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------- Carolyn Abbott Mutaz Abumathkur Santana Afton Jimboy Albaracin Yael Algom-Kfir Usman Ali Sofia Amontova Simon André Naomi Andrew Yago Antolin Raphael Appenzeller Diego ARCIS Macarena Arenas Shivam Arora Goulnara N. Arzhantseva Amy Aswani Hyungryul Baik Sahana Balasubramanya Ludovico Battista Jason Behrstock Robert Bell Paolo Bellingeri Daniel Beltita Oussama Bensaid Edgar Bering Daniel Berlyne Jon Berrick Mladen Bestvina Jonas Beyrer Hadi Bigdely Joan Birman Sasha BONTEMPS Khalid BOUTAHIR Rachael Boyd Corey Bregman Tara Brendle Martin BRIDSON Mark Brittenham Thomas Brown Joaquín Brum Michal Buran Leonardo Henrique Caldeira Pires Ferrari Aaron Calderon Matthieu Calvez Graham Campbell Pierre-Emmanuel Caprace Montserrat Casals-Ruiz Alberto Cassella Anindya Chanda Yu-Chan Chang Ruth Charney Indira Chatterji Laura Ciobanu Corina Ciobotaru Bruno Cisneros Michel Coornaert Matthew Cordes Rémi Coulon María Cumplido Francois Dahmani Pallavi DANI Arman Darbinyan Kajal Das Michael Davis Thomas Delzant Soumya Dey Luca Di Gravina François Digne Ethan Dlugie Sami Douba Theo Douvropoulos Spencer Dowdall Bruno Duchesne Andrew Duncan Martin Dunwoody Tullia Dymarz Ivan Dynnikov Eduard Einstein Gianluca Faraco Mohammad Farrokhi Derakhshandeh Ghouchan Talia Fernos Elizabeth Field Elia Fioravanti Nathan Fisher Xenia Flamm Ramon Flores Jean-Baptiste Follet Islam Foniqi Francesco Fournier Facio Elizaveta Frenkel Jean Fromentin Jordan Frost Koji FUJIWARA Tomohiro FUKAYA David Futer Damien Gaboriau Swiatoslaw GAL Carmen Galaz-Garcia Guillaume Gandolfi Jerónimo García Mejía Giles Gardam Ilya Gekhtman Thomas Gobet Eddy GODELLE Gili Golan Juan Gonzalez-Meneses Rostislav Grigorchuk Daniel Groves Samuel Grushevsky Yassine Guerch Kanan Gupta Radhika Gupta Thomas Haettel Mark Hagen Peter Haîssinsky Ian Hambleton Ursula Hamenstadt Claude Hayat Susan Hermiller Jesús Hernández Hernández Nicolaus Heuer Michael Heusener Nima Hoda Derek Holt Tal Horesh Jingyin Huang Sam Hughes Merlin Incerti-Medici Alessandra Iozzi Cesar A Ipanaque Zapata Omar Islas Victor Jaeck Andrei Jaikin Kasia Jankiewicz Arpan Kabiraj Sagar Balasaheb KALANE Ashlee Kalauli Anders Karlsson