Projects

Cox rings and resolutions of quotient singularities

• Crepant resolutions of 3-dimensional quotient singularities via Cox rings with Maksymilian Grab
  Experimental Mathematics 28(2):161-180 (2019)
• Computing resolutions of quotient singularities with Simon Keicher
  Journal of Algebra 472:546-572 (2017)
  Singular library for computing Cox rings of resolutions of quotient singularities (under development)
• Equivariant Hirzebruch classes and Molien series of quotient singularities with Andrzej Weber
  Transformation Groups 23(3):671-705 (2018)
• Cox rings of some symplectic resolutions of quotient singularities with Maksymilian Grab (preprint)
• On 81 symplectic resolutions of a 4-dimensional quotient by a group of order 32 with Jarosław A. Wiśniewski
  Kyoto Journal of Mathematics 57(2):395-434 (2017)
  Singular package for testing properties of linearizations of a torus action on an affine variety
• Cox rings of minimal resolutions of surface quotient singularities
  Glasgow Mathematical Journal 58:325-355 (2016)
  This is the main part of my PhD thesis supervised by Jarosław Wiśniewski at the University of Warsaw

Hyperkähler manifolds

• A very special EPW sextic and two IHS fourfolds with Bert van Geemen, Grzegorz Kapustka, Michał Kapustka and Jarosław A. Wiśniewski
  Geometry & Topology 21(2):1179-1230 (2017)

Algebraic approach to automata and formal languages

• On Rational Recursive Sequences with Lorenzo Clemente, Filip Mazowiecki and Michał Pilipczuk
  STACS 2023

The Kummer construction

• On Kummer 3-folds
  Revista Matemática Complutense 24:465-492 (2011)
  This is my M.Sc. project on Betti numbers of Kummer 3-folds (text in Polish), supervised by Jarosław Wiśniewski
  GAP programs for finite integral matrix groups
  Ocaml library for finite matrix groups

Combinatorial algebraic geometry

• Complexity of the usual torus action on Kazhdan-Lusztig varieties with Laura Escobar and Irem Portakal
  to appear in Algebraic Combinatorics
• Towards classifying toric degenerations of cubic surfaces with Paul Görlach and Milena Wrobel
  Le Matematiche (special issue on cubic surfaces) 75(2):537-557 (2020)
• Khovanskii bases of Cox-Nagata rings and tropical geometry with Martha Bernal, Daniel Corey, Naoki Fujita and Georg Merz
  In: Smith G., Sturmfels B. (eds) Combinatorial Algebraic Geometry. Fields Institute Communications, vol 80. Springer, New York, NY 2017 (pp. 159-179)
• Phylogenetic invariants for Z_3 scheme-theoretically
  Annals of Combinatorics 20(3):549-568 (2016)
• Phylogenetic invariants for group-based models with Mateusz Michałek (part of my PhD thesis)
  Journal of Algebraic Statistics 3:44-63 (2012)
  programs (C++) for analyzing polytopes associated with phylogenetic models
• Isotropic models of evolution with symmetries with Weronika Buczyńska and Jarosław A. Wiśniewski (part of my PhD thesis)
  Proceedings of the conference Interactions of Classical and Numerical Algebraic Geometry, Contemporary Mathematics 496:111-132 (2009)
  GAP programs for classifying small isotropic models
  a program in Prolog for determining saturated groups (not really effective - written, as an experiment, for my computer science studies)

Cones of divisors

• Cones of divisors of blow-ups of projective spaces with Salvatore Cacciola, Olivia Dumitrescu, Alessio Lo Giudice and Jinhyung Park
  Le Matematiche (Catania) 66:153-187 (2011)