Allcock\, building on the work of Greenburg\, pro ved that for any countable group \\(G\\)\, there is a a complete hyperboli c surface whose isometry group is exactly \\(G\\). When \\(G\\) is finite\ , Allcock’s construction yields a closed surface. Otherwise\, the const ruction gives an infinite-genus surface. \n\n

In this talk\, we discuss a related question. We fix any infinite-genus surface \\(S\\) and characte rise all groups that can arise as the isometry group for a complete hyperb olic structure on \\(S\\). In the process\, we give a classification type theorem for infinite-genus surfaces and\, if time allows\, two application s of the main result. \n\n

This talk is based on joint work with T. Aoug ab and N. Vlamis.\n LOCATION:https://researchseminars.org/talk/GaTO/4/ END:VEVENT BEGIN:VEVENT SUMMARY:Neil Hoffman (Oklahoma SU) DTSTART;VALUE=DATE-TIME:20200512T150000Z DTEND;VALUE=DATE-TIME:20200512T153000Z DTSTAMP;VALUE=DATE-TIME:20240222T215347Z UID:GaTO/5 DESCRIPTION:Title: Hig h crossing knot complements with few tetrahedra\nby Neil Hoffman (Okla homa 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\\) wit h \\(n\\) crossings\, one can construct a\ntriangulation of \\(S^3 - K\\) with at most \\(4n\\) tetrahedra. A natural question is then: given a tri angulation of a knot complement with \\(t\\) tetrahedra\, is the minimum c rossing number (for a diagram) of K bounded by a linear or polynomial func tion in \\(t\\)? We will answer the question in the negative by construct ing a family of hyperbolic knot complements where for each knot \\(K_n\\) in \\(S^3\\) whose the minimum crossing number goes as a function of \\(O( b^n)\\) for \\(b > 1\\)\, but the minimum number of tetrahedra in a triang ulation of \\(S^3 - K_n\\) is bounded above by \\(O(n)\\). Similar constr uctions exist for torus and satellite knot complements.\n\n