Annette Karrer Yasushi KASAHARA Fanny Kassel Takuya Katayama Atsushi Katsuda Ilya Kazachkov Dawid Kielak Thomas Koberda Yannick Krifka Rishi Kumar Christian Lange Emilio Lauret Sita Lawaju Nir Lazarovich François Ledrappier Homin Lee Xabier Legaspi Juanatey Ivan Levcovitz Daniel Levitin Gilbert Levitt NA LI Lucy Lifschitz Gabriele LINK Marco Linton Qing Liu Ye Liu Claudio Llosa Isenrich Anne Lonjou Jone Lopez de Gamiz Zearra Jiayi Lou Joel Louwsma Rylee Lyman Biao Ma Sylvain Maillot Stavroula Makri Justin Malestein Keivan Mallahi Karai Brendan Mallery Alexis Marchand Christophe MARGERIN Alex Margolis Ivan Marin Ludovic Marquis Alexandre Martin Conchita Martinez Armando Martino Jon MCCAMMOND Suraj Krishna Meda John Meier Iuliia Meshkova MurphyKate Montee Marianne Morillon Rose Morris-Wright Dr. Abhishek Mukherjee Zachary Munro Tatiana Nagnibeda Sam Nariman Christopher Natoli Georges Neaime Volodymyr Nekrashevych Walter Neumann Thomas Ng Khoi Nguyen Andrew Nicax Marialaura Noce Sangrok O Shane O Rourke Josiah Oh Semra OZTURK Frédéric Palesi Giovanni Paolini Luis Paris Irene Pasquinelli Juan Paucar Boris pawilowski Harry Petyt Christophe PITTET Tomasz PrytuÅ‚a Piotr PRZYTYCKI Doron Puder Chris Ratigan SK Rayamajhi Sarah Rees Stefano Riolo Bruno Robbio Claude ROGER Dale Rolfsen Kim Ruane Lorenzo Ruffoni Ian Runnels Jacob Russell Michah Sageev Nick Salter Eric Samperton Luis Jorge Sanchez Saldana Diego Santoro MABUD ALI SARKAR Bakul Sathaye Grégoire Schneeberger Kevin Schreve Paul Schupp Petra Schwer Sourav Sen Cagri Sert David Sheard Xiaobing Sheng Sam Shepherd Lior Silberman Marithania Silvero Rachel Skipper Mireille Soergel Ignat Soroko Davide Spriano Somphop Srisitthipaiboon Yves Stalder Emily Stark Hang Lu Su Jennifer Taback Robert Tang Jing Tao Chaitanya Tappu Anitha Thillaisundaram Philippe Tranchida Siming Tu Christian Urech Caglar Uyanik Arya Vadnere Alain Valette Vladimir Vankov Olga Varghese Nicolas Vaskou Alina Vdovina Karen Vogtmann Katie Vokes Richard Wade Genevieve Walsh Daxun Wang Richard Webb Richard Weidmann Bert Wiest Rebecca Winarski Daniel Wise Daniel Woodhouse Xiaolei Wu Yandi Wu Zhiqiang Xiao Shengkui Ye Hai Yu Alexander Zakharov abdalrazzaq zalloum Tianyi Zheng

