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:20260404T111448Z 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 geom etric group theory seminar\n\n\nAbstract\nStudying quasi-isometries betwee n groups is a major theme in geometric group theory. Of particular interes t are the situations where the existence of a quasi-isometry between two g roups implies that the groups are equivalent in a stronger algebraic sense \, such as being commensurable. I will survey some results of this type\, and then talk about recent work with Daniel Woodhouse where we prove quasi -isometric rigidity for certain graphs of virtually free groups\, which in clude "generic" cyclic HNN extensions of free groups.\n LOCATION:https://stable.researchseminars.org/talk/McGillGGT/1/ END:VEVENT BEGIN:VEVENT SUMMARY:Mikołaj Frączyk (University of Chicago) DTSTART:20200916T190000Z DTEND:20200916T200000Z DTSTAMP:20260404T111448Z UID:McGillGGT/2 DESCRIPTION:Title: Growth of mod-p homology in higher rank lattices\nby Mikołaj Frączyk (University of Chicago) as part of McGill geometric group theory seminar\n\n\nAbstract\nIt is known since the late 70s that in locally sym metric spaces of large injectivity radius\, the $k$-th real Betti number d ivided by the volume is approximately equal to the $k$-th $L^2$ Betti numb er. Is there an analogue of this fact for mod-$p$ Betti numbers? This ques tion is still very far from being solved\, except for certain special fami lies of locally symmetric spaces. In this talk\, I want to advertise a rel atively new approach to study the growth of mod-$p$ Betti numbers based on a quantitative description of minimal area representatives of mod-$p$ hom ology classes.\n LOCATION:https://stable.researchseminars.org/talk/McGillGGT/2/ END:VEVENT BEGIN:VEVENT SUMMARY:Michael Lipnowski (McGill University) DTSTART:20200923T190000Z DTEND:20200923T200000Z DTSTAMP:20260404T111448Z UID:McGillGGT/3 DESCRIPTION:Title: Algorithms for building grids\nby Michael Lipnowski (McGill U niversity) as part of McGill geometric group theory seminar\n\n\nAbstract\ nI'll describe an effective method to build grids in many metric spaces of interest in geometric group theory\, e.g. locally symmetric spaces. Joint work with Aurel Page.\n LOCATION:https://stable.researchseminars.org/talk/McGillGGT/3/ END:VEVENT BEGIN:VEVENT SUMMARY:Duncan McCoy (Université du Québec à Montréal) DTSTART:20200930T190000Z DTEND:20200930T200000Z DTSTAMP:20260404T111448Z UID:McGillGGT/4 DESCRIPTION:Title: Characterizing slopes for torus knots and hyperbolic knots\nb y Duncan McCoy (Université du Québec à Montréal) as part of McGill geo metric group theory seminar\n\n\nAbstract\nA slope $p/q$ is a characterizi ng slope for a knot $K$ in the $3$-sphere if the oriented homeomorphism ty pe 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 characteriz ing and that for hyperbolic knots all but finitely many slopes with $q>2$ are characterizing. I will discuss the proofs of these results\, which hav e a surprising amount in common.\n LOCATION:https://stable.researchseminars.org/talk/McGillGGT/4/ END:VEVENT BEGIN:VEVENT SUMMARY:Robert Kropholler (WWU Münster) DTSTART:20201007T190000Z DTEND:20201007T200000Z DTSTAMP:20260404T111448Z UID:McGillGGT/5 DESCRIPTION:Title: Groups of type $FP_2$ over fields\nby Robert Kropholler (WWU Münster) as part of McGill geometric group theory seminar\n\n\nAbstract\n Being of type $FP_2$ is an algebraic shadow of being finitely presented. A long standing question was whether these two classes are equivalent. This was shown to be false in the work of Bestvina and Brady. More recently\, there are many new examples of groups of type $FP_2$ coming with various i nteresting properties. I will begin with an introduction to the finiteness property $FP_2$. 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 $FP_2 (\\mathbb{Z})$.