This is join
t work with Robert Haraway.\n
LOCATION:https://researchseminars.org/talk/GaTO/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Martin Scharlemann (UC Santa Barbara)
DTSTART;VALUE=DATE-TIME:20200512T153000Z
DTEND;VALUE=DATE-TIME:20200512T160000Z
DTSTAMP;VALUE=DATE-TIME:20240222T215347Z
UID:GaTO/6
DESCRIPTION:Title: A s
trong Haken's theorem\nby Martin Scharlemann (UC Santa Barbara) as par
t of Geometry and topology online\n\nLecture held in N/A.\n\nAbstract\nSup
pose that \\(T\\) is a Heegaard splitting\nsurface for a compact orientabl
e three-manifold \\(M\\)\; suppose\nthat \\(S\\) is a reducing sphere for
\\(M\\). In 1968 Haken\nshowed that there is then also a reducing sphere
\\(S^*\\) for\nthe Heegaard splitting. That is\, \\(S^*\\) is a reducing s
phere\nfor \\(M\\) and the surfaces \\(T\\) and \\(S^*\\) intersect in a\n
single circle. In 1987 Casson and Gordon extended the result\nto boundary
-reducing disks in \\(M\\) and noted that in both\ncases \\(S^*\\) is obta
ined 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 w
here \\(M\\)\ncontains no \\(S^1 \\times S^2\\) summands.\n
LOCATION:https://researchseminars.org/talk/GaTO/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Henry Segerman (Oklahoma SU)
DTSTART;VALUE=DATE-TIME:20200519T150000Z
DTEND;VALUE=DATE-TIME:20200519T153000Z
DTSTAMP;VALUE=DATE-TIME:20240222T215347Z
UID:GaTO/7
DESCRIPTION:Title: Fro
m veering triangulations to Cannon-Thurston maps\nby Henry Segerman (O
klahoma SU) as part of Geometry and topology online\n\nLecture held in NA.
\n\nAbstract\nAgol introduced veering triangulations of\nmapping tori\, wh
ose combinatorics are canonically associated\nto the pseudo-Anosov monodro
my. In previous work\, Hodgson\,\nRubinstein\, Tillmann and I found examp
les of veering\ntriangulations that are not layered and therefore do not c
ome\nfrom Agol's construction.\n\n However\, non-layered veering tr
iangulations retain many of the\n good properties enjoyed by mappin
g tori. For example\,\n Schleimer and I constructed a canonical ci
rcular ordering of\n the cusps of the universal cover of a veering
triangulation.\n Its order completion gives the *veering circle\;\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 veering sp
here is the Bowditch boundary of the manifold's\n fundamental group
(with respect to its cusp groups). As an\n application we produce
Cannon-Thurston maps for all veering\n triangulations. This gives
the first examples of\n Cannon-Thurston maps that do not come\, ev
en virtually\, from\n surface subgroups.\n
LOCATION:https://researchseminars.org/talk/GaTO/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Baris Coskunuzer (UT Dallas)
DTSTART;VALUE=DATE-TIME:20200519T153000Z
DTEND;VALUE=DATE-TIME:20200519T160000Z
DTSTAMP;VALUE=DATE-TIME:20240222T215347Z
UID:GaTO/8
DESCRIPTION:Title: Min
imal surfaces in hyperbolic three-manifolds\nby Baris Coskunuzer (UT D
allas) as part of Geometry and topology online\n\n\nAbstract\nThe existenc
e of minimal surfaces in three-manifolds is a classical problem in both ge
ometric analysis and geometric topology. In the past years\, this question
has been settled for closed\, and also for finite volume\, riemannian thr
ee-manifolds. In this talk\, we will prove the existence of smoothly embed
ded\, closed\, minimal surfaces in any infinite volume hyperbolic three-ma
nifold\, barring a few special cases.\n
LOCATION:https://researchseminars.org/talk/GaTO/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daniel Allcock (UT Austin)
DTSTART;VALUE=DATE-TIME:20200526T150000Z
DTEND;VALUE=DATE-TIME:20200526T153000Z
DTSTAMP;VALUE=DATE-TIME:20240222T215347Z
UID:GaTO/9
DESCRIPTION:Title: Big
mapping class groups fail the Tits alternative\nby Daniel Allcock (UT
Austin) as part of Geometry and topology online\n\n\nAbstract\nLet \\(S\\
) be a surface with infinitely many\npunctures\, or infinitely many handle
s\, or containing a disk\nminus Cantor set. (This accounts for almost all
infinite-type\nsurfaces.) Then the mapping class group of S fails to sat
isfy\nthe Tits alternative. Namely\, we construct a finitely\ngenerated s
ubgroup which is not virtually solvable and\ncontains no free group of ran
k greater than one. The\nGrigorchuk group is a key element in the constru
ction.\n
LOCATION:https://researchseminars.org/talk/GaTO/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Talia Fernos (UNC Greensboro)
DTSTART;VALUE=DATE-TIME:20200526T153000Z
DTEND;VALUE=DATE-TIME:20200526T160000Z
DTSTAMP;VALUE=DATE-TIME:20240222T215347Z
UID:GaTO/10
DESCRIPTION:Title: Bo
undaries and CAT(0) cube complexes\nby Talia Fernos (UNC Greensboro) a
s part of Geometry and topology online\n\n\nAbstract\nThe universe of \\(\
\CAT(0)\\) cube complexes\nis rich and diverse thanks to the ease by which
they can be\nconstructed and the many of natural metrics they admit. As
a\nconsequence\, there are several associated boundaries\, such as\nthe vi