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------- A general messages board Balasubramanya's talk: Quasi-Parabolic Structures on Groups Cumplido's talk: Complexes of parabolic subgroups for Artin groups Fioravanti's talk: Spaces of cubulations Hamenstädt's talk: ​Spin mapping class groups and curve graphs Hoda's talk: Shortcut Graphs and Groups Kielak's talk: Computing fibring of 3-manifoldsand free-by-cyclic groups Levcovitz's talk: ​Right-angled Coxeter groups commensurable to right-angled Artin groups Lonjou's talk: Action of the Cremona group on a CAT(0) cube complex Margolis' talk: Quasi-actions and almost normal subgroups Morris-Wright's talk: Parabolic subgroups of Infinite type Artin groups Runnels' talk: Effectively Generating RAAGs in MCGs Skipper's talk: Finiteness properties for simple groups Soroko's talk: Intersections and joins of subgroups in free groups Stark's talk: Action rigidity for free poducts of closed hyperbolic manifold groups Varghese's talk: Automorphism groups of Coxeter groups do not have Kazhdan's property (T) Walsh's talk: Incoherence of free-by-free and surface-by-freegroups Ze open question session

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• A general messages board


• Balasubramanya's talk: Quasi-Parabolic Structures on Groups
• Are there conditions to have a "best" quasi-parabolic action, like the action of a (hyperbolic) group on its Cayley graph is "best"? (Aaron Calderon)
• Are you hoping to know more about the geometry of this poset of structures? Being more specific, does it have bounded diamater considering a path metric? (Xabier Legaspi Juanatey)
• Could you specify in what parts of your work do you discuss using hyperbolicity? Do you use something else appart from Gromov's classification of actions on hyperbolic spaces? (Xabier Legaspi Juanatey)
• Does every qp-structure (respectively qt-structure) of G always dominate every l-structure of G ? (Yves Stalder)
• Echoing Indira's Question: How does this poset behave under semidirect product? May of the examples you listed in your talk are semidirect products and I wonder if you have observed any patterns here? (Rose Morris-Wright)
• Is there a hope to describe H(G) when G is a nonamenable Baumslag-Solitar group ? (Yves Stalder)
• What's the "prototypical example" of a quasi-parabolic action look like? (Aaron Calderon)



• Cumplido's talk: Complexes of parabolic subgroups for Artin groups
• Can you please give an example of two reduction systems for a reducible element ? (Sahana Balasubramanya)
• Could you explain how the parabolic closure of an element is constructed? (Ignat Soroko)
• Do there are some group results that you get (or expect to get) with your action ? (Anne Lonjou)
• Do you understand the pseudo-Anosov elements in your group (do they share some common properties)? (Anne Lonjou)
• How far does the analogy between curves and irreducible parabolic subgroups go? Is there a way to put an ‘intersection form' on parabolic subgroups like we have for curves on surfaces by the algebraic intersection number? You use commuting centres as a way to encode isotopically disjoint curves, can we index the ‘different ways' centres of parabolics don't commute by the integers? (Jordan Frost)
• If you fix a (p,q,r) triangle group, and look at the corresponding Artin group, is there any relationship between the parabolic subgroup complex and the curve complex for cocompact lattices inside the triangle group? (Aaron Calderon)
• If you look at a parabolic subgroup P of an Artin group A, how does the parabolic subgroup complex of P sit inside that of A? Is it distorted or undistorted? (Aaron Calderon)
• In the theorem of Van der Lek, what is the presentation of the standard of the standard parabolic subgroup? Are the relations exactly the ones we would expect? (Sahana Balasubramanya)
• What about Artin groups corresponding to hyperbolic reflection groups? (Aaron Calderon)



• Fioravanti's talk: Spaces of cubulations
• 1) Would it make sense to consider two cubulations to be equivalent if there exists a 'coarsely' G- equivariant isomorphism between them ? 2) If so, would you result of getting infinitely many distinct cubulations still hold ? (Sahana Balasubramanya)
• Can you say more about the the proof that (rigid) hyperbolic groups have infinitely many cubulations? (and that Burger-Moses groups have only one) (Genevieve Walsh)
• Can you say some words on the panel collapse procedure, maybe go through an example with a cube? (Jordan Frost)
• Does every cubulated group admit an irreducible cubulation with no free faces? If not, then do you know of an alternative to the length function for topologising the space of cubulations? (Sam Shepherd)
• Does every G-action on a median space appear in the boundary of your space ? (Yves Stalder)
• Does the space of cubulations (length functions) tell you anything about the minimum dimension of a cube complex for that group? (Genevieve Walsh)
• Does there exist hyperbolic groups that one can distinguish by looking at their spaces of cubulations ? (Yves Stalder)
• How does the contact graph vary as you change the cubulation? (Daniel Berlyne)
• Is there a natural map between two cubulations of a given group, that would work even if the outer automorphism group is finite? (Suraj Krishna Meda)
• Is there a pairing coming from length functions arising from cubulations and currents on the hyperbolic group, as in the case of the free group and Outer Space? (Aaron Calderon)
• Is there a possibility of having a procedure to remove free faces, analogous to panel collapse? In dimension 2, a free edge can be removed by removing the interiors of that edge and the square containing it. (Suraj Krishna Meda)
• Is there any way to see which cubulation would be the best for a given group ? (Sahana Balasubramanya)
• What does the boundary of your space look like when there is infinitely many 'distinct' cubulations ? (Yves Stalder)
• What does the space of cubulations of a RAAG look like? (Giovanni Paolini)
• You use the fact that the Burger--Mozes group has only one essential, hyperplane essential cubulation without parallel faces to justify the assertion that there are no bad constructions other than a), b), and c). This action is on a square complex, so is there no concern that in higher dimensions there may be similar constructions that you need the full strength of "no free faces" to rule out? (Harry Petyt)