\n LOCATION:https://stable.researchseminars.org/talk/McGillGGT/5/ END:VEVENT BEGIN:VEVENT SUMMARY:Thomas Haettel (Université de Montpellier) DTSTART:20201014T190000Z DTEND:20201014T200000Z DTSTAMP:20260404T111448Z UID:McGillGGT/6 DESCRIPTION:Title: The coarse Helly property\, hierarchical hyperbolicity\, and semi hyperbolicity\nby Thomas Haettel (Université de Montpellier) as part of McGill geometric group theory seminar\n\n\nAbstract\nFor any hierarchic ally hyperbolic group\, and in particular any mapping class\ngroup\, we de fine a new metric that satisfies a coarse Helly property. This\nenables us to deduce that the group is semihyperbolic\, i.e. that it admits\na bound ed quasigeodesic bicombing\, and also that it has finitely many\nconjugacy classes 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://stable.researchseminars.org/talk/McGillGGT/6/ END:VEVENT BEGIN:VEVENT SUMMARY:Asaf Hadari (University of Hawaii at Manoa) DTSTART:20201021T190000Z DTEND:20201021T200000Z DTSTAMP:20260404T111448Z UID:McGillGGT/7 DESCRIPTION:Title: Mapping class groups that do not virtually surject to the integer s\nby Asaf Hadari (University of Hawaii at Manoa) as part of McGill ge ometric group theory seminar\n\n\nAbstract\nMapping class groups of surfac es of genus at least 3 are perfect\, but their finite-index subgroups need not be&mdash\;they can have non-trivial abelianizations. A well-known con jecture of Ivanov states that a finite-index subgroup of a mapping class g roup of a sufficiently high\ngenus has finite abelianization. We will disc uss a proof of this conjecture\, which goes through an equivalent represen tation-theoretic form of the conjecture due to Putman and Wieland.\n LOCATION:https://stable.researchseminars.org/talk/McGillGGT/7/ END:VEVENT BEGIN:VEVENT SUMMARY:Ian Runnels (University of Virginia) DTSTART:20201028T190000Z DTEND:20201028T200000Z DTSTAMP:20260404T111448Z UID:McGillGGT/8 DESCRIPTION:Title: RAAGs in MCGs\nby Ian Runnels (University of Virginia) as par t of McGill geometric group theory seminar\n\n\nAbstract\nWe give a new pr oof of a theorem of Koberda which says that right-angled Artin subgroups o f mapping class groups abound. This alternative approach uses the hierarch ical structure of the curve complex\, which allows for more explicit compu tations. Time permitting\, we will also discuss some applications to the t heory of convex cocompactness in mapping class groups.\n LOCATION:https://stable.researchseminars.org/talk/McGillGGT/8/ END:VEVENT BEGIN:VEVENT SUMMARY:Kathryn Mann (Cornell University) DTSTART:20201104T200000Z DTEND:20201104T210000Z DTSTAMP:20260404T111448Z UID:McGillGGT/9 DESCRIPTION:Title: Stability for hyperbolic groups acting on their boundaries\nb y Kathryn Mann (Cornell University) as part of McGill geometric group theo ry seminar\n\n\nAbstract\nA hyperbolic group acts naturally by homeomorphi sms on its boundary. The theme of this talk is to say that\, in many case s\, such an action has very robust dynamics. \n\nJonathan Bowden and I st udied a very special case of this\, showing if G is the fundamental group of a compact\, negatively curved Riemannian manifold\, then the action of G on its boundary is topologically stable (small perturbations of it are s emi-conjugate\, containing all the dynamical information of the original a ction). In new work with Jason Manning\, we get rid of the Riemannian geom etry and show that such a result holds for hyperbolic groups with sphere b oundary\, using purely large-scale geometric techniques. \n\nThis theme o f studying 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 approach. My talk will give some history and some picture of the large-s cale geometry involved in our work.\n LOCATION:https://stable.researchseminars.org/talk/McGillGGT/9/ END:VEVENT BEGIN:VEVENT SUMMARY:Zachary Munro (McGill University) DTSTART:20201111T200000Z DTEND:20201111T210000Z DTSTAMP:20260404T111448Z UID:McGillGGT/10 DESCRIPTION:Title: Biautomaticity of 2-dimensional Coxeter groups\nby Zachary M unro (McGill University) as part of McGill geometric group theory seminar\ n\n\nAbstract\nIt is still an open problem whether or not Coxeter groups a re biautomatic. A 2-dimensional Coxeter group is a Coxeter group whose fin ite parabolic subgroups are all dihedral groups. Damian Osajda\, Piotr Prz ytycki\, and I were able to prove that 2-dimensional Coxeter groups are bi automatic. 