Publications (updated )

Arxiv preprints

• The Hilbert scheme of points on a threefold, I with Ritvik Ramkumar and Alessio Sammartano.
  2409.17009, 2024. arXiv version
• Classification and degenerations of small minimal border rank tensors via modules with Jakub Jagiełła.
  2409.06025, 2024. arXiv version
• Symmetric powers: structure, smoothability, and applications with Cosimo Flavi and Mateusz Michałek.
  2408.02754, 2024. arXiv version
• Behrend's function is not constant on Hilb_n(C^3) with Martijn Kool and Reinier F. Schmiermann.
  2311.05408, 2023. arXiv version
• Limits of saturated ideals with Tomasz Mańdziuk.
  arXiv:2210.13579, 2022. arXiv version

To appear and published

• Generically nonreduced components of Hilbert schemes on fourfolds (for the memory volume of Gianfranco Casnati).
  To appear in special volume of Rendiconti del seminario matematico di Torino. arXiv version
• The Hilbert scheme of infinite affine space and algebraic K-theory with Marc Hoyois, Denis Nardin, Burt Totaro and Maria Yakerson.
  Journal of the European Mathematical Society, online first, 2024. Journal arXiv version
• The variety of polar simplices II with Kristian Ranestad and Frank-Olaf Schreyer.
  Experimental Math, online first, 2024. Journal arXiv version
• Open problems in deformations of Artinian algebras, Hilbert schemes and around.
  In Contemporary Mathematics (AMS) volume Deformation of Artinian Algebras and Jordan Type, 2024. Volume arXiv version
• Concise tensors of minimal border rank with Joseph Landsberg and Arpan Pal.
  Mathematische Annalen, Volume 388, pages 2473–2517, (2024). Journal arXiv version
• On the Hilbert function of Artinian local complete intersections of codimension three with Shreedevi Masuti and Maria Evelina Rossi.
  Journal of Pure and Applied Algebra Volume 227, Issue 7, July 2023. Journal arXiv version
• On construction of k-regular maps to Grassmannians via algebras of socle dimension two with Hanieh Keneshlou.
  Annali della Scuola Normale Superiore di Pisa, Classe di Scienze, (5) Vol. XXV (2024), 1763-1798.
  arXiv version Journal
• Hermitian K-theory via oriented Gorenstein algebras with Marc Hoyois, Denis Nardin and Maria Yakerson.
  Journal für die reine und angewandte Mathematik (Crelle's Journal), vol. 2022, no. 793, 2022, pp. 105-142. Journal arXiv version
• Bounds on complexity of matrix multiplication away from CW tensors with Roser Homs, Mateusz Michałek and Tim Seynnaeve.
  Journal of Pure and Applied Algebra, Volume 226, Issue 12, December 2022. Journal arXiv version
• Components and singularities of Quot schemes and varieties of commuting matrices with Klemen Šivic.
  Journal für die reine und angewandte Mathematik (Crelle's Journal), vol. 2022, no. 788, 2022, pp. 129-187. Journal arXiv version
• Białynicki-Birula decomposition for reductive groups in positive characteristic with Łukasz Sienkiewicz.
  Journal de Mathématiques Pures et Appliquées, Volume 152, August 2021, Pages 189-210. Journal arXiv version
• Pathologies on the Hilbert scheme of points.
  Inventiones mathematicae, 220(2), 581-610, 2020. Journal arXiv version
• Elementary components of Hilbert schemes.
  J. London Math. Soc., 100: 249-272. Journal arXiv version
• Smoothable zero dimensional schemes and special projections of algebraic varieties with Grzegorz Kapustka and Michał Kapustka.
  Mathematische Nachrichten. 2019; 292: 2018– 2027. Journal arXiv version
• Białynicki-Birula decomposition for reductive groups with Łukasz Sienkiewicz.
  Journal de Mathématiques Pures et Appliquées, Volume 131, November 2019, Pages 290-325. Journal arXiv version
• Constructions of k-regular maps using finite local schemes with Jarosław Buczyński, Tadeusz Januszkiewicz and Mateusz Michałek.
  Journal of the European Mathematical Society (JEMS) 21 (2019), no. 6, 1775–1808.
  Journal arXiv version
• VSPs of cubic fourfolds and the Gorenstein locus of the Hilbert scheme of 14 points on A^6.
  Linear Algebra and its Applications, Volume 557, 2018, Pages 265-286. Journal arXiv version
• On polynomials with given Hilbert function and applications with Alessandra Bernardi, Pedro Macias Marques and Kristian Ranestad.
  Collect. Math. 69 (2018) no. 1, 39-64. Journal arXiv version
• Finite schemes and secant varieties over arbitrary characteristic with Jarosław Buczyński.
  Differential Geom. Appl. 55 (2017), 13–67. Journal arXiv version
• Classifying local Artinian Gorenstein algebras.
  Collect. Math. 68 (2017) no. 1, 101-127. Journal arXiv version
• On the rationality of Poincarè series of Gorenstein algebras via Macaulay's correspondence with Gianfranco Casnati and Roberto Notari.
  Rocky Mountain J. Math. 46 (2016), no. 2, 413–433. Journal arXiv version
• On commutativity of ideal extensions (BSc thesis under the supervision of E.R.Puczyłowski),
  Communications in Algebra Vol. 44, Iss. 5, 2016. Journal arXiv version
• Irreducibility of the Gorenstein loci of Hilbert schemes via ray families, with Gianfranco Casnati and Roberto Notari.
  Algebra Number Theory, 9(7):1525–1570, 2015. Journal arXiv version
• Local finite dimensional Gorenstein k-algebras having Hilbert function (1,5,5,1) are smoothable.
  Journal of Algebra and Its Applications: Volume 13, 13(8):1450056 (7 pages), 2014.
  Journal arXiv version
• An upper bound for the Waring rank of a form.
  Archiv der Mathematik: Volume 102, Issue 4 (2014), Page 329-336. Journal arXiv version

Book chapters

• Equations and tropicalization of Enriques surfaces with Barbara Bolognese, Corey Harris.
  A project initiated during apprenticeship weeks at CombAlgGeom semester under the supervision of Greg Smith and Bernd Sturmfels.
  Appeared in Combinatorial Algebraic Geometry, Fields Institute Communications. Book chapter arXiv version
• The Hilbert scheme of 11 points in A^3 is irreducible with Theodosios Douvropoulos, Bernt Ivar Utstøl Nødland and Zach Teitler.
  A project initiated during apprenticeship weeks at CombAlgGeom semester under the supervision of Greg Smith and Bernd Sturmfels.
  Appeared in Combinatorial Algebraic Geometry, Fields Institute Communications. Book chapter arXiv version

Other - not intended for publication

• Hilbert schemes of points and applications. My PhD thesis (2017) made under the supervision of Weronika and Jarosław Buczyńscy
  arXiv version
• Deformations of zero-dimensional schemes and applications. My MSc thesis made under the supervision of Jarosław Buczyński
  arXiv version