Combinatorial Algebraic Geometry
Head:
Mateusz Michałek (Email)
Phone:
+49 (0) 341 - 9959 - 800
Fax:
+49 (0) 341 - 9959 - 658
Address:
Inselstr. 22
04103 Leipzig
Publications Mateusz Michałek
Journal Articles 
Czapliński, A. ; Michałek, M. and Seynnaeve, T.:
Uniform matrix product states from an algebraic geometer's point of view.
Advances in applied mathematics,
142 (2023), 102417 Bibtex MIS-Preprint: 38/2019 [DOI] [ARXIV] Repository Open Access
Breiding, P. ; Hodges, R. ; Ikenmeyer, C. and Michałek, M.:
Equations for GL invariant families of polynomials.
Vietnam journal of mathematics,
50 (2022) 2, p. 545-556 Bibtex [DOI] [ARXIV] Journal Open Access
D'Alì, A. ; Delucchi, E. and Michałek, M.:
Many faces of symmetric edge polytopes.
The electronic journal of combinatorics,
29 (2022) 3, P3.24 Bibtex [DOI] [ARXIV] Journal Open Access
Lim, L.-H. ; Michałek, M. and Qi, Y.:
Best \(k\)-layer neural network approximations.
Constructive approximation,
55 (2022) 1, p. 583-604 Bibtex MIS-Preprint: 55/2019 [DOI] [ARXIV] Repository Open Access
Christandl, M. ; Gesmundo, F. ; Michałek, M. and Zuiddam, J.:
Border rank non-additivity for higher order tensors.
SIAM journal on matrix analysis and applications,
42 (2021) 2, p. 503-527 Bibtex [DOI] [ARXIV] Repository Open Access
Hibi, T. ; Lasoń, M. ; Matsuda, K. ; Michałek, M. and Vodička, M.:
Gorenstein graphic matroids.
Israel journal of mathematics,
243 (2021) 1, p. 1-26 Bibtex MIS-Preprint: 22/2020 [DOI] [ARXIV] Repository Open Access
Michałek, M. ; Monin, L. and Wiśniewski, J.:
Maximum likelihood degree, complete quadrics and \({\mathbb C}^*\)-action.
SIAM journal on applied algebra and geometry,
5 (2021) 1, p. 60-85 Bibtex [DOI] [ARXIV] [CODELINK] Repository Open Access
Colmenarejo, L. ; Galuppi, F. and Michałek, M.:
Toric geometry of path signature varieties.
Advances in applied mathematics,
121 (2020), 102102 Bibtex MIS-Preprint: 28/2019 [DOI] [ARXIV] Repository Open Access
De Poi, P. ; Mezzetti, E. ; Michałek, M. ; Miró-Roig, R. M.
and Nevo, E.:
Circulant matrices and Galois-Togliatti systems.
Journal of pure and applied algebra,
224 (2020) 11, 106404 Bibtex MIS-Preprint: 74/2018 [DOI] [ARXIV] Repository Open Access
Huang, H. ; Michałek, M. and Ventura, E.:
Vanishing Hessian, wild forms and their border VSP.
Mathematische Annalen,
378 (2020) 3/4, p. 1505-1532 Bibtex MIS-Preprint: 2/2020 [DOI] [ARXIV] Journal Open Access
Khadam, M. A.
; Michałek, M. and Zwiernik, P.:
Secant varieties of toric varieties arising from simplicial complexes.
Linear algebra and its applications,
588 (2020), p. 428-457 Bibtex MIS-Preprint: 81/2019 [DOI] [ARXIV] Repository Open Access
Michałek, M.:
Book review: 'Geometry and complexity theory', by J. M. Landsberg, Cambridge University
Press, 2017.
Bulletin of the American Mathematical Society,
57 (2020) 2, p. 317-324 Bibtex [DOI] Journal Open Access
Qi, Y. ; Michałek, M. and Lim, L.-H.:
Complex best \(r\)-term approximations almost always exist in finite dimensions.
Applied and computational harmonic analysis,
49 (2020) 1, p. 180-207 Bibtex MIS-Preprint: 79/2017 [DOI] [ARXIV] Repository Open Access
Vodička, M. ; Manivel, L. ; Michałek, M. ; Monin, L. and Seynnaeve, T.:
Complete quadrics and linear spaces of symmetric matrices [In: Lefschetz properties
in algebra, geometry and combinatorics ; 27 September - 3 October 2020 ; report no.
31/2020].
