date_created: 2026-07-08T06:48:52Z date_updated: 2026-07-09T06:47:29Z doi: 10.1007/s00029-021-00651-4 intvolume: ' 27' issue: '3' language: - iso: eng page: '39' publication: Selecta Mathematica publication_identifier: issn: - 1022-1824 - 1420-9020 publication_status: published publisher: Springer Science and Business Media LLC status: public title: A non-Archimedean analogue of Teichmüller space and its tropicalization type: journal_article user_id: '82981' volume: 27 year: '2021' ... --- _id: '66333' abstract: - lang: eng text: "\r\n We use recent results by Bainbridge–Chen–Gendron–Grushevsky–Möller on compactifications of strata of abelian differentials to give a comprehensive solution to the realizability problem for effective tropical canonical divisors in equicharacteristic zero. Given a pair\r\n \r\n \ (\\Gamma, D)\r\n \r\n \ consisting of a stable tropical curve\r\n \r\n \ \\Gamma\r\n \r\n \ and a divisor\r\n \r\n \ D\r\n \r\n \ in the canonical linear system on\r\n \r\n \ \\Gamma\r\n \r\n \ , we give a purely combinatorial condition to decide whether there is a smooth curve\r\n \r\n X\r\n \ \r\n over a non-Archimedean field whose stable reduction has\r\n \r\n \ \\Gamma\r\n \r\n \ as its dual tropical curve together with an effective canonical divisor\r\n \r\n K_X\r\n \ \r\n that specializes to\r\n \r\n D\r\n \ \r\n .\r\n " author: - first_name: Martin full_name: Moeller, Martin last_name: Moeller - first_name: Martin full_name: Ulirsch, Martin id: '114697' last_name: Ulirsch - first_name: Annette full_name: Werner, Annette last_name: Werner citation: ama: Moeller M, Ulirsch M, Werner A. Realizability of tropical canonical divisors. Journal of the European Mathematical Society. 2020;23(1):185-217. doi:10.4171/JEMS/1009 apa: Moeller, M., Ulirsch, M., & Werner, A. (2020). Realizability of tropical canonical divisors. Journal of the European Mathematical Society, 23(1), 185–217. https://doi.org/10.4171/JEMS/1009 bibtex: '@article{Moeller_Ulirsch_Werner_2020, title={Realizability of tropical canonical divisors}, volume={23}, DOI={10.4171/JEMS/1009}, number={1}, journal={Journal of the European Mathematical Society}, publisher={European Mathematical Society - EMS - Publishing House GmbH}, author={Moeller, Martin and Ulirsch, Martin and Werner, Annette}, year={2020}, pages={185–217} }' chicago: 'Moeller, Martin, Martin Ulirsch, and Annette Werner. “Realizability of Tropical Canonical Divisors.” Journal of the European Mathematical Society 23, no. 1 (2020): 185–217. https://doi.org/10.4171/JEMS/1009.' ieee: 'M. Moeller, M. Ulirsch, and A. Werner, “Realizability of tropical canonical divisors,” Journal of the European Mathematical Society, vol. 23, no. 1, pp. 185–217, 2020, doi: 10.4171/JEMS/1009.' mla: Moeller, Martin, et al. “Realizability of Tropical Canonical Divisors.” Journal of the European Mathematical Society, vol. 23, no. 1, European Mathematical Society - EMS - Publishing House GmbH, 2020, pp. 185–217, doi:10.4171/JEMS/1009. short: M. Moeller, M. Ulirsch, A. Werner, Journal of the European Mathematical Society 23 (2020) 185–217. date_created: 2026-07-08T07:06:32Z date_updated: 2026-07-09T06:55:38Z doi: 10.4171/JEMS/1009 intvolume: ' 23' issue: '1' language: - iso: eng page: 185-217 publication: Journal of the European Mathematical Society publication_identifier: