BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Sam Shepherd (University of Oxford) DTSTART:20200909T190000Z DTEND:20200909T200000Z DTSTAMP:20260422T213054Z UID:McGillGGT/1 DESCRIPTION:Title: Quasi-isometric rigidity of generic cyclic HNN extensions of free groups \nby Sam Shepherd (University of Oxford) as part of McGill geometric g roup theory seminar\n\n\nAbstract\nStudying quasi-isometries between group s is a major theme in geometric group theory. Of particular interest are t he situations where the existence of a quasi-isometry between two groups i mplies that the groups are equivalent in a stronger algebraic sense\, such as being commensurable. I will survey some results of this type\, and the n talk about recent work with Daniel Woodhouse where we prove quasi-isomet ric rigidity for certain graphs of virtually free groups\, which include " generic" cyclic HNN extensions of free groups.\n LOCATION:https://researchseminars.org/talk/McGillGGT/1/ END:VEVENT BEGIN:VEVENT SUMMARY:Mikołaj Frączyk (University of Chicago) DTSTART:20200916T190000Z DTEND:20200916T200000Z DTSTAMP:20260422T213054Z UID:McGillGGT/2 DESCRIPTION:Title: Growth of mod-p homology in higher rank lattices\nby Mikołaj Frącz yk (University of Chicago) as part of McGill geometric group theory semina r\n\n\nAbstract\nIt is known since the late 70s that in locally symmetric spaces of large injectivity radius\, the $k$-th real Betti number divided by the volume is approximately equal to the $k$-th $L^2$ Betti number. Is there an analogue of this fact for mod-$p$ Betti numbers? This question is still very far from being solved\, except for certain special families of locally symmetric spaces. In this talk\, I want to advertise a relatively new approach to study the growth of mod-$p$ Betti numbers based on a quan titative description of minimal area representatives of mod-$p$ homology c lasses.\n LOCATION:https://researchseminars.org/talk/McGillGGT/2/ END:VEVENT BEGIN:VEVENT SUMMARY:Michael Lipnowski (McGill University) DTSTART:20200923T190000Z DTEND:20200923T200000Z DTSTAMP:20260422T213054Z UID:McGillGGT/3 DESCRIPTION:Title: Algorithms for building grids\nby Michael Lipnowski (McGill Universi ty) as part of McGill geometric group theory seminar\n\n\nAbstract\nI'll d escribe an effective method to build grids in many metric spaces of intere st in geometric group theory\, e.g. locally symmetric spaces. Joint work w ith Aurel Page.\n LOCATION:https://researchseminars.org/talk/McGillGGT/3/ END:VEVENT BEGIN:VEVENT SUMMARY:Duncan McCoy (Université du Québec à Montréal) DTSTART:20200930T190000Z DTEND:20200930T200000Z DTSTAMP:20260422T213054Z UID:McGillGGT/4 DESCRIPTION:Title: Characterizing slopes for torus knots and hyperbolic knots\nby Dunca n McCoy (Université du Québec à Montréal) as part of McGill geometric group theory seminar\n\n\nAbstract\nA slope $p/q$ is a characterizing slop e for a knot $K$ in the $3$-sphere if the oriented homeomorphism type of $ p/q$-surgery on $K$ determines $K$ uniquely. It is known that for a given torus knot all but finitely many non-integer slopes are characterizing and that for hyperbolic knots all but finitely many slopes with $q>2$ are cha racterizing. I will discuss the proofs of these results\, which have a sur prising amount in common.\n LOCATION:https://researchseminars.org/talk/McGillGGT/4/ END:VEVENT BEGIN:VEVENT SUMMARY:Robert Kropholler (WWU Münster) DTSTART:20201007T190000Z DTEND:20201007T200000Z DTSTAMP:20260422T213054Z UID:McGillGGT/5 DESCRIPTION:Title: Groups of type $FP_2$ over fields\nby Robert Kropholler (WWU Münste r) as part of McGill geometric group theory seminar\n\n\nAbstract\nBeing o f type $FP_2$ is an algebraic shadow of being finitely presented. A long s tanding question was whether these two classes are equivalent. This was sh own to be false in the work of Bestvina and Brady. More recently\, there a re many new examples of groups of type $FP_2$ coming with various interest ing properties. I will begin with an introduction to the finiteness proper ty $FP_2$. I will end by giving a construction to find groups that are of type $FP_2(\\mathbb{F})$ for all fields $\\mathbb{F}$ but not $FP_2(\\math bb{Z})$.