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Research Group

Numerical Algebraic Geometry - Publications

Explore the scholarly works of the "Numerical Algebraic Geometry" group. Browse journal articles, contributions in books and conference proceedings, academic theses, or discover our latest research through preprints. The names of the authors who worked on the publication during their time at the institute are shown in bold.

Preprint
2026 Repository Open Access
Andrei Balakin, Miklós Bóna, Marie-Charlotte Brandenburg, Clara Briand, Veronica Calvo Cortes, Shelby Cox, Jesús A. De Loera, Danai Deligeorgaki, Hannah Friedman, Tim Gehrunger, Chiara Giardino, Stephen Griffeth, Baran Hashemi, Elena Hoster, Alexander Ivanov, Nupur Jain, Aryaman Jal, Leonie Kayser, Joris Koefler, Kevin Kühn, Mario Kummer, Felix Lotter, René Marczinzik, Victor S. Miller, Alejandro H. Morales, Greta Panova, Gianni Petrella, Nathan Pflueger, Lakshmi Ramesh, Nikolas Rieke, Carlos Rodriguez, Andrea Rosana, Flavio Salizzoni, Otto Schmidt, Sven Ulf Schmitz, Lina Maria Simbaqueba Marin, Luca Sodomaco, Christian Stump, Bernd Sturmfels, Alexander Taveira Blomenhofer, Simon Telen, Philipp Tuchel, Emil Verkama, Carl Felix Waller, Julian Weigert, Annette Werner, Nathan Williams and Claudius Zibrowius

Benchmarks in Leipzig : a collection of questions in research-level mathematics

ArXiv: 2606.05818
Academic
2026
Leonie Kayser

Computation and complexity in algebraic geometry

Dissertation, Universität Leipzig, 2026
Preprint
2026 Repository Open Access
Eric Pichon-Pharabod and Simon Telen

Galois groups of symmetric cubic surfaces

ArXiv: 2509.06785
Preprint
2026 Repository Open Access
Barbara Betti, Sean Grate, Thiago Holleben and Flavio Salizzoni

Incidence toric ideals and three-point functions

ArXiv: 2605.23849
inJournal
2026 Journal Open Access
Francesco Maria Mascarin and Simon Telen

Lissajous varieties

In: Advances in geometry, 26 (2026) 2, pp. 263-282
DOI: 10.1515/advgeom-2026-0008 ArXiv: 2509.06844
inJournal
2026 Journal Open Access
Veronica Calvo Cortes and Simon Telen

Positive charts of toric varieties

In: Collectanea mathematica, (2026)
DOI: 10.1007/s13348-026-00518-x ArXiv: 2602.16414
Preprint
2026 Repository Open Access
Bernd Sturmfels and Simon Telen

Positive geometries from cubic surfaces

ArXiv: 2605.11909
Preprint
2026 Repository Open Access
Saiei-Jaeyeong Matsubara-Heo and Simon Telen

Principal matroid determinants

ArXiv: 2604.24667
inJournal
2026 Repository Open Access
Suresh Govindarajan, Aditya Jain, Akhila Sadanandan and Abhiram Kidambi

S-matrices in the holomorphic modular bootstrap approach

In: Physics letters / B, 878 (2026), p. 140514
DOI: 10.1016/j.physletb.2026.140514 ArXiv: 2602.14665
Preprint
2026 Repository Open Access
Monique Laurent, Francesco Maria Mascarin and Simon Telen

The algebraic boundary of graph elliptopes

ArXiv: 2605.02484
inJournal
2026 Repository Open Access
Jane Ivy Coons, Heather A. Harrington and Niharika Chakrabarty Paul

Combinatorial geometry of rational quasi-independence models as toric fiber products

In: Algebraic statistics, 17 (2026) 1, pp. 1-31
BibTex DOI: 10.2140/astat.2026.17.1 ArXiv: 2405.13897
inJournal
2026 Journal Open Access
Simon Telen

