BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Ian Agol (UC Berkeley) DTSTART:20200428T153000Z DTEND:20200428T160000Z DTSTAMP:20260404T095244Z UID:GaTO/1 DESCRIPTION:Title: Virtually algebraically fibered congruence subgroups\nby Ian Agol (UC Berkeley) as part of Geometry and topology online\n\nLecture held in N /A.\n\nAbstract\nAddressing a question of Baker and Reid\, we give a crite rion to show that an arithmetic group has a congruence subgroup that is al gebraically fibered. Some examples to which the criterion applies include: a hyperbolic four-manifold group containing infinitely many Bianchi group s and a complex hyperbolic surface group.\n\nThis is joint work with Matth ew Stover.\n LOCATION:https://stable.researchseminars.org/talk/GaTO/1/ END:VEVENT BEGIN:VEVENT SUMMARY:Genevieve Walsh (Tufts University) DTSTART:20200428T150000Z DTEND:20200428T153000Z DTSTAMP:20260404T095244Z UID:GaTO/2 DESCRIPTION:Title: Incoherence of free-by-free and surface-by-free groups\nby Genevie ve Walsh (Tufts University) as part of Geometry and topology online\n\nLec ture held in N/A.\n\nAbstract\nA group is said to be coherent if every fin itely generated subgroup is finitely presented. This property is enjoyed by free groups\, and the fundamental groups of surfaces and 3-manifolds. A group that is not coherent is incoherent\; it is very interesting to tr y and understand which groups have which property. We will discuss some o f the geometric and topological aspects of this question\, particularly qu asi-convexity and algebraic fibres. We show that free-by-free and surface -by-free groups are incoherent\, when the rank and genus are at least two. \n\nThis is joint work with Robert Kropholler and Stefano Vidussi.\n LOCATION:https://stable.researchseminars.org/talk/GaTO/2/ END:VEVENT BEGIN:VEVENT SUMMARY:Nathan Dunfield (UI Urbana-Champaign) DTSTART:20200505T150000Z DTEND:20200505T153000Z DTSTAMP:20260404T095244Z UID:GaTO/3 DESCRIPTION:Title: Counting incompressible surfaces in three-manifolds\nby Nathan Dun field (UI Urbana-Champaign) as part of Geometry and topology online\n\nLec ture held in N/A.\n\nAbstract\nCounting embedded curves on a hyperbolic su rface as a function of their length has been much studied by Mirzakhani an d others. I will discuss analogous questions about counting incompressible surfaces in a hyperbolic three-manifold\, with the key difference that no w the surfaces themselves have a more intrinsic topology. As there are onl y finitely many incompressible surfaces of bounded Euler characteristic up to isotopy in a hyperbolic three-manifold\, it makes sense to ask how the number of isotopy classes grows as a function of the Euler characteristic . Using Haken’s normal surface theory and facts about branched surfaces\ , we can characterize not just the rate of growth but show it is (essentia lly) a quasi-polynomial. Moreover\, our method allows for explicit computa tions in reasonably complicated examples.\n\nThis is joint work with Stavr os Garoufalidis and Hyam Rubinstein.\n LOCATION:https://stable.researchseminars.org/talk/GaTO/3/ END:VEVENT BEGIN:VEVENT SUMMARY:Priyam Patel (University of Utah) DTSTART:20200505T153000Z DTEND:20200505T160000Z DTSTAMP:20260404T095244Z UID:GaTO/4 DESCRIPTION:Title: Isometry groups of infinite-genus hyperbolic surfaces\nby Priyam P atel (University of Utah) as part of Geometry and topology online\n\nLectu re held in N/A.\n\nAbstract\n

Allcock\, building on the work of Greenbur g\, proved that for any countable group \\(G\\)\, there is a a complete hy perbolic surface whose isometry group is exactly \\(G\\). When \\(G\\) is finite\, Allcock’s construction yields a closed surface. Otherwise\, th e construction gives an infinite-genus surface. \n\n

In this talk\, we d iscuss a related question. We fix any infinite-genus surface \\(S\\) and c haracterise all groups that can arise as the isometry group for a complete hyperbolic structure on \\(S\\). In the process\, we give a classificatio n type theorem for infinite-genus surfaces and\, if time allows\, two appl ications of the main result. \n\n

This talk is based on joint work with T. Aougab and N. Vlamis.\n LOCATION:https://stable.researchseminars.org/talk/GaTO/4/ END:VEVENT BEGIN:VEVENT SUMMARY:Neil Hoffman (Oklahoma SU) DTSTART:20200512T150000Z DTEND:20200512T153000Z DTSTAMP:20260404T095244Z UID:GaTO/5 DESCRIPTION:Title: High crossing knot complements with few tetrahedra\nby Neil Hoffma n (Oklahoma SU) as part of Geometry and topology online\n\nLecture held in N/A.\n\nAbstract\n

It is well known that given a diagram of a knot \\(K \\) with \\(n\\) crossings\, one can construct a\ntriangulation of \\(S^3 - K\\) with at most \\(4n\\) tetrahedra. A natural question is then: give n a triangulation of a knot complement with \\(t\\) tetrahedra\, is the mi nimum crossing number (for a diagram) of K bounded by a linear or polynomi al function in \\(t\\)? We will answer the question in the negative by co nstructing a family of hyperbolic knot complements where for each knot \\( K_n\\) in \\(S^3\\) whose the minimum crossing number goes as a function o f \\(O(b^n)\\) for \\(b > 1\\)\, but the minimum number of tetrahedra in a triangulation of \\(S^3 - K_n\\) is bounded above by \\(O(n)\\). Similar constructions exist for torus and satellite knot complements.\n\n

This is joint work with Robert Haraway.\n LOCATION:https://stable.researchseminars.org/talk/GaTO/5/ END:VEVENT BEGIN:VEVENT SUMMARY:Martin Scharlemann (UC Santa Barbara) DTSTART:20200512T153000Z DTEND:20200512T160000Z DTSTAMP:20260404T095244Z UID:GaTO/6 DESCRIPTION:Title: A strong Haken's theorem\nby Martin Scharlemann (UC Santa Barbara) as part of Geometry and topology online\n\nLecture held in N/A.\n\nAbstra ct\nSuppose that \\(T\\) is a Heegaard splitting\nsurface for a compact or ientable three-manifold \\(M\\)\; suppose\nthat \\(S\\) is a reducing sphe re for \\(M\\). In 1968 Haken\nshowed that there is then also a reducing sphere \\(S^*\\) for\nthe Heegaard splitting. That is\, \\(S^*\\) is a red ucing sphere\nfor \\(M\\) and the surfaces \\(T\\) and \\(S^*\\) intersect in a\nsingle circle. In 1987 Casson and Gordon extended the result\nto b oundary-reducing disks in \\(M\\) and noted that in both\ncases \\(S^*\\) is obtained from \\(S\\) by a sequence of\noperations called one-surgeries . Here we show that in fact\none may take \\(S^* = S\\)\, at least in the case where \\(M\\)\ncontains no \\(S^1 \\times S^2\\) summands.\n LOCATION:https://stable.researchseminars.org/talk/GaTO/6/ END:VEVENT BEGIN:VEVENT SUMMARY:Henry Segerman (Oklahoma SU) DTSTART:20200519T150000Z DTEND:20200519T153000Z DTSTAMP:20260404T095244Z UID:GaTO/7 DESCRIPTION:Title: From veering triangulations to Cannon-Thurston maps\nby Henry Sege rman (Oklahoma SU) as part of Geometry and topology online\n\nLecture held in NA.\n\nAbstract\nAgol introduced veering triangulations of\nmapping to ri\, whose combinatorics are canonically associated\nto the pseudo-Anosov monodromy. In previous work\, Hodgson\,\nRubinstein\, Tillmann and I foun d examples of veering\ntriangulations that are not layered and therefore d o not come\nfrom Agol's construction.\n\n However\, non-layered vee ring triangulations retain many of the\n good properties enjoyed by mapping tori. For example\,\n Schleimer and I constructed a canon ical circular ordering of\n the cusps of the universal cover of a v eering triangulation.\n Its order completion gives the veering c ircle\;\n collapsing a pair of canonically defined laminations gives a\n surjection onto the veering sphere.\n\n In work in progress\, Manning\, Schleimer\, and I prove that the\n vee ring sphere is the Bowditch boundary of the manifold's\n fundamenta l group (with respect to its cusp groups). As an\n application we produce Cannon-Thurston maps for all veering\n triangulations. Thi s gives the first examples of\n Cannon-Thurston maps that do not co me\, even virtually\, from\n surface subgroups.\n LOCATION:https://stable.researchseminars.org/talk/GaTO/7/ END:VEVENT BEGIN:VEVENT SUMMARY:Baris Coskunuzer (UT Dallas) DTSTART:20200519T153000Z DTEND:20200519T160000Z DTSTAMP:20260404T095244Z UID:GaTO/8 DESCRIPTION:Title: Minimal surfaces in hyperbolic three-manifolds\nby Baris Coskunuze r (UT Dallas) as part of Geometry and topology online\n\n\nAbstract\nThe e xistence of minimal surfaces in three-manifolds is a classical problem in both geometric analysis and geometric topology. In the past years\, this q uestion has been settled for closed\, and also for finite volume\, riemann ian three-manifolds. In this talk\, we will prove the existence of smoothl y embedded\, closed\, minimal surfaces in any infinite volume hyperbolic t hree-manifold\, barring a few special cases.\n LOCATION:https://stable.researchseminars.org/talk/GaTO/8/ END:VEVENT BEGIN:VEVENT SUMMARY:Daniel Allcock (UT Austin) DTSTART:20200526T150000Z DTEND:20200526T153000Z DTSTAMP:20260404T095244Z UID:GaTO/9 DESCRIPTION:Title: Big mapping class groups fail the Tits alternative\nby Daniel Allc ock (UT Austin) as part of Geometry and topology online\n\n\nAbstract\nLet \\(S\\) be a surface with infinitely many\npunctures\, or infinitely many handles\, or containing a disk\nminus Cantor set. (This accounts for alm ost all infinite-type\nsurfaces.) Then the mapping class group of S fails to satisfy\nthe Tits alternative. Namely\, we construct a finitely\ngene rated subgroup which is not virtually solvable and\ncontains no free group of rank greater than one. The\nGrigorchuk group is a key element in the construction.\n LOCATION:https://stable.researchseminars.org/talk/GaTO/9/ END:VEVENT BEGIN:VEVENT SUMMARY:Talia Fernos (UNC Greensboro) DTSTART:20200526T153000Z DTEND:20200526T160000Z DTSTAMP:20260404T095244Z UID:GaTO/10 DESCRIPTION:Title: Boundaries and CAT(0) cube complexes\nby Talia Fernos (UNC Greens boro) as part of Geometry and topology online\n\n\nAbstract\nThe universe of \\(\\CAT(0)\\) cube complexes\nis rich and diverse thanks to the ease b y which they can be\nconstructed and the many of natural metrics they admi t. As a\nconsequence\, there are several associated boundaries\, such as\ nthe visual boundary and the Roller boundary. In this talk we\nwill discu ss some relationships between these boundaries\,\ntogether with the Furste nberg-Poisson boundary of a "nicely"\nacting group.\n LOCATION:https://stable.researchseminars.org/talk/GaTO/10/ END:VEVENT BEGIN:VEVENT SUMMARY:Daniel Woodhouse (Oxford) DTSTART:20200602T150000Z DTEND:20200602T153000Z DTSTAMP:20260404T095244Z UID:GaTO/11 DESCRIPTION:Title: Quasi-isometric rigidity of graphs of free groups with cyclic edge gr oups\nby Daniel Woodhouse (Oxford) as part of Geometry and topology on line\n\n\nAbstract\nLet \\(F\\) be a finitely generated free group.\nLet \ \(w_1\\) and \\(w_2\\) be suitably random/generic elements in\n\\(F\\). C onsider the HNN extension \\( G = \\langle F\, t \\\,{\\mid}\\\, t w_1\nt^ {-1} = w_2 \\rangle\\). It is already known that \\(G\\) will be\none-end ed and hyperbolic. What we have shown is that \\(G\\) is\nquasi-isomet rically rigid. That is\, if a finitely\ngenerated group \\(H\\) is qu asi-isometric to \\(G\\)\, then \\(G\\)\nand \\(H\\) are virtually isomorp hic. The main argument\ninvolves applying a new proof of Leighton's graph covering\ntheorem.\n\nOur full result is for finite graphs of groups with virtually\nfree vertex groups and and two-ended edge groups. However the \nstatement here is more technical\; in particular\, not all such\ngroups are quasi-isometrically rigid.\n\nThis is joint work with Sam Shepherd.\n LOCATION:https://stable.researchseminars.org/talk/GaTO/11/ END:VEVENT BEGIN:VEVENT SUMMARY:Rylee Lyman (Tufts) DTSTART:20200602T153000Z DTEND:20200602T160000Z DTSTAMP:20260404T095244Z UID:GaTO/12 DESCRIPTION:Title: Outer automorphisms of free Coxeter groups\nby Rylee Lyman (Tufts ) as part of Geometry and topology online\n\n\nAbstract\nA famous theorem of Birman and Hilden\nprovides a close link between the mapping class grou p of a\npunctured sphere and the centraliser\, in the mapping class\ngroup of a closed surface\, of a hyperelliptic involution.\nThere is a group th eory analogue of this in Out(\\(F_n\\))\, the\nouter automorphism group of a free group. Namely\, the outer\nautomorphism of a free Coxeter grou p is linked to the\ncentraliser\, in Out(\\(F_n\\))\, of a hyperellipt ic involution.\nIn this talk we will meet the outer automorphism group of a\nfree Coxeter group\, try to understand the analogy with mapping\nclass groups\, and survey some recent results and interesting\nquestions.\n LOCATION:https://stable.researchseminars.org/talk/GaTO/12/ END:VEVENT BEGIN:VEVENT SUMMARY:Kathryn Mann (Cornell) DTSTART:20200609T150000Z DTEND:20200609T153000Z DTSTAMP:20260404T095244Z UID:GaTO/13 DESCRIPTION:Title: Large-scale geometry of big mapping class groups\nby Kathryn Mann (Cornell) as part of Geometry and topology online\n\n\nAbstract\nMapping class groups of infinite type surfaces are not finitely generated\; they a re not even locally compact. Nonetheless\, in many cases it is still meani ngful to discuss their large scale geometry. We will explore which mapping class groups have nontrivial coarse geometry.\n\nThis is joint work with Kasra Rafi.\n LOCATION:https://stable.researchseminars.org/talk/GaTO/13/ END:VEVENT BEGIN:VEVENT SUMMARY:Eric Samperson (UIUC) DTSTART:20200609T153000Z DTEND:20200609T160000Z DTSTAMP:20260404T095244Z UID:GaTO/14 DESCRIPTION:Title: How helpful is hyperbolic geometry?\nby Eric Samperson (UIUC) as part of Geometry and topology online\n\n\nAbstract\nHyperbolic geometry se rves dual roles at the intersection of group theory and three-manifold top ology. It plays the hero of group theory — rescuing the field from a mor ass of uncomputability — but the anti-hero of low-dimensional topology —seemingly responsible for much of the complexity of three-manifolds. Wh ere do these roles overlap?\n\nI’ll give examples of group-theoretic inv ariants of three-manifolds (or knots) that are NP-hard to compute\, even f or three-manifolds (or knots) that are promised to be hyperbolic. The basi c idea is to show that the right-angled Artin semigroups of reversible cir cuits (a kind of combinatorial abstraction of particularly simple computer programs) can be quasi-isometrically embedded inside mapping class groups . Recent uniformity results concerning the coarse geometry of curve comple xes play a key role.\n\nThis is joint work with Chris Leininger that build s on previous work with Greg Kuperberg.\n LOCATION:https://stable.researchseminars.org/talk/GaTO/14/ END:VEVENT BEGIN:VEVENT SUMMARY:Corey Bregman (Brandeis) DTSTART:20200616T150000Z DTEND:20200616T153000Z DTSTAMP:20260404T095244Z UID:GaTO/15 DESCRIPTION:Title: Isotopy and equivalence of knots in three-manifolds\nby Corey Bre gman (Brandeis) as part of Geometry and topology online\n\n\nAbstract\nIt is a well-known fact that the notions of\n(ambient) isotopy and equivalence coincide for\nknots in \\(S^3\\). This is because all ori entation-preserving\nhomeomorphisms of \\(S^3\\) are isotopic to the ident ity. In\nthis talk\, we compare the notions of equivalence and isotopy\nf or knots in more general three-manifolds.\n\nWe show that the mapping clas s group of a three-manifold\n"sees" all the isotopy classes of knots\; tha t is\, if an\norientation-preserving homeomorphism fixes every isotopy\ncl ass\, then it is isotopic to the identity. In the case of\n\\(S^1 \\times S^2\\) we give infinitely many examples of knots\nwhose isotopy classes a re changed by the Gluck twist. Along\nthe way we prove that every three-m anifold group satisfies\nGrossman's Property A.\n\nThis is joint work with Paolo Aceto\, Christopher Davis\,\nJungHwan Park\, and Arunima Ray.\n LOCATION:https://stable.researchseminars.org/talk/GaTO/15/ END:VEVENT BEGIN:VEVENT SUMMARY:Caroline Series (Warwick) DTSTART:20200623T150000Z DTEND:20200623T153000Z DTSTAMP:20260404T095244Z UID:GaTO/16 DESCRIPTION:Title: Geometry in non-discrete groups of hyperbolic isometries: Primitive s tability and the Bowditch Q-conditions are equivalent.\nby Caroline Se ries (Warwick) as part of Geometry and topology online\n\n\nAbstract\nTher e are geometrical conditions on a group of hyperbolic isometries which are of interest even when the group is not discrete. We explain two such cond itions\; these are stated in terms of the images of primitive elements of the free group \\(F_2\\) under an \\(\\textrm{SL}(2\,\\mathbb{C})\\) repre sentation. One is Minsky’s condition of primitive stability\; the other is the so-called BQ-conditions introduced by Bowditch and ge neralised by Tan\, Wong\, and Zhang.\n\nThese two conditions have been sho wn to be equivalent by Jaijeong Lee and Binbin Xu (Trans AMS 2020) and ind ependently by the speaker (arxiv 2019). We will explain the ideas using an combination of both methods. If time permits\, we also explain another\, closely related\, condition which constrains the axes of palindromic primi tive elements.\n LOCATION:https://stable.researchseminars.org/talk/GaTO/16/ END:VEVENT BEGIN:VEVENT SUMMARY:Yulan Qing (Toronto) DTSTART:20200616T153000Z DTEND:20200616T160000Z DTSTAMP:20260404T095244Z UID:GaTO/17 DESCRIPTION:Title: The sub-linearly Morse boundary\nby Yulan Qing (Toronto) as part of Geometry and topology online\n\n\nAbstract\nThe Gromov boundary\, of a hyperbolic metric\nspace\, plays a central role in many aspects of geometr ic group\ntheory. In this talk\, we introduce a generalization of the\nGr omov boundary that also applies to non-hyperbolic\nspaces. For a given pro per geodesic metric space and a given\nsublinear function \\(\\kappa\\)\, we define the \\(\\kappa\\)-Morse\nboundary to be the space of all \\(\\ka ppa\\)-sublinearly-Morse\nquasi-geodesics rays starting at a given base po int.\n\nWe show that\, equipped with a coarse version of the cone\ntopolog y\, the \\(\\kappa\\)-boundary is metrizable and is a\nQI-invariant. For some groups\, we show that their Poisson\nboundaries can be realized on th e \\(\\kappa\\)-boundary of their\nCayley graphs. These groups include al l \\(\\CAT(0)\\) groups\,\nmapping class groups\, Teichmü\;ller spaces \, hierarchically\nhyperbolic groups\, and relatively hyperbolic groups.\n \nThis talk is based on joint projects with Ilya Gekhtmann\,\nKasra Rafi\, and Giulio Tiozzo.\n LOCATION:https://stable.researchseminars.org/talk/GaTO/17/ END:VEVENT BEGIN:VEVENT SUMMARY:William Worden (Rice) DTSTART:20200623T153000Z DTEND:20200623T160000Z DTSTAMP:20260404T095244Z UID:GaTO/18 DESCRIPTION:Title: Dehn filling and knot complements that do not irregularly cover\n by William Worden (Rice) as part of Geometry and topology online\n\n\nAbst ract\nIt is a longstanding conjecture of Neumann\nand Reid that exactly th ree knot complements can irregularly\ncover a hyperbolic orbifold -- the f igure-eight knot and the two\nAitchison--Rubinstein dodecahedral knots. T his conjecture\,\nwhen combined with work of Boileau--Boyer--Walsh\, impli es a\nmore recent conjecture of Reid and Walsh\, which states that\nthere are at most three knot complements in the commensurability\nclass of any h yperbolic knot. We give a Dehn filling criterion\nthat is useful for prod ucing large families of knot\ncomplements that satisfy both conjectures.\n \nThe work we will discuss is partially joint with Hoffman and\nMillichap and also partially joint with Chesebro\, Deblois\,\nHoffman\, Millichap\, and Mondal.\n LOCATION:https://stable.researchseminars.org/talk/GaTO/18/ END:VEVENT BEGIN:VEVENT SUMMARY:Michael Landry (WUSTL) DTSTART:20200721T150000Z DTEND:20200721T153000Z DTSTAMP:20260404T095244Z UID:GaTO/19 DESCRIPTION:Title: Faces of the Thurston norm ball up to isotopy\nby Michael Landry (WUSTL) as part of Geometry and topology online\n\n\nAbstract\n

