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

Michałek, Mateusz and Emanuele Ventura: Phylogenetic complexity of the Kimura 3-parameter model
In: Advances in mathematics, 343 (2019), p. 640-680
Bibtex MIS-Preprint: 27/2017 DOI: 10.1016/j.aim.2018.11.021 ARXIV: https://arxiv.org/abs/1704.02584

Buczyński, Jarosław ; Januszkiewicz, Tadeusz ; Jelisiejew, Joachim and Mateusz Michałek: Constructions of k-regular maps using finite local schemes
In: Journal of the European Mathematical Society, Vol. not yet known, pp. not yet known
Bibtex ARXIV: https://arxiv.org/abs/1511.05707

Gubeladze, Joseph and Mateusz Michałek: The poset of rational cones
In: Pacific journal of mathematics, 292 (2018) 1, p. 103-115
Bibtex DOI: 10.2140/pjm.2018.292.103 ARXIV: https://arxiv.org/abs/1606.02083

Kahle, Thomas and Mateusz Michałek: Obstructions to combinatorial formulas for plethysm
In: The electronic journal of combinatorics, 25 (2018) 1, P1.41
Bibtex ARXIV: https://arxiv.org/abs/1507.07131 LINK: http://www.combinatorics.org/ojs/index.php/eljc/article/view/v25i1p41

Landsberg, Joseph M. and Mateusz Michałek: A \(2n^2 - log_2(n) - 1\) lower bound for the border rank of matrix multiplication
In: International mathematics research notices, 2018 (2018) 15, p. 4722-4733
Bibtex DOI: 10.1093/imrn/rnx025 ARXIV: https://arxiv.org/abs/1608.07486

Michałek, Mateusz and Hyunsuk Moon: Spaces of sums of powers and real rank boundaries
In: Beiträge zur Algebra und Geometrie, Vol. not yet known, pp. not yet known
Bibtex MIS-Preprint: 9/2017 DOI: 10.1007/s13366-018-0388-4 ARXIV: https://arxiv.org/abs/1612.07900

Michałek, Mateusz ; Perepechko, Alexander and Hendrik Süß: Flexible affine cones and flexible coverings
In: Mathematische Zeitschrift, 290 (2018) 3-4, p. 1457-1478
Bibtex DOI: 10.1007/s00209-018-2069-2 ARXIV: https://arxiv.org/abs/1612.01144

Casanellas, Marta ; Fernández-Sánchez, Jesus and Mateusz Michałek: Local equations for equivariant evolutionary models
In: Advances in mathematics, 315 (2017), p. 285-323
Bibtex DOI: 10.1016/j.aim.2017.05.003 ARXIV: https://arxiv.org/abs/1512.07174

Higashitani, Akihiro ; Kummer, Mario and Mateusz Michałek: Interlacing Ehrhart polynomials of reflexive polytopes
In: Selecta mathematica, 23 (2017) 4, p. 2977-2998
Bibtex MIS-Preprint: 7/2017 DOI: 10.1007/s00029-017-0350-6 ARXIV: https://arxiv.org/abs/1612.07538

Landsberg, Joseph M. and Mateusz Michałek: On the geometry of border rank decompositions for matrix multiplication and other tensors with symmetry
In: SIAM journal on applied algebra and geometry, 1 (2017) 1, p. 2-19
Bibtex DOI: 10.1137/16M1067457 ARXIV: https://arxiv.org/abs/1601.08229

Landsberg, Joseph M. and Mateusz Michałek: Abelian tensors
In: Journal de mathématiques pures et appliquées, 108 (2017) 3, p. 333-371
Bibtex DOI: 10.1016/j.matpur.2016.11.004 ARXIV: https://arxiv.org/abs/1504.03732

Lasoń, Michał and Mateusz Michałek: Non-normal very ample polytopes : constructions and examples
In: Experimental mathematics, 26 (2017) 2, p. 130-137
Bibtex DOI: 10.1080/10586458.2015.1128370 ARXIV: https://arxiv.org/abs/1406.4070