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 talk will be largely self-contained\, although previous exposure to Coxeter groups and biautomaticity will of course be helpful.\n LOCATION:https://stable.researchseminars.org/talk/McGillGGT/10/ END:VEVENT BEGIN:VEVENT SUMMARY:Piotr Przytycki (McGill University) DTSTART:20201118T200000Z DTEND:20201118T210000Z DTSTAMP:20260404T111448Z UID:McGillGGT/11 DESCRIPTION:Title: Tail equivalence of unicorn paths\nby Piotr Przytycki (McGil l University) as part of McGill geometric group theory seminar\n\n\nAbstra ct\nLet $S$ be an orientable surface of finite type. Using Pho-On's infini te unicorn paths\, we prove hyperfiniteness of the orbit equivalence relat ion coming from the action of the mapping class group of $S$ on the Gromov boundary of the arc graph of $S$. This is joint work with Marcin Sabok.\n LOCATION:https://stable.researchseminars.org/talk/McGillGGT/11/ END:VEVENT BEGIN:VEVENT SUMMARY:Mitul Islam (University of Michigan) DTSTART:20201125T200000Z DTEND:20201125T210000Z DTSTAMP:20260404T111448Z UID:McGillGGT/12 DESCRIPTION:Title: Convex co-compact representations of 3-manifold groups\nby M itul Islam (University of Michigan) as part of McGill geometric group theo ry seminar\n\n\nAbstract\nConvex co-compact representations are a generali zation of convex co-compact Kleinian groups. A discrete faithful represent ation into the projective linear group is called convex co-compact if its image acts co-compactly on a properly convex domain in real projective spa ce. In this talk\, I will discuss such representations of 3-manifold group s. I will prove that a closed irreducible orientable 3-manifold group admi ts such a representation only when the manifold is geometric (with Euclide an\, hyperbolic\, or Euclidean $\\times$ hyperbolic geometry) or when each component in its geometric decomposition is hyperbolic. This extends a re sult of Benoist about convex real projective structures on closed 3-manifo lds. In each case\, I will also describe the structure of the representati on and the properly convex domain. This is joint work with Andrew Zimmer.\ n LOCATION:https://stable.researchseminars.org/talk/McGillGGT/12/ END:VEVENT BEGIN:VEVENT SUMMARY:Florestan Brunck (McGill University) DTSTART:20210113T200000Z DTEND:20210113T210000Z DTSTAMP:20260404T111448Z UID:McGillGGT/13 DESCRIPTION:Title: Iterated medial subdivision in surfaces of constant curvature an d applications to acute triangulations of hyperbolic and spherical simplic ial complexes\nby Florestan Brunck (McGill University) as part of McGi ll geometric group theory seminar\n\n\nAbstract\nConsider a triangle in th e Euclidean plane and subdivide it recursively into 4 sub-triangles by joi ning its midpoints. Each generation of this iterated subdivision yields tr iangles which are all similar to the original one and exactly twice as sma ll as the triangle(s) of the previous generation. What happens when we per form this iterated medial triangle subdivision on a geodesic triangle when the underlying space is not Euclidean? I will first produce examples of v arious unfamiliar and unexpected behaviours of this subdivision in non-Euc lidean geometries. I will then show that this iterated subdivision neverth eless "stabilizes in the limit" (in a sense that will be made precise) whe n the underlying space is of constant non-zero curvature. My aim is to com bine this result with a forthcoming result of Christopher Bishop on confor ming triangulations of PSLGs to construct acute triangulations of hyperbol ic and spherical simplicial complexes.