Let \\( M\\) be a three-manifold with\n nondegenerate Thurston norm \\(x\\) on its second homology.\n There is a partial dictionary between th e combinatorics\n of the polyhedral unit ball of \\(x\\) and \n the topological features of \\(M\\). This dictionary is\ n quite incomplete\, but its existing entries are tantalizing.\n

\n

\n Currently\, most of the entries of this dictio nary concern\n fibered faces of the unit ball. Thurston proved tha t these\n organize all fibrations of \\(M\\) over the circle. Frie d and\n Mosher tell us more: for each fibered face \\(F\\) there is a\n (canonical) pseudo-Anosov flow whose Euler class computes the\ n norm \\(x\\) in the cone over \\(F\\). Furthermore\, the flow\n "sees" certain least-complexity surfaces. Further work of\n Mosher shows that\, under certain conditions\, pseudo-Anosov\n flow s can naturally specify nonfibered faces of the unit ball.\n

\n

\n After giving some of this background I will discuss resul ts\n from my recent preprint (see link). I\n show that Agol 's veering triangulations can be used to\n determine faces of Thurs ton norm balls\, to compute the\n Thurston norm over those faces\, and to collate all isotopy\n classes of least-complexity surfaces o ver those faces. This\n analysis includes nonfibered faces.\n

\n\nNo password is required.\n LOCATION:https://stable.researchseminars.org/talk/GaTO/19/ END:VEVENT BEGIN:VEVENT SUMMARY:Rich Schwartz (Brown) DTSTART:20200728T150000Z DTEND:20200728T153000Z DTSTAMP:20260404T095244Z UID:GaTO/20 DESCRIPTION:Title: The spheres of Sol\nby Rich Schwartz (Brown) as part of Geometry and topology online\n\n\nAbstract\nWe give a complete characterization of the cut locus of the identity in Sol\, one of the strangest of the eight T hurston geometries. As a corollary we prove that the metric spheres in Sol are in fact topological spheres.\n\nThis is joint work with Matei Coicule scu\n LOCATION:https://stable.researchseminars.org/talk/GaTO/20/ END:VEVENT BEGIN:VEVENT SUMMARY:Scott Taylor (Colby) DTSTART:20200728T153000Z DTEND:20200728T160000Z DTSTAMP:20260404T095244Z UID:GaTO/21 DESCRIPTION:Title: Equivariant Heegaard genus of reducible three-manifolds\nby Scott Taylor (Colby) as part of Geometry and topology online\n\n\nAbstract\n

\n Suppose that \\(M\\) is a closed\, connected\,\n oriented three-manifold which comes with a group action by a\n finite group of (orientation preserving) diffeomorphisms.\n The equivariant Heegaard genus of \\(M\\) is then the\n minimal genus of an equ ivariant Heegaard surface. The\n equivariant sphere theorem\, toge ther with recent work of\n Scharlemann\, suggests that equivariant Heegaard genus might be\n additive under equivariant connected sum\ , while analogies with\n tunnel number suggest it should not be.\n

\n

\n I will describe some examples showing that e quivariant\n Heegaard genus can be sub-additive\, additive\, or\n super-additive. Building on recent work with Tomova\, I’ll\n sketch machinery that gives rise both to sharp bounds on the\n a ddivity of equivariant Heegaard genus and to a closely\n related in variant that is in fact additive.\n

\n LOCATION:https://stable.researchseminars.org/talk/GaTO/21/ END:VEVENT BEGIN:VEVENT SUMMARY:Marissa Loving (Georgia Tech) DTSTART:20200804T150000Z DTEND:20200804T153000Z DTSTAMP:20260404T095244Z UID:GaTO/22 DESCRIPTION:Title: Covers and curves\nby Marissa Loving (Georgia Tech) as part of Ge ometry and topology online\n\n\nAbstract\n

\n It is a celebrated result of Scott that every\n closed curve on a hyperbolic surface \ \(S\\) lifts to a simple\n closed curve on some finite cover. In t he spirit of this work\n we pose the following question: "What info rmation about two\n covers \\(X\\) and \\(Y\\) of \\(S\\) can be de rived by\n understanding how curves on \\(S\\) lift simply to \\(X\ \) and\n \\(Y\\)?" In this talk\, we will explore the answer to th is\n question for regular finite covers of a closed hyperbolic\n surface.\n

\n

\n This is joint work with Tari k Aougab\, Max Lahn\, and Yang\n (Sunny) Xiao.\n

\n LOCATION:https://stable.researchseminars.org/talk/GaTO/22/ END:VEVENT BEGIN:VEVENT SUMMARY:Sarah Dean Rasmussen (Cambridge) DTSTART:20200804T153000Z DTEND:20200804T160000Z DTSTAMP:20260404T095244Z UID:GaTO/23 DESCRIPTION:Title: Taut foliations from left orders\, in Heegaard genus two\nby Sara h Dean Rasmussen (Cambridge) as part of Geometry and topology online\n\n\n Abstract\n

\n Suppose that \\(M\\) is a closed\, connected\,\n oriented three-manifold which is not graph. All previously\n known constructions of taut foliations on such \\(M\\) used\n branc hed surfaces. These branched surfaces come from sutured\n manifold hierarchies\, following Gabai\, come from spanning\n surfaces of k not exteriors\, following Roberts\, or come from\n one-vertex trian gulations with foliar orientations\, following\n Dunfield.\n < /p>\n

\n In this talk\, we give a new construction that doe s not use\n branched surfaces. Instead\, we build a taut foliation from\n the data of a Heegaard diagram for \\(M\\) and a left order on\n the fundamental group \\(\\pi_1(M)\\). We glue an\n \ \(\\mathbb{R}\\)-transverse foliation (over a thickened Heegaard\n surface) to a pair of handlebody foliations\; we then suitably\n ca ncel any singularities. For Heegaard diagrams satisfying\n mild co nditions\, this can be done reliably in Heegaard genus\n two. In s ome cases this construction can be extended to\n higher Heegaard ge nus. This helps explain numerical results\n of Dunfield: (i) tens of thousands of Heegaard-genus two\n hyperbolic L-spaces certifiabl y fail to admit fundamental\n group left orders and (ii) no hyperbo lic L-space is known to\n admit a fundamental group left order.\n

\n LOCATION:https://stable.researchseminars.org/talk/GaTO/23/ END:VEVENT BEGIN:VEVENT SUMMARY:Kasia Jankiewicz (Chicago) DTSTART:20200818T150000Z DTEND:20200818T153000Z DTSTAMP:20260404T095244Z UID:GaTO/24 DESCRIPTION:Title: Generalized Tits conjecture for Artin groups\nby Kasia Jankiewicz (Chicago) as part of Geometry and topology online\n\n\nAbstract\n

\n The Tits conjecture\, proved by Crisp and\n Paris\, states tha t the subgroup of an Artin group generated by\n powers of the stand ard generators is the "obvious"\n right-angled Artin group (RAAG). We aim to generalize this: the\n subgroup generated by a collectio n of naturally distinguished\n elements\, specifically powers of th e Garside elements\, is a\n RAAG. I will discuss our partial resul ts\, for certain families\n of Artin groups.\n

\n

\n This is joint work with Kevin Schreve.\n

\n LOCATION:https://stable.researchseminars.org/talk/GaTO/24/ END:VEVENT BEGIN:VEVENT SUMMARY:Andras Stipsicz (Renyi) DTSTART:20200811T150000Z DTEND:20200811T153000Z DTSTAMP:20260404T095244Z UID:GaTO/25 DESCRIPTION:Title: Connected Floer homology of covering involutions\nby Andras Stips icz (Renyi) as part of Geometry and topology online\n\n\nAbstract\n

\n We use the covering involution of double\n branched covers of knots to define a knot invariant inspired\n by connected Heegaard Floer homology. Using this\, we obtain\n novel concordance results .\n

\n

\n This is joint work with Antonio Alfieri and Sungkyung Kang.\n

\n LOCATION:https://stable.researchseminars.org/talk/GaTO/25/ END:VEVENT BEGIN:VEVENT SUMMARY:Jing Tao (Oklahoma) DTSTART:20200818T153000Z DTEND:20200818T160000Z DTSTAMP:20260404T095244Z UID:GaTO/26 DESCRIPTION:Title: The Nielsen-Thurston classification\, revisited\nby Jing Tao (Okl ahoma) as part of Geometry and topology online\n\n\nAbstract\n

\n I will explain a new proof of the\n Nielsen-Thurston classificatio n of mapping classes\, using the\n Thurston metric on Teichmuller s pace.\n

\n

\n This is joint work with Camille Horb ez.\n

\n LOCATION:https://stable.researchseminars.org/talk/GaTO/26/ END:VEVENT BEGIN:VEVENT SUMMARY:Dawid Kielak (Oxford) DTSTART:20200825T153000Z DTEND:20200825T160000Z DTSTAMP:20260404T095244Z UID:GaTO/27 DESCRIPTION:Title: Poincaré duality groups\nby Dawid Kielak (Oxford) as part of Geo metry and topology online\n\n\nAbstract\n

\n It is a classical fa ct that a Poincaré\;\n duality group\, in dimension two\, is a surface group. In this\n talk I will discuss a relatively short new proof of this.\n

\n

\n This is joint work with Peter Kropholler.\n

\n LOCATION:https://stable.researchseminars.org/talk/GaTO/27/ END:VEVENT BEGIN:VEVENT SUMMARY:Mehdi Yazdi (Oxford) DTSTART:20201008T140000Z DTEND:20201008T143000Z DTSTAMP:20260404T095244Z UID:GaTO/28 DESCRIPTION:Title: The complexity of determining knot genus in a fixed three-manifold\nby Mehdi Yazdi (Oxford) as part of Geometry and topology online\n\n\nAb stract\n

\n The genus of a knot in a three-manifold is\n defined to be the minimum genus of a compact\, orientable\n s urface bounding that knot\, if such a surface exists. In\n particu lar a knot can be untangled if and only if it has genus\n zero. We consider the computational complexity of determining\n knot genus. Such problems have been studied by several\n mathematicians\; amo ng them are the works of\n Hass-Lagarias-Pippenger\, Agol-Hass-Thur ston\, Agol and\n Lackenby. For a fixed three-manifold the knot ge nus problem asks\,\n given a knot \\(K\\) and an integer \\(g\\)\, whether the genus of \\(K\\) is\n equal to \\(g\\). Marc Lackenby proved that the knot genus problem\n for the three-sphere lies in N P. In joint work with Lackenby\, we\n prove that this can be gener alised to any fixed\, compact\,\n orientable three-manifold\, answe ring a question of\n Agol-Hass-Thurston from 2002.\n

\n LOCATION:https://stable.researchseminars.org/talk/GaTO/28/ END:VEVENT BEGIN:VEVENT SUMMARY:David Gabai (Princeton) DTSTART:20201008T143000Z DTEND:20201008T150000Z DTSTAMP:20260404T095244Z UID:GaTO/29 DESCRIPTION:Title: The fully marked surface theorem\nby David Gabai (Princeton) as p art of Geometry and topology online\n\n\nAbstract\n

\n In his sem inal 1976 paper Bill Thurston\n observed that a closed leaf \\(S\\) of a foliation has Euler\n characteristic equal\, up to sign\, to the Euler class of the\n foliation evaluated on \\([S]\\)\, the hom ology class represented\n by \\(S\\). We give a converse for taut foliations: if the\n underlying manifold is hyperbolic and if the E uler class of a\n taut foliation \\(F\\) evaluated on \\([S]\\) equ als\, up to sign\,\n the Euler characteristic of \\(S\\)\, then the re exists another\n taut foliation \\(F'\\) such that \\(S\\) is ho mologous to a union\n of leaves and such that the plane field of \\ (F'\\) is homotopic\n to that of \\(F\\). In particular\, \\(F\\) and \\(F'\\) have the\n same Euler class.\n

\n

\n In the same paper Thurston proved that taut foliations on\n closed hyperbolic three-manifolds have Euler class of norm at\n mos t one\, and conjectured that\, conversely\, any integral\n cohomolo gy class with norm equal to one is the Euler class of\n a taut foli ation. Work of Yazdi\, together with our main\n result\, give a ne gative answer to Thurston's conjecture.\n

\n

\n Th is is joint work with Mehdi Yazdi.\n

\n LOCATION:https://stable.researchseminars.org/talk/GaTO/29/ END:VEVENT BEGIN:VEVENT SUMMARY:Esmee te Winkel (Warwick) DTSTART:20201015T140000Z DTEND:20201015T143000Z DTSTAMP:20260404T095244Z UID:GaTO/30 DESCRIPTION:Title: Knots in the curve graph\nby Esmee te Winkel (Warwick) as part of Geometry and topology online\n\n\nAbstract\n

\n By a famous theo rem of Thurston the space\n \\(\\PML\\) of projective (measured) la minations on a five-times\n punctured sphere is a three-sphere. An elementary example of a\n projective lamination is a simple closed geodesic with the\n counting measure. This defines a map from the s et of curves to\n \\(\\PML\\)\, which extends to an injective map f rom the curve\n graph to \\(\\PML\\). The topology of the image of the curve\n graph in \\(\\PML\\) and its complement were previously studied\n by Gabai.\n

\n

In this talk we will in troduce certain finite subgraphs of\n the curve graph of the five-t imes punctured sphere and\n determine whether their image in \\(\\P ML\\) is knotted.\n

\n LOCATION:https://stable.researchseminars.org/talk/GaTO/30/ END:VEVENT BEGIN:VEVENT SUMMARY:Rudradip Biswas (Manchester) DTSTART:20201015T143000Z DTEND:20201015T150000Z DTSTAMP:20260404T095244Z UID:GaTO/31 DESCRIPTION:Title: Generation of unbounded derived categories of modules over groups in Kropholler's hierarchy\nby Rudradip Biswas (Manchester) as part of Geo metry and topology online\n\n\nAbstract\n

\n For a group $G$ in Krophol ler's hierarchy and\n a commutative ring $R$\, we will go through some re cently\n discovered generation properties of $D(\\rm{Mod}(RG))$ in terms of\n localising and colocalising subcategories. If time permits\, we\n w ill try to include a few comments on how these generation\n properties sh ed some light on some deep properties of\n $D(\\rm{Mod}(RG))$ as a triang ulated category.\n

\n LOCATION:https://stable.researchseminars.org/talk/GaTO/31/ END:VEVENT BEGIN:VEVENT SUMMARY:Yair Minsky (Yale) DTSTART:20201022T140000Z DTEND:20201022T143000Z DTSTAMP:20260404T095244Z UID:GaTO/32 DESCRIPTION:Title: Veering triangulations and their polynomials\nby Yair Minsky (Yal e) as part of Geometry and topology online\n\n\nAbstract\n

\n Thi s is an introduction to Sam's talk.\n McMullen introduced certain p olynomials associated to fibered\n three-manifolds\, which package together the dynamical data\n associated to all the fibrations in a given fibered face of\n Thurston's norm ball. Agol's veering tria ngulations provide a\n good setting in which similar invariants can be defined. I\n will review this background\, explain the definit ion of the\n "veering Polynomial" and the "taut Polynomial"\, the\n relationship between them\, and how they recover McMullen's\n polynomial in the fibered face.\n

\n

\n This is joint work with Michael Landry and Sam Taylor.\n

\n LOCATION:https://stable.researchseminars.org/talk/GaTO/32/ END:VEVENT BEGIN:VEVENT SUMMARY:Sam Taylor (Temple) DTSTART:20201022T143000Z DTEND:20201022T150000Z DTSTAMP:20260404T095244Z UID:GaTO/33 DESCRIPTION:Title: The veering polynomial\, the flow graph\, and the Thurston norm\n by Sam Taylor (Temple) as part of Geometry and topology online\n\n\nAbstra ct\n

\n This is a continuation of Yair’s talk on the\n v eering polynomial. Here we show how the veering polynomial\n can b e constructed as the Perron polynomial of a certain\n combinatorial ly defined directed graph\, which we call\n the flow graph. This perspective will allows us to\n relate our polynomial to a fac e \\(F\\) of the Thurston norm ball\n and to see that the cone over \\(F\\) is spanned by surfaces that\n are "carried" by the veering triangulation. We’ll also discuss\n criteria for when the face \\(F\\) is fibered.\n

\n

\n This is joint work wit h Michael Landry and Yair Minsky.\n

\n LOCATION:https://stable.researchseminars.org/talk/GaTO/33/ END:VEVENT BEGIN:VEVENT SUMMARY:Mark Bell (Independent) DTSTART:20201029T150000Z DTEND:20201029T153000Z DTSTAMP:20260404T095244Z UID:GaTO/34 DESCRIPTION:Title: Computations in big mapping class groups\nby Mark Bell (Independe nt) as part of Geometry and topology online\n\n\nAbstract\n

\n We will take a brief look at some of the\n computations that are poss ible in big mapping class groups. In\n particular we will discuss t he implementation\n of Bigger\n - a Python package which allows you to study and ma nipulate\n laminations and mapping classes on infinite-type surface s.\n

\n LOCATION:https://stable.researchseminars.org/talk/GaTO/34/ END:VEVENT BEGIN:VEVENT SUMMARY:Chenxi Wu (Rutgers) DTSTART:20201105T150000Z DTEND:20201105T153000Z DTSTAMP:20260404T095244Z UID:GaTO/35 DESCRIPTION:Title: Bounds on asymptotic translation length on free factor and free split ting complexes\nby Chenxi Wu (Rutgers) as part of Geometry and topolog y online\n\n\nAbstract\n