Oberwolfach reports,
17 (2020) 4, p. 1577-1579 Bibtex [DOI] [FREELINK] Repository Open Access
Beck, M. ; Haase, C. ; Higashitani, A. ; Hofscheier, J. ; Jochemko, K. ; Katthän, L. and Michałek, M.:
Smooth centrally symmetric polytopes in dimension 3 are IDP.
Annals of combinatorics,
23 (2019) 2, p. 255-262 Bibtex MIS-Preprint: 18/2018 [DOI] [ARXIV] Repository Open Access
Buczyński, J. ; Januszkiewicz, T. ; Jelisiejew, J. and Michałek, M.:
Constructions of \(k\)-regular maps using finite local schemes.
Journal of the European Mathematical Society,
21 (2019) 6, p. 1775-1808 Bibtex [DOI] [ARXIV] Repository Open Access
Harris, C. ; Michałek, M. and Sertöz, E. C.
:
Computing images of polynomial maps.
Advances in computational mathematics,
45 (2019) 5/6, p. 2845-2865 Bibtex MIS-Preprint: 2/2018 [DOI] [ARXIV] Journal Open Access
Higashitani, A. ; Jochemko, K. and Michałek, M.:
Arithmetic aspects of symmetric edge polytopes.
Mathematika : a journal of pure and applied mathematics,
65 (2019) 3, p. 763-784 Bibtex MIS-Preprint: 59/2018 [DOI] [ARXIV] Repository Open Access
Katthän, L. ; Michałek, M. and Miller, E.:
When is a polynomial ideal binomial after an ambient automorphism?.
Foundations of computational mathematics,
19 (2019) 6, p. 1363-1385 Bibtex MIS-Preprint: 36/2017 [DOI] [ARXIV] Journal Open Access
Michałek, M.:
Can local cohomology prevent injections? [In: Singularities and homological aspects
of commutative algebra ; 10 February - 16 February 2019 ; report no. 6/2019].
Oberwolfach reports,
16 (2019) 1, p. 443-445 Bibtex [DOI] [FREELINK] Repository Open Access
Michałek, M. ; Higashitani, A. ; Jochemko, K. and Kummer, M.:
Symmetric edge polytopes [In: Toric geometry ; 22 September - 28 September 2019 ;
report no. 43/2019].
Oberwolfach reports,
16 (2019) 3, p. 2710-2711 Bibtex [DOI] [FREELINK] Repository Open Access
Michałek, M. ; Seynnaeve, T. and Verstraete, F.:
A tensor version of the quantum Wielandt theorem.
SIAM journal on matrix analysis and applications,
40 (2019) 3, p. 1125-1130 Bibtex MIS-Preprint: 96/2018 [DOI] [ARXIV] Journal Open Access
Michałek, M. and Shitov, Y.:
Quantum version of Wielandt's inequality revisited.
IEEE transactions on information theory,
65 (2019) 8, p. 5239-5242 Bibtex MIS-Preprint: 79/2018 [DOI] [ARXIV] Repository Open Access
Michałek, M. and Ventura, E.:
Phylogenetic complexity of the Kimura 3-parameter model.
Advances in mathematics,
343 (2019), p. 640-680 Bibtex MIS-Preprint: 27/2017 [DOI] [ARXIV] Repository Open Access
Gubeladze, J. and Michałek, M.:
The poset of rational cones.
Pacific journal of mathematics,
292 (2018) 1, p. 103-115 Bibtex [DOI] [ARXIV] Repository Open Access
Kahle, T. and Michałek, M.:
Obstructions to combinatorial formulas for plethysm.
The electronic journal of combinatorics,
25 (2018) 1, P1.41 Bibtex [DOI] [ARXIV] Journal Open Access
Landsberg, J. M. and Michałek, M.:
A \(2n^2 - log_2(n) - 1\) lower bound for the border rank of matrix multiplication.
International mathematics research notices,
2018 (2018) 15, p. 4722-4733 Bibtex [DOI] [ARXIV] Journal Open Access
Michałek, M. and Moon, H.:
Spaces of sums of powers and real rank boundaries.
Beiträge zur Algebra und Geometrie,
59 (2018) 4, p. 645-663 Bibtex MIS-Preprint: 9/2017 [DOI] [ARXIV] Journal Open Access
Michałek, M. ; Perepechko, A. and Süß, H.:
Flexible affine cones and flexible coverings.