sual boundary and the Roller boundary. In this talk we\nwill discuss some
relationships between these boundaries\,\ntogether with the Furstenberg-P
oisson boundary of a "nicely"\nacting group.\n
LOCATION:https://researchseminars.org/talk/GaTO/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daniel Woodhouse (Oxford)
DTSTART;VALUE=DATE-TIME:20200602T150000Z
DTEND;VALUE=DATE-TIME:20200602T153000Z
DTSTAMP;VALUE=DATE-TIME:20240222T215347Z
UID:GaTO/11
DESCRIPTION:Title: Qu
asi-isometric rigidity of graphs of free groups with cyclic edge groups\nby Daniel Woodhouse (Oxford) as part of Geometry and topology online\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\\). Consider
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-ended and
hyperbolic. What we have shown is that \\(G\\) is\nquasi-isometrically
rigid. That is\, if a finitely\ngenerated group \\(H\\) is quasi-iso
metric to \\(G\\)\, then \\(G\\)\nand \\(H\\) are virtually isomorphic. T
he main argument\ninvolves applying a new proof of Leighton's graph coveri
ng\ntheorem.\n\nOur full result is for finite graphs of groups with virtua
lly\nfree vertex groups and and two-ended edge groups. However the\nstate
ment here is more technical\; in particular\, not all such\ngroups are qua
si-isometrically rigid.\n\nThis is joint work with Sam Shepherd.\n
LOCATION:https://researchseminars.org/talk/GaTO/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rylee Lyman (Tufts)
DTSTART;VALUE=DATE-TIME:20200602T153000Z
DTEND;VALUE=DATE-TIME:20200602T160000Z
DTSTAMP;VALUE=DATE-TIME:20240222T215347Z
UID:GaTO/12
DESCRIPTION:Title: Ou
ter automorphisms of free Coxeter groups\nby Rylee Lyman (Tufts) as pa
rt of Geometry and topology online\n\n\nAbstract\nA famous theorem of Birm
an and Hilden\nprovides a close link between the mapping class group of a\
npunctured sphere and the centraliser\, in the mapping class\ngroup of a c
losed surface\, of a hyperelliptic involution.\nThere is a group theory an
alogue of this in Out(\\(F_n\\))\, the\nouter automorphism group of a free
group. Namely\, the outer\nautomorphism of a free Coxeter group i
s linked to the\ncentraliser\, in Out(\\(F_n\\))\, of a hyperelliptic invo
lution.\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://researchseminars.org/talk/GaTO/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kathryn Mann (Cornell)
DTSTART;VALUE=DATE-TIME:20200609T150000Z
DTEND;VALUE=DATE-TIME:20200609T153000Z
DTSTAMP;VALUE=DATE-TIME:20240222T215347Z
UID:GaTO/13
DESCRIPTION:Title: La
rge-scale geometry of big mapping class groups\nby Kathryn Mann (Corne
ll) as part of Geometry and topology online\n\n\nAbstract\nMapping class g
roups of infinite type surfaces are not finitely generated\; they are not
even locally compact. Nonetheless\, in many cases it is still meaningful t
o discuss their large scale geometry. We will explore which mapping class
groups have nontrivial coarse geometry.\n\nThis is joint work with Kasra R
afi.\n
LOCATION:https://researchseminars.org/talk/GaTO/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eric Samperson (UIUC)
DTSTART;VALUE=DATE-TIME:20200609T153000Z
DTEND;VALUE=DATE-TIME:20200609T160000Z
DTSTAMP;VALUE=DATE-TIME:20240222T215347Z
UID:GaTO/14
DESCRIPTION:Title: Ho
w helpful is hyperbolic geometry?\nby Eric Samperson (UIUC) as part of
Geometry and topology online\n\n\nAbstract\nHyperbolic geometry serves du
al roles at the intersection of group theory and three-manifold topology.
It plays the hero of group theory — rescuing the field from a morass of
uncomputability — but the anti-hero of low-dimensional topology—seemin
gly responsible for much of the complexity of three-manifolds. Where do th
ese roles overlap?\n\nI’ll give examples of group-theoretic invariants o
f three-manifolds (or knots) that are NP-hard to compute\, even for three-
manifolds (or knots) that are promised to be hyperbolic. The basic idea is
to show that the right-angled Artin semigroups of reversible circuits (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 complexes play
a key role.\n\nThis is joint work with Chris Leininger that builds on prev
ious work with Greg Kuperberg.\n
LOCATION:https://researchseminars.org/talk/GaTO/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Corey Bregman (Brandeis)
DTSTART;VALUE=DATE-TIME:20200616T150000Z
DTEND;VALUE=DATE-TIME:20200616T153000Z
DTSTAMP;VALUE=DATE-TIME:20240222T215347Z
UID:GaTO/15
DESCRIPTION:Title: Is
otopy and equivalence of knots in three-manifolds\nby Corey Bregman (B
randeis) as part of Geometry and topology online\n\n\nAbstract\nIt is a we
ll-known fact that the notions of\n(ambient) isotopy and equival
ence coincide for\nknots in \\(S^3\\). This is because all orientatio
n-preserving\nhomeomorphisms of \\(S^3\\) are isotopic to the identity. I
n\nthis talk\, we compare the notions of equivalence and isotopy\nfor knot
s in more general three-manifolds.\n\nWe show that the mapping class group
of a three-manifold\n"sees" all the isotopy classes of knots\; that is\,
