Publications
101 items — books, preprints, journal articles, refereed conference papers and surveys. Entries link to arXiv and, where published, to the DOI.
Books (1) Preprints (8) Journal articles (80) Refereed conference publications (1) Other (11)
Curriculum vitae
Full curriculum vitae — positions, education, honours, funding, students, invited talks and service.
Books
- Invitation to Nonlinear Algebra
Preprints
- A counterexample to Purdy's inequality for hyperplane arrangements in projective three-space
- The Gröbner Version of White's Conjecture is False
- Vertex Posets, Monotone Path Polytopes, and Chow Polynomials
- Nonlinear methods for tensors: determinantal equations for secant varieties beyond cactus
- Linear operators preserving volume polynomials
- Realizations of homology classes and projection areas
- Mixed Eulerian numbers and beyond
- White's conjecture for matroids and inner projections
Journal articles
2026
- On the maximum likelihood degree of Gaussian graphical modelsto appear in Bulletin of the London Mathematical Society (2026)
- Degree of the Gaussian graphical model of the cycleto appear in Forum of Mathematics: Sigma (2026)
- Characteristic numbers and chromatic polynomial of a tensorForum of Mathematics: Sigma 14 (2026), e108
- Sullivant-Talaska ideal of the cyclic Gaussian Graphical ModelAdvances in Applied Mathematics 179 (2026)
2025
- The Algebraic Degree of Coupled OscillatorsAdvances in Mathematics 480 (2025)
- Topological classification of driven-dissipative nonlinear systemsScience Advances Vol 11, Issue 33 (2025)
- Towards finding hay in a haystack: explicit tensors of border rank greater than 2.02m in ℂm⊗ℂm⊗ℂmTheory of Computing 21.1 (2025)
- Symmetric powers: structure, smoothability, and applicationsInternational Mathematics Research Notices, Issue 18 (2025)
- On the codimension of permanental varietiesAdvances in Mathematics 461 (2025)
- Applications of intersection theory: from maximum likelihood to chromatic polynomialsEinstein Semester Proceedings ”Varieties, Polyhedra, Computation”, EMS (2025)
- Polynomial systems admitting a simultaneous solutionJournal of Algebra 667 (2025)
2024
- Complete quadrics: Schubert calculus for Gaussian models and semidefinite programmingJournal of the European Mathematical Society 26, no. 8, (2024), 3091-3135
- Khovanskii bases for semimixed systems of polynomial equations – a case of approximating stationary nonlinear Newtonian dynamicsJournal de Mathématiques Pures et Appliquées 182, (2024), 195-222
2023
- Equivariant Euler characteristics on permutohedral varietiesto appear in the proceedings of the workshop: The Strong and Weak Lefschetz Properties 12-16 September 2022, Springer INdAM Series, (2023)
- Identifiability for mixtures of centered Gaussians and sums of powers of quadraticsBulletin of the London Mathematical Society 55, (2023), 2407-2424
- Algebraic compressed sensingApplied and Computational Harmonic Analysis 65, (2023), 374-406
- Enumerative geometry meets statistics, combinatorics and topologyNotices of the American Mathematical Society 70(4) (2023)
- Uniform matrix product states from an algebraic geometer's point of viewAdvances in Applied Mathematics 142 (2023)
- Gorenstein MatroidsInternational Mathematics Research Notices, 2023, Issue 18, (2023) 15687-15728
2022
- Many faces of symmetric edge polytopesThe Electronic Journal of Combinatorics 29(3)(2022), 1-42
- Bounds on complexity of matrix multiplication away from CW tensorsJournal of Pure and Applied Algebra 226 (12) (2022)
- Equations for GL-invariant families of polynomialsVietnam Journal of Mathematics 50 (2022), 545-556
- A note on seminormality of cut polytopesSIAM J. on Discrete Mathematics 36 (1) (2022)
- Ideals of Spaces of Degenerate MatricesLinear Algebra and its Applications 648 (2022), 56-69