Mathematische Zeitschrift,
290 (2018) 3-4, p. 1457-1478 Bibtex [DOI] [ARXIV] Journal Open Access
Michałek, M. and Sturmfels, B.:
Tensoren und ihre Zerlegungen.
Jahrbuch der Max-Planck-Gesellschaft,
2018 (2018), Forschungsbericht - Max-Planck-Institut für Mathematik in den Naturwissenschaften Bibtex [FREELINK] Repository Open Access
Casanellas, M. ; Fernández-Sánchez, J. and Michałek, M.:
Local equations for equivariant evolutionary models.
Advances in mathematics,
315 (2017), p. 285-323 Bibtex [DOI] [ARXIV] Repository Open Access
Higashitani, A. ; Kummer, M. and Michałek, M.:
Interlacing Ehrhart polynomials of reflexive polytopes.
Selecta mathematica,
23 (2017) 4, p. 2977-2998 Bibtex MIS-Preprint: 7/2017 [DOI] [ARXIV] Journal Open Access
Landsberg, J. M. and Michałek, M.:
On the geometry of border rank decompositions for matrix multiplication and other
tensors with symmetry.
SIAM journal on applied algebra and geometry,
1 (2017) 1, p. 2-19 Bibtex [DOI] [ARXIV] Journal Open Access
Landsberg, J. M. and Michałek, M.:
Abelian tensors.
Journal de mathématiques pures et appliquées,
108 (2017) 3, p. 333-371 Bibtex [DOI] [ARXIV] Repository Open Access
Lasoń, M. and Michałek, M.:
Non-normal very ample polytopes : constructions and examples.
Experimental mathematics,
26 (2017) 2, p. 130-137 Bibtex [DOI] [ARXIV] Repository Open Access
Michałek, M.:
Finite phylogenetic complexity of \(\mathbb{Z}_p\) and invariants for \(\mathbb{Z}_3\).
European journal of combinatorics,
59 (2017), p. 169-186 Bibtex [DOI] [ARXIV] Repository Open Access
Michałek, M. and Miller, C.:
Examples of k-regular maps and interpolation spaces.
Linear algebra and its applications,
530 (2017), p. 94-108 Bibtex [DOI] [ARXIV] Repository Open Access
Michałek, M. ; Moon, H. ; Sturmfels, B. and Ventura, E.:
Real rank geometry of ternary forms.
Annali di matematica pura ed applicata,
196 (2017) 3, p. 1025-1054 Bibtex [DOI] [ARXIV] Journal Open Access
Michałek, M. and Ventura, E.:
Finite phylogenetic complexity and combinatorics of tables.
Algebra and number theory,
11 (2017) 1, p. 235-252 Bibtex [DOI] [ARXIV] Repository Open Access
Bruns, W. ; Gubeladze, J. and Michałek, M.:
Quantum jumps of normal polytopes.
Discrete and computational geometry,
56 (2016) 1, p. 181-215 Bibtex [DOI] [ARXIV] Repository Open Access
Kahle, T. and Michałek, M.:
Plethysm and lattice point counting.
Foundations of computational mathematics,
16 (2016) 5, p. 1241-1261 Bibtex [DOI] [ARXIV] Repository Open Access
Michałek, M.:
Toric structures in nontoric varieties [In: Toric geometry ; 27 March - 2 April 2016
; report no. 19/2016].
Oberwolfach reports,
13 (2016) 2, p. 999-1001 Bibtex [DOI] [FREELINK] Repository Open Access
Michałek, M. and Miró-Roig, R. M.
:
Smooth monomial Togliatti systems of cubics.
Journal of combinatorial theory / A,
143 (2016), p. 66-87 Bibtex [DOI] [ARXIV] Repository Open Access
Michałek, M. ; Sturmfels, B. ; Uhler, C. and Zwiernik, P.:
Exponential varieties.
Proceedings of the London Mathematical Society,
112 (2016) 1, p. 27-56 Bibtex [DOI] [ARXIV] Repository Open Access
Beck, M. ; Delgado, J. ; Gubeladze, J. and Michałek, M.:
Very ample and Koszul segmental fibrations.
Journal of algebraic combinatorics,
42 (2015) 1, p. 165-182 Bibtex [DOI] [ARXIV] Repository Open Access
Buczyńska, W. ; Buczyński, J. and Michałek, M.:
The Hackbusch conjecture on tensor formats.