\n LOCATION:https://researchseminars.org/talk/McGillGGT/5/ END:VEVENT BEGIN:VEVENT SUMMARY:Thomas Haettel (Université de Montpellier) DTSTART:20201014T190000Z DTEND:20201014T200000Z DTSTAMP:20260422T213054Z UID:McGillGGT/6 DESCRIPTION:Title: The coarse Helly property\, hierarchical hyperbolicity\, and semihyperbo licity\nby Thomas Haettel (Université de Montpellier) as part of McGi ll geometric group theory seminar\n\n\nAbstract\nFor any hierarchically hy perbolic group\, and in particular any mapping class\ngroup\, we define a new metric that satisfies a coarse Helly property. This\nenables us to ded uce that the group is semihyperbolic\, i.e. that it admits\na bounded quas igeodesic bicombing\, and also that it has finitely many\nconjugacy classe s of finite subgroups. This has several other consequences\nfor the group. This is a joint work with Nima Hoda and Harry Petyt.\n LOCATION:https://researchseminars.org/talk/McGillGGT/6/ END:VEVENT BEGIN:VEVENT SUMMARY:Asaf Hadari (University of Hawaii at Manoa) DTSTART:20201021T190000Z DTEND:20201021T200000Z DTSTAMP:20260422T213054Z UID:McGillGGT/7 DESCRIPTION:Title: Mapping class groups that do not virtually surject to the integers\n by Asaf Hadari (University of Hawaii at Manoa) as part of McGill geometric group theory seminar\n\n\nAbstract\nMapping class groups of surfaces of g enus at least 3 are perfect\, but their finite-index subgroups need not be &mdash\;they can have non-trivial abelianizations. A well-known conjecture of Ivanov states that a finite-index subgroup of a mapping class group of a sufficiently high\ngenus has finite abelianization. We will discuss a p roof of this conjecture\, which goes through an equivalent representation- theoretic form of the conjecture due to Putman and Wieland.\n LOCATION:https://researchseminars.org/talk/McGillGGT/7/ END:VEVENT BEGIN:VEVENT SUMMARY:Ian Runnels (University of Virginia) DTSTART:20201028T190000Z DTEND:20201028T200000Z DTSTAMP:20260422T213054Z UID:McGillGGT/8 DESCRIPTION:Title: RAAGs in MCGs\nby Ian Runnels (University of Virginia) as part of Mc Gill geometric group theory seminar\n\n\nAbstract\nWe give a new proof of a theorem of Koberda which says that right-angled Artin subgroups of mappi ng class groups abound. This alternative approach uses the hierarchical st ructure of the curve complex\, which allows for more explicit computations . Time permitting\, we will also discuss some applications to the theory o f convex cocompactness in mapping class groups.\n LOCATION:https://researchseminars.org/talk/McGillGGT/8/ END:VEVENT BEGIN:VEVENT SUMMARY:Kathryn Mann (Cornell University) DTSTART:20201104T200000Z DTEND:20201104T210000Z DTSTAMP:20260422T213054Z UID:McGillGGT/9 DESCRIPTION:Title: Stability for hyperbolic groups acting on their boundaries\nby Kathr yn Mann (Cornell University) as part of McGill geometric group theory semi nar\n\n\nAbstract\nA hyperbolic group acts naturally by homeomorphisms on its boundary. The theme of this talk is to say that\, in many cases\, suc h an action has very robust dynamics. \n\nJonathan Bowden and I studied a very special case of this\, showing if G is the fundamental group of a co mpact\, negatively curved Riemannian manifold\, then the action of G on it s boundary is topologically stable (small perturbations of it are semi-con jugate\, containing all the dynamical information of the original action). In new work with Jason Manning\, we get rid of the Riemannian geometry an d show that such a result holds for hyperbolic groups with sphere boundary \, using purely large-scale geometric techniques. \n\nThis theme of study ing topological dynamics of boundary actions dates back at least as far as work of Sullivan in the 1980's\, although we take a very different approa ch. My talk will give some history and some picture of the large-scale ge ometry involved in our work.