if an\norientation-preserving homeomorphism fixes every isotopy\nclass\, t
hen 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 are chan
ged by the Gluck twist. Along\nthe way we prove that every three-manifold
group satisfies\nGrossman's Property A.\n\nThis is joint work with Paolo
Aceto\, Christopher Davis\,\nJungHwan Park\, and Arunima Ray.\n
LOCATION:https://researchseminars.org/talk/GaTO/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Caroline Series (Warwick)
DTSTART;VALUE=DATE-TIME:20200623T150000Z
DTEND;VALUE=DATE-TIME:20200623T153000Z
DTSTAMP;VALUE=DATE-TIME:20240222T215347Z
UID:GaTO/16
DESCRIPTION:Title: Ge
ometry in non-discrete groups of hyperbolic isometries: Primitive stabilit
y and the Bowditch Q-conditions are equivalent.\nby Caroline Series (W
arwick) as part of Geometry and topology online\n\n\nAbstract\nThere are g
eometrical conditions on a group of hyperbolic isometries which are of int
erest even when the group is not discrete. We explain two such conditions\
; these are stated in terms of the images of primitive elements of the fre
e group \\(F_2\\) under an \\(\\textrm{SL}(2\,\\mathbb{C})\\) representati
on. One is Minsky’s condition of primitive stability\; the other
is the so-called BQ-conditions introduced by Bowditch and generalis
ed by Tan\, Wong\, and Zhang.\n\nThese two conditions have been shown to b
e equivalent by Jaijeong Lee and Binbin Xu (Trans AMS 2020) and independen
tly by the speaker (arxiv 2019). We will explain the ideas using an combin
ation of both methods. If time permits\, we also explain another\, closely
related\, condition which constrains the axes of palindromic primitive el
ements.\n
LOCATION:https://researchseminars.org/talk/GaTO/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yulan Qing (Toronto)
DTSTART;VALUE=DATE-TIME:20200616T153000Z
DTEND;VALUE=DATE-TIME:20200616T160000Z
DTSTAMP;VALUE=DATE-TIME:20240222T215347Z
UID:GaTO/17
DESCRIPTION:Title: Th
e sub-linearly Morse boundary\nby Yulan Qing (Toronto) as part of Geom
etry and topology online\n\n\nAbstract\nThe Gromov boundary\, of a hyperbo
lic metric\nspace\, plays a central role in many aspects of geometric grou
p\ntheory. In this talk\, we introduce a generalization of the\nGromov bo
undary that also applies to non-hyperbolic\nspaces. For a given proper geo
desic metric space and a given\nsublinear function \\(\\kappa\\)\, we defi
ne the \\(\\kappa\\)-Morse\nboundary to be the space of all \\(\\kappa\\)-
sublinearly-Morse\nquasi-geodesics rays starting at a given base point.\n\
nWe show that\, equipped with a coarse version of the cone\ntopology\, the
\\(\\kappa\\)-boundary is metrizable and is a\nQI-invariant. For some gr
oups\, we show that their Poisson\nboundaries can be realized on the \\(\\
kappa\\)-boundary of their\nCayley graphs. These groups include all \\(\\
CAT(0)\\) groups\,\nmapping class groups\, Teichmü\;ller spaces\, hier
archically\nhyperbolic groups\, and relatively hyperbolic groups.\n\nThis
talk is based on joint projects with Ilya Gekhtmann\,\nKasra Rafi\, and Gi
ulio Tiozzo.\n
LOCATION:https://researchseminars.org/talk/GaTO/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:William Worden (Rice)
DTSTART;VALUE=DATE-TIME:20200623T153000Z
DTEND;VALUE=DATE-TIME:20200623T160000Z
DTSTAMP;VALUE=DATE-TIME:20240222T215347Z
UID:GaTO/18
DESCRIPTION:Title: De
hn filling and knot complements that do not irregularly cover\nby Will
iam Worden (Rice) as part of Geometry and topology online\n\n\nAbstract\nI
t is a longstanding conjecture of Neumann\nand Reid that exactly three kno
t complements can irregularly\ncover a hyperbolic orbifold -- the figure-e
ight knot and the two\nAitchison--Rubinstein dodecahedral knots. This con
jecture\,\nwhen combined with work of Boileau--Boyer--Walsh\, implies a\nm
ore recent conjecture of Reid and Walsh\, which states that\nthere are at
most three knot complements in the commensurability\nclass of any hyperbol
ic knot. We give a Dehn filling criterion\nthat is useful for producing l
arge families of knot\ncomplements that satisfy both conjectures.\n\nThe w
ork we will discuss is partially joint with Hoffman and\nMillichap and als
o partially joint with Chesebro\, Deblois\,\nHoffman\, Millichap\, and Mon
dal.\n
LOCATION:https://researchseminars.org/talk/GaTO/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michael Landry (WUSTL)
DTSTART;VALUE=DATE-TIME:20200721T150000Z
DTEND;VALUE=DATE-TIME:20200721T153000Z
DTSTAMP;VALUE=DATE-TIME:20240222T215347Z
UID:GaTO/19
DESCRIPTION:Title: Fa
ces 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 the co
mbinatorics\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 Currently\, most of the entries of this dictionary co ncern\n fibered faces of the unit ball. Thurston proved that these \n organize all fibrations of \\(M\\) over the circle. Fried 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 flows can n aturally specify nonfibered faces of the unit ball.\n