Toric amplitudes and universal adjoints

In: The journal of the London Mathematical Society, 113 (2026) 2, e70468
BibTex DOI: 10.1112/jlms.70468 ArXiv: 2504.00897 Code: mathrepo.mis.mpg.de
Academic
2025 Repository Open Access
Barbara Betti

Khovanskii and Gröbner degenerations in computational commutative algebra

Dissertation, Universität Leipzig, 2025
Link: nbn-resolving.org
inJournal
2025
Celia Hacker, Leonie Kayser and Mireille Soergel

Queer in Math Day 2024 : held at the Max Planck Institute for Mathematics in the Sciences (MPI-MiS), Leipzig, June 6, 2024

In: Mitteilungen der Deutschen Mathematiker-Vereinigung, 33 (2025) 1, pp. 51-55
DOI: 10.1515/dmvm-2025-0015
inJournal
2025 Repository Open Access
Kathlén Kohn, Ragni Piene, Kristian Ranestad, Felix Rydell, Boris Shapiro, Rainer Sinn, Miruna-Stefana Sorea and Simon Telen

Adjoints and canonical forms of polypols

In: Documenta mathematica, 30 (2025) 2, pp. 275-346
BibTex DOI: 10.4171/DM/991 ArXiv: 2108.11747 Code: mathrepo.mis.mpg.de
inJournal
2025 Journal Open Access
Eliana Duarte, Dmitrii Pavlov and Maximilian Wiesmann

Algebraic geometry of quantum graphical models

In: Advances in applied mathematics, 170 (2025), p. 102930
BibTex DOI: 10.1016/j.aam.2025.102930 ArXiv: 2308.11538 Code: mathrepo.mis.mpg.de
inJournal
2025 Repository Open Access
Zaïneb Bel-Afia, Chiara Meroni and Simon Telen

Chebyshev varieties

In: Mathematics of computation, 95 (2026), pp. 2061-2089
BibTex DOI: 10.1090/mcom/4125 ArXiv: 2401.12140
inBook
2025 Journal Open Access
Leonie Kayser

Computational complexity of polynomial subalgebras

In: ISSAC '25 : proceedings of the 2025 international symposium on symbolic and algebraic computation / Carlos D’Andrea... (eds.)
New York, NY : ACM, 2025. - pp. 337 - 344
BibTex DOI: 10.1145/3747199.3747578 ArXiv: 2502.05278 Code: mathrepo.mis.mpg.de
Preprint
2025 Repository Open Access
Marta Casanellas, Jennifer Garbett, Roser Homs, Annachiara Korchmaros and Niharika Chakrabarty Paul

Computing phylogenetic invariants for time-reversible models : from TN93 to its submodels

BibTex ArXiv: 2505.20526
Preprint
2025 Repository Open Access
Abhiram Kidambi, Elke Neuhaus and İrem Portakal

Elliptic curves in game theory

BibTex ArXiv: 2501.14612 Code: mathrepo.mis.mpg.de
inJournal
2025 Journal Open Access
Barbara Betti, Alessio Moscariello, Francesco Romeo and Jyoti Singh

F-threshold of determinantal rings

In: Communications in algebra, 53 (2025) 6, pp. 2278-2291
BibTex DOI: 10.1080/00927872.2024.2434666 ArXiv: 2309.17376
Preprint
2025 Repository Open Access
Barbara Betti, Viktoriia Borovik, Bella Finkel, Bernd Sturmfels and Bailee Zacovic

Graphical scattering equations

BibTex ArXiv: 2511.07316
inJournal
2025 Journal Open Access
Fulvio Gesmundo, Leonie Kayser and Simon Telen

Hilbert functions of chopped ideals

In: Journal of algebra, 666 (2025), pp. 415-445
BibTex DOI: 10.1016/j.jalgebra.2024.11.017 ArXiv: 2307.02560 MiS Preprint Code: mathrepo.mis.mpg.de
inJournal
2025 Journal Open Access
Elia Mazzucchelli, Dmitrii Pavlov and Kexin Wang