\n LOCATION:https://researchseminars.org/talk/McGillGGT/9/ END:VEVENT BEGIN:VEVENT SUMMARY:Zachary Munro (McGill University) DTSTART:20201111T200000Z DTEND:20201111T210000Z DTSTAMP:20260422T213054Z UID:McGillGGT/10 DESCRIPTION:Title: Biautomaticity of 2-dimensional Coxeter groups\nby Zachary Munro (M cGill University) as part of McGill geometric group theory seminar\n\n\nAb stract\nIt is still an open problem whether or not Coxeter groups are biau tomatic. A 2-dimensional Coxeter group is a Coxeter group whose finite par abolic subgroups are all dihedral groups. Damian Osajda\, Piotr Przytycki\ , and I were able to prove that 2-dimensional Coxeter groups are biautomat ic. In this talk\, I will present the outline of our proof and some of the difficulties of generalizing it to other classes of Coxeter groups. The t alk will be largely self-contained\, although previous exposure to Coxeter groups and biautomaticity will of course be helpful.\n LOCATION:https://researchseminars.org/talk/McGillGGT/10/ END:VEVENT BEGIN:VEVENT SUMMARY:Piotr Przytycki (McGill University) DTSTART:20201118T200000Z DTEND:20201118T210000Z DTSTAMP:20260422T213054Z UID:McGillGGT/11 DESCRIPTION:Title: Tail equivalence of unicorn paths\nby Piotr Przytycki (McGill Unive rsity) as part of McGill geometric group theory seminar\n\n\nAbstract\nLet $S$ be an orientable surface of finite type. Using Pho-On's infinite unic orn paths\, we prove hyperfiniteness of the orbit equivalence relation com ing from the action of the mapping class group of $S$ on the Gromov bounda ry of the arc graph of $S$. This is joint work with Marcin Sabok.\n LOCATION:https://researchseminars.org/talk/McGillGGT/11/ END:VEVENT BEGIN:VEVENT SUMMARY:Mitul Islam (University of Michigan) DTSTART:20201125T200000Z DTEND:20201125T210000Z DTSTAMP:20260422T213054Z UID:McGillGGT/12 DESCRIPTION:Title: Convex co-compact representations of 3-manifold groups\nby Mitul Is lam (University of Michigan) as part of McGill geometric group theory semi nar\n\n\nAbstract\nConvex co-compact representations are a generalization of convex co-compact Kleinian groups. A discrete faithful representation i nto the projective linear group is called convex co-compact if its image a cts co-compactly on a properly convex domain in real projective space. In this talk\, I will discuss such representations of 3-manifold groups. I wi ll prove that a closed irreducible orientable 3-manifold group admits such a representation only when the manifold is geometric (with Euclidean\, hy perbolic\, or Euclidean $\\times$ hyperbolic geometry) or when each compon ent in its geometric decomposition is hyperbolic. This extends a result of Benoist about convex real projective structures on closed 3-manifolds. In each case\, I will also describe the structure of the representation and the properly convex domain. This is joint work with Andrew Zimmer.\n LOCATION:https://researchseminars.org/talk/McGillGGT/12/ END:VEVENT BEGIN:VEVENT SUMMARY:Florestan Brunck (McGill University) DTSTART:20210113T200000Z DTEND:20210113T210000Z DTSTAMP:20260422T213054Z UID:McGillGGT/13 DESCRIPTION:Title: Iterated medial subdivision in surfaces of constant curvature and appli cations to acute triangulations of hyperbolic and spherical simplicial com plexes\nby Florestan Brunck (McGill University) as part of McGill geom etric group theory seminar\n\n\nAbstract\nConsider a triangle in the Eucli dean plane and subdivide it recursively into 4 sub-triangles by joining it s midpoints. Each generation of this iterated subdivision yields triangles which are all similar to the original one and exactly twice as small as t he triangle(s) of the previous generation. What happens when we perform th is iterated medial triangle subdivision on a geodesic triangle when the un derlying space is not Euclidean? I will first produce examples of various unfamiliar and unexpected behaviours of this subdivision in non-Euclidean geometries. I will then show that this iterated subdivision nevertheless " stabilizes in the limit" (in a sense that will be made precise) when the u nderlying space is of constant non-zero curvature. My aim is to combine th is result with a forthcoming result of Christopher Bishop on conforming tr iangulations of PSLGs to construct acute triangulations of hyperbolic and spherical simplicial complexes.