Journal de mathématiques pures et appliquées,
104 (2015) 4, p. 749-761 Bibtex [DOI] [ARXIV] Repository Open Access
Casanellas, M. ; Fernández-Sánchez, J. and Michałek, M.:
Low degree equations for phylogenetic group-based models.
Collectanea mathematica,
66 (2015) 2, p. 203-225 Bibtex [DOI] [ARXIV] Repository Open Access
Manivel, L. and Michałek, M.:
Secants of minuscule and cominuscule minimal orbits.
Linear algebra and its applications,
481 (2015), p. 288-312 Bibtex [DOI] [ARXIV] Repository Open Access
Michałek, M.:
Toric varieties in phylogenetics.
Dissertationes mathematicae,
2015 (2015) 511, p. 1-86 Bibtex [DOI]
Michałek, M. ; Oeding, L. and Zwiernik, P.:
Secant cumulants and toric geometry.
International mathematics research notices,
2015 (2015) 12, p. 4019-4063 Bibtex [DOI] [ARXIV] Repository Open Access
Lasoń, M. and Michałek, M.:
On the toric ideal of a matroid.
Advances in mathematics,
259 (2014), p. 1-12 Bibtex [DOI] [ARXIV] Repository Open Access
Manivel, L. and Michałek, M.:
Effective constructions in plethysms and Weintraub's conjecture.
Algebras and representation theory,
17 (2014) 2, p. 433-443 Bibtex [DOI] [ARXIV] Repository Open Access
Michałek, M.:
Toric geometry of the 3-Kimura model for any tree.
Advances in geometry,
14 (2014) 1, p. 11-30 Bibtex [DOI] [ARXIV] Repository Open Access
Buczyńska, W. ; Buczyński, J. ; Kubjas, K. and Michałek, M.:
On the graph labellings arising from phylogenetics.
Open mathematics,
11 (2013) 9, p. 1577-1592 Bibtex [DOI] [ARXIV] Journal Open Access
Michałek, M.:
Constructive degree bounds for group-based models.
Journal of combinatorial theory / A,
120 (2013) 7, p. 1672-1694 Bibtex [DOI] [ARXIV] Repository Open Access
Donten-Bury, M. and Michałek, M.:
Phylogenetic invariants for group-based models.
Journal of algebraic statistics,
3 (2012) 1, p. 44-63 Bibtex [DOI] [ARXIV] Journal Open Access
Michałek, M.:
Birational maps between Calabi-Yau manifolds associated to webs of quadrics.
Journal of algebra,
370 (2012), p. 186-197 Bibtex [DOI] [ARXIV] Repository Open Access
Lasoń, M. and Michałek, M.:
On the full, strongly exceptional collections on toric varieties with Picard number
three.
Collectanea mathematica,
62 (2011) 3, p. 275-296 Bibtex [DOI] [ARXIV] Journal Open Access
Michałek, M.:
Geometry of phylogenetic group-based models.
Journal of algebra,
339 (2011) 1, p. 339-356 Bibtex [DOI] [ARXIV] Repository Open Access
Michałek, M.:
Family of counterexamples to King's conjecture.
Comptes rendus mathematique,
349 (2011) 1, p. 67-69 Bibtex [DOI] [ARXIV] Repository Open Access
Michałek, M.:
A short proof of combinatorial Nullstellensatz.
The American mathematical monthly,
117 (2010) 9, p. 821-823 Bibtex [DOI] [ARXIV] Repository Open Access
Alon, N. ; Grytczuk, J. ; Lasoń, M. and Michałek, M.:
Splitting necklaces and measurable colorings of the real line.
Proceedings of the American Mathematical Society,
137 (2009) 5, p. 1593-1599 Bibtex [DOI] [ARXIV] Repository Open Access
Dey, A. ; Lasoń, M. and Michałek, M.:
Derived category of toric varieties with Picard number three.
Le Matematiche,
64 (2009) 2, p. 99-116 Bibtex [ARXIV] [FREELINK] Journal Open Access
Publications in Books and Conference Proceedings
Cameron, A. ; Dinu, R. ; Michałek, M. and Seynnaeve, T.:
Flag matroids : algebra and geometry.
Interactions with lattice polytopes : Magdeburg, Germany, September 2017 / A.
M. Kasprzyk... (eds.). Springer, 2022. - P. 73-114
(Springer proceedings in mathematics and statistics ; 386)
Bibtex MIS-Preprint: 93/2018 [DOI] [ARXIV] Repository Open Access
Kozhasov, K. ; Michałek, M. and Sturmfels, B.:
Positivity certificates via integral representations.