\n\n After giving some of this background I will discuss results\n from my recent preprint (see link). I\n show that Agol's veer ing triangulations can be used to\n determine faces of Thurston nor m balls\, to compute the\n Thurston norm over those faces\, and to collate all isotopy\n classes of least-complexity surfaces over tho se faces. This\n analysis includes nonfibered faces.\n

\n \nNo password is required.\n LOCATION:https://researchseminars.org/talk/GaTO/19/ END:VEVENT BEGIN:VEVENT SUMMARY:Rich Schwartz (Brown) DTSTART;VALUE=DATE-TIME:20200728T150000Z DTEND;VALUE=DATE-TIME:20200728T153000Z DTSTAMP;VALUE=DATE-TIME:20240222T215347Z UID:GaTO/20 DESCRIPTION:Title: Th e spheres of Sol\nby Rich Schwartz (Brown) as part of Geometry and top ology 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 Thurston geometries. As a corollary we prove that the metric spheres in Sol are in fact topological spheres.\n\nThis is joint work with Matei Coiculescu\n LOCATION:https://researchseminars.org/talk/GaTO/20/ END:VEVENT BEGIN:VEVENT SUMMARY:Scott Taylor (Colby) DTSTART;VALUE=DATE-TIME:20200728T153000Z DTEND;VALUE=DATE-TIME:20200728T160000Z DTSTAMP;VALUE=DATE-TIME:20240222T215347Z UID:GaTO/21 DESCRIPTION:Title: Eq uivariant 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 (or
ientation preserving) diffeomorphisms.\n The *equivariant Heegaar
d genus* of \\(M\\) is then the\n minimal genus of an equivarian
t Heegaard surface. The\n equivariant sphere theorem\, together wi
th recent work of\n Scharlemann\, suggests that equivariant Heegaar
d 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 equivari ant\n Heegaard genus can be sub-additive\, additive\, or\n s uper-additive. Building on recent work with Tomova\, I’ll\n sket ch machinery that gives rise both to sharp bounds on the\n addivity of equivariant Heegaard genus and to a closely\n related invariant that is in fact additive.\n