issn: - 1435-9855 - 1435-9863 publication_status: published publisher: European Mathematical Society - EMS - Publishing House GmbH status: public title: Realizability of tropical canonical divisors type: journal_article user_id: '82981' volume: 23 year: '2020' ... --- _id: '66324' author: - first_name: Madeline full_name: Brandt, Madeline last_name: Brandt - first_name: Martin full_name: Ulirsch, Martin id: '114697' last_name: Ulirsch citation: ama: Brandt M, Ulirsch M. Divisorial motivic zeta functions for marked stable curves. Michigan Mathematical Journal. 2020;71(2). doi:10.1307/mmj/20195792 apa: Brandt, M., & Ulirsch, M. (2020). Divisorial motivic zeta functions for marked stable curves. Michigan Mathematical Journal, 71(2). https://doi.org/10.1307/mmj/20195792 bibtex: '@article{Brandt_Ulirsch_2020, title={Divisorial motivic zeta functions for marked stable curves}, volume={71}, DOI={10.1307/mmj/20195792 }, number={2}, journal={Michigan Mathematical Journal}, publisher={Michigan Mathematical Journal}, author={Brandt, Madeline and Ulirsch, Martin}, year={2020} }' chicago: Brandt, Madeline, and Martin Ulirsch. “Divisorial Motivic Zeta Functions for Marked Stable Curves.” Michigan Mathematical Journal 71, no. 2 (2020). https://doi.org/10.1307/mmj/20195792 . ieee: 'M. Brandt and M. Ulirsch, “Divisorial motivic zeta functions for marked stable curves,” Michigan Mathematical Journal, vol. 71, no. 2, 2020, doi: 10.1307/mmj/20195792 .' mla: Brandt, Madeline, and Martin Ulirsch. “Divisorial Motivic Zeta Functions for Marked Stable Curves.” Michigan Mathematical Journal, vol. 71, no. 2, Michigan Mathematical Journal, 2020, doi:10.1307/mmj/20195792 . short: M. Brandt, M. Ulirsch, Michigan Mathematical Journal 71 (2020). date_created: 2026-07-08T06:50:16Z date_updated: 2026-07-09T06:49:12Z doi: '10.1307/mmj/20195792 ' intvolume: ' 71' issue: '2' language: - iso: eng publication: Michigan Mathematical Journal publication_identifier: issn: - 0026-2285 publication_status: published publisher: Michigan Mathematical Journal status: public title: Divisorial motivic zeta functions for marked stable curves type: journal_article user_id: '82981' volume: 71 year: '2020' ... --- _id: '66336' abstract: - lang: eng text: "We contribute to the foundations of tropical geometry with a view toward formulating tropical moduli problems, and with the moduli space of curves as our main example. We propose a moduli functor for the moduli space of curves and show that it is representable by a geometric stack over the category of rational polyhedral cones. In this framework, the natural forgetful morphisms between moduli spaces of curves with marked points function as universal curves.\r\n\t \ Our approach to tropical geometry permits tropical moduli problems—moduli of curves or otherwise—to be extended to logarithmic schemes. We use this to construct a smooth tropicalization morphism from the moduli space of algebraic curves to the moduli space of tropical curves, and we show that this morphism commutes with all of the tautological morphisms." article_number: e23 author: - first_name: Renzo full_name: Cavalieri, Renzo last_name: Cavalieri - first_name: Melody full_name: Chan, Melody last_name: Chan - first_name: Martin full_name: Ulirsch, Martin id: '114697' last_name: Ulirsch - first_name: Jonathan full_name: Wise, Jonathan last_name: Wise citation: ama: Cavalieri R, Chan M, Ulirsch M, Wise J. A MODULI STACK OF TROPICAL CURVES. Forum of Mathematics, Sigma. 