\n LOCATION:https://stable.researchseminars.org/talk/McGillGGT/13/ END:VEVENT BEGIN:VEVENT SUMMARY:Anne Lonjou (University of Basel) DTSTART:20210203T200000Z DTEND:20210203T210000Z DTSTAMP:20260404T111448Z UID:McGillGGT/14 DESCRIPTION:Title: Action of the Cremona group on a CAT(0) cube complex\nby Ann e Lonjou (University of Basel) as part of McGill geometric group theory se minar\n\n\nAbstract\nThe Cremona group is the group of birational transfor mations of the projective plane. Even if this group comes from algebraic g eometry\, tools from geometric group theory have been powerful to study it . In this talk\, based on a joint work with Christian Urech\, we will buil d a natural action of the Cremona group on a CAT(0) cube complex. We will then explain how we can obtain new and old group theoretical and dynamical results on the Cremona group.\n LOCATION:https://stable.researchseminars.org/talk/McGillGGT/14/ END:VEVENT BEGIN:VEVENT SUMMARY:Damian Orlef (IMPAN) DTSTART:20201202T200000Z DTEND:20201202T210000Z DTSTAMP:20260404T111448Z UID:McGillGGT/15 DESCRIPTION:Title: Non-orderability of random triangular groups by using random 3 CNF formulas\nby Damian Orlef (IMPAN) as part of McGill geometric grou p theory seminar\n\n\nAbstract\nA random group in the triangular binomial model\n $\\Gamma(n\,p)$ is given by the presentation $\\langle S|R \\rang le$\,\n where $S$ is a set of $n$ generators and $R$ is a random set of\n cyclically reduced relators of length 3 over $S$\, with each relator\n included 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 a nd Żuk\, there exist constants $C\, C'$\,\n such that a random triangula r 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 fin ding a constant $c$ such that\, if\n $p\\in(cn^{-2}\, n^{-3/2-\\varepsil on})$\, 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 the satisfiability of\n a random propositional formula\, constructed from the presentation of\n $\\Gamma$. The left-orderability of quotients will be also discussed.\n LOCATION:https://stable.researchseminars.org/talk/McGillGGT/15/ END:VEVENT BEGIN:VEVENT SUMMARY:Anush Tserunyan (McGill University) DTSTART:20210120T200000Z DTEND:20210120T210000Z DTSTAMP:20260404T111448Z UID:McGillGGT/16 DESCRIPTION:Title: The structure of hyperfinite subequivalence relations of treed e quivalence relations\nby Anush Tserunyan (McGill University) as part o f McGill geometric group theory seminar\n\n\nAbstract\nA large part of mea sured group theory studies structural properties of countable groups that hold "on average". This is made precise by studying the orbit equivalence relations induced by free measurable actions of these groups on a standard probability space. In this vein\, the amenable groups correspond to hyper finite equivalence relations\, and the free groups to the treeable ones. I n joint work with R. Tucker-Drob\, we give a detailed analysis of the stru cture of hyperfinite subequivalence relations of a treed equivalence relat ion on a standard probability space\, deriving the analogues of structural properties of amenable subgroups (copies of $\\mathbb{Z}$) of a free grou p. Most importantly\, just like every such subgroup is contained in a uniq ue maximal one\, we show that even in the non-measure-preserving setting\, every hyperfinite subequivalence relation is contained in a unique maxima l one.\n LOCATION:https://stable.researchseminars.org/talk/McGillGGT/16/ END:VEVENT BEGIN:VEVENT SUMMARY:Jean-Philippe Burelle (Université de Sherbrooke) DTSTART:20210127T200000Z DTEND:20210127T210000Z DTSTAMP:20260404T111448Z UID:McGillGGT/17 DESCRIPTION:Title: Local rigidity of diagonally embedded triangle groups\nby Je an-Philippe Burelle (Université de Sherbrooke) as part of McGill geometri c group theory seminar\n\n\nAbstract\nIn studying moduli spaces of represe ntations of surface groups\, and more generally of hyperbolic groups\, tri angle groups are simple examples which can provide insight into the more g eneral theory. Recent work of Alessandrini&ndash\;Lee&ndash\;Schaffhauser generalized the theory of higher Teichmü\;ller spaces to the