\n The free factor and free splitting co mplexes\n are analogies for the curve complex on surfaces. We found some\n upper bound on the asymptotic translation length on these\n complexes when the train track maps have homotopic mapping\n tori\, analogous to an upper bound we found earlier in the\n sett ing of curve complexes.\n

\n

\n This is joint work with Hyungryul Baik and Dongryul Kim.\n

\n LOCATION:https://stable.researchseminars.org/talk/GaTO/35/ END:VEVENT BEGIN:VEVENT SUMMARY:Ivan Dynnikov (Steklov) DTSTART:20201105T153000Z DTEND:20201105T160000Z DTSTAMP:20260404T095244Z UID:GaTO/36 DESCRIPTION:Title: An algorithm to compare Legendrian knots\nby Ivan Dynnikov (Stekl ov) as part of Geometry and topology online\n\n\nAbstract\n

\n We have worked out a general method to decide\n whether two given Leg endrian knots are Legendrian\n equivalent. The method yields a form al algorithmic solution to\n the problem (with very high algorithmi c complexity) and\, in\n certain circumstances\, allows one to dist inguish Legendrian\n knots practically\, including some cases in wh ich the\n computation of any known algebraic invariant except for t he\n two classical ones (Thurston--Bennequin's and Maslov's) is\n infeasible. We use this\, in particular\, to provide an example\n of an annulus embedded in the three-sphere and tangent to the\n contact structure along the whole boundary\, such that the two\n connected components of the boundary are not equivalent as\n Legend rian knots.\n

\n

\n The talk is based on joint wor ks with Maxim Prasolov and Vladimir Shastin.\n

\n LOCATION:https://stable.researchseminars.org/talk/GaTO/36/ END:VEVENT BEGIN:VEVENT SUMMARY:Tara Brendle (Glasgow) DTSTART:20201203T150000Z DTEND:20201203T153000Z DTSTAMP:20260404T095244Z UID:GaTO/37 DESCRIPTION:Title: The mapping class group of connect sums of \\(S^2 \\times S^1\\)\ nby Tara Brendle (Glasgow) as part of Geometry and topology online\n\n\nAb stract\n

\n Let \\(M_n\\) denote the connect sum of \\(n\\)\n copies of \\(S^2 \\times S^1\\). Laudenbach showed that the\n mapping class group \\(\\Mod(M_n)\\) is an extension of the group\n \\(\\Out(F_n)\\) by \\((\\ZZ/2)^n\\)\, where the latter group is the\n "sphere twist" subgroup of \\(\\Mod(M_n)\\).\n

\n

\n We prove that this extension splits. In this talk\, I will\n describe the splitting and discuss some simplifications of\n Lau denbach's original proof that arise from our techniques.\n

\n

\n This is joint work with N. Broaddus and A. Putman.\n < /p>\n LOCATION:https://stable.researchseminars.org/talk/GaTO/37/ END:VEVENT BEGIN:VEVENT SUMMARY:Ying Hu (UNO) DTSTART:20201203T153000Z DTEND:20201203T160000Z DTSTAMP:20260404T095244Z UID:GaTO/38 DESCRIPTION:Title: Euler class of taut foliations on Q-homology spheres and Dehn filling s\nby Ying Hu (UNO) as part of Geometry and topology online\n\n\nAbstr act\n

\n The Euler class of an oriented plane field\n over a three-manifold is a second cohomology class\, which\n determines the plane field up to isomorphism. In this talk\,\n we will discu ss the Euler class of taut foliations on a\n \\(\\QQ\\)-homology sp here. We view \\(\\QQ\\)-homology spheres as\n Dehn fillings on kno t manifolds and give necessary and\n sufficient conditions for the Euler class of taut foliations\n on such manifolds to vanish. We wi ll also apply these results\n to study the orderability of three-ma nifold groups.\n

\n LOCATION:https://stable.researchseminars.org/talk/GaTO/38/ END:VEVENT BEGIN:VEVENT SUMMARY:Ruth Charney (Brandeis) DTSTART:20201210T150000Z DTEND:20201210T153000Z DTSTAMP:20260404T095244Z UID:GaTO/39 DESCRIPTION:Title: Outer space for right-angled Artin groups\nby Ruth Charney (Brand eis) as part of Geometry and topology online\n\n\nAbstract\n

\n R ight-angled Artin groups (RAAGs) span a\n range of groups from free groups to free abelian groups.\n Thus\, their (outer) automorphism groups range from \\(\\Out(F_n)\\) to\n \\(\\GL(n\,\\ZZ)\\). Automorphis m groups of RAAGs have been well-studied\n over the past decade fro m a purely algebraic viewpoint. To\n allow for a more geometric ap proach\, one needs to construct a\n contractible space with a prope r action of the group.\n

\n

\n In this pair of tal ks we will construct such a space\, namely an\n analogue of Culler- Vogtmann’s Outer Space for arbitrary RAAGs.\n

\n

\n This is joint work with Corey Bregman and Karen Vogtmann.\n

\ n LOCATION:https://stable.researchseminars.org/talk/GaTO/39/ END:VEVENT BEGIN:VEVENT SUMMARY:Corey Bregman (Brandeis) DTSTART:20201210T153000Z DTEND:20201210T160000Z DTSTAMP:20260404T095244Z UID:GaTO/40 DESCRIPTION:Title: Outer space for right-angled Artin groups\nby Corey Bregman (Bran deis) as part of Geometry and topology online\n\n\nAbstract\n

\n Right-angled Artin groups (RAAGs) span a\n range of groups from fre e groups to free abelian groups.\n Thus\, their (outer) automorphism group s range from \\(\\Out(F_n)\\) to\n \\(\\GL(n\,\\ZZ)\\). Automorphi sm groups of RAAGs have been well-studied\n over the past decade fr om a purely algebraic viewpoint. To\n allow for a more geometric a pproach\, one needs to construct a\n contractible space with a prop er action of the group.\n

\n

\n In this pair of ta lks we will construct such a space\, namely an\n analogue of Culler -Vogtmann’s Outer Space for arbitrary RAAGs.\n

\n

\n This is joint work with Ruth Charney and Karen Vogtmann.\n

\ n LOCATION:https://stable.researchseminars.org/talk/GaTO/40/ END:VEVENT BEGIN:VEVENT SUMMARY:Robert Kropholler (University of Warwick) DTSTART:20211007T140500Z DTEND:20211007T145500Z DTSTAMP:20260404T095244Z UID:GaTO/41 DESCRIPTION:Title: Coarse embeddings and homological filling functions\nby Robert Kr opholler (University of Warwick) as part of Geometry and topology online\n \n\nAbstract\n

\n The homological filling function of a\n finitely presented group \\(G\\) measures the difficulty of\n filli ng loops with surfaces in a classifying space. The\n behaviour of t his function when passing to finitely presented\n subgroups is rath er wild. If one adds assumptions on the\n dimension of \\(G\\)\, t hen one can bound the homological filling\n function of the subgrou p by that of \\(G\\). I will discuss how\n to generalise these res ults from subgroups to coarse\n embeddings and also to higher dimen sional filling functions.\n

\n

\n This is joint wo rk with Mark Pengitore.\n

\n\nWe start five minutes after the hou r.\n LOCATION:https://stable.researchseminars.org/talk/GaTO/41/ END:VEVENT BEGIN:VEVENT SUMMARY:Ian Leary (Southampton) DTSTART:20211014T140500Z DTEND:20211014T145500Z DTSTAMP:20260404T095244Z UID:GaTO/42 DESCRIPTION:Title: Graphical small cancellation and groups of type \\(\\mathrm{FP}\\)\nby Ian Leary (Southampton) as part of Geometry and topology online\n\n\ nAbstract\n

\n Graphical small cancellation was introduced\n by Gromov to embed an expanding family inside the Cayley graph\n of a finitely generated group. We use this technique to\n constru ct a large family of groups of type \\(\\mathrm{FP}\\)\, most of\n which are not finitely presented. This is the first time\n non-fin itely presented groups of type \\(\\mathrm{FP}\\) have been\n const ructed without using Bestvina-Brady Morse theory.\n I will g ive an idea of how graphical small cancellation works\n and how we use it.\n

\n

\n This is joint work with Tom Brown. \n

\n LOCATION:https://stable.researchseminars.org/talk/GaTO/42/ END:VEVENT BEGIN:VEVENT SUMMARY:Giles Gardam (Münster) DTSTART:20211125T150500Z DTEND:20211125T155500Z DTSTAMP:20260404T095244Z UID:GaTO/43 DESCRIPTION:Title: The Kaplansky conjectures\nby Giles Gardam (Münster) as part of Geometry and topology online\n\n\nAbstract\nThree conjectures on group rin gs of torsion-free groups are commonly attributed to Kaplansky\, namely th e unit\, zero divisor and idempotent conjectures. For example\, the zero d ivisor conjecture predicts that if $K$ is a field and $G$ is a torsion-fre e group\, then the group ring $K[G]$ has no zero divisors. I will discuss these conjectures and their relationship to other conjectures and properti es of groups. I will then explain how modern solvers for Boolean satisfiab ility can be applied to them\, producing the first counterexample to the u nit conjecture.\n LOCATION:https://stable.researchseminars.org/talk/GaTO/43/ END:VEVENT BEGIN:VEVENT SUMMARY:Sam Kim (KIAS) DTSTART:20211118T150500Z DTEND:20211118T155500Z DTSTAMP:20260404T095244Z UID:GaTO/44 DESCRIPTION:Title: Optimal regularity of mapping class group actions on the circle\n by Sam Kim (KIAS) as part of Geometry and topology online\n\n\nAbstract\nW e prove that for each finite index subgroup $H$ of the mapping class group of a closed hyperbolic surface\, and for each real number $r>1$ there doe s not exist a faithful $C^r$-action (in Hölder's sense) of $H$ on a circl e. For this\, we partially determine the optimal regularity of faithful ac tions by right-angled Artin groups on a circle. (Joint with Thomas Koberda and Cristobal Rivas)\n LOCATION:https://stable.researchseminars.org/talk/GaTO/44/ END:VEVENT BEGIN:VEVENT SUMMARY:Camille Horbez (Orsay) DTSTART:20211021T140500Z DTEND:20211021T145500Z DTSTAMP:20260404T095244Z UID:GaTO/45 DESCRIPTION:Title: Orbit equivalence rigidity of irreducible actions of right-angled Art in groups\nby Camille Horbez (Orsay) as part of Geometry and topology online\n\n\nAbstract\n

A central goal in measured group theory is to cla ssify free\, ergodic\, measure-preserving actions of countable groups on p robability spaces up to orbit equivalence: that is\, up to the existence o f a measure space isomorphism sending orbits to orbits. Rigidity occurs wh en orbit equivalence of two actions forces them to be conjugate through a group isomorphism. In this talk\, I will present orbit equivalence rigidit y phenomena for actions of (centerless\, one-ended) right-angled Artin gro ups\, upon imposing that every standard generator acts ergodically on the space.\n\n

This is joint work with Jingyin Huang.\n LOCATION:https://stable.researchseminars.org/talk/GaTO/45/ END:VEVENT BEGIN:VEVENT SUMMARY:Rachel Skipper (OSU) DTSTART:20211104T150500Z DTEND:20211104T155500Z DTSTAMP:20260404T095244Z UID:GaTO/46 DESCRIPTION:Title: Braiding groups of homeomorphisms of Cantor sets\nby Rachel Skipp er (OSU) as part of Geometry and topology online\n\n\nAbstract\n

\n We will discuss some ways in which one can\n braid some classica l subgroups of the homeomorphism group of\n the Cantor set. This i ncludes Higman-Thompson groups and\n self-similar groups\, as well as the topological finiteness\n properties of the resulting groups. \n

\n

\n The talk will include some joint work wit h Xiaolei Wu and\n Matthew Zaremsky.\n

\n LOCATION:https://stable.researchseminars.org/talk/GaTO/46/ END:VEVENT BEGIN:VEVENT SUMMARY:Emily Stark (Wesleyan University) DTSTART:20211202T150500Z DTEND:20211202T155500Z DTSTAMP:20260404T095244Z UID:GaTO/47 DESCRIPTION:Title: Graphically discrete groups and rigidity\nby Emily Stark (Wesleya n University) as part of Geometry and topology online\n\n\nAbstract\nRigid ity theorems prove that a group's geometry determines its algebra\, typica lly up to virtual isomorphism. Motivated by rigidity problems\, we study g raphically discrete groups\, which impose a discreteness criterion on the automorphism group of any graph the group acts on geometrically. Classic e xamples of graphically discrete groups include virtually nilpotent groups and fundamental groups of closed hyperbolic manifolds. We will present new examples\, proving this property is not a quasi-isometry invariant. We wi ll discuss action rigidity for free products of residually finite graphica lly discrete groups. This is joint work with Alex Margolis\, Sam Shepherd\ , and Daniel Woodhouse.\n LOCATION:https://stable.researchseminars.org/talk/GaTO/47/ END:VEVENT BEGIN:VEVENT SUMMARY:Arnaud de Mesmay (Laboratoire d'Informatique Gaspard-Monge) DTSTART:20211209T150500Z DTEND:20211209T155500Z DTSTAMP:20260404T095244Z UID:GaTO/48 DESCRIPTION:Title: Short canonical decompositions of non-orientable surfaces\nby Arn aud de Mesmay (Laboratoire d'Informatique Gaspard-Monge) as part of Geomet ry and topology online\n\n\nAbstract\nSuppose that $S$ is a surface and $G \\subset S$ is an embedded graph. In many applications\, during algorith m design\, and even when representing the embedding\, there is a basic tas k: to cut $S$ into a single disk. When $S$ is orientable\, it has long be en known how to compute a canonical cutting system that is also "short": e ach arc of the system runs along each edge of $G$ at most a constant numbe r of times. \n\nIn this talk we survey what is known about such cutting pr oblems. We then explain how to obtain a short canonical system when $S$ i s non-orientable. \n\nThis is joint work with Niloufar Fuladi and Alfredo Hubard.\n LOCATION:https://stable.researchseminars.org/talk/GaTO/48/ END:VEVENT BEGIN:VEVENT SUMMARY:Benjamin Ward (BGSU) DTSTART:20211111T150500Z DTEND:20211111T155500Z DTSTAMP:20260404T095244Z UID:GaTO/49 DESCRIPTION:Title: Massey Products for Graph Homology.\nby Benjamin Ward (BGSU) as p art of Geometry and topology online\n\n\nAbstract\nThis talk is about grap h complexes and their homology. A graph complex can be thought of as a ge neralization of a dg associative algebra\, but with more sophisticated com position operations allowing for particles to collide along any graph\, no t just along a line. Is every graph complex quasi-isomorphic to its homol ogy? Continuing the analogy with associative algebras the answer is no\, but we will see how an A-infinity analog of graph complexes can be used to rectify this situation. We will then discuss what these higher operation s can tell us in the particular cases of Lie and commutative graph homolog y.\n LOCATION:https://stable.researchseminars.org/talk/GaTO/49/ END:VEVENT BEGIN:VEVENT SUMMARY:Kim Ruane (Tufts University) DTSTART:20220113T150500Z DTEND:20220113T155500Z DTSTAMP:20260404T095244Z UID:GaTO/50 DESCRIPTION:Title: Torsion-free groups acting geometrically on the product of two trees< /a>\nby Kim Ruane (Tufts University) as part of Geometry and topology onli ne\n\n\nAbstract\nGiven a group acting geometrically on product of two tre es\, we know that one visual boundary is the topological join of two Canto r sets. We prove that these groups are "boundary rigid": any CAT(0) space on which the group acts has visual boundary homeomorphic to such a join. \n \nSince there is no hyperbolicity going on here\, one cannot expect tha t the natural equivariant quasi-isometry between an arbitrary CAT(0) space and the product of two trees to extend to any sort of map on boundaries\, thus the proof requires new techniques. The proof uses work of Ricks on recognising product splittings from the Tits boundary as well as work of G uralnik and Swenson on general dynamics of a CAT(0) group on both the visu al and Tits boundary. \n\nThis is (recent) joint work with Jankiewicz\, Ka rrer\, and Sathaye.\n LOCATION:https://stable.researchseminars.org/talk/GaTO/50/ END:VEVENT BEGIN:VEVENT SUMMARY:Vladimir Vankov (Southampton) DTSTART:20220120T150500Z DTEND:20220120T155500Z DTSTAMP:20260404T095244Z UID:GaTO/51 DESCRIPTION:Title: Uncountably many quasi-isometric torsion-free groups\nby Vladimir Vankov (Southampton) as part of Geometry and topology online\n\n\nAbstrac t\nThe study of quasi-isometries between finitely generated groups has tra ditionally been one of the more common questions of geometric group theory \, which includes understanding the possible nature of quasi-isometry clas ses in general. There are several precedents for sets of uncountable cardi nality to exhibit surprising behaviour differing from countable sets\, esp ecially when it comes to subgroups. We explore generalising constructions of uncountably many torsion groups falling into the same quasi-isometry cl ass via commensurability\, to the torsion-free setting. This is done by co nsidering bounded cohomology and appealing to algebraic concepts classical ly found in finite group theory\, in order to produce examples of a contin uum of quasi-isometric and torsion-free\, but pairwise non-isomorphic fini tely generated groups.\n LOCATION:https://stable.researchseminars.org/talk/GaTO/51/ END:VEVENT BEGIN:VEVENT SUMMARY:Davide Spriano (Oxford) DTSTART:20220127T150500Z DTEND:20220127T155500Z DTSTAMP:20260404T095244Z UID:GaTO/52 DESCRIPTION:Title: Hyperbolic spaces for $\\mathrm{CAT}(0)$ groups\nby Davide Sprian o (Oxford) as part of Geometry and topology online\n\n\nAbstract\n$\\mathr m{CAT}(0)$ spaces\, as avatars of non-positive curvature\, are both old an d widely studied. Making up an important subclass are the $\\mathrm{CAT}( 0)$ cube complexes: spaces obtained by gluing Euclidean $n$-cubes along fa ces and satisfying an additional combinatorial conditions. Given such a s pace $X$\, there are several techniques to construct associated spaces tha t "detect the hyperbolic behaviour" of $X$. All of these techniques rely on the combinatorial structure coming from the cubes. \n\nIn this talk we will present a new approach to construct hyperbolic spaces on which $\\mat hrm{CAT}(0)$ groups act. We thus obtain characterisations of rank-one ele ments and recover rank-rigidity results. \n\nThis is joint work with H. Pe tyt and A. Zalloum.\n LOCATION:https://stable.researchseminars.org/talk/GaTO/52/ END:VEVENT BEGIN:VEVENT SUMMARY:Annette Karrer (Technion) DTSTART:20220217T150500Z DTEND:20220217T155500Z DTSTAMP:20260404T095244Z UID:GaTO/53 DESCRIPTION:Title: Connected components of Morse boundaries of graphs of groups\nby Annette Karrer (Technion) as part of Geometry and topology online\n\n\nAbs tract\n

Each finitely generated group has a\n topological space associated to it called the Morse boundary.\n This boundary general izes the Gromov boundary of\n Gromov-hyperbolic groups and captures how similar the group is\n to a Gromov-hyperbolic group.\n \n

\n In this talk\, we will study connected components o f Morse\n boundaries of a graph of groups \\(G\\). We will focus o n the\n case where the edge groups are undistorted and do not\n contribute to the Morse boundary of \\(G\\). We will describe\n the connected components of the Morse boundary of \\(G\\) using\n the associated Bass-Serre tree. We will see that every\n connecte d component of the Morse boundary with at least two\n points origin ates from the Morse boundary of a vertex group.\n