• Hamenstädt's talk: ​Spin mapping class groups and curve graphs
• Can we see some examples of spin structures? (Francesco Fournier Facio)
• Can you work out, starting from an admissible diagram on a genus 3 surface, a concrete spin structure it defines? (Biao Ma)
• Do spin mapping class groups have trivial abelianization? (Sami Douba)
• Does the torelli group sits inside the spin mcg? (Luis Paris)
• What are the spin structures on the torus and how does the mapping class group act on them? (Sami Douba)



• Hoda's talk: Shortcut Graphs and Groups
• A technical question: why in your proof of the alternative characterization the shortcuts (see your picture) do not interact? (Goulnara N. Arzhantseva)
• Are Schreier graphs of strongly shortcut Cayley graphs still strongly shortcut? (Xabier Legaspi Juanatey)
• Do you have any combination results for strongly shortcut groups? It seems like being strongly shortcut will be preserved under free products, what about other graphs of groups? (Sam Shepherd)
• Does there exist a group with a polynomial Dehn function having the same properties as the Baumslag-Solitar group BS(1,2) in your last theorem? (Goulnara N. Arzhantseva)
• Does there exist a non shortcut Cayley graph of a Coxeter group? (Goulnara N. Arzhantseva)
• Following Francesco Fournier Facio's question about the interval, as hyperbolicity is a QI invariant, do you know what values of \xi \in (1/3, \sqrt(2) - 1) are in the same quasi-isometry class? (Jordan Frost)
• If a graph is strongly shortcut for {xi_n} converging to 1, then is it shortcut ? (Sahana Balasubramanya)
• In the characterization of strong shortcut graphs in terms of K-bilipschitz cycles, what happens if you replace these with (K, C)-QI embedded cycles? Do you now get a notion which is invariant under QI? Is it interesting at all? (Francesco Fournier Facio)
• Is there a result characterizing the setting when the subdivision (i.e. taking a barycentric subdivision) of the complex is sufficient to guarantee an isometric embedding of the cycle (as in your Example)? (Goulnara N. Arzhantseva)
• Is there any intuition in knowing which is an 'appropriate' generating set to have a shortcut Cayley graph? For example, in the case of BS(1,2)? (Jone Lopez de Gamiz Zearra)
• Let S be the set of values of \xi such that G is \xi-strongly shortcut if and only if it is hyperbolic. You prove that (1/3, \sqrt(2) - 1) \subset S and 1/2 \notin S, and ask about what is the supremum of S. How about the infimum, is it equal to 1/3? Is it clear that this set should be an interval? (Francesco Fournier Facio)
• Please could you clarify the interplay between strict and non-strict inequalities on \xi and K (e.g. \xi < 1 versus \xi \leq 1) in different cases? (Goulnara N. Arzhantseva)
• Please give more details on the connection to the wall distance. (Goulnara N. Arzhantseva)
• What are interesting examples of (non)-systolic complexes? (Goulnara N. Arzhantseva)
• What can be a high-dimensional generalization (from square to cubical?) of your result on quadric complexes? (Goulnara N. Arzhantseva)
• What is the multiplicative constant (analogous to $2/\pi$) for the distortion of the distance between images of some antipodal points of the circle under a 1-Lipschitz map to a hyperbolic space? (Goulnara N. Arzhantseva)
• Where the notion of systolicity has been introduced first, in combinatorics or in groups? When and by whom it was done? (Goulnara N. Arzhantseva)
• You mention at the end that being strongly shortcut is not a QI-invariant of graphs. Can you give an example? (Francesco Fournier Facio)