Hyperplane arrangements in the Grassmannian

In: Le Matematiche, 80 (2025) 1, pp. 387-408
BibTex ArXiv: 2409.04288 Link: lematematiche.dmi.unict.it Code: mathrepo.mis.mpg.de
inJournal
2025 Journal Open Access
Leonie Kayser, Andreas Kretschmer and Simon Telen

Logarithmic discriminants of hyperplane arrangements

In: Le Matematiche, 80 (2025) 1, pp. 325-346
BibTex ArXiv: 2410.11675 Link: lematematiche.dmi.unict.it Code: mathrepo.mis.mpg.de
inJournal
2025 Journal Open Access
Barbara Betti and Leonie Kayser

Mukai lifting of self-dual points in \(\mathbb{P}^6\)

In: Experimental mathematics, (2025)
BibTex DOI: 10.1080/10586458.2025.2513603 ArXiv: 2406.02734 Code: mathrepo.mis.mpg.de
inJournal
2025 Journal Open Access
Abhiram Kidambi, Masaki Okada and Taizan Watari

Notes on characterizations of 2d rational SCFTs : algebraicity, mirror symmetry, and complex multiplication

In: Fortschritte der Physik, 73 (2025) 1/2, p. 2400161
BibTex DOI: 10.1002/prop.202400161 ArXiv: 2408.00861
inJournal
2025 Journal Open Access
Sebastian Falkensteiner, Dmitrii Pavlov and Rafael Sendra

On real and observable rational realizations of input-output equations

In: Systems and control letters, 198 (2025), p. 106059
BibTex DOI: 10.1016/j.sysconle.2025.106059 ArXiv: 2303.16799
Preprint
2025 Repository Open Access
Eric Pichon-Pharabod

Periods of fibre products of elliptic surfaces and the Gamma conjecture

BibTex ArXiv: 2505.07685
Preprint
2025 Repository Open Access
Simon Telen

Positive geometry of polytopes and polypols

BibTex ArXiv: 2506.05510
inJournal
2025 Journal Open Access
Barbara Betti, Viktoriia Borovik and Simon Telen

Proudfoot-Speyer degenerations of scattering equations

In: Le Matematiche, 80 (2025) 1, pp. 143-165
BibTex ArXiv: 2410.03614 Link: lematematiche.dmi.unict.it Code: mathrepo.mis.mpg.de
inJournal
2025 Repository Open Access
Dmitrii Pavlov and Simon Telen

Santaló geometry of convex polytopes

In: SIAM journal on applied algebra and geometry, 9 (2025) 1, pp. 58-82
BibTex DOI: 10.1137/24M1643566 ArXiv: 2402.18955 Code: mathrepo.mis.mpg.de
inJournal
2025 Journal Open Access
Barbara Betti, Marta Panizzut and Simon Telen

Solving equations using Khovanskii bases

In: Journal of symbolic computation, 126 (2025), p. 102340
BibTex DOI: 10.1016/j.jsc.2024.102340 ArXiv: 2306.14871 Code: mathrepo.mis.mpg.de
inJournal
2025 Repository Open Access
Paul Breiding, Mateusz Michałek, Leonid Monin and Simon Telen

The algebraic degree of coupled oscillators

In: Advances in mathematics, 480 (2025) Part B, p. 110492
BibTex DOI: 10.1016/j.aim.2025.110492 ArXiv: 2208.08179
Preprint
2025 Repository Open Access
Barbara Betti and Viktoriia Borovik

The SagbiHomotopy.jl package for solving polynomial systems

BibTex ArXiv: 2506.06264 Code: mathrepo.mis.mpg.de
Preprint
2025 Repository Open Access
Elke Neuhaus, İrem Portakal and Niharika Chakrabarty Paul

Torus actions on matrix Schubert and Kazhdan-Lusztig varieties, and their links to statistical models

BibTex ArXiv: 2510.00250
inBook
2025 Repository Open Access
Kemal Rose, Bernd Sturmfels and Simon Telen