2020;8. doi:10.1017/fms.2020.16 apa: Cavalieri, R., Chan, M., Ulirsch, M., & Wise, J. (2020). A MODULI STACK OF TROPICAL CURVES. Forum of Mathematics, Sigma, 8, Article e23. https://doi.org/10.1017/fms.2020.16 bibtex: '@article{Cavalieri_Chan_Ulirsch_Wise_2020, title={A MODULI STACK OF TROPICAL CURVES}, volume={8}, DOI={10.1017/fms.2020.16}, number={e23}, journal={Forum of Mathematics, Sigma}, publisher={Cambridge University Press (CUP)}, author={Cavalieri, Renzo and Chan, Melody and Ulirsch, Martin and Wise, Jonathan}, year={2020} }' chicago: Cavalieri, Renzo, Melody Chan, Martin Ulirsch, and Jonathan Wise. “A MODULI STACK OF TROPICAL CURVES.” Forum of Mathematics, Sigma 8 (2020). https://doi.org/10.1017/fms.2020.16. ieee: 'R. Cavalieri, M. Chan, M. Ulirsch, and J. Wise, “A MODULI STACK OF TROPICAL CURVES,” Forum of Mathematics, Sigma, vol. 8, Art. no. e23, 2020, doi: 10.1017/fms.2020.16.' mla: Cavalieri, Renzo, et al. “A MODULI STACK OF TROPICAL CURVES.” Forum of Mathematics, Sigma, vol. 8, e23, Cambridge University Press (CUP), 2020, doi:10.1017/fms.2020.16. short: R. Cavalieri, M. Chan, M. Ulirsch, J. Wise, Forum of Mathematics, Sigma 8 (2020). date_created: 2026-07-08T07:07:13Z date_updated: 2026-07-09T07:06:55Z doi: 10.1017/fms.2020.16 intvolume: ' 8' language: - iso: eng publication: Forum of Mathematics, Sigma publication_identifier: issn: - 2050-5094 publication_status: published publisher: Cambridge University Press (CUP) status: public title: A MODULI STACK OF TROPICAL CURVES type: journal_article user_id: '82981' volume: 8 year: '2020' ... --- _id: '66339' author: - first_name: Martin full_name: Ulirsch, Martin id: '114697' last_name: Ulirsch citation: ama: Ulirsch M. Non-Archimedean geometry of Artin fans. Advances in Mathematics. 2019;345:346-381. doi:10.1016/j.aim.2019.01.008 apa: Ulirsch, M. (2019). Non-Archimedean geometry of Artin fans. Advances in Mathematics, 345, 346–381. https://doi.org/10.1016/j.aim.2019.01.008 bibtex: '@article{Ulirsch_2019, title={Non-Archimedean geometry of Artin fans}, volume={345}, DOI={10.1016/j.aim.2019.01.008}, journal={Advances in Mathematics}, publisher={Elsevier BV}, author={Ulirsch, Martin}, year={2019}, pages={346–381} }' chicago: 'Ulirsch, Martin. “Non-Archimedean Geometry of Artin Fans.” Advances in Mathematics 345 (2019): 346–81. https://doi.org/10.1016/j.aim.2019.01.008.' ieee: 'M. Ulirsch, “Non-Archimedean geometry of Artin fans,” Advances in Mathematics, vol. 345, pp. 346–381, 2019, doi: 10.1016/j.aim.2019.01.008.' mla: Ulirsch, Martin. “Non-Archimedean Geometry of Artin Fans.” Advances in Mathematics, vol. 345, Elsevier BV, 2019, pp. 346–81, doi:10.1016/j.aim.2019.01.008. short: M. Ulirsch, Advances in Mathematics 345 (2019) 346–381. date_created: 2026-07-08T07:09:58Z date_updated: 2026-07-09T06:58:37Z doi: 10.1016/j.aim.2019.01.008 intvolume: ' 345' language: - iso: eng page: 346-381 publication: Advances in Mathematics publication_identifier: issn: - 0001-8708 publication_status: published publisher: Elsevier BV status: public title: Non-Archimedean geometry of Artin fans type: journal_article user_id: '82981' volume: 345 year: '2019' ...