setting o f orbifold surfaces\, including triangle groups. In particular\, they defi ned a "Hitchin component" of representations into $\\mathrm{PGL}(n\,\\math bb{R})$ which is homeomorphic to a ball and consists entirely of discrete and faithful representations. They compute the dimension of Hitchin compon ents for triangle groups\, and find that this dimension is positive except for a finite number of low-dimensional examples where the representations are rigid. In contrast with these results and with the torsion-free surfa ce group case\, we show that the composition of the geometric representati on of a hyperbolic triangle group with a diagonal embedding into $\\mathrm {PGL}(2n\,\\mathbb{R})$ or $\\mathrm{PSp}(2n\,\\mathbb{R})$ is always loca lly rigid.\n LOCATION:https://stable.researchseminars.org/talk/McGillGGT/17/ END:VEVENT BEGIN:VEVENT SUMMARY:Jingyin Huang (Ohio State University) DTSTART:20210210T200000Z DTEND:20210210T210000Z DTSTAMP:20260404T111448Z UID:McGillGGT/18 DESCRIPTION:Title: Measure equivalence rigidity of 2-dimensional Artin groups of hy perbolic type\nby Jingyin Huang (Ohio State University) as part of McG ill geometric group theory seminar\n\n\nAbstract\nThe notion of measure eq uivalence between countable groups was introduced by Gromov as a measure-t heoretic analogue of quasi-isometry. We study the class of 2-dimensional A rtin groups of hyperbolic type from the viewpoint of measure equivalence\, and show that if two groups from this class are measure equivalent\, then their "curve graphs" are isomorphic. This reduces the question of measure equivalence of these groups to a combinatorial rigidity question concerni ng their curve graphs\; in particular\, we deduce measure equivalence supe rrigidity 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 concerning boundary amenability of groups acting on certain CAT(-1) spaces . The second is a structural similarity between these Artin groups and map ping class groups from the viewpoint of measure equivalence.\n LOCATION:https://stable.researchseminars.org/talk/McGillGGT/18/ END:VEVENT BEGIN:VEVENT SUMMARY:Kevin Schreve (University of Chicago) DTSTART:20210217T200000Z DTEND:20210217T210000Z DTSTAMP:20260404T111448Z UID:McGillGGT/19 DESCRIPTION:Title: Generalized Tits conjecture for Artin groups\nby Kevin Schre ve (University of Chicago) as part of McGill geometric group theory semina r\n\n\nAbstract\nIn 2001\, Crisp and Paris showed the squares of the stand ard generators of an Artin group generate an "obvious" right-angled Artin subgroup. \nThis resolved an earlier conjecture of Tits. I will introduce a generalization of this conjecture\, where we ask that a larger set of el ements generates another "obvious" right-angled Artin subgroup.\nI will gi ve evidence that this is a good generalization\, explain what classes of A rtin groups we can prove it for\, and give some applications. Joint with K asia Jankiewicz.\n LOCATION:https://stable.researchseminars.org/talk/McGillGGT/19/ END:VEVENT BEGIN:VEVENT SUMMARY:Carolyn Abbott (Columbia University) DTSTART:20210310T200000Z DTEND:20210310T210000Z DTSTAMP:20260404T111448Z UID:McGillGGT/20 DESCRIPTION:Title: Random walks and quasiconvexity in acylindrically hyperbolic gro ups\nby Carolyn Abbott (Columbia University) as part of McGill geometr ic group 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 acylindricall y hyperbolic groups\, a class of groups which includes mapping class group s\, $\\mathrm{Out}(F_n)$\, and right-angled Artin and Coxeter groups\, amo ng many others. I will discuss how a random element of such a group intera cts with fixed subgroups\, especially so-called hyperbolically embedded su bgroups. In particular\, I will discuss when the subgroup generated by a r andom element and a fixed subgroup is a free product\, and I will also des cribe some of the geometric properties of that free product. This is joint work with Michael Hull.