Tropical implicitization revisited

In: The computer algebra system OSCAR : algorithms and examples / Wolfram Decker... (eds.)
Cham : Springer, 2025. - pp. 429-450
(Algorithms and computation in mathematics ; 32)
BibTex DOI: 10.1007/978-3-031-62127-7_17 ArXiv: 2306.13015 Code: mathrepo.mis.mpg.de
inJournal
2025 Repository Open Access
Saiei-Jaeyeong Matsubara-Heo and Simon Telen

Twisted cohomology and likelihood ideals

In: Advances in applied mathematics, 165 (2025), p. 102832
BibTex DOI: 10.1016/j.aam.2024.102832 ArXiv: 2301.13579 Code: mathrepo.mis.mpg.de
inJournal
2025 Journal Open Access
Kristian Ranestad, Bernd Sturmfels and Simon Telen

What is positive geometry?

In: Le Matematiche, 80 (2025) 1, pp. 3-16
BibTex DOI: 10.4418/2025.80.1.1 ArXiv: 2502.12815
inBook
2025 Repository Open Access
Matías R. Bender and Simon Telen

Yet another eigenvalue algorithm for solving polynomial systems

In: Varieties, polyhedra, computation / Peter Bürgisser... (eds.)
Berlin : EMS Press, 2025. - pp. 355-394
(EMS series of congress reports ; 22)
BibTex DOI: 10.4171/ECR/22 ArXiv: 2105.08472
inJournal
2024 Repository Open Access
Kristian Ranestad, Rainer Sinn and Simon Telen

Adjoints and canonical forms of tree amplituhedra

In: Mathematica Scandinavica, 130 (2024) 3, pp. 433-466
BibTex DOI: 10.7146/math.scand.a-149816 ArXiv: 2402.06527
inJournal
2024 Repository Open Access
Mareike Dressler, Marina Garrote-López, Guido Montúfar, Kemal Rose and Johannes Müller

Algebraic optimization of sequential decision problems

In: Journal of symbolic computation, 121 (2024), p. 102241
BibTex DOI: 10.1016/j.jsc.2023.102241 ArXiv: 2211.09439
Preprint
2024 Repository Open Access
Simon Telen and Maximilian Wiesmann

Euler stratifications of hypersurface families

BibTex ArXiv: 2407.18176 Code: mathrepo.mis.mpg.de
inJournal
2024 Journal Open Access
Dmitrii Pavlov, Bernd Sturmfels and Simon Telen

Gibbs manifolds

In: Information geometry, 7 (2024) 2 supplement, pp. 691-717
BibTex DOI: 10.1007/s41884-023-00111-2 ArXiv: 2211.15490 Code: mathrepo.mis.mpg.de
inJournal
2024 Repository Open Access
Claudia Fevola, Sebastian Mizera and Simon Telen

Landau singularities revisited : computational algebraic geometry for Feynman integrals

In: Physical review letters, 132 (2024) 10, p. 101601
BibTex DOI: 10.1103/PhysRevLett.132.101601 ArXiv: 2311.14669 Code: mathrepo.mis.mpg.de
inJournal
2024 Journal Open Access
Dmitrii Pavlov

Logarithmically sparse symmetric matrices

In: Beiträge zur Algebra und Geometrie, 65 (2024) 4, pp. 907-922
BibTex DOI: 10.1007/s13366-024-00753-y ArXiv: 2301.10042
inJournal
2024 Repository Open Access
Timothy Duff, Simon Telen, Elise Walker and Thomas Yahl

Polyhedral homotopies in Cox coordinates

In: Journal of algebra and its applications, 23 (2024) 4, p. 2450073
BibTex DOI: 10.1142/S0219498824500737 ArXiv: 2012.04255 Code: mathrepo.mis.mpg.de
inJournal
2024 Repository Open Access
Claudia Fevola, Sebastian Mizera and Simon Telen

Principal Landau determinants

In: Computer physics communications, 303 (2024), p. 109278
BibTex DOI: 10.1016/j.cpc.2024.109278 ArXiv: 2311.16219 Code: mathrepo.mis.mpg.de
Academic
2024 Repository Open Access
Dmitrii Pavlov

Real algebraic geometry for physics and optimization

Dissertation, Universität Leipzig, 2024
BibTex Link: nbn-resolving.org
Academic
2024 Repository Open Access
Kemal Rose