\n LOCATION:https://researchseminars.org/talk/McGillGGT/13/ END:VEVENT BEGIN:VEVENT SUMMARY:Anne Lonjou (University of Basel) DTSTART:20210203T200000Z DTEND:20210203T210000Z DTSTAMP:20260422T213054Z UID:McGillGGT/14 DESCRIPTION:Title: Action of the Cremona group on a CAT(0) cube complex\nby Anne Lonjo u (University of Basel) as part of McGill geometric group theory seminar\n \n\nAbstract\nThe Cremona group is the group of birational transformations of the projective plane. Even if this group comes from algebraic geometry \, tools from geometric group theory have been powerful to study it. In th is talk\, based on a joint work with Christian Urech\, we will build a nat ural action of the Cremona group on a CAT(0) cube complex. We will then ex plain how we can obtain new and old group theoretical and dynamical result s on the Cremona group.\n LOCATION:https://researchseminars.org/talk/McGillGGT/14/ END:VEVENT BEGIN:VEVENT SUMMARY:Damian Orlef (IMPAN) DTSTART:20201202T200000Z DTEND:20201202T210000Z DTSTAMP:20260422T213054Z UID:McGillGGT/15 DESCRIPTION:Title: Non-orderability of random triangular groups by using random 3CNF for mulas\nby Damian Orlef (IMPAN) as part of McGill geometric group theor y seminar\n\n\nAbstract\nA random group in the triangular binomial model\n $\\Gamma(n\,p)$ is given by the presentation $\\langle S|R \\rangle$\,\n where $S$ is a set of $n$ generators and $R$ is a random set of\n cycli cally reduced relators of length 3 over $S$\, with each relator\n include d in $R$ independently with probability $p$. When\n $n\\rightarrow\\infty $\, the asymptotic properties of groups in\n $\\Gamma(n\,p)$ vary widely with the choice of $p=p(n)$. By\n Antoniuk-Łuczak-Świątkowski and Żuk \, there exist constants $C\, C'$\,\n such that a random triangular group is asymptotically almost surely\n (a.a.s.) free\, if $p < Cn^{-2}$\, and a.a.s. infinite\, hyperbolic\, but\n not free\, if $p\\in (C'n^{-2}\, n^ {-3/2-\\varepsilon})$. We generalize\n the second statement by finding a constant $c$ such that\, if\n $p\\in(cn^{-2}\, n^{-3/2-\\varepsilon})$\, then a random triangular group\n is a.a.s. not left-orderable. We prove this by linking\n left-orderability of $\\Gamma \\in \\Gamma(n\,p)$ to th e satisfiability of\n a random propositional formula\, constructed from t he presentation of\n $\\Gamma$. The left-orderability of quotients will b e also discussed.\n LOCATION:https://researchseminars.org/talk/McGillGGT/15/ END:VEVENT BEGIN:VEVENT SUMMARY:Anush Tserunyan (McGill University) DTSTART:20210120T200000Z DTEND:20210120T210000Z DTSTAMP:20260422T213054Z UID:McGillGGT/16 DESCRIPTION:Title: The structure of hyperfinite subequivalence relations of treed equivale nce relations\nby Anush Tserunyan (McGill University) as part of McGil l geometric group theory seminar\n\n\nAbstract\nA large part of measured g roup theory studies structural properties of countable groups that hold "o n average". This is made precise by studying the orbit equivalence relatio ns induced by free measurable actions of these groups on a standard probab ility space. In this vein\, the amenable groups correspond to hyperfinite equivalence relations\, and the free groups to the treeable ones. In joint work with R. Tucker-Drob\, we give a detailed analysis of the structure o f hyperfinite subequivalence relations of a treed equivalence relation on a standard probability space\, deriving the analogues of structural proper ties of amenable subgroups (copies of $\\mathbb{Z}$) of a free group. Most importantly\, just like every such subgroup is contained in a unique maxi mal one\, we show that even in the non-measure-preserving setting\, every hyperfinite subequivalence relation is contained in a unique maximal one.