• Kielak's talk: Computing fibring of 3-manifoldsand free-by-cyclic groups
• 1) Is there a "canonical" (in some sense) splitting of a free-by-cyclic group? 2) How concrete are the results given by your algorithm in the one-relator case? What would be the description of all splittings for the mapping torus of a->a, b->ba? (Ignat Soroko)
• At the end of your talk you have a Theorem which says your conjecture is true for one-relator groups. Is there an algorithm which computes the element \psi \in Aut(F_n) which realises this? What \psi can arise? (Marco Linton)
• Can something be said when we replace `free-by-cyclic' with `ascending HNN-extension of a free group'? (Marco Linton)
• Can you explain more about the l2 Euler characteristic? Why is it always defined? In the conjecture, are there restrictions on the group G? What if such an A doesn't have its Euler characteristic defined? (Genevieve Walsh)
• Can you explain more about the proof in the 1-relator free by cyclic case? (Genevieve Walsh)
• How much more of the Thurston norm theory generalizes to (hyperbolic) free-by-Z groups? For example, do the boundaries of the fibered faces correspond to interesting structures on the group? Is there an associated notion of entropy for the atoroidal automorphism, and if so, does it extend continuously over the entire fibered face (in the closed surface case, this is a theorem of Fried)? Is there an associated polynomial for any of your fibered faces (a la McMullen's Teichmüller polynomial)? (Aaron Calderon)
• If a free-by-cyclic group has a fibering, is it possible to determine if it corresponds to a 3-manifold ? If so, is it possible to determine which 3-manifold ? (Sahana Balasubramanya)
• Is there any hope of generalizing this L2 definition of the Thurston norm to hyperbolic-by-Z groups? (Aaron Calderon)
• One can build some sort of combinatorial analogue of a mapping torus in your case; take a rose with n loops x I and then glue the boundaries according to the automorphism. Do other algebraic fiberings of the group correspond to geometric information in this space (or vice versa)? (Aaron Calderon)



• Levcovitz's talk: ​Right-angled Coxeter groups commensurable to right-angled Artin groups
• A choice seems to be involved in G_\Lambda starting from \Lambda, namely given an edge (s, t) you can take either st or ts as a generator. It looks like you need the order to be a certain way in the proof of condition R_2. Does this choice really matter? (Francesco Fournier Facio)
• Can the techniques used for detecting RAAG subgroups of RACGs be adapted to the setting of graph products of finite groups (asked by Luis Paris)? (Ivan Levcovitz)
• Can you explain why (st) is an infinite order element of the RACG, when s and t are non-adjacent vertices of the defining graph ? (Sahana Balasubramanya)
• Can you say something about the "dual curve" in the disk diagram and the hyperplane in NPCCC? (Hai Yu)
• Do you know if there is a class of RAAGs where you can characterize finite index subgroups by looking to subgraphs of the extension graph? Similar to the conditions F1 and F2 that you have (Jone Lopez de Gamiz Zearra)
• Give a characterization of finite-index subgroups of RAAGs which correspond to subgraphs of the extension graph (asked by Jone Lopez de Gamiz Zearra). (Ivan Levcovitz)
• In your theorem, is it known if there is any relation between the RAAG that the RACG is quasi-isometric to and the RAAG that the RACG is commensurable to ? (Sahana Balasubramanya)
• What are some obstructions to a RACG being commensurable/quasi-isometric to a RAAG? (Ivan Levcovitz)



• Lonjou's talk: Action of the Cremona group on a CAT(0) cube complex
• 1. Throughout, I gather that you're using the “combinatorial distance” = distance in 1-skeleton. If you set each cube to be a unit cube use the “geometric distance,” does the complex have finite or infinite diameter? 2. What happens if you restrict to blowups of some uniformly bounded height? (by “uniformly bounded height,” I mean what happens if you look at only the complex consisting of those marked surfaces so that the minimal dominating surface is obtained by at most k blowups, where each blowup can blow up arbitrarily many points) Is the corresponding complex still connected? Will it still be CAT(0)? Does this even make sense? (Aaron Calderon)
• Are there similarities between your construction and Farley's construction of a CAT(0) cube complex for digram groups ? Is it known whether the Cremona group is a diagram group ? (Yves Stalder)
• Given an element of the Cremona group acting elliptically on the cube complex, can you describe the set of vertices that are fixed by it? Is this a convex subcomplex (in the combinatorial metric)? (Elia Fioravanti)
• Is the action that you construct proper? Do you know whether the group has property PW? (Tatiana Nagnibeda)