\n

\n This is joint work with Elia Fioravanti.\n

\n LOCATION:https://stable.researchseminars.org/talk/GaTO/53/ END:VEVENT BEGIN:VEVENT SUMMARY:Luke Jeffreys (Bristol) DTSTART:20220224T150500Z DTEND:20220224T155500Z DTSTAMP:20260404T095244Z UID:GaTO/54 DESCRIPTION:Title: Non-planarity of SL(2\,Z)-orbits of origamis in genus two\nby Luk e Jeffreys (Bristol) as part of Geometry and topology online\n\n\nAbstract \n

Origamis (also known as square-tiled\n surfaces) arise naturally in a variety of settings in\n low-dimensional topology. They can be thought of as surfaces\n obtained by gluing the sides of a collection of unit squares.\n As such\, they generalise the to rus which can be obtained by\n gluing the sides of a single square. An origami is said to be\n primitive if it is not a cover of a lower genus\n origami.\n

\n

\n In this talk\, I will describe how one can define an action of\n the matri x group \\(\\mathrm{SL}(2\,\\mathbb{Z})\\) on primitive origamis. In\n genus two (with one singularity)\, the orbits of this action\n were classified by Hubert-Lelièvre and McMullen. By\n considerin g a generating set of size two for \\(\\mathrm{SL}(2\,\\mathbb{Z})\\)\,\n we can turn these orbits into an infinite family of\n four-v alent graphs. For a specific generating set\, I will\n explain how all but two of these graphs are non-planar. I\n will also discuss why this gives indirect evidence for\n McMullen's conjecture that these graphs form a family of\n expanders.\n

\n

\ n This is joint work with Carlos Matheus.\n

\n LOCATION:https://stable.researchseminars.org/talk/GaTO/54/ END:VEVENT BEGIN:VEVENT SUMMARY:Armando Martino (Southampton) DTSTART:20220303T150500Z DTEND:20220303T155500Z DTSTAMP:20260404T095244Z UID:GaTO/55 DESCRIPTION:Title: On automorphisms of free groups and nearly canonical trees\nby Ar mando Martino (Southampton) as part of Geometry and topology online\n\n\nA bstract\n

\n I will discuss some open problems for\n autom orphisms of free groups\; whether centralisers are\n finitely gener ated\, whether their mapping tori have\n well-behaved automorphism group\, and whether the conjugacy\n problem is solvable. I will exp lain some new partial results\,\n using techniques involving canoni cal trees.\n

\n

\n This is joint work Naomi Andrew \, and various others.\n

\n LOCATION:https://stable.researchseminars.org/talk/GaTO/55/ END:VEVENT BEGIN:VEVENT SUMMARY:Macarena Arenas (Cambridge) DTSTART:20220210T150500Z DTEND:20220210T155500Z DTSTAMP:20260404T095244Z UID:GaTO/56 DESCRIPTION:Title: A cubical Rips construction\nby Macarena Arenas (Cambridge) as pa rt of Geometry and topology online\n\n\nAbstract\nThe Rips exact sequence is a useful tool for\n producing examples of groups satisfying comb inations of\n properties that are not obviously compatible. It wor ks by\n taking as an input an arbitrary finitely presented group\n \\(Q\\)\, and producing as an output a hyperbolic group \\(G\\)\n that maps onto \\(Q\\) with finitely generated kernel. The\n "output group" \\(G\\) is crafted by adding generators and\n relat ions to a presentation of \\(Q\\)\, in such a way that these\n rela tions create enough "noise" in the presentation to ensure\n hyperbo licity. One can then lift pathological properties of\n \\(Q\\) to (some subgroup of) \\(G\\). Among other things\, Rips\n used his c onstruction to produce the first examples of\n incoherent hyperboli c groups\, and of hyperbolic groups with\n unsolvable generalised w ord problem.\n\n In this talk\, I will explain Rips' result\, menti on some of its\n variations\, and survey some tools and concepts re lated to\n these constructions\, including small cancellation theor y\,\n cubulated groups\, and asphericity. Time permitting\, I will \n describe a variation of the Rips construction that produces\n cubulated hyperbolic groups of any desired cohomological\n dim ension.\n LOCATION:https://stable.researchseminars.org/talk/GaTO/56/ END:VEVENT BEGIN:VEVENT SUMMARY:Sam Hughes (Oxford) DTSTART:20220310T150500Z DTEND:20220310T155500Z DTSTAMP:20260404T095244Z UID:GaTO/57 DESCRIPTION:Title: Irreducible lattices fibring over the circle\nby Sam Hughes (Oxfo rd) as part of Geometry and topology online\n\n\nAbstract\nLet \\(n \\geq 2\\) and let \\(\\Lambda\\) be a\n lattice in a product of simple n on-compact Lie groups with\n finite centre. An application of the Margulis normal subgroup\n theorem implies that if \\(H^1(\\Lambda)\\) is non-zero\, then\n \\(\\Gamma\\) is reducible. In the more general\ n \\(\\mathrm{CAT}(0)\\) setting there are many irreducible\n lattices with non-vanishing first cohomology. In this case we\n can deploy the BNSR invariants and investigate how far these\n coho mology classes are from a fibration of finite type CW\n complexes. In this talk we will combine the groups of Leary\n and Minasyan wi th the technology of Bestvina and Brady to\n construct the first ex amples of irreducible lattices which\n fibre over the circle.\n LOCATION:https://stable.researchseminars.org/talk/GaTO/57/ END:VEVENT BEGIN:VEVENT SUMMARY:Rylee Lyman (Rutgers) DTSTART:20220317T150500Z DTEND:20220317T155500Z DTSTAMP:20260404T095244Z UID:GaTO/58 DESCRIPTION:Title: Folding-like techniques for CAT(0) cube complexes\nby Rylee Lyman (Rutgers) as part of Geometry and topology online\n\n\nAbstract\nIn a sem inal paper\, Stallings introduced folding of morphisms of graphs. One cons equence of folding is the representation of finitely generated subgroups o f a finite-rank free group as immersions of finite graphs. Stallings's met hods allow one to construct this representation algorithmically\, giving e ffective\, algorithmic answers and proofs to classical questions about sub groups of free groups. Recently Dani–Levcovitz used Stallings-like metho ds to study subgroups of right-angled Coxeter groups\, which act geometric ally on \\(\\mathrm{CAT}(0)\\) cube complexes. We extend their techniques to fundamental groups of non-positively curved cube complexes.\n LOCATION:https://stable.researchseminars.org/talk/GaTO/58/ END:VEVENT BEGIN:VEVENT SUMMARY:Marco Linton (Warwick) DTSTART:20220428T140500Z DTEND:20220428T145500Z DTSTAMP:20260404T095244Z UID:GaTO/59 DESCRIPTION:Title: Hyperbolicity of certain one-relator groups\nby Marco Linton (War wick) as part of Geometry and topology online\n\n\nAbstract\nThe primitivi ty rank of an element \\(w\\) of a free group \\(F\\) is defined as the mi nimal rank of a subgroup containing w as an imprimitive element. Recent w ork of Louder and Wilton has shown that there is a strong connection betwe en this quantity and the subgroup structure of the one-relator group \\(F/ \\langle \\langle w \\rangle \\rangle\\). In particular\, they show that one-relator groups whose defining relation has primitivity rank at least t hree cannot contain Baumslag—Solitar subgroups\, leading them to conject ure that such groups are hyperbolic. In this talk\, I will confirm and st rengthen this conjecture\, providing some applications.\n LOCATION:https://stable.researchseminars.org/talk/GaTO/59/ END:VEVENT BEGIN:VEVENT SUMMARY:Susan Hermiller (Nebraska) DTSTART:20220519T140500Z DTEND:20220519T145500Z DTSTAMP:20260404T095244Z UID:GaTO/60 DESCRIPTION:Title: Formal conjugacy growth for graph products\nby Susan Hermiller (N ebraska) as part of Geometry and topology online\n\n\nAbstract\n

\n The conjugacy growth series of a finitely\n generated group meas ures the growth of conjugacy classes\, in\n analogy with the standa rd growth series that measures the\n growth of elements of the grou p. In contrast\, though\,\n conjugacy growth series are rarely rat ional\, and even for free\n groups with standard generating sets\, the series are\n transcendental and their formulas are rather compl icated. In\n this talk I will discuss several results on conjugacy growth\n and languages in graph products\, including a recursive f ormula\n for computing the conjugacy growth series of a graph produ ct\n in terms of the conjugacy growth and standard growth series of \n subgraph products. In the special case of right-angled Artin\n groups I will also discuss a another formula for the conjugacy\n growth series based on a natural language of conjugacy\n repre sentatives.\n

\n

\n This is joint work with Laura Ciobanu and Valentin Mercier.\n

\n LOCATION:https://stable.researchseminars.org/talk/GaTO/60/ END:VEVENT BEGIN:VEVENT SUMMARY:Marco Barberis (Warwick) DTSTART:20220505T140500Z DTEND:20220505T145500Z DTSTAMP:20260404T095244Z UID:GaTO/61 DESCRIPTION:Title: Curve graphs: exhaustions by rigid sets and the co-Hopfian property\nby Marco Barberis (Warwick) as part of Geometry and topology online\n\ n\nAbstract\nSince Ivanov's celebrated first result\, many rigidity theore ms for various variants of the curve graph of surfaces have been proven. A mong these\, there is a cluster of results regarding the existence of exha ustion via finite subgraphs which are rigid (that is such that every embed ding is induced by an automorphism of the whole graph). From this property \, interesting per se\, the co-Hopfian property of the graphs immediately follows. In this talk I will present the classical results in the fields\, as well as some new cases\, which point toward conjecturing that most cur ve graphs on finite-type surfaces should admit exhaustions by rigid sets\, in line with Ivanov's Metaconjecture.\n LOCATION:https://stable.researchseminars.org/talk/GaTO/61/ END:VEVENT BEGIN:VEVENT SUMMARY:Jean Pierre Mutanguha (IAS) DTSTART:20220512T140500Z DTEND:20220512T145500Z DTSTAMP:20260404T095244Z UID:GaTO/62 DESCRIPTION:Title: Canonical forms for free group automorphisms\nby Jean Pierre Muta nguha (IAS) as part of Geometry and topology online\n\n\nAbstract\nThe Nie lsen-–Thurston theory of surface homeomorphisms can be thought of as a s urface analogue to the Jordan canonical form. I will discuss my progress in developing a similar decomposition for free group automorphisms. (Un)f ortunately\, free group automorphisms can have arbitrarily complicated beh aviour. This forms a significant barrier to translating specific argument s that worked for surfaces into the free group setting\; nevertheless\, th e overall ideas/strategies do translate!\n LOCATION:https://stable.researchseminars.org/talk/GaTO/62/ END:VEVENT BEGIN:VEVENT SUMMARY:Jone Lopez de Gamiz (Warwick) DTSTART:20220526T140500Z DTEND:20220526T145500Z DTSTAMP:20260404T095244Z UID:GaTO/63 DESCRIPTION:Title: On finitely generated normal subgroups of right-angled Artin groups\nby Jone Lopez de Gamiz (Warwick) as part of Geometry and topology onli ne\n\n\nAbstract\n

\n In general\, subgroups of RAAGs are known t o\n have wild structure and bad algorithmic behaviour. However\,\n in this talk we will see that finitely generated normal\n s ubgroups are much more tame. More precisely\, we will show\n that a finitely generated normal subgroup of a RAAG is\n virtually co-ab elian.\n

\n

\n We will then discuss some algorithm ic consequences\, such as\n the decidability of the conjugacy and t he membership problems.\n We will finally discuss residual properti es\, such as conjugacy\n separability\, for finitely generated norm al subgroups of\n RAAGs.\n

\n LOCATION:https://stable.researchseminars.org/talk/GaTO/63/ END:VEVENT BEGIN:VEVENT SUMMARY:Naomi Andrew (Southampton) DTSTART:20220616T140500Z DTEND:20220616T145500Z DTSTAMP:20260404T095244Z UID:GaTO/64 DESCRIPTION:Title: Baumslag-Solitar groups\, automorphisms and generalisations\nby N aomi Andrew (Southampton) as part of Geometry and topology online\n\n\nAbs tract\nBaumslag-Solitar groups are a well known family in geometric group theory\, providing useful (counter)examples - such as groups that are Hopf ian but not residually finite. Recently\, Ian Leary and Ashot Minasyan int roduced a generalisation\, finding even more counterexamples - notably gro ups that are \\(\\CAT(0)\\) but not biautomatic. Outer automorphism groups of Baumslag-Solitar groups range from finite to not even finitely generat ed\, with proofs (and re-proofs) across several authors and years.\n\nIn t his talk I will summarise (some) of what is known about the automorphisms of Baumslag-Solitar groups\, and the more modern\, Bass-Serre theoretic te chniques that can be used to prove them. I'll then discuss my work with Sa m Hughes to extend these results to the automorphisms of Leary-Minasyan gr oups.\n LOCATION:https://stable.researchseminars.org/talk/GaTO/64/ END:VEVENT BEGIN:VEVENT SUMMARY:Lorenzo Ruffoni (Tufts) DTSTART:20220623T140500Z DTEND:20220623T145500Z DTSTAMP:20260404T095244Z UID:GaTO/65 DESCRIPTION:Title: Strict hypbolisation and special cubulation\nby Lorenzo Ruffoni ( Tufts) as part of Geometry and topology online\n\n\nAbstract\n

\n Gromov introduced some "hyperbolisation"\n procedures that turn a given polyhedron into a space of\n non-positive curvature. Charney and Davis developed a refined\n "strict hyperbolisation" procedure that outputs a space of\n strictly negative curvature. Their proc edure has been used to\n construct new examples of manifolds and gr oups with negative\n curvature\, and other prescribed features. We construct actions\n of the resulting groups on CAT(0) cube complexe s. As an\n application\, we obtain that they are virtually special \, hence\n linear over the integers and residually finite.\n < /p>\n

\n This is joint work with J. Lafont.\n

\n LOCATION:https://stable.researchseminars.org/talk/GaTO/65/ END:VEVENT BEGIN:VEVENT SUMMARY:Gareth Wilkes (Cambridge) DTSTART:20220630T140500Z DTEND:20220630T145500Z DTSTAMP:20260404T095244Z UID:GaTO/66 DESCRIPTION:Title: Residual properties of graphs of \\(p\\)-groups\nby Gareth Wilkes (Cambridge) as part of Geometry and topology online\n\nLecture held in Ro om B3.03 in the Zeeman Building\, University of Warwick.\n\nAbstract\n

\ n When groups may be built up as graphs of\n 'simpler' group s\, it is often of interest to study how good\n residual finiteness properties of the simpler groups can imply\n residual properties o f the whole. The essential case of this\n theory is the study of r esidual properties of finite groups.\n In this talk I will discuss the question of when a graph of\n finite \\(p\\)-groups is residual ly \\(p\\)-finite\, for \\(p\\) a\n prime. I will describe the pre vious theorems in this area for\n one-edge and finite graphs of gro ups\, and their method of\n proof. I will then state a generalisat ion of these theorems to\n potentially infinite graphs of groups\, together with an\n alternative and perhaps more natural method of p roof. Finally\n I will briefly describe a usage of these results i n the study\n of accessibility—namely the existence of a finitely generated\n inaccessible group which is residually \\(p\\)-finite. \n

\n LOCATION:https://stable.researchseminars.org/talk/GaTO/66/ END:VEVENT BEGIN:VEVENT SUMMARY:Grace Garden (University of Sydney) DTSTART:20221006T130500Z DTEND:20221006T140000Z DTSTAMP:20260404T095244Z UID:GaTO/67 DESCRIPTION:Title: Earthquakes on the once-punctured torus\nby Grace Garden (Univers ity of Sydney) as part of Geometry and topology online\n\n\nAbstract\nWe s tudy earthquake deformations on Teichmüller space associated with simple closed curves of the once-punctured torus. We describe two methods to get an explicit form of the earthquake deformation for any simple closed curve . The first method is rooted in hyperbolic geometry\, the second represent ation theory. The two methods align\, providing both a geometric and an al gebraic interpretation of the earthquake deformations. Pictures are given for earthquakes across multiple coordinate systems for Teichmüller space. Two families of curves are used as examples. Examining the limiting behav iour of each gives insight into earthquakes about measured geodesic lamina tions\, of which simple closed curves are a special case.\n LOCATION:https://stable.researchseminars.org/talk/GaTO/67/ END:VEVENT BEGIN:VEVENT SUMMARY:Claudio Llosa Isenrich (KIT) DTSTART:20221013T130500Z DTEND:20221013T140000Z DTSTAMP:20260404T095244Z UID:GaTO/68 DESCRIPTION:Title: Finiteness properties\, subgroups of hyperbolic groups\, and complex hyperbolic lattices\nby Claudio Llosa Isenrich (KIT) as part of Geomet ry and topology online\n\nLecture held in Room B3.02 in the Zeeman Buildin g\, University of Warwick.\n\nAbstract\nHyperbolic groups form an importan t class of finitely generated groups that has attracted much attention in geometric group theory. We call a group of finiteness type \\(F_n\\) if it has a classifying space with finitely many cells of dimension at most \\( n\\). This generalises finite presentability\, which is equivalent to typ e \\(F_2\\). Hyperbolic groups are of type \\(F_n\\) for all \\(n\\). It is natural to ask if subgroups of hyperbolic groups inherit these strong f initeness properties. We use methods from complex geometry to show that e very uniform arithmetic lattice with positive first Betti number in \\(\\m athrm{PU}(n\, 1)\\) admits a finite index subgroup\, which maps onto the i ntegers with kernel of type \\(F_{n−1}\\) but not \\(F_n\\). This answer s an old question of Brady and produces many finitely presented non-hyperb olic subgroups of hyperbolic groups. This is joint work with Pierre Py.\n LOCATION:https://stable.researchseminars.org/talk/GaTO/68/ END:VEVENT BEGIN:VEVENT SUMMARY:Henry Bradford (Cambridge) DTSTART:20221020T130500Z DTEND:20221020T140000Z DTSTAMP:20260404T095244Z UID:GaTO/69 DESCRIPTION:Title: Local permutation stability\nby Henry Bradford (Cambridge) as par t of Geometry and topology online\n\nLecture held in Room B3.02 in the Zee man Building\, University of Warwick.\n\nAbstract\nA group \\(\\Gamma\\) i s sofic if elements of \\(\\Gamma\\) can be distinguished by almost-action s on finite sets. It is a major unsolved problem to determine whether all groups are sofic. One approach to this problem which has gained much recen t attention is that of “permutation stability”\, that is\, showing tha t almost-actions of a group are controlled by its actions. We introduce a “local” generalization of permutation stability\, under which actions are replaced by partial actions. We exhibit an uncountable family of group s which are locally permutation stable but not permutation stable\, coming from topological dynamics. The proof is based on a criterion for local st ability of amenable groups\, in terms of invariant random subgroups.\n LOCATION:https://stable.researchseminars.org/talk/GaTO/69/ END:VEVENT BEGIN:VEVENT SUMMARY:Becca Winarski (College of the Holy Cross) DTSTART:20221103T140500Z DTEND:20221103T150000Z DTSTAMP:20260404T095244Z UID:GaTO/70 DESCRIPTION:Title: Polynomials\, branched covers\, and trees\nby Becca Winarski (Col lege of the Holy Cross) as part of Geometry and topology online\n\nLecture held in Room B3.02 in the Zeeman Building\, University of Warwick.\n\nAbs tract\nThurston proved that a post-critically finite branched cover of the plane is either equivalent to a polynomial (that is: conjugate via a mapp ing class) or it has a topological obstruction. We use topological techniq ues – adapting tools used to study mapping class groups – to produce a n algorithm that determines when a branched cover is equivalent to a polyn omial. When it is\, we determine which polynomial it is equivalent to. \n \nThis is joint work with Jim Belk\, Justin Lanier\, and Dan Margalit.\n LOCATION:https://stable.researchseminars.org/talk/GaTO/70/ END:VEVENT BEGIN:VEVENT SUMMARY:Bradley Zykoski (Michigan) DTSTART:20221117T140500Z DTEND:20221117T150000Z DTSTAMP:20260404T095244Z UID:GaTO/71 DESCRIPTION:Title: A polytopal decomposition of strata of translation surfaces\nby B radley Zykoski (Michigan) as part of Geometry and topology online\n\nLectu re held in Room B3.02 in the Zeeman Building\, University of Warwick.\n\nA bstract\nA closed surface can be endowed with a certain locally Euclidean metric structure called a translation surface. Moduli spaces that paramet rize such structures are called strata. There is a GL(2\,R)-action on str ata\, and orbit closures of this action are rare gems\, the classification of which has been given a huge boost in the past decade by landmark resul ts such as the "Magic Wand" theorem of Eskin-Mirzakhani-Mohammadi and the Cylinder Deformation theorem of Wright. Investigation of the topology of strata is still in its nascency\, although recent work of Calderon-Salter and Costantini-Möller-Zachhuber indicate that this field is rapidly bloss oming. \n\nIn this talk\, I will discuss a way of decomposing strata into finitely many higher-dimensional polytopes. I will discuss how I have us ed this decomposition to study the topology of strata\, and my ongoing wor k using this decomposition to study the orbit closures of the GL(2\,R)-act ion.\n LOCATION:https://stable.researchseminars.org/talk/GaTO/71/ END:VEVENT BEGIN:VEVENT SUMMARY:Koji Fujiwara (Kyoto) DTSTART:20221201T140500Z DTEND:20221201T150000Z DTSTAMP:20260404T095244Z UID:GaTO/73 DESCRIPTION:Title: Growth rates in a hyperbolic group\nby Koji Fujiwara (Kyoto) as p art of Geometry and topology online\n\nLecture held in Room B3.02 in the Z eeman Building\, University of Warwick.\n\nAbstract\nI discuss the set of rates of growth of a finitely generated group with respect to all its fini te generating sets. In a joint work with Sela\, for a hyperbolic group\, w e showed that the set is well-ordered\, and that each number can be the ra te of growth of at most finitely many generating sets up to automorphism o f the group. If there is time\, I may also discuss generalisation to acyli ndrically hyperbolic groups.\n LOCATION:https://stable.researchseminars.org/talk/GaTO/73/ END:VEVENT BEGIN:VEVENT SUMMARY:Daniel Berlyne (Bristol) DTSTART:20221027T130500Z DTEND:20221027T140000Z DTSTAMP:20260404T095244Z UID:GaTO/74 DESCRIPTION:Title: Braid groups of graphs\nby Daniel Berlyne (Bristol) as part of Ge ometry and topology online\n\nLecture held in Room B3.02 in the Zeeman Bui lding\, University of Warwick.\n\nAbstract\nThe braid group of a space \\( X\\) is the fundamental group of its configuration space\, which tracks th e motion of some number of particles as they travel through \\(X\\). When \\(X\\) is a graph\, the configuration space turns out to be a special cub e complex\, in the sense of Haglund and Wise. I show how these cube comple xes are constructed and use graph of groups decompositions to provide meth ods for computing braid groups of various graphs\, as well as criteria for a graph braid group to split as a free product. This has various applicat ions\, such as characterising various forms of hyperbolicity in graph brai d groups and determining when a graph braid group is isomorphic to a right -angled Artin group.\n LOCATION:https://stable.researchseminars.org/talk/GaTO/74/ END:VEVENT BEGIN:VEVENT SUMMARY:Ric Wade (Oxford) DTSTART:20221208T140500Z DTEND:20221208T150000Z DTSTAMP:20260404T095244Z UID:GaTO/75 DESCRIPTION:Title: Aut-invariant quasimorphisms on groups\nby Ric Wade (Oxford) as p art of Geometry and topology online\n\nLecture held in Room B3.02 in the Z eeman Building\, University of Warwick.\n\nAbstract\n