Sparse polynomial system(s) in optimization

Dissertation, Universität Leipzig, 2024
BibTex Link: nbn-resolving.org
Preprint
2024 Repository Open Access
Kemal Rose

The polyhedral type of a polynomial map on the plane

BibTex ArXiv: 2402.08993 Code: mathrepo.mis.mpg.de
inJournal
2024 Repository Open Access
Bernd Sturmfels, Simon Telen, François-Xavier Vialard and Max von Renesse

Toric geometry of entropic regularization

In: Journal of symbolic computation, 120 (2024), p. 102221
BibTex DOI: 10.1016/j.jsc.2023.102221 ArXiv: 2202.01571
inJournal
2024 Repository Open Access
Daniele Agostini, Claudia Fevola, Anna-Laura Sattelberger and Simon Telen

Vector spaces of generalized Euler integrals

In: Communications in number theory and physics, 18 (2024) 2, pp. 327-370
BibTex DOI: 10.4310/CNTP.2024.v18.n2.a2 ArXiv: 2208.08967 Code: mathrepo.mis.mpg.de
inJournal
2023 Journal Open Access
Yannik Mahlau, Leonie Kayser and Lukas Berg

[Re] On explainability of graph neural networks via subgraph explorations

In: ReScience C, 9 (2023) 2, p. 41
BibTex DOI: 10.5281/zenodo.8173753 Link: rescience.github.io Code: github.com
Preprint
2023 Repository Open Access
Julia Lindberg, Leonid Monin and Kemal Rose

A polyhedral homotopy algorithm for computing critical points of polynomial programs

BibTex ArXiv: 2302.04117
inJournal
2023 Repository Open Access
Michael Borinsky, Anna-Laura Sattelberger, Bernd Sturmfels and Simon Telen

Bayesian integrals on toric varieties

In: SIAM journal on applied algebra and geometry, 7 (2023) 1, pp. 77-103
BibTex DOI: 10.1137/22M1490569 ArXiv: 2204.06414 Code: mathrepo.mis.mpg.de
Preprint
2023 Repository Open Access
Yelena Mandelshtam, Dmitrii Pavlov and Elizabeth Pratt

Combinatorics of \(m=1\) Grasstopes

BibTex ArXiv: 2307.09603 Code: mathrepo.mis.mpg.de
inJournal
2023 Repository Open Access
Rob Claes, Karl Meerbergen and Simon Telen

Contour integration for eigenvector nonlinearities

In: SIAM journal on matrix analysis and applications, 44 (2023) 4, pp. 1619-1644
BibTex DOI: 10.1137/22M1497985 ArXiv: 2205.12367
inJournal
2023 Journal Open Access
Saiei-Jaeyeong Matsubara-Heo, Sebastian Mizera and Simon Telen

Four lectures on Euler integrals

In: SciPost physics lecture notes, 2023 (2023), p. 75
BibTex DOI: 10.21468/SciPostPhysLectNotes.75 ArXiv: 2306.13578
inJournal
2023 Repository Open Access
Daniele Agostini, Taylor Brysiewicz, Claudia Fevola, Lukas Kühne, Bernd Sturmfels and Simon Telen

Likelihood degenerations

In: Advances in mathematics, 414 (2023), p. 108863
BibTex DOI: 10.1016/j.aim.2023.108863 ArXiv: 2107.10518 Code: mathrepo.mis.mpg.de
inJournal
2023 Repository Open Access
Rida Ait El Manssour, Yassine El Maazouz, Enis Kaya and Kemal Rose

Lines on \(p\)-adic and real cubic surfaces

In: Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg, 93 (2023) 2, pp. 149-162
BibTex DOI: 10.1007/s12188-023-00269-7 ArXiv: 2202.03489 Code: mathrepo.mis.mpg.de
Preprint
2023 Repository Open Access
Julia Lindberg, Leonid Monin and Kemal Rose

The algebraic degree of sparse polynomial optimization

BibTex ArXiv: 2308.07765