Michałek, Mateusz: Finite phylogenetic complexity of \(\mathbb{Z}_p\) and invariants for \(\mathbb{Z}_3\)
In: European journal of combinatorics, 59 (2017), p. 169-186
Bibtex DOI: 10.1016/j.ejc.2016.08.007 ARXIV: https://arxiv.org/abs/1508.04177

Michałek, Mateusz and Chris Miller: Examples of k-regular maps and interpolation spaces
In: Linear algebra and its applications, 530 (2017), p. 94-108
Bibtex DOI: 10.1016/j.laa.2017.05.003 ARXIV: https://arxiv.org/abs/1512.00609

Michałek, Mateusz ; Moon, Hyunsuk ; Sturmfels, Bernd and Emanuele Ventura: Real rank geometry of ternary forms
In: Annali di matematica pura ed applicata, 196 (2017) 3, p. 1025-1054
Bibtex DOI: 10.1007/s10231-016-0606-3 ARXIV: http://arxiv.org/abs/1601.06574

Michałek, Mateusz and Emanuele Ventura: Finite phylogenetic complexity and combinatorics of tables
In: Algebra and number theory, 11 (2017) 1, p. 235-252
Bibtex DOI: 10.2140/ant.2017.11.235 ARXIV: https://arxiv.org/abs/1606.07263

Bruns, Winfried ; Gubeladze, Joseph and Mateusz Michałek: Quantum jumps of normal polytopes
In: Discrete and computational geometry, 56 (2016) 1, p. 181-215
Bibtex DOI: 10.1007/s00454-016-9773-7 ARXIV: https://arxiv.org/abs/1504.01036

Kahle, Thomas and Mateusz Michałek: Plethysm and lattice point counting
In: Foundations of computational mathematics, 16 (2016) 5, p. 1241-1261
Bibtex DOI: 10.1007/s10208-015-9275-7 ARXIV: https://arxiv.org/abs/1408.5708

Michałek, Mateusz: Toric structures in nontoric varieties
In: Oberwolfach reports, 13 (2016) 2, p. 999-1001
Bibtex DOI: 10.4171/OWR/2016/19

Michałek, Mateusz and Rosa Maria Miró-Roig: Smooth monomial Togliatti systems of cubics
In: Journal of combinatorial theory / A, 143 (2016), p. 66-87
Bibtex DOI: 10.1016/j.jcta.2016.05.004 ARXIV: https://arxiv.org/abs/1310.2529

Michałek, Mateusz ; Sturmfels, Bernd ; Uhler, Caroline and Piotr Zwiernik: Exponential varieties
In: Proceedings of the London Mathematical Society, 112 (2016) 1, p. 27-56
Bibtex DOI: 10.1112/plms/pdv066 ARXIV: http://arxiv.org/abs/1412.6185

Beck, Matthias ; Delgado, Jessica ; Gubeladze, Joseph and Mateusz Michałek: Very ample and Koszul segmental fibrations
In: Journal of algebraic combinatorics : an international journal, 42 (2015) 1, p. 165-182
Bibtex DOI: 10.1007/s10801-014-0577-7 ARXIV: https://arxiv.org/abs/1307.7422

Buczyńska, Weronika ; Buczyński, Jarosław and Mateusz Michałek: The Hackbusch conjecture on tensor formats
In: Journal de mathématiques pures et appliquées, 104 (2015) 4, p. 749-761
Bibtex DOI: 10.1016/j.matpur.2015.05.002 ARXIV: https://arxiv.org/abs/1501.01120

Casanellas, Marta ; Fernández-Sánchez, Jesus and Mateusz Michałek: Low degree equations for phylogenetic group-based models
In: Collectanea mathematica, 66 (2015) 2, p. 203-225
Bibtex DOI: 10.1007/s13348-014-0120-0 ARXIV: https://arxiv.org/abs/1402.6945