\nFor a large clas s of groups\, we exhibit an infinite-dimensional space of homogeneous quas i-morphisms that are invariant under the action of the automorphism group. This class includes non-elementary hyperbolic groups\, infinitely-ended f initely generated groups\, some relatively hyperbolic groups\, and a class of graph products of groups that includes all right-angled Artin and Coxe ter groups that are not virtually abelian.\n

\n

\nThis is joint work with Francesco Fournier-Facio.\n

\n LOCATION:https://stable.researchseminars.org/talk/GaTO/75/ END:VEVENT BEGIN:VEVENT SUMMARY:Davide Spriano (Oxford) DTSTART:20230126T140500Z DTEND:20230126T150000Z DTSTAMP:20260404T095244Z UID:GaTO/76 DESCRIPTION:Title: Combinatorial criteria for hyperbolicity\nby Davide Spriano (Oxfo rd) as part of Geometry and topology online\n\nLecture held in Room B3.02 in the Zeeman Building\, University of Warwick.\n\nAbstract\nPerhaps one o f the most fascinating properties of hyperbolic groups is that they admit equivalent definitions coming from different areas of mathematics. In this talk\, we will survey some interesting definitions\, and discuss a new on e that\, perhaps surprisingly\, was previously unknown\, namely that fact that hyperbolicity can be detected by the language of quasi-geodesics in t he Cayley graph. As an application\, we will discuss some progress towards a conjecture of Shapiro concerning groups with uniquely geodesic Cayley g raphs.\n LOCATION:https://stable.researchseminars.org/talk/GaTO/76/ END:VEVENT BEGIN:VEVENT SUMMARY:Saul Schleimer (Warwick) DTSTART:20230223T140500Z DTEND:20230223T150000Z DTSTAMP:20260404T095244Z UID:GaTO/77 DESCRIPTION:Title: From loom spaces to veering triangulations\nby Saul Schleimer (Wa rwick) as part of Geometry and topology online\n\nLecture held in Room B3. 02 in the Zeeman Building\, University of Warwick.\n\nAbstract\nA ``loom s pace'' is a copy of $\\mathbb{R}^2$ equipped with a pair of transverse fol iations satisfying certain axioms. These arise as the link spaces associa ted to veering triangulations and also as the flow spaces of (drilled) pse udo-Anosov flows without perfect fits. Following work of Guéritaud\, we prove a converse: namely\, every loom space gives rise\, canonically\, to a locally veering triangulation. Furthermore\, the realisation of this tri angulation (minus the vertices) is homeomorphic to $\\mathbb{R}^3$. I wil l sketch the proof\, giving many pictures.\n\nThis is joint work with Henr y Segerman.\n LOCATION:https://stable.researchseminars.org/talk/GaTO/77/ END:VEVENT BEGIN:VEVENT SUMMARY:Malavika Mukundan (Michigan) DTSTART:20230302T140500Z DTEND:20230302T150000Z DTSTAMP:20260404T095244Z UID:GaTO/78 DESCRIPTION:Title: Dynamical approximation of entire functions\nby Malavika Mukundan (Michigan) as part of Geometry and topology online\n\nLecture held in Roo m B3.02 in the Zeeman Building\, University of Warwick.\n\nAbstract\nPosts ingularly finite holomorphic functions are entire functions for which the forward orbit of the set of critical and asymptotic values is finite. Moti vated by previous work on approximating entire functions dynamically by po lynomials\, we ask the following question: given a postsingularly finite e ntire function $f$\, can $f$ be realised as the locally uniform limit of a sequence of postcritically finite polynomials?\n\nIn joint work with Niko lai Prochorov and Bernhard Reinke\, we show how we may answer this questio n in the affirmative.\n LOCATION:https://stable.researchseminars.org/talk/GaTO/78/ END:VEVENT BEGIN:VEVENT SUMMARY:Elia Fioravanti (MPIM Bonn) DTSTART:20230309T140500Z DTEND:20230309T150000Z DTSTAMP:20260404T095244Z UID:GaTO/79 DESCRIPTION:Title: Coarse cubical rigidity\nby Elia Fioravanti (MPIM Bonn) as part o f Geometry and topology online\n\nLecture held in Room D1.07 in the Zeeman Building\, University of Warwick.\n\nAbstract\nWhen a group $G$ admits ni ce actions on $\\mathrm{CAT}(0)$ cube complexes\, understanding the space of all such actions can provide useful information on the outer automorphi sm group $\\mathrm{Out}(G)$. As a classical example\, the Culler-Vogtmann outer space is (roughly) the space of all geometric actions of the free gr oup $F_n$ on a $1$-dimensional cube complex (a tree). In general\, however \, spaces of cubulations tend to be awkwardly vast\, even for otherwise ri gid groups such as the hexagon RAAG. In an attempt to tame these spaces\, we show that all cubulations of many right-angled Artin and Coxeter groups coarsely look the same\, in a strong sense: they all induce the same coar se median structure on the group. \n\nThis is joint work with Ivan Levcovi tz and Michah Sageev.\n LOCATION:https://stable.researchseminars.org/talk/GaTO/79/ END:VEVENT BEGIN:VEVENT SUMMARY:Nansen Petrosyan (Southampton) DTSTART:20230309T150500Z DTEND:20230309T160000Z DTSTAMP:20260404T095244Z UID:GaTO/80 DESCRIPTION:Title: Hyperbolicity and $L$-infinity cohomology\nby Nansen Petrosyan (S outhampton) as part of Geometry and topology online\n\nLecture held in Roo m D1.07 in the Zeeman Building\, University of Warwick.\n\nAbstract\n$L$-i nfinity cohomology is a quasi-isometry invariant of finitely generated gro ups. It was introduced by Gersten as a tool to find lower bounds for the D ehn function of some finitely presented groups. I will discuss a generalis ation of a theorem of Gersten on surjectivity of the restriction map in $L $-infinity cohomology of groups. This leads to applications on subgroups o f hyperbolic groups\, quasi-isometric distinction of finitely generated gr oups and $L$-infinity cohomology calculations for some well-known classes of groups such as RAAGs\, Bestvina-Brady groups and $\\mathrm{Out}(F_n)$. Along the way\, we obtain hyperbolicity criteria for groups of type $FP_2( Q)$ and for those satisfying a rational homological linear isoperimetric i nequality.\n\nI will first define L-infinity cohomology and discuss some o f its properties. I will then sketch some of the main ideas behind the pro ofs. This is joint work with Vladimir Vankov.\n LOCATION:https://stable.researchseminars.org/talk/GaTO/80/ END:VEVENT BEGIN:VEVENT SUMMARY:Alan Logan (Heriot-Watt University) DTSTART:20230427T130500Z DTEND:20230427T140000Z DTSTAMP:20260404T095244Z UID:GaTO/81 DESCRIPTION:Title: Dynamics and algorithms for endomorphisms of free groups\nby Alan Logan (Heriot-Watt University) as part of Geometry and topology online\n\ nLecture held in Room B3.02 in the Zeeman Building\, University of Warwick .\n\nAbstract\nRecent work of Mutanguha has given a topological insight in to endomorphisms of free groups and their dynamics. The purpose of this ta lk is to sketch this theory\, and to explain how it can be applied to reso lve the conjugacy problem for ascending HNN-extensions of free groups.\n LOCATION:https://stable.researchseminars.org/talk/GaTO/81/ END:VEVENT BEGIN:VEVENT SUMMARY:Michael Borinsky (ETH-ITS) DTSTART:20230525T130500Z DTEND:20230525T140000Z DTSTAMP:20260404T095244Z UID:GaTO/82 DESCRIPTION:Title: The commutative graph complex and the amount of top-weight cohomology in the moduli space of curves\nby Michael Borinsky (ETH-ITS) as part of Geometry and topology online\n\nLecture held in Room B3.02 in the Zeema n Building\, University of Warwick.\n\nAbstract\nI will present new result s on the asymptotic growth rate of\nthe Euler characteristic of Kontsevich 's commutative graph complex. By\nwork of Chan\, Galatius and Payne\, thes e results imply the same\nasymptotic growth rate for the top-weight Euler characteristic of M_g\,\nthe moduli space of curves\, and establish the ex istence of a large amount\nof unexplained top-weight cohomology in this sp ace.\n LOCATION:https://stable.researchseminars.org/talk/GaTO/82/ END:VEVENT BEGIN:VEVENT SUMMARY:Raphael Zentner (Durham University) DTSTART:20231005T130500Z DTEND:20231005T140000Z DTSTAMP:20260404T095244Z UID:GaTO/83 DESCRIPTION:Title: Rational homology ribbon cobordism is a partial order\nby Raphael Zentner (Durham University) as part of Geometry and topology online\n\nLe cture held in Room B3.02 in the Zeeman Building\, University of Warwick.\n \nAbstract\nLast year\, Ian Agol proved that ribbon knot concordance is a partial order on knots\; this resolves a conjecture that has been open for more than three decades. His proof is beautiful and surprisingly simple. There is an analogous notion of ribbon cobordism for closed 3-manifolds. W e use Agol's method to show that this is also a partial order within the c lass of irreducible 3-manifolds. \n\nThis is joint work with Stefan Friedl and Filip Misev.\n LOCATION:https://stable.researchseminars.org/talk/GaTO/83/ END:VEVENT BEGIN:VEVENT SUMMARY:Mark Pengitore (University of Virginia) DTSTART:20231012T130500Z DTEND:20231012T140000Z DTSTAMP:20260404T095244Z UID:GaTO/84 DESCRIPTION:Title: Residual finiteness growth functions of surface groups with respect t o characteristic quotients\nby Mark Pengitore (University of Virginia) as part of Geometry and topology online\n\nLecture held in Room B3.02 in the Zeeman Building\, University of Warwick.\n\nAbstract\nResidual finiten ess growth functions of groups have attracted much interest in recent year s. \nThese are functions that roughly measure the complexity of the finite quotients needed to separate particular group elements from the identity in terms of word length. In this talk\, we study the growth rate of these functions adapted to finite characteristic quotients. One potential applic ation of this result is towards linearity of the mapping class group.\n LOCATION:https://stable.researchseminars.org/talk/GaTO/84/ END:VEVENT BEGIN:VEVENT SUMMARY:Clement Legrand (University of Bordeaux) DTSTART:20231019T130500Z DTEND:20231019T140000Z DTSTAMP:20260404T095244Z UID:GaTO/85 DESCRIPTION:Title: Reconfiguration of square-tiled surfaces\nby Clement Legrand (Uni versity of Bordeaux) as part of Geometry and topology online\n\nLecture he ld in Room B3.02 in the Zeeman Building\, University of Warwick.\n\nAbstra ct\nA square-tiled surface is a special case of a quadrangulation of a sur face\, that can be encoded as a pair of permutations in \\(S_n \\times S_n \\) that generates a transitive subgroup of \\(S_n\\). Square-tiled surfa ces can be classified into different strata according to the total angles around their conical singularities. Among other parameters\, strata fix t he genus and the size of the quadrangulation. Generating a random square- tiled surface in a fixed stratum is a widely open question. We propose a M arkov chain approach using "shearing moves": \na natural reconfiguration o peration preserving the stratum of a square-tiled surface. In a subset of strata\, we prove that this Markov chain is irreducible and has diameter \\(O(n^2)\\)\, where \\(n\\) is the number of squares in the quadrangulati on.\n LOCATION:https://stable.researchseminars.org/talk/GaTO/85/ END:VEVENT BEGIN:VEVENT SUMMARY:Adele Jackson (University of Oxford) DTSTART:20231102T140500Z DTEND:20231102T150000Z DTSTAMP:20260404T095244Z UID:GaTO/86 DESCRIPTION:Title: Algorithms for Seifert fibered spaces\nby Adele Jackson (Universi ty of Oxford) as part of Geometry and topology online\n\nLecture held in R oom B3.02 in the Zeeman Building\, University of Warwick.\n\nAbstract\nGiv en two mathematical objects\, the most basic question is whether they are the same. We will discuss this question for triangulations of three-manif olds. In practice there is fast software to answer this question and theo retically the problem is known to be decidable. However\, our understandi ng is limited and known theoretical algorithms could have extremely long r un-times. I will describe a programme to show that the three-manifold hom eomorphism problem is in the complexity class NP\, and discuss the importa nt sub-case of Seifert fibered spaces.\n LOCATION:https://stable.researchseminars.org/talk/GaTO/86/ END:VEVENT BEGIN:VEVENT SUMMARY:Monika Kudlinska (University of Oxford) DTSTART:20231109T140500Z DTEND:20231109T150000Z DTSTAMP:20260404T095244Z UID:GaTO/87 DESCRIPTION:Title: Subgroup separability in 3-manifold and free-by-cyclic groups\nby Monika Kudlinska (University of Oxford) as part of Geometry and topology online\n\nLecture held in Room B3.02 in the Zeeman Building\, University o f Warwick.\n\nAbstract\nA group \\(G\\) is said to be subgroup separable i f every finitely generated subgroup of \\(G\\) is the intersection of fini te index subgroups. It is known that a fundamental group of a compact\, ir reducible\, closed 3-manifold \\(M\\) is subgroup separable if and only if \\(M\\) is geometric. We will discuss the problem of subgroup separabilit y in free-by-cyclic groups by drawing a parallel between free-by-cyclic an d 3-manifold groups. Time permitting\, we will discuss how to extend these ideas to find non-separable subgroups in random groups.\n LOCATION:https://stable.researchseminars.org/talk/GaTO/87/ END:VEVENT BEGIN:VEVENT SUMMARY:Rob Kropholler (University of Warwick) DTSTART:20231116T140500Z DTEND:20231116T150000Z DTSTAMP:20260404T095244Z UID:GaTO/88 DESCRIPTION:Title: The landscape of Dehn functions\nby Rob Kropholler (University of Warwick) as part of Geometry and topology online\n\nLecture held in Room B3.02 in the Zeeman Building\, University of Warwick.\n\nAbstract\nThe Deh n function of a finitely presented group \\(G\\) can be used to measure th e complexity of its word problem. Specifically the Dehn function measures the minimal area required to fill loops in the Cayley graph of \\(G\\). Th ere are various analogues of the Dehn function for wider classes of groups . These all correspond to fillings of different loops in the Cayley graph. I will carefully introduce the various analogues and discuss how the vari ous Dehn functions can be used to prove interesting results. I will be par ticularly interested in the case of subgroups of hyperbolic groups.\n LOCATION:https://stable.researchseminars.org/talk/GaTO/88/ END:VEVENT BEGIN:VEVENT SUMMARY:Jeffrey Giansiracusa (Durham University) DTSTART:20231123T140500Z DTEND:20231123T150000Z DTSTAMP:20260404T095244Z UID:GaTO/89 DESCRIPTION:Title: Topology of the matroid Grassmannian\nby Jeffrey Giansiracusa (Du rham University) as part of Geometry and topology online\n\nLecture held i n Room B3.02 in the Zeeman Building\, University of Warwick.\n\nAbstract\n The matroid Grassmannian is the moduli space of oriented matroids\; this i s an important combinatorial analogue of the ordinary oriented real Grassm annian. Thirty years ago MacPherson showed us that understanding the homo topy type of this space can have significant implications in manifold topo logy\, such as providing combinatorial formulae for the Pontrjagin classes . In some easy cases\, the matroid Grassmannian is homotopy equivalent to the oriented real Grassmannian\, but in most cases we have no idea whethe r or not they are equivalent. This question is known as MacPherson's conj ecture. I'll show that one of the important homotopical structures of the oriented Grassmannians has an analogue on the matroid Grassmannian: the d irect sum monoidal product (which gives rise to topological K-theory) is E -infinity.\n LOCATION:https://stable.researchseminars.org/talk/GaTO/89/ END:VEVENT BEGIN:VEVENT SUMMARY:Cameron Gates Rudd (MPI Bonn) DTSTART:20231130T140500Z DTEND:20231130T150000Z DTSTAMP:20260404T095244Z UID:GaTO/90 DESCRIPTION:Title: Stretch laminations and hyperbolic Dehn surgery\nby Cameron Gates Rudd (MPI Bonn) as part of Geometry and topology online\n\nLecture held i n Room B3.02 in the Zeeman Building\, University of Warwick.\n\nAbstract\n Given a hyperbolic manifold \\(M\\) and a homotopy class of maps from \\(M \\) to the circle\, there is an associated geodesic "stretch" lamination e ncoding at which points in \\(M\\) the Lipschitz constant of any map in th e homotopy class must be large. Recently\, Farre-Landesberg-Minsky related these laminations to horocycle orbit closures in infinite cyclic covers a nd when \\(M\\) is a surface\, they analyzed the possible structure of the se laminations. I will discuss the case where \\(M\\) is a 3-manifold and give the first 3-dimensional examples where these laminations can be ident ified. The argument uses the Thurston norm and tools from quantitative Deh n surgery.\n LOCATION:https://stable.researchseminars.org/talk/GaTO/90/ END:VEVENT BEGIN:VEVENT SUMMARY:Francesco Fournier-Facio (University of Cambridge) DTSTART:20240125T140500Z DTEND:20240125T150000Z DTSTAMP:20260404T095244Z UID:GaTO/92 DESCRIPTION:Title: Infinite simple characteristic quotients\nby Francesco Fournier-F acio (University of Cambridge) as part of Geometry and topology online\n\n Lecture held in Room B3.02 in the Zeeman Building\, University of Warwick. \n\nAbstract\nThe rank of a finitely generated group is the minimal size o f a generating set. Several questions that received a lot of attention aro und 50 years ago ask about the rank of finitely generated groups\, and how this relates to the rank of their direct powers. In this context\, Wiegol d asked about the existence of infinite simple characteristic quotients of free groups. I will review this framework\, present several open question s - old and new - and present a solution to Wiegold's problem. \n\nThis is joint with Remi Coulon.\n LOCATION:https://stable.researchseminars.org/talk/GaTO/92/ END:VEVENT BEGIN:VEVENT SUMMARY:Sam Hughes (University of Oxford) DTSTART:20231207T140500Z DTEND:20231207T150000Z DTSTAMP:20260404T095244Z UID:GaTO/93 DESCRIPTION:Title: Centralisers and classifying spaces for $\\mathrm{Out}(F_N)$\nby Sam Hughes (University of Oxford) as part of Geometry and topology online\ n\nLecture held in Room B3.02 in the Zeeman Building\, University of Warwi ck.