\ n LOCATION:https://researchseminars.org/talk/McGillGGT/16/ END:VEVENT BEGIN:VEVENT SUMMARY:Jean-Philippe Burelle (Université de Sherbrooke) DTSTART:20210127T200000Z DTEND:20210127T210000Z DTSTAMP:20260422T213054Z UID:McGillGGT/17 DESCRIPTION:Title: Local rigidity of diagonally embedded triangle groups\nby Jean-Phil ippe Burelle (Université de Sherbrooke) as part of McGill geometric group theory seminar\n\n\nAbstract\nIn studying moduli spaces of representation s of surface groups\, and more generally of hyperbolic groups\, triangle g roups are simple examples which can provide insight into the more general theory. Recent work of Alessandrini&ndash\;Lee&ndash\;Schaffhauser general ized the theory of higher Teichmü\;ller spaces to the setting of orbif old surfaces\, including triangle groups. In particular\, they defined a " Hitchin component" of representations into $\\mathrm{PGL}(n\,\\mathbb{R})$ which is homeomorphic to a ball and consists entirely of discrete and fai thful representations. They compute the dimension of Hitchin components fo r triangle groups\, and find that this dimension is positive except for a finite number of low-dimensional examples where the representations are ri gid. In contrast with these results and with the torsion-free surface grou p case\, we show that the composition of the geometric representation of a hyperbolic triangle group with a diagonal embedding into $\\mathrm{PGL}(2 n\,\\mathbb{R})$ or $\\mathrm{PSp}(2n\,\\mathbb{R})$ is always locally rig id.\n LOCATION:https://researchseminars.org/talk/McGillGGT/17/ END:VEVENT BEGIN:VEVENT SUMMARY:Jingyin Huang (Ohio State University) DTSTART:20210210T200000Z DTEND:20210210T210000Z DTSTAMP:20260422T213054Z UID:McGillGGT/18 DESCRIPTION:Title: Measure equivalence rigidity of 2-dimensional Artin groups of hyperboli c type\nby Jingyin Huang (Ohio State University) as part of McGill geo metric group theory seminar\n\n\nAbstract\nThe notion of measure equivalen ce between countable groups was introduced by Gromov as a measure-theoreti c analogue of quasi-isometry. We study the class of 2-dimensional Artin gr oups of hyperbolic type from the viewpoint of measure equivalence\, and sh ow that if two groups from this class are measure equivalent\, then their "curve graphs" are isomorphic. This reduces the question of measure equiva lence of these groups to a combinatorial rigidity question concerning thei r curve graphs\; in particular\, we deduce measure equivalence superrigidi ty results for a class of Artin groups whose curve graphs are known to be rigid from a previous work of Crisp. There are two main ingredients in the proof of independent interest. The first is a more general result concern ing boundary amenability of groups acting on certain CAT(-1) spaces. The s econd is a structural similarity between these Artin groups and mapping cl ass groups from the viewpoint of measure equivalence.\n LOCATION:https://researchseminars.org/talk/McGillGGT/18/ END:VEVENT BEGIN:VEVENT SUMMARY:Kevin Schreve (University of Chicago) DTSTART:20210217T200000Z DTEND:20210217T210000Z DTSTAMP:20260422T213054Z UID:McGillGGT/19 DESCRIPTION:Title: Generalized Tits conjecture for Artin groups\nby Kevin Schreve (Uni versity of Chicago) as part of McGill geometric group theory seminar\n\n\n Abstract\nIn 2001\, Crisp and Paris showed the squares of the standard gen erators of an Artin group generate an "obvious" right-angled Artin subgrou p. \nThis resolved an earlier conjecture of Tits. I will introduce a gener alization of this conjecture\, where we ask that a larger set of elements generates another "obvious" right-angled Artin subgroup.\nI will give evid ence that this is a good generalization\, explain what classes of Artin gr oups we can prove it for\, and give some applications. Joint with Kasia Ja nkiewicz.