Manivel, Laurent and Mateusz Michałek: Secants of minuscule and cominuscule minimal orbits
In: Linear algebra and its applications, 481 (2015), p. 288-312
Bibtex DOI: 10.1016/j.laa.2015.04.027 ARXIV: https://arxiv.org/abs/1401.1956

Michałek, Mateusz: Toric varieties in phylogenetics
In: Dissertationes mathematicae, 2015 (2015) 511, p. 1-86
Bibtex DOI: 10.4064/dm511-0-1

Michałek, Mateusz ; Oeding, Luke and Piotr Zwiernik: Secant cumulants and toric geometry
In: International mathematics research notices, 2015 (2015) 12, p. 4019-4063
Bibtex DOI: 10.1093/imrn/rnu056 ARXIV: https://arxiv.org/abs/1212.1515

Lasoń, Michał and Mateusz Michałek: On the toric ideal of a matroid
In: Advances in mathematics, 259 (2014), p. 1-12
Bibtex DOI: 10.1016/j.aim.2014.03.004 ARXIV: https://arxiv.org/abs/1302.5236

Manivel, Laurent and Mateusz Michałek: Effective constructions in plethysms and Weintraub's conjecture
In: Algebras and representation theory, 17 (2014) 2, p. 433-443
Bibtex DOI: 10.1007/s10468-012-9402-y ARXIV: https://arxiv.org/abs/1207.5748

Michałek, Mateusz: Toric geometry of the 3-Kimura model for any tree
In: Advances in geometry, 14 (2014) 1, p. 11-30
Bibtex DOI: 10.1515/advgeom-2013-0018 ARXIV: https://arxiv.org/abs/1102.4733

Buczyńska, Weronika ; Buczyński, Jarosław ; Kubjas, Kaie and Mateusz Michałek: On the graph labellings arising from phylogenetics
In: Open mathematics, 11 (2013) 9, p. 1577-1592
Bibtex DOI: 10.2478/s11533-013-0263-3 ARXIV: https://arxiv.org/abs/1105.5382

Michałek, Mateusz: Constructive degree bounds for group-based models
In: Journal of combinatorial theory / A, 120 (2013) 7, p. 1672-1694
Bibtex DOI: 10.1016/j.jcta.2013.06.003 ARXIV: https://arxiv.org/abs/1207.0930

Donten-Bury, Maria and Mateusz Michałek: Phylogenetic invariants for group-based models
In: Journal of algebraic statistics, 3 (2012) 1, p. 44-63
Bibtex DOI: 10.18409/jas.v3i1.15 ARXIV: https://arxiv.org/abs/1011.3236

Michałek, Mateusz: Birational maps between Calabi-Yau manifolds associated to webs of quadrics
In: Journal of algebra, 370 (2012), p. 186-197
Bibtex DOI: 10.1016/j.jalgebra.2012.07.019 ARXIV: https://arxiv.org/abs/0904.4404

Lasoń, Michał and Mateusz Michałek: On the full, strongly exceptional collections on toric varieties with Picard number three
In: Collectanea mathematica, 62 (2011) 3, p. 275-296
Bibtex DOI: 10.1007/s13348-011-0044-x ARXIV: https://arxiv.org/abs/1003.2047

Michałek, Mateusz: Geometry of phylogenetic group-based models
In: Journal of algebra, 339 (2011) 1, p. 339-356
Bibtex DOI: 10.1016/j.jalgebra.2011.05.016 ARXIV: https://arxiv.org/abs/1004.3012

Michałek, Mateusz: Family of counterexamples to King's conjecture
In: Comptes rendus mathematique, 349 (2011) 1, p. 67-69
Bibtex DOI: 10.1016/j.crma.2010.11.027 ARXIV: https://arxiv.org/abs/1009.0821