\n\nAbstract\nIn this talk I will outline reduction theory for mapping classes and explain various attempts to construct similar machinery for el ements of $\\mathrm{Out}(F_N)$. I will then present a new reduction theor y for studying centralisers of elements in $\\mathrm{IA}_3(N)$\, the finit e index level three congruence subgroup of $\\mathrm{Out}(F_N)$. Using th is I will explain an application to the classifying space for virtually cy clic subgroups\, a space notable for its appearance in the Farrell--Jones Conjecture. \n\nBased on joint work with Yassine Guerch and Luis Jorge San chez Saldana.\n LOCATION:https://stable.researchseminars.org/talk/GaTO/93/ END:VEVENT BEGIN:VEVENT SUMMARY:Richard Wade (University of Oxford) DTSTART:20240111T140500Z DTEND:20240111T150000Z DTSTAMP:20260404T095244Z UID:GaTO/94 DESCRIPTION:Title: Quasi-flats in the Aut free factor complex\nby Richard Wade (Univ ersity of Oxford) as part of Geometry and topology online\n\nLecture held in Room B3.02 in the Zeeman Building\, University of Warwick.\n\nAbstract\ nWe will describe families of quasi-flats in the "$\\mathrm{Aut}(F_n)$ ver sion" of the free factor complex. This shows that\, unlike its more popula r "Outer" cousin\, the $\\mathrm{Aut}$ free factor complex is not hyperbol ic. The flats are reasonably simple to describe and are shown to be q.i. e mbedded via the construction of a coarse Lipschitz retraction. This leaves many open problems about the coarse geometry of this space\, and I hope t o talk about a few of them. \n\nThis is joint work with Mladen Bestvina an d Martin Bridson.\n LOCATION:https://stable.researchseminars.org/talk/GaTO/94/ END:VEVENT BEGIN:VEVENT SUMMARY:Ian Leary (University of Southampton) DTSTART:20240118T140500Z DTEND:20240118T150000Z DTSTAMP:20260404T095244Z UID:GaTO/95 DESCRIPTION:Title: Residual finiteness of generalized Bestvina-Brady groups\nby Ian Leary (University of Southampton) as part of Geometry and topology online\ n\nLecture held in Room B3.02 in the Zeeman Building\, University of Warwi ck.\n\nAbstract\nI discovered/created generalized Bestvina-Brady groups to give an uncountable family of groups with surprising homological properti es. In this talk\, I will introduce the groups and address the following questions: when are they virtually torsion-free? when are they residually finite? This leads naturally to a third question: when do they virtually e mbed in right-angled Artin groups? There are nice conjectural answers to a ll three questions\, which we have proved in some cases.\n\nThis is joint work with Vladimir Vankov.\n LOCATION:https://stable.researchseminars.org/talk/GaTO/95/ END:VEVENT BEGIN:VEVENT SUMMARY:Samuel Shepherd (Vanderbilt University) DTSTART:20240201T140500Z DTEND:20240201T150000Z DTSTAMP:20260404T095244Z UID:GaTO/96 DESCRIPTION:Title: One-ended halfspaces in group splittings\nby Samuel Shepherd (Van derbilt University) as part of Geometry and topology online\n\nLecture hel d in Room B3.02 in the Zeeman Building\, University of Warwick.\n\nAbstrac t\nI will introduce the notion of halfspaces in group splittings and discu ss the problem of when these halfspaces are one-ended. I will also discuss connections to JSJ splittings of groups\, and to determining whether grou ps are simply connected at infinity. \n\nThis is joint work with Michael M ihalik.\n LOCATION:https://stable.researchseminars.org/talk/GaTO/96/ END:VEVENT BEGIN:VEVENT SUMMARY:Joeseph MacManus (Oxford) DTSTART:20240229T140500Z DTEND:20240229T150000Z DTSTAMP:20260404T095244Z UID:GaTO/97 DESCRIPTION:Title: Groups quasi-isometric to planar graphs\nby Joeseph MacManus (Oxf ord) as part of Geometry and topology online\n\nLecture held in Room B3.02 in the Zeeman Building\, University of Warwick.\n\nAbstract\nA classic an d important theorem\, originating in work of Mess\, states that a finitely generated group is quasi-isometric to a complete Riemannian plane if and only if it is a virtual surface group. Another related result obtained by Maillot states that a finitely generated group is virtually free if and o nly if it is quasi-isometric to a complete planar simply connected Riemann ian surface with non-compact geodesic boundary. These results illustrate the general philosophy that planarity is a very `rigid' property amongst f initely generated groups.\n\nIn this talk I will build on the above and sk etch how to characterise those finitely generated groups which are quasi-i sometric to planar graphs. Such groups are virtually free products of fre e and surface groups\, and thus virtually admit a planar Cayley graph. Th e main technical step is proving that such a group is accessible\, in the sense of Dunwoody and Wall. This is achieved through a careful study of t he dynamics of quasi-actions on planar graphs.\n LOCATION:https://stable.researchseminars.org/talk/GaTO/97/ END:VEVENT BEGIN:VEVENT SUMMARY:Marco Linton (Oxford) DTSTART:20240307T140500Z DTEND:20240307T150000Z DTSTAMP:20260404T095244Z UID:GaTO/98 DESCRIPTION:Title: The coherence of one-relator groups\nby Marco Linton (Oxford) as part of Geometry and topology online\n\nLecture held in Room B3.02 in the Zeeman Building\, University of Warwick.\n\nAbstract\nA group is 'coherent ' if all of its finitely generated subgroups are finitely presented. In t his talk I will sketch a proof of Baumslag’s conjecture that all one-rel ator groups are coherent\, discussing connections with the non-positive im mersions property and the vanishing of the second L^2 Betti number.\n\nThi s is joint work with Andrei Jaikin-Zapirain.\n LOCATION:https://stable.researchseminars.org/talk/GaTO/98/ END:VEVENT BEGIN:VEVENT SUMMARY:Davide Spriano (Oxford) DTSTART:20240314T140500Z DTEND:20240314T150000Z DTSTAMP:20260404T095244Z UID:GaTO/99 DESCRIPTION:Title: Uniquely geodesic groups\nby Davide Spriano (Oxford) as part of G eometry and topology online\n\nLecture held in Room B3.02 in the Zeeman Bu ilding\, University of Warwick.\n\nAbstract\nA group is 'uniquely geodesic ' (also called 'geodetic') if it admits a locally finite Cayley graphs whe re any two vertices can be connected by a unique shortest path. Despite t his being a very natural geometric property\, an algebraic characterisatio n of uniquely geodetic groups has been elusive for quite some time\, even for simple questions such as “are uniquely geodesic groups finitely pres ented”? We provide the first algebraic classification of uniquely geode sic groups.\n\nThis is joint work with Murray Elder\, Giles Gardam\, Adam Piggott\, and Kane Townsend.\n LOCATION:https://stable.researchseminars.org/talk/GaTO/99/ END:VEVENT BEGIN:VEVENT SUMMARY:Rohini Ramadas (Warwick) DTSTART:20240509T130500Z DTEND:20240509T140000Z DTSTAMP:20260404T095244Z UID:GaTO/100 DESCRIPTION:Title: Thurston theory in complex dynamics: a tropical perspective\nby Rohini Ramadas (Warwick) as part of Geometry and topology online\n\nLectur e held in Room B3.02 in the Zeeman Building\, University of Warwick.\n\nAb stract\nA rational function in one complex variable defines a branched cov ering from Riemann sphere $\\mathbb{CP}^1$ to itself. In the 1980s\, Willi am Thurston proved a theorem addressing the question: which branched cover ings of the topological sphere $S^2$ are (suitably equivalent to) rational functions on $\\mathbb{CP}^1$? Thurston’s theorem is still central in o ne-variable complex and arithmetic dynamics.\n\nTropical geometry is a fie ld in which polyhedral geometry and combinatorics are used to describe deg enerations in algebraic geometry. There are connections with geometric gro up theory\; for example\, Culler-Vogtmann Outer Space is closely related t o the space of tropical curves.\n\nI will introduce Thurston’s theorem a nd describe a connection with tropical geometry.\n LOCATION:https://stable.researchseminars.org/talk/GaTO/100/ END:VEVENT BEGIN:VEVENT SUMMARY:Nikolai Prochorov (Marseille) DTSTART:20240425T130500Z DTEND:20240425T140000Z DTSTAMP:20260404T095244Z UID:GaTO/101 DESCRIPTION:Title: Thurston theory for critically fixed branched covering maps\nby Nikolai Prochorov (Marseille) as part of Geometry and topology online\n\nL ecture held in Room B3.02 in the Zeeman Building\, University of Warwick.\ n\nAbstract\nIn the 1980’s\, William Thurston obtained his celebrated ch aracterisation of rational mappings. This result laid the foundation of su ch a field as Thurston's theory of holomorphic maps\, which has been activ ely developing in the last few decades. One of the most important problems in this area is the questions about characterisation\, which is understan ding when a topological map is equivalent (in a certain dynamical sense) t o a holomorphic one\, and classification\, which is an enumeration of all possible topological models of holomorphic maps from a given class.\n\nIn my talk\, I am going to focus on the characterisation and classification p roblems for the family of post-critically finite branched coverings\, i.e. \, branched coverings of the two-dimensional sphere $S^2$ with all critica l points being fixed. Maps of this family can be defined by combinatorial models based on planar embedded graphs\, and it provides an elegant answer to the classification problem for this family. Further\, I plan to explai n how to understand whether a given critically fixed branched cover is equ ivalent to a critically fixed rational map of the Riemann sphere and provi de an algorithm of combinatorial nature that allows us to answer this ques tion. Finally\, if time permits\, I will briefly mention the connections b etween Thurston's theory\, Teichmüller spaces and Mapping Class Groups of marked spheres.\n\nThis is a joint work with Mikhail Hlushchanka.\n LOCATION:https://stable.researchseminars.org/talk/GaTO/101/ END:VEVENT BEGIN:VEVENT SUMMARY:Henry Segerman (Oklahoma University) DTSTART:20240523T130500Z DTEND:20240523T140000Z DTSTAMP:20260404T095244Z UID:GaTO/102 DESCRIPTION:Title: Avoiding inessential edges\nby Henry Segerman (Oklahoma Universi ty) as part of Geometry and topology online\n\nLecture held in Room B3.02 in the Zeeman Building\, University of Warwick.\n\nAbstract\nResults of Ma tveev\, Piergallini\, and Amendola show that any two triangulations of a t hree-manifold with the same number of vertices are related to each other b y a sequence of local combinatorial moves (namely\, 2-3 and 3-2 moves). Fo r some applications however\, we need our triangulations to have certain p roperties\, for example that all edges are essential. (An edge is inessent ial if both ends are incident to a single vertex\, into which the edge can be homotoped.) We show that if the universal cover of the manifold has in finitely many boundary components\, then the set of essential ideal triang ulations is connected under 2-3\, 3-2\, 0-2\, and 2-0 moves. Our results h ave applications to veering triangulations and to quantum invariants such as the 1-loop invariant. \n\nThis is joint work with Tejas Kalelkar and Sa ul Schleimer.\n LOCATION:https://stable.researchseminars.org/talk/GaTO/102/ END:VEVENT BEGIN:VEVENT SUMMARY:David Hume (University of Birmingham) DTSTART:20240530T130500Z DTEND:20240530T140000Z DTSTAMP:20260404T095244Z UID:GaTO/103 DESCRIPTION:Title: Coarse embeddings\, and yet more ways to avoid them\nby David Hu me (University of Birmingham) as part of Geometry and topology online\n\nL ecture held in Room B3.02 in the Zeeman Building\, University of Warwick.\ n\nAbstract\nCoarse embeddings (maps between metric spaces whose distortio n can be controlled by some function) occur naturally in various areas of pure mathematics\, most notably in topology and algebra. It may therefore come as a surprise to discover that it is not known whether there is a coa rse embedding of three-dimensional real hyperbolic space into the direct p roduct of a real hyperbolic plane and a 3-regular tree. One reason for thi s is that there are very few invariants which behave monotonically with re spect to coarse embeddings\, and thus could be used to obstruct coarse emb eddings.\n\nIn this talk I will discuss some new invariants which combine two very classical invariants‚ asymptotic dimension and growth\, to give different obstructions to coarse embeddings. \n\nThis is joint work with John Mackay and Romain Tessera.\n LOCATION:https://stable.researchseminars.org/talk/GaTO/103/ END:VEVENT BEGIN:VEVENT SUMMARY:Ramón Flores (Universidad de Sevilla) DTSTART:20240620T130500Z DTEND:20240620T140000Z DTSTAMP:20260404T095244Z UID:GaTO/104 DESCRIPTION:Title: Characterizing graph properties via RAAGs\nby Ramón Flores (Uni versidad de Sevilla) as part of Geometry and topology online\n\nLecture he ld in Room B3.02 in the Zeeman Building\, University of Warwick.\n\nAbstra ct\nIn the last years\, thorough research has been conducted in order to u nderstand graph properties in terms of group properties of the associated right-angled Artin group (RAAG). These properties should be intrinsic\, in the sense that they should not depend on a concrete system of generators of the group. In this talk\, we will give a general review of the topic\, with emphasis on planarity\, self-complementarity\, and existence of surje ctions. In particular\, we will highlight the crucial role of the cohomolo gy algebra of the group in our approach.\n\nThis is joint work with Delara m Kahrobaei (CUNY New York) and Thomas Koberda (Virginia).\n LOCATION:https://stable.researchseminars.org/talk/GaTO/104/ END:VEVENT BEGIN:VEVENT SUMMARY:Carl-Fredrik Nyberg Brodda (KIAS) DTSTART:20240620T150500Z DTEND:20240620T160000Z DTSTAMP:20260404T095244Z UID:GaTO/105 DESCRIPTION:Title: Free growth\, free counting\nby Carl-Fredrik Nyberg Brodda (KIAS ) as part of Geometry and topology online\n\nLecture held in Room B3.02 in the Zeeman Building\, University of Warwick.\n\nAbstract\nI will discuss some recent forays into some counting problems for free objects. I will fo cus on free inverse semigroups and free regular ∗-semigroups. I will fir st discuss recent results giving a precise rate of exponential growth of t he free inverse monoid of arbitrary (finite) rank\, which turns out to be given by a surprisingly complicated but algebraic number. I will then disc uss a useful tool for counting algebraic things – rewriting systems – and an elegant bijection which proves a surprising result about the rate o f growth of the monogenic free regular ∗-semigroup. Then\, and again usi ng the theory of rewriting systems\, I will discuss just how non-finitely presented some of these free objects are\, and some homological corollarie s.\n\nThis is joint (in part) with M. Kambites\, N. Szakács\, and R. Webb .\n LOCATION:https://stable.researchseminars.org/talk/GaTO/105/ END:VEVENT BEGIN:VEVENT SUMMARY:Valentina Disarlo (Heidelberg) DTSTART:20240704T130500Z DTEND:20240704T140000Z DTSTAMP:20260404T095244Z UID:GaTO/106 DESCRIPTION:Title: The model theory of the curve graph\nby Valentina Disarlo (Heide lberg) as part of Geometry and topology online\n\nLecture held in Room B3. 02 in the Zeeman Building\, University of Warwick.\n\nAbstract\nThe curve graph of a surface of finite type is a graph that encodes the combinatoric s of isotopy classes of simple closed curves. It is a fundamental tool for the study of the geometric group theory of the mapping class group. In 19 87 N.K. Ivanov proved that the automorphism group of the curve graph is th e extended mapping class group. In the following decades\, many people pro ved analogous results for many "similar" graphs\, such as the pants graph\ , the arc graph\, and so on. In response to these results\, N.V. Ivanov fo rmulated a meta-conjecture which asserts that any "natural and sufficientl y rich" object associated to a surface has automorphism group isomorphic t o the extended mapping class group. \n\nWe provide a model theoretical fra mework for Ivanov’s meta-conjecture and conduct a thorough study of curv e graphs from the model theoretic point of view\, with particular emphasis in the problem of interpretability between different "similar" geometric complexes. In particular\, we prove that the curve graph of a surface of f inite type is w-stable. This talk does not assume any prior knowledge in m odel theory.\n\nThis is joint work with Thomas Koberda (Virginia) and Javi er de la Nuez Gonzalez (KIAS).\n LOCATION:https://stable.researchseminars.org/talk/GaTO/106/ END:VEVENT BEGIN:VEVENT SUMMARY:Saul Schleimer (Warwick) DTSTART:20241003T123000Z DTEND:20241003T133000Z DTSTAMP:20260404T095244Z UID:GaTO/107 DESCRIPTION:Title: Solving the word problem in the mapping class group in quasi-linear time\nby Saul Schleimer (Warwick) as part of Geometry and topology onl ine\n\nLecture held in Room B3.02 in the Zeeman Building\, University of W arwick.\n\nAbstract\nMapping class groups of surfaces are of fundamental i mportance in dynamics\, geometric group theory\, and low-dimensional topol ogy. The word problem for groups in general\, the definition of the mappi ng class group\, its finite generation by twists\, and the solution to its word problem were all set out by Dehn [1911\, 1922\, 1938]. Some of this material was rediscovered by Lickorish [1960's] and then by Thurston [197 0-80's] - they gave important applications of the mapping class group to t he topology and geometry of three-manifolds. In the past fifty years\, va rious mathematicians (including Penner\, Mosher\, Hamidi-Tehrani\, Dylan T hurston\, Dynnikov) have given solutions to the word problem in the mappin g class group\, using a variety of techniques. All of these algorithms ar e quadratic-time.\n\nWe give an algorithm requiring only $O(n \\log^3(n))$ time. We do this by combining Dynnikov's approach to curves on surfaces\ , Möller's version of the half-GCD algorithm\, and a delicate error analy sis in interval arithmetic.\n\nThis is joint work with Mark Bell.\n LOCATION:https://stable.researchseminars.org/talk/GaTO/107/ END:VEVENT BEGIN:VEVENT SUMMARY:Mireille Soergel (MPI MiS Leipzig) DTSTART:20241017T123000Z DTEND:20241017T133000Z DTSTAMP:20260404T095244Z UID:GaTO/108 DESCRIPTION:Title: Dyer groups: Coxeter groups\, right-angled Artin groups and more...< /a>\nby Mireille Soergel (MPI MiS Leipzig) as part of Geometry and topolog y online\n\nLecture held in Room B3.02 in the Zeeman Building\, University of Warwick.