\n LOCATION:https://researchseminars.org/talk/GaTO/21/ END:VEVENT BEGIN:VEVENT SUMMARY:Marissa Loving (Georgia Tech) DTSTART;VALUE=DATE-TIME:20200804T150000Z DTEND;VALUE=DATE-TIME:20200804T153000Z DTSTAMP;VALUE=DATE-TIME:20240222T215347Z UID:GaTO/22 DESCRIPTION:Title: Co vers and curves\nby Marissa Loving (Georgia Tech) as part of Geometry 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 the spir it of this work\n we pose the following question: "What information about two\n covers \\(X\\) and \\(Y\\) of \\(S\\) can be derived b y\n understanding how curves on \\(S\\) lift simply to \\(X\\) and\ n \\(Y\\)?" In this talk\, we will explore the answer to this\n question for regular finite covers of a closed hyperbolic\n su rface.\n

\n\n This is joint work with Tarik Aouga b\, Max Lahn\, and Yang\n (Sunny) Xiao.\n

\n LOCATION:https://researchseminars.org/talk/GaTO/22/ END:VEVENT BEGIN:VEVENT SUMMARY:Sarah Dean Rasmussen (Cambridge) DTSTART;VALUE=DATE-TIME:20200804T153000Z DTEND;VALUE=DATE-TIME:20200804T160000Z DTSTAMP;VALUE=DATE-TIME:20240222T215347Z UID:GaTO/23 DESCRIPTION:Title: Ta ut foliations from left orders\, in Heegaard genus two\nby Sarah Dean Rasmussen (Cambridge) as part of Geometry and topology online\n\n\nAbstrac t\n\n Suppose that \\(M\\) is a closed\, connected\,\n or iented three-manifold which is not graph. All previously\n known c onstructions of taut foliations on such \\(M\\) used\n branched sur faces. These branched surfaces come from sutured\n manifold hierar chies\, following Gabai\, come from spanning\n surfaces of knot ext eriors\, following Roberts\, or come from\n one-vertex triangulatio ns with foliar orientations\, following\n Dunfield.\n

\n\n In this talk\, we give a new construction that does not u se\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 \\(\\mat hbb{R}\\)-transverse foliation (over a thickened Heegaard\n surface ) to a pair of handlebody foliations\; we then suitably\n cancel an y singularities. For Heegaard diagrams satisfying\n mild condition s\, this can be done reliably in Heegaard genus\n two. In some cas es this construction can be extended to\n higher Heegaard genus. T his helps explain numerical results\n of Dunfield: (i) tens of thou sands of Heegaard-genus two\n hyperbolic L-spaces certifiably fail to admit fundamental\n group left orders and (ii) no hyperbolic L-s pace is known to\n admit a fundamental group left order.\n

\n LOCATION:https://researchseminars.org/talk/GaTO/23/ END:VEVENT BEGIN:VEVENT SUMMARY:Kasia Jankiewicz (Chicago) DTSTART;VALUE=DATE-TIME:20200818T150000Z DTEND;VALUE=DATE-TIME:20200818T153000Z DTSTAMP;VALUE=DATE-TIME:20240222T215347Z UID:GaTO/24 DESCRIPTION:Title: Ge neralized Tits conjecture for Artin groups\nby Kasia Jankiewicz (Chica go) as part of Geometry and topology online\n\n\nAbstract\n\n Th e Tits conjecture\, proved by Crisp and\n Paris\, states that the s ubgroup of an Artin group generated by\n powers of the standard gen erators is the "obvious"\n right-angled Artin group (RAAG). We aim to generalize this: the\n subgroup generated by a collection of na turally distinguished\n elements\, specifically powers of the Garsi de elements\, is a\n RAAG. I will discuss our partial results\, fo r certain families\n of Artin groups.\n

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

\n LOCATION:https://researchseminars.org/talk/GaTO/24/ END:VEVENT BEGIN:VEVENT SUMMARY:Andras Stipsicz (Renyi) DTSTART;VALUE=DATE-TIME:20200811T150000Z DTEND;VALUE=DATE-TIME:20200811T153000Z DTSTAMP;VALUE=DATE-TIME:20240222T215347Z UID:GaTO/25 DESCRIPTION:Title: Co nnected Floer homology of covering involutions\nby Andras Stipsicz (Re nyi) as part of Geometry and topology online\n\n\nAbstract\n\n W e use the covering involution of double\n branched covers of knots to define a knot invariant inspired\n by connected Heegaard Floer h omology. Using this\, we obtain\n novel concordance results.\n

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

\n LOCATION:https://researchseminars.org/talk/GaTO/25/ END:VEVENT BEGIN:VEVENT SUMMARY:Jing Tao (Oklahoma) DTSTART;VALUE=DATE-TIME:20200818T153000Z DTEND;VALUE=DATE-TIME:20200818T160000Z DTSTAMP;VALUE=DATE-TIME:20240222T215347Z UID:GaTO/26 DESCRIPTION:Title: Th e Nielsen-Thurston classification\, revisited\nby Jing Tao (Oklahoma) as part of Geometry and topology online\n\n\nAbstract\n\n I will explain a new proof of the\n Nielsen-Thurston classification of ma pping classes\, using the\n Thurston metric on Teichmuller space.\n