\n LOCATION:https://stable.researchseminars.org/talk/McGillGGT/20/ END:VEVENT BEGIN:VEVENT SUMMARY:Daniel Wise (McGill University) DTSTART:20210224T200000Z DTEND:20210224T210000Z DTSTAMP:20260404T111448Z UID:McGillGGT/21 DESCRIPTION:Title: Complete square complexes\nby Daniel Wise (McGill University ) as part of McGill geometric group theory seminar\n\n\nAbstract\nA com plete square complex is a 2-complex $X$ whose universal cover is the p roduct of two trees. Obvious examples are when $X$ is itself the product o f two graphs but there are many other examples. I will give a quick survey of complete square complexes with an aim towards describing some problems about them and describing some small examples that are "irreducible" in t he sense that they do not have a finite cover that is a product.\n LOCATION:https://stable.researchseminars.org/talk/McGillGGT/21/ END:VEVENT BEGIN:VEVENT SUMMARY:Sami Douba (McGill University) DTSTART:20210317T190000Z DTEND:20210317T200000Z DTSTAMP:20260404T111448Z UID:McGillGGT/22 DESCRIPTION:Title: Virtually unipotent elements of 3-manifold groups\nby Sami D ouba (McGill University) as part of McGill geometric group theory seminar\ n\n\nAbstract\nSuppose a group $G$ contains an infinite-order element $g$ such that every finite-dimensional linear representation of $G$ maps some nontrivial power of $g$ to a unipotent matrix. Since unitary matrices are diagonalizable\, and since a unipotent matrix is torsion if its entries li e in a field of positive characteristic\, such a group $G$ does not admit a faithful finite-dimensional unitary representation\, nor is $G$ linear o ver a field of positive characteristic. We discuss manifestations of the a bove phenomenon in various finitely generated groups\, with an emphasis on 3-manifold groups.\n LOCATION:https://stable.researchseminars.org/talk/McGillGGT/22/ END:VEVENT BEGIN:VEVENT SUMMARY:Eduardo Oregon Reyes (University of California\, Berkeley) DTSTART:20210324T190000Z DTEND:20210324T200000Z DTSTAMP:20260404T111448Z UID:McGillGGT/23 DESCRIPTION:Title: Cubulated relatively hyperbolic groups and virtual specialness\nby Eduardo Oregon Reyes (University of California\, Berkeley) as part of McGill geometric group theory seminar\n\n\nAbstract\nIan Agol showed th at hyperbolic groups acting geometrically on CAT(0) cube complexes are vir tually 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 generalization of this result (also obtained independently by Groves and Manning)\, which states that cubulated relatively hyperbolic groups are v irtually special provided the peripheral subgroups are virtually special i n a way that is compatible with the cubulation. In particular\, we deduce virtual specialness for cubulated groups that are hyperbolic relative to v irtually abelian groups\, extending Wise's results for limit groups and fu ndamental groups of cusped hyperbolic 3-manifolds. The main ingredient of the proof is a relative version of Wise's quasi-convex hierarchy theorem\, obtained using recent results by Einstein\, Groves\, and Manning.\n LOCATION:https://stable.researchseminars.org/talk/McGillGGT/23/ END:VEVENT BEGIN:VEVENT SUMMARY:Steve Trettel (Stanford University) DTSTART:20210331T190000Z DTEND:20210331T200000Z DTSTAMP:20260404T111448Z UID:McGillGGT/24 DESCRIPTION:Title: Raymarching the Thurston geometries: visual intuition for geomet ric topology in 3 dimensions\nby Steve Trettel (Stanford University) a s part of McGill geometric group theory seminar\n\n\nAbstract\n

The geom etrization theorem of Thurston and Perelman provides a roadmap to understa nding topology in dimension 3 via geometric means. Specifically\, it state s that every closed 3-manifold has a decomposition into geometric pieces\, and the zoo of these geometric pieces is quite constrained: each is built from one of only eight homogeneous 3-dimensional Riemannian model spaces\ , called the Thurston geometries. So to begin to understand what 3-manifol ds "are like\," we may reduce the problem to first understanding these geo metric pieces.