• Margolis' talk: Quasi-actions and almost normal subgroups
• How important is the assumption that X is proper when you show that if G quasi-acts coboundedly on X with coarse stabiliser H then this is quasi-conjugate to the action on G/H? (Harry Petyt)
• If we know that the conjugates of an almost normal subgroup H are all uniformly commensurate, then does this tell us anything stronger than the almost normal hypothesis? (Aaron Calderon)
• In the dichotomy for finitely generated hyperbolic groups, why is there no mixed case? (Francesco Fournier Facio)
• In your theorem about a space X QI to a f.g. hyperbolic group you have two cases. In the continuous case, every cobounded quasi-action on X is quasi-conjugate to an isometric action on a rank one symmetric space - is there one symmetric space that works for all quasi-actions? We can ask the same question in the discrete case, is there one locally finite graph Y such that any quasi-action on X is quasi-conjugate to an isometric action on Y? I think the answer to the second question is no even when X is a free group. (Sam Shepherd)
• Thanks for your beautiful talk alex. I got interest in these concepts. Can you suggest me some references to get an essence of this line of research. Does it have a general view hyperbolic geometry ? (Dr. Abhishek Mukherjee)
• What happens if you weaken the hyperbolicity constraint (relatively hyperbolic, acylindrical, etc.)? For example, are there examples of quasi-actions on relatively hyperbolic spaces which aren't quasi-conjugate to isometric actions on relatively hyperbolic spaces? (Aaron Calderon)



• Morris-Wright's talk: Parabolic subgroups of Infinite type Artin groups
• 1) Do we have a way to tell when the parabolic closure of an element of an FC-type Artin group is actually of finite type? 2) Are the problems of triviality of center and torsion freeness solved for FC-type Artin groups? (Ignat Soroko)
• Are parabolic subgroups convex in some sense when they sit inside the Cayley graph of its ambient Artin-Tits group? (Rose Morris-Wright)
• Are parabolic subgroups convex in some sense when they sit inside the Cayley graph of its ambient Artin-Tits group? (Xabier Legaspi Juanatey)
• Could you give some examples of properties which are true for finite-type Artin groups but are false (or unknown) for FC type? (Aaron Calderon)
• Do you prove somewhere that, if P is a finite type parabolic subgroup of the whole group siting inside a finite type parabolic subgroup R, then P is a parabolic subgroup of R? (Luis Paris)
• Is the Deligne complex not CAT(0) for Artin groups that are not of FC type? (Giovanni Paolini)
• What are the known properties of the action of the FC type Artin groups on the Delinge complex? (Sahana Balasubramanya)



• Runnels' talk: Effectively Generating RAAGs in MCGs
• Can you say a few words about the proof of the undistortion? (Biao Ma)
• Do you know which elements of the right-angled Artin groups that you build in MCG(S) are pseudo-Anosov or reducible? (Jacob Russell)
• Does the power you produce depend on the specific collection of mapping class group elements given or just on the subsurfaces that they are supported on? (Jacob Russell)
• In the Clay-Leininger-Mangahas theorem, the bound depends only on the subsurfaces, while in your theorem it looks like it also depends on the mapping classes. Is there a reason for this? (Sam Shepherd)
• Some of your "enemy relations" come from the braid group of the surface. Can surface braids play a role in this kind of results? (María Cumplido)



• Skipper's talk: Finiteness properties for simple groups
• Can you give an explicit construction of an n-connected space in which your group acts. Do you know if someone has tried to compute higher isoperimetric inequalities for these groups?. (Juan Paucar)
• Could say a few words about the Stein-Farley complex? (Xiaobing Sheng)
• How does the valency d (of the tree on which G_n acts) vary as n grows? (Francesco Fournier Facio)



