Piotr Przytycki

Geometric Group Theory at McGill

Videos

• Slim unicorns
• Arcs intersecting at most once
• Tame automorphism group
• Torsion groups do not act on 2-dimensional CAT(0) complexes
• Subgraphs of diameter 1 in graphs of girth 2
• Coxeter groups are biautomatic (minicourse): part 1, part 2, part 3
• A pair of Garside shadows

Papers

• A pair of Garside shadows, joint with Yeeka Yau, Algebraic Combinatorics 7, no.6 (2024), 1879-1885.
• The moduli space of cactus flower curves and the virtual cactus group, joint with Aleksei Ilin, Joel Kamnitzer, Yu Li, and Leonid Rybnikov, submitted (2024).
• Finitely generated subgroups of algebraic elements of plane Cremona groups are bounded, joint with Anne Lonjou and Christian Urech, Journal de l'Ecole polytechnique - Mathematiques 11 (2024), 1011-1028.
• Weak Tits alternative for groups acting geometrically on buildings, joint with Chris Karpinski and Damian Osajda, Journal of Algebra 656 (2024), special volume in memory of Jacques Tits, 259-275.
• Coxeter groups are biautomatic, joint with Damian Osajda, to appear in Inventiones mathematicae (2025).
• Tits Alternative for the 3-dimensional tame automorphism group , joint with Stephane Lamy, submitted (2022).
• Tits Alternative for 2-dimensional CAT(0) complexes, joint with Damian Osajda, Forum of Mathematics, Pi 10 (2022), e25.
• Unicorn paths and hyperfiniteness for the mapping class group, joint with Marcin Sabok, Forum of Mathematics, Sigma Vol.9:e36 (2021) 1-10.
• 2-dimensional Coxeter groups are biautomatic, joint with Zachary Munro and Damian Osajda, Proceedings of the Royal Society of Edinburgh Section A: Mathematics 152 no.2 (2022), 382-401.
• Dihedral twists in the Twist Conjecture, Mathematische Zeitschrift 299 (2021), 1741-1765.
• Tits alternative for Artin groups of type FC, joint with Alexandre Martin, Journal of Group Theory 23, no.4 (2020), 563-573.
• Abelian subgroups of two-dimensional Artin groups, joint with Alexandre Martin, Bulletin of the LMS 53, no.5 (2021), 1338-1350.
• Acylindrical actions for two-dimensional Artin groups of hyperbolic type, joint with Alexandre Martin, International Mathematics Research Notices 17 (2022), 13099-13127.
• Tits Alternative for groups acting properly on 2-dimensional recurrent complexes, joint with Damian Osajda , with an appendix written jointly with Jon McCammond, Advances in Mathematics 391 (2021), paper no. 107976.
• Torsion groups do not act on 2-dimensional CAT(0) complexes, joint with Sergey Norin and Damian Osajda , Duke Mathematical Journal 171, no.6 (2022), 1379-1415.
• Presqu'un immeuble pour le groupe des automorphismes moderes, joint with Stephane Lamy, Annales Henri Lebesgue 4 (2021), 605-651.
• A step towards Twist Conjecture, joint with Jingyin Huang, Documenta Mathematica 23 (2018), 2081-2100.
• Mixed 3-manifolds are virtually special, joint with Daniel T. Wise, Journal of the AMS 31 (2018) 318-347.
• Acylindrical hyperbolicity of the three-dimensional tame automorphism group, joint with Stephane Lamy, Annales Scientifiques de l'ENS (4) 52, no.2 (2019), 367-392.
• Arcs on spheres intersecting at most twice, joint with Christopher Smith, Indiana Univ Math J 68, no.1 (2019), 157-178.
• Dismantlable classifying space for the family of parabolic subgroups of a relatively hyperbolic group, joint with Eduardo Martinez-Pedroza, J Inst Math Jussieu 18, no.2 (2019), 329-345.