\n\nAbstract\nDyer groups are a family encompassing both Coxet er groups and right-angled Artin groups. Among many common properties\, th ese two families admit the same solution to the word problem. Each of thes e two classes of groups also have natural piecewise Euclidean CAT(0) space s associated to them. In this talk I will introduce Dyer groups\, give som e of their properties.\n LOCATION:https://stable.researchseminars.org/talk/GaTO/108/ END:VEVENT BEGIN:VEVENT SUMMARY:Sami Douba (IHES) DTSTART:20241107T133000Z DTEND:20241107T143000Z DTSTAMP:20260404T095244Z UID:GaTO/109 DESCRIPTION:Title: Zariski closures of linear reflection groups\nby Sami Douba (IHE S) as part of Geometry and topology online\n\nLecture held in Room B3.02 i n the Zeeman Building\, University of Warwick.\n\nAbstract\nWe show that l inear reflection groups in the sense of Vinberg are often Zariski dense in \\(\\mathrm{PGL}(n)\\). Among the applications are examples of low-dimens ional closed hyperbolic manifolds whose fundamental groups virtually embed as Zariski-dense subgroups of \\(\\mathrm{SL}(n\,\\mathbb{Z})\\)\, as wel l as some one-ended Zariski-dense subgroups of \\(\\mathrm{SL}(n\,\\mathbb {Z})\\) that are finitely generated but infinitely presented\, for all suf ficiently large \\(n\\). \n\nThis is joint work with Jacques Audibert\, Gy e-Seon Lee\, and Ludovic Marquis.\n LOCATION:https://stable.researchseminars.org/talk/GaTO/109/ END:VEVENT BEGIN:VEVENT SUMMARY:Simon Machado (ETH Zurich) DTSTART:20241128T133000Z DTEND:20241128T143000Z DTSTAMP:20260404T095244Z UID:GaTO/110 DESCRIPTION:Title: Approximate lattices: structure and beyond\nby Simon Machado (ET H Zurich) as part of Geometry and topology online\n\nLecture held in Room B3.02 in the Zeeman Building\, University of Warwick.\n\nAbstract\nApproxi mate lattices are aperiodic generalisations of lattices in locally compact groups. Yves Meyer first introduced them in abelian groups before studyin g them as mathematical models for quasi-crystals. Since then\, their struc ture has been thoroughly investigated in both abelian and non-abelian sett ings. The primary motivation behind this research was to extend Meyer’s foundational theorem to non-abelian locally compact groups.\n\nThis genera lisation has now been established\, and I will discuss the resulting struc ture theory. I will highlight certain concepts\, including a notion of coh omology that lies between group cohomology and bounded cohomology\, which plays a significant role in their study. Additionally\, I will formulate o pen problems and conjectures related to approximate lattices.\n LOCATION:https://stable.researchseminars.org/talk/GaTO/110/ END:VEVENT BEGIN:VEVENT SUMMARY:Peter Patzt (Oklahoma) DTSTART:20241205T133000Z DTEND:20241205T143000Z DTSTAMP:20260404T095244Z UID:GaTO/111 DESCRIPTION:Title: Unstable cohomology of \\(\\mathrm{SL}_n(\\mathbb{Z})\\) and Hopf al gebras\nby Peter Patzt (Oklahoma) as part of Geometry and topology onl ine\n\nLecture held in Room B3.02 in the Zeeman Building\, University of W arwick.\n\nAbstract\nThe cohomology of \\(\\mathrm{SL}_n(\\mathbb{Z})\\) h as many connections to geometry and number theory and is largely unknown. In this talk\, I will give a survey about what is known about it. In parti cular\, I will include newly found unstable classes which come from a Hopf algebra structure. \n\nThis talk is on joint work with Avner Ash and Jere my Miller.\n LOCATION:https://stable.researchseminars.org/talk/GaTO/111/ END:VEVENT BEGIN:VEVENT SUMMARY:Shaked Bader (Oxford) DTSTART:20241010T123000Z DTEND:20241010T133000Z DTSTAMP:20260404T095244Z UID:GaTO/112 DESCRIPTION:Title: Hyperbolic subgroups of type FP_2(Ring)\nby Shaked Bader (Oxford ) as part of Geometry and topology online\n\nLecture held in Room B3.02 in the Zeeman Building\, University of Warwick.\n\nAbstract\nIn 1996 Gersten proved that if $G$ is a word hyperbolic group of cohomological dimension two and $H$ is a subgroup of type $\\mathrm{FP}_2$\, then $H$ is hyperboli c as well. I will generalise this result to show that the same is true if $G$ is only assumed to have cohomological dimension two over some ring $R $ and $H$ is of type $\\mathrm{FP}_2(R)$.\n\nThis is joint work with Rober t Kropholler and Vlad Vankov.\n LOCATION:https://stable.researchseminars.org/talk/GaTO/112/ END:VEVENT BEGIN:VEVENT SUMMARY:Stefanie Zbinden (Heriot-Watt) DTSTART:20241031T133000Z DTEND:20241031T143000Z DTSTAMP:20260404T095244Z UID:GaTO/113 DESCRIPTION:Title: Morse directions in classical small cancellation groups\nby Stef anie Zbinden (Heriot-Watt) as part of Geometry and topology online\n\nLect ure held in Room B3.02 in the Zeeman Building\, University of Warwick.\n\n Abstract\nMorse geodesics are geodesics that capture the hyperbolic-like f eatures of not necessarily hyperbolic spaces. They were studied in order t o generalize proofs about hyperbolic groups. However\, it quickly became c lear that having a Morse geodesic is not enough to exclude various types o f pathological behaviours\, which makes many genearlizations impossible. L uckily\, it turns out that having slightly stronger assumptions on the gro up\, such as having a WPD element or being "Morse-local-to-global" makes certain pathologies impossible. In this talk\, we explore how those strong er assumptions relate to each other in the case of small cancellation grou ps.\n LOCATION:https://stable.researchseminars.org/talk/GaTO/113/ END:VEVENT BEGIN:VEVENT SUMMARY:Mikhail Hlushchanka (Amsterdam) DTSTART:20241114T133000Z DTEND:20241114T143000Z DTSTAMP:20260404T095244Z UID:GaTO/114 DESCRIPTION:Title: Canonical decomposition of rational maps\nby Mikhail Hlushchanka (Amsterdam) as part of Geometry and topology online\n\nLecture held in Ro om B3.02 in the Zeeman Building\, University of Warwick.\n\nAbstract\nTher e are various classical and more recent decomposition results in mapping c lass group theory\, geometric group theory\, and complex dynamics (which i nclude celebrated results by Bill Thurston). The goal of this talk is to i ntroduce a powerful decomposition of rational maps based on the topologica l structure of their Julia sets. Namely\, we will discuss the following re sult: every postcritically-finite rational map with non-empty Fatou set ca n be canonically decomposed into crochet maps (these have very "thinly con nected" Julia sets) and Sierpinski carpet maps (these have very "heavily c onnected" Julia sets). If time permits\, I will discuss applications of th is result in various aspects of geometric group theory. \n\nThis is based on joint work with Dima Dudko and Dierk Schleicher.\n LOCATION:https://stable.researchseminars.org/talk/GaTO/114/ END:VEVENT BEGIN:VEVENT SUMMARY:Harry Petyt (Oxford) DTSTART:20241121T133000Z DTEND:20241121T143000Z DTSTAMP:20260404T095244Z UID:GaTO/115 DESCRIPTION:Title: Obstructions to cubulation\nby Harry Petyt (Oxford) as part of G eometry and topology online\n\nLecture held in Room B3.02 in the Zeeman Bu ilding\, University of Warwick.\n\nAbstract\nOne can get a lot of informat ion about a group by getting it to act geometrically on a \\(\\mathrm{CAT} (0)\\) cube complex. When this is possible there is a standard framework f or trying to find the action\, known as Sageev's construction. On the othe r hand\, whilst most groups will not admit such actions\, there is a real lack of ways to actually rule out the possibility that they exist. In this talk we give a geometric obstruction to the possibility of cubulating gro ups.\n\nThis is joint work with Zach Munro.\n LOCATION:https://stable.researchseminars.org/talk/GaTO/115/ END:VEVENT BEGIN:VEVENT SUMMARY:Rob Kropholler (Warwick) DTSTART:20250109T133000Z DTEND:20250109T143000Z DTSTAMP:20260404T095244Z UID:GaTO/116 DESCRIPTION:Title: An explicit bound on the Dehn function of a subgroup of a hyperbolic group\nby Rob Kropholler (Warwick) as part of Geometry and topology o nline\n\nLecture held in Room B3.02 in the Zeeman Building\, University of Warwick.\n\nAbstract\nHyperbolic groups are characterised by having a lin ear Dehn function. This property does not pass to finitely presented subgr oups\, by work of Brady. This opens the question of what Dehn functions o f finitely presented subgroups of hyperbolic groups can be. In this talk I will detail what is known and give an explicit upper bound for the Dehn f unction of Brady’s example.\n\nThis is joint work with Claudio Llosa Ise nrich and Ignat Soroko.\n LOCATION:https://stable.researchseminars.org/talk/GaTO/116/ END:VEVENT BEGIN:VEVENT SUMMARY:Alessandro Sisto (Heriot-Watt) DTSTART:20250116T133000Z DTEND:20250116T143000Z DTSTAMP:20260404T095244Z UID:GaTO/117 DESCRIPTION:Title: Asymptotically CAT(0) metrics and applications\nby Alessandro Si sto (Heriot-Watt) as part of Geometry and topology online\n\nLecture held in Room B3.02 in the Zeeman Building\, University of Warwick.\n\nAbstract\ nWe construct metrics that satisfy a CAT(0)-like inequality involving a su blinear error for a large class of groups including mapping class groups a nd a lot of their quotients\, most 3-manifold groups\, extra-large Artin g roups\, extension of Veech groups and multicurve stabilisers\, and many ot hers. These metrics in turn allow one to construct contractible Rips compl exes with "nice" compactifications\, and to use those to show that the gro ups in our large class satisfy the Farrell-Jones conjecture.\n\nThis is jo int work-in progress with Matt Durham and Yair Minsky.\n LOCATION:https://stable.researchseminars.org/talk/GaTO/117/ END:VEVENT BEGIN:VEVENT SUMMARY:Ismael Morales (Oxford) DTSTART:20250306T133000Z DTEND:20250306T143000Z DTSTAMP:20260404T095244Z UID:GaTO/118 DESCRIPTION:Title: Fixed points\, splittings and division rings\nby Ismael Morales (Oxford) as part of Geometry and topology online\n\nLecture held in Room B 3.02 in the Zeeman Building\, University of Warwick.\n\nAbstract\nLet $G$ be a free group of rank $N$\, let $f$ be an automorphism of $G$ and let $\ \mathrm{Fix}(f)$ be the corresponding subgroup of fixed points. Bestvina a nd Handel showed that the rank of $\\mathrm{Fix}(f)$ is at most $N$\, for which they developed the theory of train track maps on free groups. Differ ent arguments were provided later on by Sela\, Paulin and Gaboriau-Levitt- Lustig. In this talk\, we present a new proof which involves the Linnell d ivision ring of $G$. We also discuss how our approach relates to previous ones and how it gives new insight into variations of the problem.\n LOCATION:https://stable.researchseminars.org/talk/GaTO/118/ END:VEVENT BEGIN:VEVENT SUMMARY:Macarena Arena (Cambridge) DTSTART:20250320T133000Z DTEND:20250320T143000Z DTSTAMP:20260404T095244Z UID:GaTO/119 DESCRIPTION:Title: Taut smoothings and shortest geodesics\nby Macarena Arena (Cambr idge) as part of Geometry and topology online\n\nLecture held in Room B3.0 2 in the Zeeman Building\, University of Warwick.\n\nAbstract\nIn this tal k we will discuss the connection between combinatorial properties of minim ally self-intersecting curves on a surface \\(S\\) and the geometric behav iour of geodesics on \\(S\\) when \\(S\\) is endowed with a riemannian met ric. In particular\, we will explain the interplay between a smoothing\, w hich is a type of surgery on a curve that resolves a self-intersection\, a nd k-systoles\, which are shortest geodesics having at least k self-inters ections\, and we will present some results that partially elucidate this i nterplay.\n LOCATION:https://stable.researchseminars.org/talk/GaTO/119/ END:VEVENT BEGIN:VEVENT SUMMARY:Anna Felikson (Durham) DTSTART:20250508T123000Z DTEND:20250508T133000Z DTSTAMP:20260404T095244Z UID:GaTO/120 DESCRIPTION:Title: Hyperbolic geometry of friezes\nby Anna Felikson (Durham) as par t of Geometry and topology online\n\nLecture held in Room B3.02 in the Zee man Building\, University of Warwick.\n\nAbstract\nFrieze patterns were in troduced by Coxeter in the 1970s who\, with Conway\, established a corresp ondence between frieze patterns and triangulated polygons. It turned out l ater that this object is very rich in connections with different fields in mathematics. We use hyperbolic geometry to provide a classification of po sitive integral friezes on marked bordered surfaces.\n\nThis is a joint wo rk with Pavel Tumarkin.\n LOCATION:https://stable.researchseminars.org/talk/GaTO/120/ END:VEVENT BEGIN:VEVENT SUMMARY:Naomi Andrew (Oxford) DTSTART:20250626T123000Z DTEND:20250626T133000Z DTSTAMP:20260404T095244Z UID:GaTO/121 DESCRIPTION:Title: The Farrell--Tate K-theory of $\\mathrm{Out}(F_n)$\nby Naomi And rew (Oxford) as part of Geometry and topology online\n\nLecture held in Ro om B3.02 in the Zeeman Building\, University of Warwick.\n\nAbstract\nGive n a (nice enough) group\, there is an isomorphism\, due to Lück\, relatin g the rationalised K-theory groups of its classifying space to a large pro duct of cohomology groups\, some with rational and some with $p$-adic coef ficients.\n\nWe identify a generalised cohomology theory capturing the $p$ -adic part of this product. Working in $\\mathrm{Out}(F_n)$\, in ranks clo se to $p$ we can fully compute this $p$-adic part and in this way produce an infinite family of odd-dimensional summands in the rationalised K-theor y of $\\mathrm{Out}(F_n)$. I will discuss these results and the tools tha t go into them\, which range from spherical group rings to the lemma that is not Burnside's\, via results about centralisers in $\\mathrm{Out}(F_n)$ : I will try to explain how all these various ideas fit together!\n\nThis is joint work with Irakli Patchkoria.\n LOCATION:https://stable.researchseminars.org/talk/GaTO/121/ END:VEVENT BEGIN:VEVENT SUMMARY:Davide Spriano (Warwick) DTSTART:20251016T123000Z DTEND:20251016T133000Z DTSTAMP:20260404T095244Z UID:GaTO/122 DESCRIPTION:Title: Curtains\, walls\, and stable cylinders\nby Davide Spriano (Warw ick) as part of Geometry and topology online\n\nLecture held in Room B3.02 in the Zeeman Building\, University of Warwick.\n\nAbstract\nIn this talk we will discuss a generalization of Sageev’s wallspace construction tha t allows to study the geometry of certain spaces by combinatorial properti es of certain walls. Specifically\, we’ll look at the interactions with hyperbolicity and focus on two applications. In CAT(0) spaces\, these tech niques allow to construct a “universal hyperbolic quotient”\, called t he curtain model\, that is analogous to the curve graph of a surface. When focusing on a space that is already hyperbolic\, the construction can be used to improve its fine properties\, and in particular we address a conje cture of Rips and Sela and show that residually finite hyperbolic groups a dmit globally stable cylinders. \n\nThis is joint work with Petyt and Zall oum.\n LOCATION:https://stable.researchseminars.org/talk/GaTO/122/ END:VEVENT BEGIN:VEVENT SUMMARY:Mahan Mj (Tata Institute of Fundamental Research) DTSTART:20251023T123000Z DTEND:20251023T133000Z DTSTAMP:20260404T095244Z UID:GaTO/123 DESCRIPTION:Title: Hyperbolic and elliptic commensurations\nby Mahan Mj (Tata Insti tute of Fundamental Research) as part of Geometry and topology online\n\nL ecture held in Room B3.02 in the Zeeman Building\, University of Warwick.\ n\nAbstract\nA group $G$ is said to commensurate a subgroup $H$\, if for a ll $g$ in $G$\, the intersection $H^g \\cap H$ has finite index in both $H $ and $H^g$. (Here $H^g$ denotes the conjugate of $H$ by $g$.) The commen suration action of $G$ on $H$ can be studied dynamically. This gives rise to two extreme behaviours: hyperbolic and elliptic. We will discuss what t hese mean and survey a range of theorems and conjectures in this context\, starting with work of Mostow and Margulis\, and coming to the present day .\n LOCATION:https://stable.researchseminars.org/talk/GaTO/123/ END:VEVENT BEGIN:VEVENT SUMMARY:Islam Foniqi (University of East Anglia) DTSTART:20251106T134500Z DTEND:20251106T144500Z DTSTAMP:20260404T095244Z UID:GaTO/124 DESCRIPTION:Title: Submonoid membership problems in one-relator groups and monoids\, su rface groups\, and beyond\nby Islam Foniqi (University of East Anglia) as part of Geometry and topology online\n\nLecture held in Room B3.02 in the Zeeman Building\, University of Warwick.\n\nAbstract\nThe word problem for one-relator monoids remains one of the long-standing open questions i n combinatorial algebra. One way to approach it is by studying related dec ision problems\, in particular the submonoid membership problem\, in both monoids and groups. In this talk\, I will discuss how these problems are c onnected\, drawing on classical work by Adian and Guba. I will also highli ght the role of embeddings of right-angled Artin groups and trace monoids\ , which offer useful insights into the structure of these questions. Final ly\, I will present recent joint results with Robert D. Gray on the submon oid membership problem in surface groups\, and in the broader hyperbolic s etting.\n LOCATION:https://stable.researchseminars.org/talk/GaTO/124/ END:VEVENT BEGIN:VEVENT SUMMARY:Sebastian Hensel (LMU Munich) DTSTART:20251120T133000Z DTEND:20251120T143000Z DTSTAMP:20260404T095244Z UID:GaTO/125 DESCRIPTION:Title: Dynamics of torus homeomorphisms and the fine curve graph\nby Se bastian Hensel (LMU Munich) as part of Geometry and topology online\n\nLec ture held in Room B3.02 in the Zeeman Building\, University of Warwick.\n\ nAbstract\nThe fine curve graph is a Gromov hyperbolic graph on which the homeomorphism group of a surface acts. We relate the surface dynamics of a torus homeomorphism to its action on the fine curve graph. In particula r we show that the shape of a “big" rotation set is determined by the fi xed points on the Gromov boundary of the graph. A key ingredient is a met ric version of the WPD property for the homeomorphism group of the torus.\ n\nThis is joint work with Frédéric Le Roux.\n LOCATION:https://stable.researchseminars.org/talk/GaTO/125/ END:VEVENT BEGIN:VEVENT SUMMARY:Jing Tao (University of Oklahoma) DTSTART:20251127T133000Z DTEND:20251127T143000Z DTSTAMP:20260404T095244Z UID:GaTO/126 DESCRIPTION:Title: Tame maps of surfaces of infinite type\nby Jing Tao (University of Oklahoma) as part of Geometry and topology online\n\nLecture held in Ro om B3.02 in the Zeeman Building\, University of Warwick.