• Soroko's talk: Intersections and joins of subgroups in free groups
• Could you explain a bit where does this partially linear, partially quadratic bound in your result come from (which you conjecture to be the actual border line), and why it behaves like this? (Alexander Zakharov)
• Friedman and Mineyev proved the "strengthened" Hanna Neumann conjuecture, which also deals with intersections of H with certain conjugates of K (one per double coset). These intersections are visible in the pullback - each connected component corresponds to a different double coset. What effect (if any) do they have on the topological pushout? (Naomi Andrew)
• If H and K are both finite index subgroups of F, then do we have a more complete understanding of which quadruples (rr(H),rr(K),rr(H intersect K),rr(H join K)) are realisable? (Sam Shepherd)
• Is there a moral reason why the group-theoretic conjecture first fails for m=5? (Giles Gardam)
• S.Ivanov and W.Dicks proved some Hanna Neumann type bounds for the Kurosh rank of subgroup intersection in free products (in particular, it's always true with coefficient 6, as proved by Ivanov). Are there any relations between Kurosh ranks of join and intersection known for free products? Or maybe in the particular case when the subgroups intersect trivially with the conjugates to the factors (such subgroups are free)? (Alexander Zakharov)



• Stark's talk: Action rigidity for free poducts of closed hyperbolic manifold groups
• Are there any known one-ended examples of torsion-free abstractly commensurable groups with no common model geometry? What if we remove torsion-free condition? Or some candidates perhaps? (Alexander Zakharov)
• Can two quasi-isometric Baumslag-Solitar groups have no common model geometry? (The full q.i. classification of Baumslag-Solitar groups is known, due to Farb, Mosher and Whyte). What about same question for RAAGs? (Alexander Zakharov)
• Do you know if your methods would work in case the action is not proper, but something weaker (like acylindrical) ? (Sahana Balasubramanya)
• How would hyperbolicity play a role in question #2 (that if two hyperbolic groups act geometrically on the same simplicial complex then they are abstractly commensurable)? (Genevieve Walsh)
• In your slide defining QI rigidity and action rigidity it seemed like there was a missing arrow: the converse of the Milnor-Schwarz Lemma. Does this kind of rigidity have a name? Is it studied? (Francesco Fournier Facio)



• Varghese's talk: Automorphism groups of Coxeter groups do not have Kazhdan's property (T)
• Are there groups Aut(W_\Gamma) known to have the Haagerup property (that is, known to admit a metrically proper action on a Hilbert space) ? (Yves Stalder)
• Does the following conjecture sound reasonable? For every infinite Coxeter group W, the automorphism group Aut(W) virtually maps onto some infinite Coxeter group. (Alain Valette)
• For a Coxeter group $W_\Gamma$, what is an example of an automorphism that is NOT in the subgroup generated by inner automorphisms and automorphisms of the labeled graph $\Gamma$? (Alain Valette)
• In the open question at 21:30: what happens if you take just one connected component? (Alain Valette)
• What are maximal FA subgroups of Artin groups of finite type? (Biao Ma)



• Walsh's talk: Incoherence of free-by-free and surface-by-freegroups
• Is anything known about topological coherence? Say a locally compact group is coherent if all compactly generated subgroups are compactly presented (Francesco Fournier Facio)
• The base case in the inductive argument you shared uses the result that F_2-by-F_m is incoherent (from other work of yours). Could you say a few words about this case and what ingredients in the proof of the F_2-by-F_n case do not generalize to the F_m-by-F_n case? (Ivan Levcovitz)
• The examples of incoherent groups in your talk come from fibrings. Are there known substantially different examples? For instance, is there an example of an incoherent group with finite abelianization? Simple? (Francesco Fournier Facio)



