Young Geometric Group Theory IX Saint-Jacut-de-la-Mer February 24-28, 2020 Photo © Ronan Jacut / Dinan Cap-Fréhel Tourisme Page size: 148.0x210.0 mm Introduction Welcome to the ninth edition of the Young Geometric Group The- ory meeting! In this booklet, apart from the abstracts of the mini-courses and research talks, you will find the research statements of all the par- ticipants. We strongly encourage you to read through all of them. In this way, you will get a panoramic view of the current subjects of research in the field of geometric group theory. You will surely discover subjects you never knew existed. Maybe, you will discover as well that someone else has some common interests with you. So, this could be the beginning of passionate scientific discussions! This winter school is thought as a forum for sharing ideas in a friendly atmosphere. Feel free to ask the speakers, the organizers and other participants. In this way, you will certainly make the best of your week in Saint-Jacut-de-la-mer. We wish you a pleasant and fruitful winter school! The organizers. 1 2 Contents Mini-courses 11 Cantat Serge Groups of polynomial transformations . 13 Erschler Anna Growth and amenability of groups . 13 Haïssinsky Peter Convergence groups ................... 14 Monod Nicolas Spaces of the third kind . 14 Junior speakers 15 Fanoni Federica Big mapping class groups and their actions on graphs 17 Frączyk Mikołaj Growth of mod-p homology groups in higher rank lat- tices. .......................... 17 Gupta Radhika Non-uniquely ergodic arational trees in the boundary of outer space ...................... 17 Hartman Yair Which groups have bounded harmonic functions? . 18 Le Boudec Adrien Commensurated subgroups and micro-supported actions 19 Pozzetti Beatrice Surface subgroups of semisimple Lie groups . 19 Research statements 21 3 Alekseev Ilya Geodesic words for finitely generated groups . 23 Appenzeller Raphael Generalized buildings arising from symmetric spaces over non-Archimedean real closed fields . 25 Arenas Macarena Hyperbolicity and cubical small-cancellation theory . 26 Arora Shivam Hyperbolic groups .................... 27 Ashcroft Calum Cubulating Groups ................... 32 Barberis Marco Rigidity of k-separating curve graphs . 33 Barrett Benjamin Boundaries of hyperbolic groups . 35 Bell Nicholas Generalising Mirzakhani’s curve counting . 37 Bensaid Oussama Average Dehn function of finitely generated groups and LG-rigidity of transitive graphs . 38 Bertolotti Federica Maximal representations in higher Teichmuller theory 39 Biz Leonardo Properties of the coarse boundary groupoid . 40 Blufstein Martín Axel Curvature tests and hyperbolicity . 42 Brown Thomas Some groups of type FP . 44 Brunck Florestan Acute triangulations of polyhedra . 45 Buran Michal Separability within the class of alternating groups . 47 Chopra Holli Boundaries of Hyperbolic Spaces . 48 Conder Matthew Discrete and free two-generated subgroups of SL2 . 49 Darbinyan Arman Groups, computability, and computational complexity 50 de Souza Lucas H. R. Research in perspective compactifications . 51 4 Dickmann Ryan Big mapping class groups . 54 Dlugie Ethan Big mapping class groups and complexes . 55 Domat George Big mapping class groups . 56 Douba Sami Linearity of graph manifold groups . 58 Duda Karol Geometric group theory and computability . 59 Elkiaer Émilie Groups actions on Banach spaces . 60 Escalier Amandine Local-to-global rigidity of transitive graphs . 61 Faber Josh Anarchy in the Hanna Neumann conjecture . 62 Ferragut Tom Horocycle product of hyperbolique metric spaces . 64 Fioravanti Elia Spaces of actions on CAT(0) cube complexes . 65 Flamm Xenia Semialgebraic methods in geometric group theory . 67 Flechsig Jonas Artin groups acting on arc matching complexes . 68 Francoeur Dominik Groups acting on rooted trees . 69 Frisch Joshua Dynamical properties of groups . 71 Fruchter Jonathan The first order theory of acylindrically hyperbolic groups 73 Gerasimova Maria Isoperimetry, Littlewood functions, and unitarisabil- ity of groups ....................... 75 Glorieux Olivier Geometry in higher rank . 77 Gheysens Maxime Big topological groups . 79 Goffer Gil Totally disconnected groups . 80 Gohla Lukas Group stability in the context of group approximations 82 5 Grau Leonid Higher Dehn functions of solvable Lie groups . 83 Grayevsky Ido Quasi-isometries of right angled groups . 85 Guerch Yassine Geometry and rigidity of relative automorphisms groups 86 H Balasubramanya Sahana Group actions on hyperbolic spaces . 87 Hayez Laurent Analytical and asymptotical aspects of finitely gener- ated groups ....................... 93 Hoda Nima Non-positive curvature in groups . 95 Hoganson Hannah Lp metrics on Teichmüller space . 97 Hughes Sam Lattices in products of Lie groups and trees . 