Piotr Przytycki

email: piotr.przytycki(you know what)mcgill.ca
pronouns: he/him/his

Associate Professor at
Department of Mathematics and Statistics, McGill University
Burnside Hall, 805 Sherbrooke Street West, Montreal, QC, Canada H3A 0B9
curriculum vitae

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

Papers

A pair of Garside shadows, joint with Yeeka Yau, accepted to Algebraic Combinatorics (2024).
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, submitted (2022).
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)