\n LOCATION:https://researchseminars.org/talk/McGillGGT/19/ END:VEVENT BEGIN:VEVENT SUMMARY:Carolyn Abbott (Columbia University) DTSTART:20210310T200000Z DTEND:20210310T210000Z DTSTAMP:20260422T213054Z UID:McGillGGT/20 DESCRIPTION:Title: Random walks and quasiconvexity in acylindrically hyperbolic groups \nby Carolyn Abbott (Columbia University) as part of McGill geometric grou p theory seminar\n\n\nAbstract\nThe properties of a random walk on a group which acts on a hyperbolic metric space have been well-studied in recent years. In this talk\, I will focus on random walks on acylindrically hyper bolic groups\, a class of groups which includes mapping class groups\, $\\ mathrm{Out}(F_n)$\, and right-angled Artin and Coxeter groups\, among many others. I will discuss how a random element of such a group interacts wit h fixed subgroups\, especially so-called hyperbolically embedded subgroups . In particular\, I will discuss when the subgroup generated by a random e lement and a fixed subgroup is a free product\, and I will also describe s ome of the geometric properties of that free product. This is joint work w ith Michael Hull.\n LOCATION:https://researchseminars.org/talk/McGillGGT/20/ END:VEVENT BEGIN:VEVENT SUMMARY:Daniel Wise (McGill University) DTSTART:20210224T200000Z DTEND:20210224T210000Z DTSTAMP:20260422T213054Z UID:McGillGGT/21 DESCRIPTION:Title: Complete square complexes\nby Daniel Wise (McGill University) as pa rt of McGill geometric group theory seminar\n\n\nAbstract\nA complete s quare complex is a 2-complex $X$ whose universal cover is the product of two trees. Obvious examples are when $X$ is itself the product of two g raphs but there are many other examples. I will give a quick survey of com plete square complexes with an aim towards describing some problems about them and describing some small examples that are "irreducible" in the sens e that they do not have a finite cover that is a product.\n LOCATION:https://researchseminars.org/talk/McGillGGT/21/ END:VEVENT BEGIN:VEVENT SUMMARY:Sami Douba (McGill University) DTSTART:20210317T190000Z DTEND:20210317T200000Z DTSTAMP:20260422T213054Z UID:McGillGGT/22 DESCRIPTION:Title: Virtually unipotent elements of 3-manifold groups\nby Sami Douba (M cGill University) as part of McGill geometric group theory seminar\n\n\nAb stract\nSuppose a group $G$ contains an infinite-order element $g$ such th at every finite-dimensional linear representation of $G$ maps some nontriv ial power of $g$ to a unipotent matrix. Since unitary matrices are diagona lizable\, and since a unipotent matrix is torsion if its entries lie in a field of positive characteristic\, such a group $G$ does not admit a faith ful finite-dimensional unitary representation\, nor is $G$ linear over a f ield of positive characteristic. We discuss manifestations of the above ph enomenon in various finitely generated groups\, with an emphasis on 3-mani fold groups.\n LOCATION:https://researchseminars.org/talk/McGillGGT/22/ END:VEVENT BEGIN:VEVENT SUMMARY:Eduardo Oregon Reyes (University of California\, Berkeley) DTSTART:20210324T190000Z DTEND:20210324T200000Z DTSTAMP:20260422T213054Z UID:McGillGGT/23 DESCRIPTION:Title: Cubulated relatively hyperbolic groups and virtual specialness\nby Eduardo Oregon Reyes (University of California\, Berkeley) as part of McGi ll geometric group theory seminar\n\n\nAbstract\nIan Agol showed that hype rbolic groups acting geometrically on CAT(0) cube complexes are virtually special in the sense of Haglund–Wise\, the last step in the proof of the virtual Haken and virtual fibering conjectures. I will talk about a gener alization of this result (also obtained independently by Groves and Mannin g)\, which states that cubulated relatively hyperbolic groups are virtuall y special provided the peripheral subgroups are virtually special in a way that is compatible with the cubulation. In particular\, we deduce virtual specialness for cubulated groups that are hyperbolic relative to virtuall y abelian groups\, extending Wise's results for limit groups and fundament al groups of cusped hyperbolic 3-manifolds. The main ingredient of the pro of is a relative version of Wise's quasi-convex hierarchy theorem\, obtain ed using recent results by Einstein\, Groves\, and Manning.\n LOCATION:https://researchseminars.org/talk/McGillGGT/23/ END:VEVENT BEGIN:VEVENT SUMMARY:Steve Trettel (Stanford University) DTSTART:20210331T190000Z DTEND:20210331T200000Z DTSTAMP:20260422T213054Z UID:McGillGGT/24 DESCRIPTION:Title: Raymarching the Thurston geometries: visual intuition for geometric top ology in 3 dimensions\nby Steve Trettel (Stanford University) as part of McGill geometric group theory seminar\n\n\nAbstract\n