98 Joseph Matthieu Isometric orbit equivalence . 99 Jurina Simon Decision problems in finitely presented groups . 100 Karrer Annette Spaces of nonpositive curvature and their boundaries 104 Kerr Alice Product set growth . 105 Klinge Kevin Vanishing of `2-cohomology . 106 Kolodner Noam Free groups and core graphs . 107 Kontogeorgiou Georgios Cayley complex embeddings . 108 Lacourte Octave IET, subgroups and generalizations . 111 Ladjali Amina Assouda Generalisations of CAT(0) cube complexes . 112 Legaspi-Juanatey Xabier Growth and its connections . 113 Leibtag Elyasheev Topological properties of algebraic groups . 115 Levine Alex Group equations . 116 6 Li Kevin Bredon cohomology and classifying spaces . 117 Lotz Marco The combinatorics of hyperbolic Coxeter groups . 118 Lowen Alex Algorithmic problems for Out(Fn) . 120 Magnani Maria Character variety and Teichmüller space . 121 Miller Marissa Characterizations of stable subgroups . 122 Moeller Philip Semisimple locally compact groups and duality . 123 Munro Zachary Yi-Jeng Weak Modularity . 124 Ng Thomas Uniform exponential growth in groups with non-positive curvature . 125 Nicolás Cardona Francisco Finitely generated normal subgroups of Kähler groups 126 Oh Josiah QI rigidity and relative ends . 128 Oregón-Reyes Eduardo Isometric actions on metric spaces with non-positive curvature . 129 Pallier Gabriel Large-scale geometry of Lie groups . 133 Papin Chloé Hyperbolic spaces for the outer automorphism group of Baumslag-Solitar groups . 135 Plenz Sebastian Minimal volume entropy . 136 Rauzy Emmanuel Embeddings in finitely presented groups . 137 Robbio Bruno Hierarchically hyperbolic spaces, cubulating groups and RAAGs . 138 Ron Liran Horoboundary theory for Cayley graphs . 139 Santos Rego Yuri Matrix groups, Thompson groups, and 3-manifolds . 141 7 Sarti Filippo Superrigidity of measurable cocycle of complex hyper- bolic lattices into SU(m; n) . 143 Sasaki Dounnu Subset currents on hyperbolic groups and surfaces . 144 Sathaye Bakul Non-positively curved groups and manifolds . 146 Schaffer-Cohen Anschel Big mapping class groups acting on simplicial things 152 Schiavo Vasco What I’m interested in . 153 Seidel Matan Word maps and word measures . 154 Semal Lancelot About unitary representations of locally compact groups157 Sheard David Accessibility of Groups . 159 Shepherd Sam Leighton’s Theorem and cube complexes . 161 Shinkle Emily Finite rigidity Problems . 163 Slutsky Raz Co-volume of lattices in Lie groups controls their com- plexity . 164 Soergel Mireille Actions of Artin groups on CAT(0) spaces and the K(π; 1) conjecture . 165 Stadlöder Stefan Relations between the Bogomolov property and the property (^τ) of groups . 166 Stankov Bogdan Random walks on Cayley and Schreier graphs . 169 Su Hang Lu Left orders and formal languages . 171 Sun Bin Acylindrically hyperbolic groups . 173 Szőke Nóra Gabriella Amenability of topological full groups . 176 Tee Paul Tits Alternative for 2-Dimensional Artin Groups . 178 8 Tranchida Philippe Right-angled Artin groups, CAT(0) cube complexes and mapping class groups. 179 Tsai Tsung-Hsuan Random triangular groups at density 1/3 . 181 Vankov Vladimir Special cube complexes and generalised Bestvina-Brady Groups . 183 Vaskou Nicolas Algebraic structure of groups from a geometric per- spective . 185 Vigdorovich Itamar Asymptotic behaviour of locally symmetric spaces and harmonic analysis . 186 Young Samuel Local subgroup properties of abstract commensurators 187 Zhu Feng Hyperbolic(-ish) subgroups in higher rank . 189 Organization 191 9 10 Mini-courses 11 12 Serge Cantat CNRS / Université de Rennes 1, France Groups of polynomial transformations Consider the affine space of dimension k > 1, say over the field of complex numbers, and the group of all its polynomial transfor- mations with a polynomial inverse. By definition, this is the group of polynomial automorphisms of the affine space: it contains all affine transformations, but also non linear automorphisms of arbi- trary large degrees. What properties of linear (finitely generated) groups remain valid in this larger group? This will be the main topic of the mini-course. Anna Erschler CNRS / ENS Paris, France Growth and amenability of groups Growth function counts the number of elements of word length at most n in the word metric. While many known groups have ei- ther polynomial or exponential growth, a rich and interesting class of groups of intermediate growth was discovered in the eighties by Grigorchuk. Despite some progress in understanding such groups in recents decades, there is still some mystery about these groups and many fundamental questions remain open. Amenable groups are groups admitting an invariant finitely additive measure defined on all their subsets.