• Cocompactly cubulated 2-dimensional Artin groups, joint with Jingyin Huang and Kasia Jankiewicz, Commentarii Mathematici Helvetici 91 no.3 (2016), 519-542.
• A note on acylindrical hyperbolicity of Mapping Class Groups, joint with Alessandro Sisto, Advanced Studies in Pure Mathematics 73, Hyperbolic Geometry and Geometric Group Theory (2017), 255-264.
• Balanced walls for random groups, joint with John Mackay, Mich Math J 64 (2015), 396-419.
• Arcs intersecting at most once, GAFA 25 (2015), 658-670.
• Systolizing buildings, joint with Petra Schwer, Groups, Geometry, and Dynamics 10 no.1 (2016) 241-277.
• Cocompactly cubulated graph manifolds, joint with Mark Hagen, Israel Journal of Mathematics 207 no.1 (2015), 377-394. Erratum (2016).
• 1-slim triangles and uniform hyperbolicity for arc graphs and curve graphs, joint with Sebastian Hensel and Richard C.H. Webb, Journal of the EMS 17 no.4 (2015), 755-762.
• Separability of embedded surfaces in 3-manifolds, joint with Daniel T. Wise, Compositio Mathematica 150 (2014), 1623-1630.
• Realisation and dismantlability, joint with Sebastian Hensel and Damian Osajda , Geometry & Topology 18 (2014), 2079-2126.
• Graph manifolds with boundary are virtually special, joint with Daniel T. Wise, Journal of Topology 7 no.2 (2014), 419-435.
• Square complexes and simplicial nonpositive curvature, joint with Tomasz Elsner, Proceedings of the AMS 141 (2013), 2997-3004.
• Contractibility of the Kakimizu complex and symmetric Seifert surfaces, joint with Jennifer Schultens, Transactions of the AMS 364 no.3 (2012), 1489-1508.
• Bipolar Coxeter groups, joint with Pierre-Emmanuel Caprace, Journal of Algebra 338 no.1 (2011), 35-55.
• Twist-rigid Coxeter groups, joint with Pierre-Emmanuel Caprace, Geometry & Topology 14 (2010) 2243-2275.
• The ending lamination space of the five-punctured sphere is the Noebeling curve joint with Sebastian Hensel, Journal of the LMS 84 no.1 (2011), 103-119.
• Acute triangulations of polyhedra and R^n, joint with Eryk Kopczynski and Igor Pak, Combinatorica 32 no.1 (2012) 85-110, extended abstract in Proceedings of the 2010 annual symposium on computational geometry.
• Veech groups of Loch Ness monsters, joint with Gabriela Schmithuesen and Ferran Valdez, Annales de l'Institut Fourier 61 no.2 (2011), 673-687.
• Random groups do not split, joint with Francois Dahmani and Vincent Guirardel, Mathematische Annalen 349 no.3 (2011), 657-673.
• Boundaries of systolic groups, joint with Damian Osajda, Geometry & Topology 13 (2009), 2807-2880.
• EG for systolic groups, Commentarii Mathematici Helvetici 84 no.1 (2009), 159-169.
• Flag-no-square triangulations and Gromov boundaries in dimension 3, joint with Jacek Swiatkowski, Groups, Geometry, and Dynamics 3 (2009), 453-468.
• The fixed point theorem for simplicial nonpositive curvature, Mathematical Proceedings of Cambridge Philosophical Society 144 (2008), 683-695.
• Gaussian thermostats as geodesic flows of nonsymmetric linear connections, joint with Maciej P. Wojtkowski, Communications in Mathematical Physics 277 no.3 (2008), 759-769.
• Systolic groups with no flats are hyperbolic, Fundamenta Mathematicae 193 (2007), 277-283.

• Translation of sections IV-VI of Francis Bonahon's Boutes des varietes hyperboliques, joint with Ingrid Irmer and Samuel Tapie (2008).
• PhD thesis (2008).
• Krzywizna pseudosfery, Delta 6 (2006).
• Powierzchnie: zajecia praktyczno-techniczne, Delta 10 (2008).

Teaching (Poland)