- Positivity Certificates via Integral Representationsin Facets of Algebraic Geometry: A Volume in Honour of William Fulton's 80th Birthday, Vol 2, Cambridge University Press (2022), 84–114
- Flag matroids: algebra and geometryInteractions with Lattice Polytopes, A. Kasprzyk and B. Nill eds., Springer (2022)
2021
- Best k-layer neural network approximationsConstructive Approximation 55 (2021), 583-604
- Maximum likelihood degree and space of orbits of a ℂ* actionSIAM Journal on Applied Algebra and Geometry 5, no. 1 (2021), 60-85
- Border rank non-additivity for higher order tensorsSIAM Journal on Matrix Analysis and Applications 42, no. 2 (2021), 503-527
- Gorenstein graphic matroidsIsrael Journal of Mathematics 243 (2021), 1-26
2020
- Toric geometry of path signature varietiesAdvances in Applied Mathematics 121, (2020)
- Circulant matrices and Galois-Togliatti systemsJournal of Pure and Applied Algebra 224, no. 11, (2020)
- Vanishing Hessian, wild forms and their border VSPMathematische Annalen 378, (2020), 1505-1532
- Complex best r-term approximations almost always exist in finite dimensionsApplied and Computational Harmonic Analysis 49, no. 1, (2020), 180-207
- Secant varieties of toric varieties arising from simplicial complexesLinear Algebra and its Applications 588, (2020), 428-457
2019
- Computing images of polynomial mapsAdvances in Computational Mathematics 45, no. 5, (2019), 2845-2865
- A tensor version of the quantum Wielandt theoremSIAM Journal on Matrix Analysis and Applications 40, (2019),1125-1130
- When is a polynomial ideal binomial after an ambient automorphism?Foundations of Computational Mathematics 19, (2019),1363-1385
- Quantum version of Wielandt's Inequality revisitedIEEE Transactions on Information Theory 65, no. 8, (2019), 5239-5242
- Arithmetic aspects of symmetric edge polytopesMathematika 65, no. 3, (2019), 763-784
- Constructions of k-regular maps using finite local schemesJournal of the European Mathematical Society 21, no. 6, (2019), 1775-1808
- Phylogenetic complexity of the Kimura 3-parameter modelAdvances in Mathematics 343, (2019), 640-680
- Smooth centrally symmetric polytopes in dimension 3 are IDPAnnals of Combinatorics 23, no. 2, (2019), 255-262
2018
- Spaces of Sums of Powers and Real Rank BoundariesContributions to Algebra and Geometry 59, no. 4, (2018), 645-663
- Flexible affine cones and flexible coveringsMathematische Zeitschrift 290, no. 3-4, (2018), 1457-1478
- A 2n2−log(n)−1 lower bound for the border rank of matrix multiplicationInternational Mathematics Research Notices 2018, no. 15, (2018), 4722-4733
- Obstructions to combinatorial formulas for plethysmElectronic Journal of Combinatorics 25 no. 1, (2018)
- The poset of rational conesPacific Journal of Mathematics 292, (2018), 103-115
2017
- Interlacing Ehrhart Polynomials of Reflexive PolytopesSelecta Mathematica 23 no. 4, (2017), 2977–2998
- Abelian tensorsJournal de Mathématiques Pures et Appliquées 108 no. 3, (2017), 333–371
- Local equations for equivariant evolutionary modelsAdvances in Mathematics 315, (2017), 285–323
- Examples of k-regular maps and interpolation spacesLinear Algebra and its Applications 530, (2017), 94–108
- Real Rank Geometry of Ternary FormsAnnali di Matematica Pura ed Applicata 196 no. 3, (2017), 1025–1054
- On the geometry of border rank algorithms for matrix multiplication and other tensors with symmetrySIAM Journal on Applied Algebra and Geometry 1 no. 1 (2017), 2–19
- Finite phylogenetic complexity and combinatorics of tablesAlgebra & Number Theory 11 no. 1 (2017), 235-252
- Finite phylogenetic complexity of ℤp and invariants for ℤ3European Journal of Combinatorics 59 (2017), 169-186
- Non-normal very ample polytopes - constructions and examplesExperimental Mathematics 26 no. 2 (2017), 130–137
2016
- Quantum jumps of normal polytopesDiscrete and Computational Geometry 56 no. 1 (2016), 181-215