Michałek, Mateusz: A short proof of combinatorial Nullstellensatz
In: The American mathematical monthly, 117 (2010) 9, p. 821-823
Bibtex DOI: 10.4169/000298910X521689 ARXIV: https://arxiv.org/abs/0904.4573

Alon, Noga ; Grytczuk, Jarosław ; Lasoń, Michał and Mateusz Michałek: Splitting necklaces and measurable colorings of the real line
In: Proceedings of the American Mathematical Society, 137 (2009) 5, p. 1593-1599
Bibtex DOI: 10.1090/S0002-9939-08-09699-8 ARXIV: https://arxiv.org/abs/1412.7996

Dey, Arijit ; Lasoń, Michał and Mateusz Michałek: Derived category of toric varieties with Picard number three

Publications in Books and Conference Proceedings

Buczyński, Jarosław ; Michałek, Mateusz and Elisa Postinghel: Introduction to 'Schubert varieties, equivariant cohomology and characteristic classes, IMPANGA15 volume'
In: Schubert varieties, equivariant cohomology and characteristic classes : impanga 15 / JarosławBuczyński... (eds.)
Zürich : Euroean Mathematical Society, 2018. - P. 1-8
(EMS series of congress reports)
Bibtex DOI: 10.4171/182

Michałek, Mateusz: Selected topics on toric varieties
In: 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 / TakayukiHibi (ed.)
Toko : Mathematical Society of Japan, 2018. - P. 207-252
(Advanced studies in pure mathematics ; 77)
Bibtex ARXIV: https://arxiv.org/abs/1702.03125

Michałek, Mateusz: Notes on Kebekus' lectures on differential forms on singular spaces
In: Contributions to algebraic geometry : impanga lecture notes / PiortrPragacz (ed.)
Zürich : European Mathematical Society, 2012. - P. 375-388
(EMS series of congress reports)
Bibtex

Preprints

Beck, Matthias ; Haase, Christian ; Higashitani, Akihiro ; Hofscheier, Johannes ; Jochemko, Katharina ; Katthaen, Lukas and Mateusz Michałek: Smooth centrally symmetric polytopes in dimension 3 are IDP

Cameron, Amanda ; Dinu, Rodica ; Michałek, Mateusz and Tim Seynnaeve: Flag matroids : algebra and geometry

De Poi, Pietro ; Mezzetti, Emilia ; Michałek, Mateusz ; Miró-Roig, Rosa Maria and Eran Nevo: Circulant matrices and Galois-Togliatti systems

Harris, Corey ; Michałek, Mateusz and Emre Can Sertöz: Computing images of polynomial maps

Higashitani, Akihiro ; Jochemko, Katharina and Mateusz Michałek: Arithmetic aspects of symmetric edge polytopes

Michałek, Mateusz ; Seynnaeve, Tim and Frank Verstraete: A tensor version of the quantum Wielandt theorem

Michałek, Mateusz and Yaroslav Shitov: Quantum version of Wielandt's inequality revisited

Katthaen, Lukas ; Michałek, Mateusz and Ezra Miller: When is a polynomial ideal binomial after an ambient automorphism?

Qi, Yang ; Michałek, Mateusz and Lek-Heng Lim: Complex tensors almost always have best low-rank approximations

Books

Buczyński, Jarosław ; Michałek, Mateusz and Elisa Postinghel (eds.): Schubert varieties, equivariant cohomology and characteristic classes : impanga 15
Zürich : Euroean Mathematical Society, 2018
(EMS series of congress reports)
ISBN 978-3-03719-182-8 ISBN 978-3-03719-682-3
Bibtex DOI: 10.4171/182

Michałek, Mateusz: Wprowadzenie do algebry komutatywnej = [Translation of the book 'Introduction to commutative algebra' / M. Atiyah and I. Macdonald (polish)]
Kraków : Wydawnictwo Uniwersytetu Jagiellonskiego, 2008. - 149 p.
ISBN 978-83-233-2350-1
Bibtex

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