\n\nAbstract\nA co rnerstone in low-dimensional topology is the Nielsen-Thurston Classificati on Theorem\, which provides a blueprint for understanding homeomorphisms o f compact surfaces up to homotopy. However\, extending this theory to non- compact surfaces of infinite type remains an elusive goal. The complexity arises from the behavior of curves on surfaces with infinite type\, which can become increasingly intricate with each iteration of a homeomorphism. To address some of the challenges\, we introduce the notion of tame maps\, a class of homeomorphisms that exhibit non-mixing dynamics. In this talk\ , I will present some recent progress on extending the classification theo ry to such maps. \n\nThis is joint work with Mladen Bestvina and Federica Fanoni.\n LOCATION:https://stable.researchseminars.org/talk/GaTO/126/ END:VEVENT BEGIN:VEVENT SUMMARY:Philipp Bader (University of Glasgow) DTSTART:20251211T133000Z DTEND:20251211T143000Z DTSTAMP:20260404T095244Z UID:GaTO/127 DESCRIPTION:Title: Teichmüller curves via the Hurwitz-Hecke construction\nby Phili pp Bader (University of Glasgow) as part of Geometry and topology online\n \nLecture held in Room B3.02 in the Zeeman Building\, University of Warwic k.\n\nAbstract\nTeichmüller curves are totally geodesic algebraic curves inside the moduli space of Riemann surfaces of genus $g$. There are fascin ating connections between Teichmüller curves and billiard flows on polygo ns.\n\nGiven a Teichmüller curve\, there is a way to construct another\, in higher genus\, by taking a branched cover. If a Teichmüller curve does not arise in this way\, we call it primitive. The classification o f primitive Teichmüller curves is a problem that has been widely explored in the past decades but still leaves many questions unanswered. In fact\, only in genus two there exists a complete classification. In every genus starting from five and higher only finitely many examples of primitive Tei chmüller curves have been found.\n\nIn this talk\, we introduce the notio ns described above and present the so-called Hurwitz-Hecke construction\; a method that can be used to construct Teichmüller curves. We will see th at this construction gives rise to many of the known examples of Teichmül ler curves. \n\nThis is joint work in progress with Paul Apisa and Luke Je ffreys.\n LOCATION:https://stable.researchseminars.org/talk/GaTO/127/ END:VEVENT BEGIN:VEVENT SUMMARY:Will Cohen (University of Cambridge) DTSTART:20251113T133000Z DTEND:20251113T143000Z DTSTAMP:20260404T095244Z UID:GaTO/128 DESCRIPTION:Title: Improving acylindrical actions on trees\nby Will Cohen (Universi ty of Cambridge) as part of Geometry and topology online\n\nLecture held i n Room B3.02 in the Zeeman Building\, University of Warwick.\n\nAbstract\n Loosely speaking\, an action of a group on a tree is acylindrical if long enough paths must have small stabilisers. Groups admitting such actions f orm a natural subclass of acylindrically hyperbolic groups\, and an intere sting feature of acylindrical actions on trees is that many properties of groups are inherited from their vertex stabilisers. In order to make use of this\, it is important to have some degree of control over these stabil isers. For example\, can we ask for these stabilisers to be finitely gene rated? Even stronger\, if our group is hyperbolic\, can we ask for the st abilisers to be quasiconvex?\n\nI will introduce acylindrical actions as w ell as some stronger and related concepts. I will also discuss a method k nown as the Dunwoody—Sageev resolution. We use this to move between the se concepts and provide positive answers to the above questions in some ca ses.\n LOCATION:https://stable.researchseminars.org/talk/GaTO/128/ END:VEVENT BEGIN:VEVENT SUMMARY:Jannis Weis (Karlsruhe Institute of Technology) DTSTART:20251204T133000Z DTEND:20251204T143000Z DTSTAMP:20260404T095244Z UID:GaTO/129 DESCRIPTION:Title: From finiteness properties to polynomial filling via homological alg ebra\nby Jannis Weis (Karlsruhe Institute of Technology) as part of Ge ometry and topology online\n\nLecture held in Room B3.02 in the Zeeman Bui lding\, University of Warwick.\n\nAbstract\nIf a group has type $\\textrm{ FP}_n$ one can define higher filling functions\, which give a quantitative refinement of $\\textrm{FP}_n$ by measuring the size of fillings of $k$ ‑cycles ($k \\leq n$). We develop a homological‑algebra framework tha t extends existing tools for finiteness properties to produce polynomial b ounds for these filling functions. The goal is to make deducing polynomia lity as straightforward as proving $\\textrm{FP}_n$.\n\nThis is based on j oint work with Roman Sauer.\n LOCATION:https://stable.researchseminars.org/talk/GaTO/129/ END:VEVENT BEGIN:VEVENT SUMMARY:Jerónimo García Mejía (Warwick) DTSTART:20260115T133000Z DTEND:20260115T143000Z DTSTAMP:20260404T095244Z UID:GaTO/130 DESCRIPTION:Title: Complete classification of the Dehn functions of Bestvina—Brady gr oups\nby Jerónimo García Mejía (Warwick) as part of Geometry and to pology online\n\nLecture held in Room B3.02 in the Zeeman Building\, Unive rsity of Warwick.\n\nAbstract\nIntroduced by Bestvina and Brady in 1997\, Bestvina–Brady groups form a rich class of examples in geometric group t heory\, notable for their exotic finiteness properties. We will focus on their Dehn functions: a fundamental quasi-isometry invariant that provides a quantitative measure of the group's finite presentability. After recall ing previous results\, We give a classification of the Dehn functions of B estvina—Brady groups. \n\nThis talk is based on joint work with Yu-Chan Chang and Matteo Migliorini.\n LOCATION:https://stable.researchseminars.org/talk/GaTO/130/ END:VEVENT BEGIN:VEVENT SUMMARY:Nansen Petrosyan (University of Southampton) DTSTART:20260122T133000Z DTEND:20260122T143000Z DTSTAMP:20260404T095244Z UID:GaTO/131 DESCRIPTION:Title: The kernel knows\nby Nansen Petrosyan (University of Southampton ) as part of Geometry and topology online\n\nLecture held in Room B3.02 in the Zeeman Building\, University of Warwick.\n\nAbstract\nFor a graph pro duct of groups\, the canonical map to the direct product of the vertex gro ups has a kernel whose structure is not immediately apparent. Remarkably\, this kernel turns out to be oblivious to most of the algebra one builds i nto the construction\, yet it is sensitive to the underlying combinatorics . This has applications to the Baum--Connes conjecture\, Brown's question\ , the Eilenberg-Ganea conjecture and inheritance properties of graph produ cts of groups.\n\nThis is joint work with Ian Leary.\n LOCATION:https://stable.researchseminars.org/talk/GaTO/131/ END:VEVENT BEGIN:VEVENT SUMMARY:Carolyn Abbott (Brandeis University) DTSTART:20260129T133000Z DTEND:20260129T143000Z DTSTAMP:20260404T095244Z UID:GaTO/132 DESCRIPTION:Title: A non-acylindrically hyperbolic Morse local-to-global group\nby Carolyn Abbott (Brandeis University) as part of Geometry and topology onli ne\n\nLecture held in Room B3.02 in the Zeeman Building\, University of Wa rwick.\n\nAbstract\nHyperbolic spaces satisfy two defining properties: eve ry geodesic is Morse\, and every local quasi-geodesic (on a sufficiently l arge local scale) is a global quasi-geodesic. In non-hyperbolic spaces\, s ome geodesics may be Morse and others not\, and local quasi- geodesics may or may not be global quasi-geodesics. Intuitively\, the Morse geodesics p ick out the “hyperbolic-like” directions in the space. Morse local-to- global (MLTG) spaces generalize hyperbolic spaces by requiring that the lo cal-to-global property for hyperbolic spaces holds for all Morse elements. MLTG groups (groups whose Cayley graph is a MLTG space) include hyperboli c groups\, Zn\, many classes of Artin groups\, including right-angled\, ma pping class groups\, and groups hyperbolic relative to MLTG groups. All kn own examples that contain a Morse element are acylindrically hyperbolic\; in light of which Russell\, Spriano\, and Tran asked whether this was alwa ys the case. In this talk\, I’ll explain why the answer to this question is no by describing the construction of a non-acylindrically hyperbolic M LTG group with a Morse element. Along the way\, I’ll describe how to gen eralize several techniques from small cancellation groups to general finit ely generated groups. \n\nThis is joint work with Stefanie Zbinden.\n LOCATION:https://stable.researchseminars.org/talk/GaTO/132/ END:VEVENT BEGIN:VEVENT SUMMARY:Luke Jeffreys (University of Bristol) DTSTART:20260205T133000Z DTEND:20260205T143000Z DTSTAMP:20260404T095244Z UID:GaTO/133 DESCRIPTION:Title: Euler characteristics of SL(2\,Z)-orbit graphs of square-tiled surfa ces\nby Luke Jeffreys (University of Bristol) as part of Geometry and topology online\n\nLecture held in Room B3.02 in the Zeeman Building\, Uni versity of Warwick.\n\nAbstract\nSquare-tiled surfaces (aptly named) are s urfaces obtained by gluing together a collection of unit squares along the ir sides (the square torus being the simplest example). These surfaces are special cases of translation surfaces\, whose moduli space carries a natu ral action of the group $SL(2\,\\mathbb{R})$. The famous works of Eskin– Mirzakhani and Eskin–Mirzakhani–Mohammadi were concerned with understa nding the orbits of this action.\n\nThis $SL(2\,\\mathbb{R})$-action restr icts to an action of $SL(2\,\\mathbb{Z})$ on square-tiled surfaces\, and t he orbits under this restricted action can be transformed into finite regu lar graphs. It is a long-standing conjecture of McMullen that a specific f amily of these orbit graphs in genus two forms a family of expander graphs . Providing indirect evidence for this conjecture\, I will describe joint work with Carlos Matheus in which we prove that the absolute values of the Euler characteristics of the graphs in this family go to infinity (a requ irement for any expander family). To do this\, we are required to count a variety of objects\, including integer points on algebraic hypersurfaces\, pseudo-Anosov homeomorphisms of fixed dilatation\, and orbifold points on certain algebraic curves in moduli space.\n LOCATION:https://stable.researchseminars.org/talk/GaTO/133/ END:VEVENT BEGIN:VEVENT SUMMARY:Giovanni Italiano (University of Oxford) DTSTART:20260212T133000Z DTEND:20260212T143000Z DTSTAMP:20260404T095244Z UID:GaTO/134 DESCRIPTION:Title: Improved virtual algebraic fibrations of high dimensional hyperbolic Coxeter groups\nby Giovanni Italiano (University of Oxford) as part o f Geometry and topology online\n\nLecture held in Room B3.02 in the Zeeman Building\, University of Warwick.\n\nAbstract\nIn a recent paper\, Lafont \, Minemyer\, Sorcar\, Stover\, and Wells built hyperbolic right-angled Co xeter groups that virtually algebraically fibre in any virtual cohomologic al dimension. We provide a new construction that allows us to construct gr oups that virtually fibre with finitely presented kernel. Obtaining finite presentability is usually a big step forward\, since it allows to use hom ological methods (due to Kielak and Fisher) to leverage even stronger fini teness properties. However\, our technique is quite in dissonance with thi s\, so these particular examples do not seem to be upgradable in general. \n\nThis is joint work with Matteo Migliorini and Andrew Ng.\n LOCATION:https://stable.researchseminars.org/talk/GaTO/134/ END:VEVENT BEGIN:VEVENT SUMMARY:Gabriel Corrigan (University of Glasgow) DTSTART:20260219T133000Z DTEND:20260219T143000Z DTSTAMP:20260404T095244Z UID:GaTO/135 DESCRIPTION:Title: Finiteness properties of some automorphism groups of right-angled Ar tin groups\nby Gabriel Corrigan (University of Glasgow) as part of Geo metry and topology online\n\nLecture held in Room B3.02 in the Zeeman Buil ding\, University of Warwick.\n\nAbstract\nRight-angled Artin groups (RAAG s) can be viewed as a generalisation of free groups. To what extent\, then \, do the techniques used to study automorphisms of free groups generalise to the setting of RAAGs? One significant advance in this direction is the construction of 'untwisted Outer space' for RAAGs\, a generalisation of t he influential Culler-Vogtmann Outer space for free groups. A consequence of this construction is an upper bound on the virtual cohomological dimens ion of the 'untwisted subgroup' of outer automorphisms of a RAAG. However\ , this bound is sometimes larger than one expects\; I present work showing that in fact it can be arbitrarily so\, by forming a new complex as a def ormation retraction of the untwisted Outer space. In a different direction \, another subgroup of interest is that consisting of symmetric automorphi sms. Generalising work in the free groups setting from 1989\, I present an Outer space for the symmetric automorphism group of a RAAG. A consequence of the proof is a strong finiteness property for many other subgroups of the outer automorphism group.\n LOCATION:https://stable.researchseminars.org/talk/GaTO/135/ END:VEVENT BEGIN:VEVENT SUMMARY:Matteo Migliorini (Karlsruher Institut für Technologie) DTSTART:20260226T133000Z DTEND:20260226T143000Z DTSTAMP:20260404T095244Z UID:GaTO/136 DESCRIPTION:Title: The Dehn function of Thompson's group $T$\nby Matteo Migliorini (Karlsruher Institut für Technologie) as part of Geometry and topology on line\n\nLecture held in Room B3.02 in the Zeeman Building\, University of Warwick.\n\nAbstract\nThompson’s groups\, introduced by Thompson in 1965 \, have had a lot of attention in the last fifty years. Being finitely pre sented\, a natural question is to compute their Dehn function. All three groups are conjectured to have quadratic Dehn function\; this conjecture w as confirmed for Thompson’s group $F$ by Guba in 2006. During this talk \, we show how to deduce from Guba’s result that Thompson’s group $T$ has quadratic Dehn function as well.\n LOCATION:https://stable.researchseminars.org/talk/GaTO/136/ END:VEVENT BEGIN:VEVENT SUMMARY:Tobias Hartnick (Karlsruher Institut für Technologie) DTSTART:20260305T133000Z DTEND:20260305T143000Z DTSTAMP:20260404T095244Z UID:GaTO/137 DESCRIPTION:Title: Geometry of approximate subgroups\nby Tobias Hartnick (Karlsruhe r Institut für Technologie) as part of Geometry and topology online\n\nLe cture held in Room B3.02 in the Zeeman Building\, University of Warwick.\n \nAbstract\nIn this lecture\, which is independent of the first two ones\, we will explain some of the more geometric aspects of approximate subgrou ps related to geometric group theory\, measure equivalence and bounded coh omology. A key player in this game is a certain ample groupoid constructed from the local patterns of the underlying point set. \n\nThis is based on joint works with Björklund\, Cordes\, Sarti and Tonić.\n LOCATION:https://stable.researchseminars.org/talk/GaTO/137/ END:VEVENT BEGIN:VEVENT SUMMARY:Genevieve Walsh (Tufts University) DTSTART:20260206T110500Z DTEND:20260206T115500Z DTSTAMP:20260404T095244Z UID:GaTO/138 DESCRIPTION:Title: Drilling and what it is good for\nby Genevieve Walsh (Tufts Univ ersity) as part of Geometry and topology online\n\nLecture held in Room B3 .02 in the Zeeman Building\, University of Warwick.\n\nAbstract\nA drillin g of a group is a relatively hyperbolic group pair\, which is a generaliza tion of the fundamental group of a drilled manifold. We define this and sh ow that drillings exist for residually finite hyperbolic groups with two-s phere boundaries. We also present some preliminary work which shows drilli ng can be used to understand the non-quasi convex surface subgroups of a r esidually finite hyperbolic group with two-sphere boundary.\n\nThe first p art of this talk is joint work with D. Groves\, P. Haïssinsky\, J. Mannin g\, D. Osajda\, and A. Sisto. The second part is joint with D. Groves.\n LOCATION:https://stable.researchseminars.org/talk/GaTO/138/ END:VEVENT BEGIN:VEVENT SUMMARY:Layne Hall (University of Warwick) DTSTART:20260312T133000Z DTEND:20260312T143000Z DTSTAMP:20260404T095244Z UID:GaTO/139 DESCRIPTION:Title: Flows and ideal triangulations of three-manifolds\nby Layne Hall (University of Warwick) as part of Geometry and topology online\n\nLectur e held in Room B3.02 in the Zeeman Building\, University of Warwick.\n\nAb stract\nPseudo-Anosov flows are a class of dynamical systems on three-mani folds with deep connections to the topology and geometry of their underlyi ng spaces. For instance\, features of the flow are closely related to the manifold’s hyperbolic geometry\, embedded surfaces\, and fundamental gro up. A modern approach to studying these flows is with veering triangulatio ns. These are rigid combinatorial objects that have provided new computati onal and algorithmic techniques to study the flows. In this talk\, I will first give a broad overview of the correspondence between these flows and triangulations. I will then discuss my work on more flexible triangulation s that capture a larger class of pseudo-Anosov flows and yield new explici t examples.\n LOCATION:https://stable.researchseminars.org/talk/GaTO/139/ END:VEVENT BEGIN:VEVENT SUMMARY:Ray Sliazkaite (University of Warwick) DTSTART:20260319T133000Z DTEND:20260319T143000Z DTSTAMP:20260404T095244Z UID:GaTO/140 DESCRIPTION:Title: The world of graph braid groups\nby Ray Sliazkaite (University o f Warwick) as part of Geometry and topology online\n\nLecture held in Room B3.02 in the Zeeman Building\, University of Warwick.\n\nAbstract\nGraph braid groups are fundamental groups of special\, non-positively curved cub e complexes. As a result\, they are interesting groups sharing some proper ties with classical braid groups\, right-angled Artin groups\, and more. I n this talk I will explore various examples illustrating the complicated b ut beautiful nature of graph braid groups.\n LOCATION:https://stable.researchseminars.org/talk/GaTO/140/ END:VEVENT END:VCALENDAR