- Smooth monomial Togliatti systems of cubicsJournal of Combinatorial Theory, Series A 143 (2016), 66-87
- Exponential varietiesProceedings of London Mathematical Society 112 no. 1 (2016), 27-56
- Plethysm and lattice point countingFoundations of Computational Mathematics 16 no. 5 (2016), 1241-1261
2015
- Hackbusch Conjecture on tensor formatsJournal de Mathématiques Pures et Appliquées 104 (2015) no. 4, 749–761
- Secant cumulants and toric geometryInternational Mathematics Research Notices 2015 no. 12 (2015) 4019-4063
- Secants of minuscule and cominuscule minimal orbitsLinear Algebra and its Applications 481 (2015) 288–312
- Very ample and Koszul segmental fibrationsJournal of Algebraic Combinatorics 42 (2015) no. 1, 165–182
- Toric varieties in phylogeneticsDissertationes Mathematicae 511 (2015), 3–86
- Low degree equations for phylogenetic group-based modelsCollectanea Mathematica 66 (2015), no. 2, 203–225
2014
- On the toric ideal of a matroidAdvances in Mathematics 259 (2014), 1–12
- Effective constructions in plethysms and Weintraub's conjectureAlgebras and Representation Theory (2014), 1–11
- Toric geometry of the 3-Kimura model for any treeAdvances in Geometry 14 (2014), no. 1, 11-30
2013
- Constructive degree bounds for group-based modelsJournal of Combinatorial Theory, Series A 120 (2013), no. 7, 1672–1694
- On the graph labellings arising from phylogeneticsCentral European Journal of Mathematics 11.9 (2013), 1577-1592
2012
- Birational maps between Calabi-Yau manifolds associated to webs of quadricsJournal of Algebra 370 (2012), 186-197
- Phylogenetic invariants for group-based modelsJournal of Algebraic Statistics 3 (2012), no. 1, 44-63
2011
- Geometry of phylogenetic group-based modelsJournal of Algebra 339 (2011), no. 1, 339–356
- On the full, strongly exceptional collections on toric varieties with Picard number threeCollectanea Mathematica 62, no. 3 (2011), 275-296
- Family of counterexamples to King's conjectureComptes Rendus Mathematique 349, no. 1 (2011), 67-69
2010
- A short proof of Combinatorial NullstellensatzThe American Mathematical Monthly 117, no. 9 (2010), 821-823
2009
- Splitting necklaces and measurable colorings of the real lineProceedings of the American Mathematical Society 137.5 (2009), 1593-1599
- Derived category of toric varieties with Picard number threeLe Matematiche 64(2) (2009), 99-116
Refereed conference publications
In theoretical computer science, refereed conference proceedings are the primary form of publication, with acceptance rates comparable to or below those of leading journals.
- A universal sequence of tensors for the asymptotic rank conjectureInnovations in Theoretical Computer Science (ITCS 2025), New York, LIPIcs, article no. 64
Other
- Tensors: From complex problems to real applications.Combinatorial, Computational, and Applied Algebraic Geometry: A Tribute to Bernd Sturmfels 111 (2025): 307
- Oberwolfach report 'Symmetric Edge Polytopes'
- Oberwolfach report 'Can local cohomology prevent injections?'
- Tensoren und ihre ZerlegungenForschungsbericht 2018 MPI MiS
- Review of the book “Geometry and Complexity Theory” by JM LandsbergBulletin of the American Mathematical Society - invited review
- Introduction to "Schubert varieties, equivariant cohomology and characteristic classes, IMPANGA15 volume"EMS Ser. Congr. Rep., Eur. Math. Soc., 2018
- Selected Topics on Toric VarietiesProceedings of the MSJ SI 2015
- Oberwolfach report 'Normal and Very Ample Polytopes – old and new open problems'
- Oberwolfach report No. 19/2016 'Toric structures in nontoric varieties'
- Notes on Kebekus lectures on differential forms on singular spacesImpanga Lecture Notes: Contributions to algebraic geometry, 375-388, EMS Ser. Congr. Rep., Eur. Math. Soc., 2012
- Introduction to commutative algebrafrom English to Polish, jointly with Wojciech Lubawski