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 To top of page

Breiding, P. ; Gesmundo, F. ; Michałek, M. and Vannieuwenhoven, N.: Algebraic compressed sensing. Applied and computational harmonic analysis, 65 (2023), p. 374-406 Bibtex [DOI] [ARXIV] Repository Open Access

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

Manivel, L. ; Monin, L. ; Michałek, M. ; Seynnaeve, T. and Vodička, M.: Complete quadrics : Schubert calculus for Gaussian models and semidefinite programming. Journal of the European Mathematical Society, Vol. not yet known, pp. not yet known Bibtex MIS-Preprint: 107/2020 [DOI] [ARXIV] [CODELINK] 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 To top of page

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 To top of page

Breiding, P. ; Michałek, M. ; Monin, L. and Telen, S.: The algebraic degree of coupled oscillators. 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

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 To top of page

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 To top of page

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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