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For me\, the happy fact that our day-to-day life takes place in three dimensions is a major asset here\; while we can visua lize surfaces extrinsically\, and reason about 4-manifolds via slicing\, o nly for 3-manifolds can we really attempt to answer "what would it feel li ke/look like/be like" to live inside of one. To leverage our natural visua l intuition in three dimensions\, in joint work with Ré\;mi Coulon\, Sabetta Matsumoto\, and Henry Segerman\, we have adapted the computer gra phics technique of raymarching to homogeneous Riemannian metrics. We use t his to produce accurate and real-time intrinsic views of Riemannian 3-mani folds\; specifically the eight Thurston geometries and assorted compact qu otients. In this talk\, I will take you on a tour of these spaces\, and ta lk a bit about the mathematical challenges of actually implementing this.< /p>\n LOCATION:https://stable.researchseminars.org/talk/McGillGGT/24/ END:VEVENT BEGIN:VEVENT SUMMARY:Joshua Frisch (California Institute of Technology) DTSTART:20210407T190000Z DTEND:20210407T200000Z DTSTAMP:20260404T111448Z UID:McGillGGT/25 DESCRIPTION:Title: The ICC property in random walks and dynamics\nby Joshua Fri sch (California Institute of Technology) as part of McGill geometric group theory seminar\n\n\nAbstract\n

A topological dynamical system (i.e. a g roup acting by homeomorphisms on a compact Hausdorff space) is said to be proximal if for any two points $p$ and $q$ we can simultaneously "push th em together" (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\, Glas ner noted that whenever $\\mathbb{Z}$ acts proximally\, that action will h ave a fixed point. He termed groups with this fixed point property “stro ngly amenable”. \nThe Poisson boundary of a random walk on a group is a measure space that corresponds to the space of different asymptotic traje ctories that the random walk might take. Given a group $G$ and a probabili ty measure $\\mu$ on $G$\, the Poisson boundary is trivial (i.e. has no no n-trivial events) if and only if $G$ supports a bounded $\\mu$-harmonic fu nction. A group is called Choquet&ndash\;Deny if its Poisson boundary is t rivial for every $\\mu$.

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In this talk I will discuss work giving a n explicit classification of which groups are Choquet&ndash\;Deny\, which groups are strongly amenable\, and what these mysteriously equivalent clas ses of groups have to do with the ICC property. I will also discuss why st rongly amenable groups can be viewed as strengthening amenability in at le ast three distinct ways\, thus proving the name is extremely well deserved . This is joint work with Yair Hartman\, Omer Tamuz\, and Pooya Vahidi Fer dowsi.

\n LOCATION:https://stable.researchseminars.org/talk/McGillGGT/25/ END:VEVENT END:VCALENDAR