Facets of algebraic geometry : a collection in honor of William Fulton's 80th birthday
; Volume 2 / P.
Aluffi... (eds.). Cambridge University Press, 2022. - P. 84-114 Bibtex MIS-Preprint: 66/2019 [DOI] [ARXIV] Repository Open Access
Buczyński, J. ; Michałek, M. and Postinghel, E.:
Introduction to 'Schubert varieties, equivariant cohomology and characteristic classes,
IMPANGA15 volume'.
Schubert varieties, equivariant cohomology and characteristic classes : impanga 15 / J.
Buczyński... (eds.). European Mathematical Society, 2018. - P. 1-7
(EMS series of congress reports)
Bibtex [DOI]
Michałek, M.:
Selected topics on toric varieties.
The 50th anniversary of Gröbner bases : proceedings of the 8th Mathematical
Society of Japan Seasonal Institute (MSJ SI 2015) : July 1-10, 2015, at Hotel Nikko
Osaka / T.
Hibi (ed.). Mathematical Society of Japan, 2018. - P. 207-252
(Advanced studies in pure mathematics ; 77)
Bibtex [DOI] [ARXIV] Repository Open Access
Michałek, M.:
Notes on Kebekus' lectures on differential forms on singular spaces.
Contributions to algebraic geometry : impanga lecture notes / P.
Pragacz (ed.). European Mathematical Society, 2012. - P. 375-388
(EMS series of congress reports)
Bibtex
Preprints
Breiding, P. ; Michałek, M. ; Monin, L. and Telen, S.:
The algebraic degree of coupled oscillators.
Bibtex [ARXIV] Repository Open Access
Breiding, P. ; Gesmundo, F. ; Michałek, M. and Vannieuwenhoven, N.:
Algebraic compressed sensing.
Bibtex [ARXIV] Repository Open Access
Dinu, R. ; Michałek, M. and Vodička, M.:
Geometry of the Gaussian graphical model of the cycle.
Bibtex [ARXIV] Repository Open Access
Lasoń, M. and Michałek, M.:
On algebraic properties of matroid polytopes.
Bibtex [ARXIV] Repository Open Access
Manivel, L. ; Monin, L. ; Michałek, M. ; Seynnaeve, T. and Vodička, M.:
Complete quadrics : Schubert calculus for Gaussian models and semidefinite programming.
Bibtex MIS-Preprint: 107/2020 [ARXIV] [CODELINK] Repository Open Access
Michałek, M. ; Monin, L. and Wiśniewski, J.:
The Gaussian moduli [Supplementary resources to 'Maximum likelihood degree, complete
quadrics and C*-action'].
Bibtex [ARXIV] [CODELINK] Repository Open Access
Landsberg, J. M. and Michałek, M.:
Towards finding hay in a haystack : explicit tensors of border rank greater than \(2.02m\)
in \(C^{m}\otimes C^{m}\otimes C^{m}\).
Bibtex MIS-Preprint: 1/2020 [ARXIV] Repository Open Access
Academic Theses
Vodička, M.:
Combinatorial methods in algebraic geometry.
Dissertation, Universität Konstanz, 2022 Bibtex
Görlach, P.:
Projective geometry, toric algebra and tropical computations.
Dissertation, Universität Leipzig, 2020 Bibtex [FREELINK] Repository Open Access
Seynnaeve, T.:
Algebraic geometry for tensor networks, matrix multiplication, and flag matroids.
Dissertation, Universität Leipzig, 2020 Bibtex [FREELINK] Repository Open Access
Books
Michałek, M. and Sturmfels, B.:
Invitation to nonlinear algebra.
American Mathematical Society, 2021. - 226 p.
(Graduate studies in mathematics ; 211)
ISBN 978-1-4704-5367-1 Bibtex [CODELINK]
Buczyński, J. ; Michałek, M. and Postinghel, E. (eds.):
Schubert varieties, equivariant cohomology and characteristic classes : impanga 15.
European Mathematical Society, 2018. - VI, 348 p.
(EMS series of congress reports)
ISBN 978-3-03719-182-8 Bibtex [DOI]
Michałek, M.:
Wprowadzenie do algebry komutatywnej = [Translation of the book 'Introduction to commutative
algebra' / M. Atiyah and I. Macdonald (polish)].
Wydawnictwo Uniwersytetu Jagiellonskiego, 2008. - 149 p. ISBN 978-83-233-2350-1 Bibtex
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