The geometrizat ion theorem of Thurston and Perelman provides a roadmap to understanding t opology in dimension 3 via geometric means. Specifically\, it states that every closed 3-manifold has a decomposition into geometric pieces\, and th e zoo of these geometric pieces is quite constrained: each is built from o ne of only eight homogeneous 3-dimensional Riemannian model spaces\, calle d the Thurston geometries. So to begin to understand what 3-manifolds "are like\," we may reduce the problem to first understanding these geometric pieces.

\n

For me\, the happy fact that our day-to-day life takes p lace in three dimensions is a major asset here\; while we can visualize su rfaces extrinsically\, and reason about 4-manifolds via slicing\, only for 3-manifolds can we really attempt to answer "what would it feel like/look like/be like" to live inside of one. To leverage our natural visual intui tion in three dimensions\, in joint work with Ré\;mi Coulon\, Sabett a Matsumoto\, and Henry Segerman\, we have adapted the computer graphics t echnique of raymarching to homogeneous Riemannian metrics. We use this to produce accurate and real-time intrinsic views of Riemannian 3-manifolds\; specifically the eight Thurston geometries and assorted compact quotients . In this talk\, I will take you on a tour of these spaces\, and talk a bi t about the mathematical challenges of actually implementing this.

\n LOCATION:https://researchseminars.org/talk/McGillGGT/24/ END:VEVENT BEGIN:VEVENT SUMMARY:Joshua Frisch (California Institute of Technology) DTSTART:20210407T190000Z DTEND:20210407T200000Z DTSTAMP:20260422T213054Z UID:McGillGGT/25 DESCRIPTION:Title: The ICC property in random walks and dynamics\nby Joshua Frisch (Ca lifornia Institute of Technology) as part of McGill geometric group theory seminar\n\n\nAbstract\n

A topological dynamical system (i.e. a group ac ting by homeomorphisms on a compact Hausdorff space) is said to be proxim al if for any two points $p$ and $q$ we can simultaneously "push them toge ther" (rigorously\, there is a net $g_n$ such that $\\lim g_n(p) = \\lim g _n(q)$). In his paper introducing the concept of proximality\, Glasner not ed that whenever $\\mathbb{Z}$ acts proximally\, that action will have a f ixed point. He termed groups with this fixed point property “strongly am enable”. \nThe Poisson boundary of a random walk on a group is a measur e space that corresponds to the space of different asymptotic trajectories that the random walk might take. Given a group $G$ and a probability meas ure $\\mu$ on $G$\, the Poisson boundary is trivial (i.e. has no non-trivi al events) if and only if $G$ supports a bounded $\\mu$-harmonic function. A group is called Choquet&ndash\;Deny if its Poisson boundary is trivial for every $\\mu$.

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In this talk I will discuss work giving an expli cit classification of which groups are Choquet&ndash\;Deny\, which groups are strongly amenable\, and what these mysteriously equivalent classes of groups have to do with the ICC property. I will also discuss why strongly amenable groups can be viewed as strengthening amenability in at least thr ee distinct ways\, thus proving the name is extremely well deserved. This is joint work with Yair Hartman\, Omer Tamuz\, and Pooya Vahidi Ferdowsi.< /p>\n LOCATION:https://researchseminars.org/talk/McGillGGT/25/ END:VEVENT END:VCALENDAR