• Ze open question session
• Let G and G' be hyperbolic groups acting geometrically on a proper simplicial complex X. Are G and G' commensurable? (Daniel Woodhouse)
• Are there any interesting computational and geometric questions in group theory? (Talia Fernos)
• Can the techniques used for detecting RAAG subgroups of RACGs be adapted to the setting of graph products of finite groups (asked by Luis Paris)? (Ivan Levcovitz) (Ivan Levcovitz)
• Coherence: It was proven by Droms that a RAAG A_Gamma is coherent iff Gamma is chordal. There are some results in the literature concerning coherence of Coxeter groups but no full characterization in terms of graphs. Is there any hope to characterize coherence of Coxeter groups? (Olga Varghese)
• Do you have any ideas/suggestions for putting on a boundary on an acylindrically hyperbolic group (one that hopefully 'witnesses' the acylindrical behavior) ? (Sahana Balasubramanya)
• Does every finitely presented group with polynomial Dehn function admit a shortcut Cayley graph? (Goulnara N. Arzhantseva)
• Fio1 - Does there exist a cubulated group G such that all its cubulations have free faces? And such that every cubulation of every finite-index subgroup of G also has free faces? For instance, what happens for (i) right-angled Coxeter groups, (ii) hyperbolic 3-manifold groups? (Elia Fioravanti)
• Fio2 - Does every special group admit infinitely many essential, hyperplane-essential cubulations? (Elia Fioravanti)
• Fio3 - Does there exist a hyperbolic group G and an essential, hyperplane-essential cubulation X such that X is isolated (in the length function topology) within the space of essential, hyperplane-essential cubulations of G? (Elia Fioravanti)
• For Cayley graphs, is the strong shortcut property invariant under change of generating sets? (Nima Hoda)
• Give a characterization of finite-index subgroups of RAAGs which correspond to subgraphs of the extension graph (asked by Jone Lopez de Gamiz Zearra). (Ivan Levcovitz)
• How can a group quasi-isometric to a (non-solvable) Baumslag-Solitar group look like? For solvable Baumslag-Solitar groups there are strong rigidity results by Farb and Mosher, but non-solvable ones seem to be way less rigid, in particular, they are all quasi-isometric to each other (except BS(n,n), which are virtually F_n x Z), due to Whyte. (Alexander Zakharov)
• ISO: different ways of getting non-quasi-convex subgroups. (Genevieve Walsh)
• Let G be a one-ended hyperbolic group that is not QI to a rank-1 symmetric space of dimension > 2, and does not contain a quadratically hanging subgroup in its JSJ decomposition. Is G QI-rigid (if G' is QI to G, are they commensurable?) Special cases: random groups? free-by cyclic groups? (Daniel Woodhouse)
• Open questions from Dawid Kielak's talk (gracefully provided by him): 1) Is there an algorithm deciding whether an automorphism of a free group is geometric, i.e., comes from a mapping class of a surface with boundary? 2) Is there a god notion of a `canonical way' of writing a given free-by-cyclic group? 3) What do monodromies corresponding to 1-coclasses lying in the same fibred face have in common? (Alessandra Iozzi)
• Two free factors A,B in a free group F are {\it complementary} if F=A*B*C for some (possibly trivial) free factor C. Whitehead's algorithm decides if given A,B are complementary. Is there an algorithm to decide if given free factors A,B there is a nontrivial free factor C that is complementary to both A and B? This is analogous to an algorithm that determines if two curves in a surface are at distance at most 2 in the curve complex. (Mladen Bestvina)
• What are some obstructions to a RACG being commensurable/quasi-isometric to a RAAG? (Ivan Levcovitz) (Ivan Levcovitz)
• What positive cultural changes will occur / are occurring in the mathematical community as a result of corona? Will the need to physically attend conferences in order to stay in the loop be reduced? (Giles Gardam)
• When is the subgroup membership problem decidable for a RAAG? In particular, is it decidable for the pentagon graph RAAG? Known cases: undecidable when the graph contains an induced square (which happens iff the RAAG contains F_2xF_2), decidable when the graph contains no induced cycles of length 4 or more (due to I.Kapovich, Weidmann and Myasnikov, and these are exactly the coherent RAAGs). (Alexander Zakharov)