\n\n This is joint work with Camille Horbez.\n

\n LOCATION:https://researchseminars.org/talk/GaTO/26/ END:VEVENT BEGIN:VEVENT SUMMARY:Dawid Kielak (Oxford) DTSTART;VALUE=DATE-TIME:20200825T153000Z DTEND;VALUE=DATE-TIME:20200825T160000Z DTSTAMP;VALUE=DATE-TIME:20240222T215347Z UID:GaTO/27 DESCRIPTION:Title: Po incaré duality groups\nby Dawid Kielak (Oxford) as part of Geometry a nd topology online\n\n\nAbstract\n\n It is a classical fact that a Poincaré\;\n duality group\, in dimension two\, is a surfa ce group. In this\n talk I will discuss a relatively short new pro of of this.\n

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

\n LOCATION:https://researchseminars.org/talk/GaTO/27/ END:VEVENT BEGIN:VEVENT SUMMARY:Mehdi Yazdi (Oxford) DTSTART;VALUE=DATE-TIME:20201008T140000Z DTEND;VALUE=DATE-TIME:20201008T143000Z DTSTAMP;VALUE=DATE-TIME:20240222T215347Z UID:GaTO/28 DESCRIPTION:Title: Th e complexity of determining knot genus in a fixed three-manifold\nby M ehdi Yazdi (Oxford) as part of Geometry and topology online\n\n\nAbstract\ n\n The *genus* of a knot in a three-manifold is\n d
efined to be the minimum genus of a compact\, orientable\n surface
bounding that knot\, if such a surface exists. In\n particular a k
not can be untangled if and only if it has genus\n zero. We consid
er the computational complexity of determining\n knot genus. Such
problems have been studied by several\n mathematicians\; among them
are the works of\n Hass-Lagarias-Pippenger\, Agol-Hass-Thurston\,
Agol and\n Lackenby. For a fixed three-manifold the knot genus pro
blem 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 NP. In
joint work with Lackenby\, we\n prove that this can be generalised
to any fixed\, compact\,\n orientable three-manifold\, answering a
question of\n Agol-Hass-Thurston from 2002.\n

\n In his seminal 19 76 paper Bill Thurston\n observed that a closed leaf \\(S\\) of a f oliation has Euler\n characteristic equal\, up to sign\, to the Eul er class of the\n foliation evaluated on \\([S]\\)\, the homology c lass represented\n by \\(S\\). We give a converse for taut foliati ons: if the\n underlying manifold is hyperbolic and if the Euler cl ass of a\n taut foliation \\(F\\) evaluated on \\([S]\\) equals\, u p to sign\,\n the Euler characteristic of \\(S\\)\, then there exis ts another\n taut foliation \\(F'\\) such that \\(S\\) is homologou s 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 most one\, and conjectured that\, conversely\, any integral\n cohomology clas s with norm equal to one is the Euler class of\n a taut foliation. Work of Yazdi\, together with our main\n result\, give a negative answer to Thurston's conjecture.\n

\n\n This is j oint work with Mehdi Yazdi.\n

\n LOCATION:https://researchseminars.org/talk/GaTO/29/ END:VEVENT BEGIN:VEVENT SUMMARY:Esmee te Winkel (Warwick) DTSTART;VALUE=DATE-TIME:20201015T140000Z DTEND;VALUE=DATE-TIME:20201015T143000Z DTSTAMP;VALUE=DATE-TIME:20240222T215347Z UID:GaTO/30 DESCRIPTION:Title: Kn ots in the curve graph\nby Esmee te Winkel (Warwick) as part of Geomet ry and topology online\n\n\nAbstract\n\n By a famous theorem of Thurston the space\n \\(\\PML\\) of projective (measured) laminatio ns on a five-times\n punctured sphere is a three-sphere. An element ary example of a\n projective lamination is a simple closed geodesi c with the\n counting measure. This defines a map from the set of c urves to\n \\(\\PML\\)\, which extends to an injective map from the curve\n graph to \\(\\PML\\). The topology of the image of the cur ve\n graph in \\(\\PML\\) and its complement were previously studie d\n by Gabai.\n

\nIn this talk we will introduce certain finite subgraphs of\n the curve graph of the five-times pu nctured sphere and\n determine whether their image in \\(\\PML\\) i s knotted.\n

\n LOCATION:https://researchseminars.org/talk/GaTO/30/ END:VEVENT BEGIN:VEVENT SUMMARY:Rudradip Biswas (Manchester) DTSTART;VALUE=DATE-TIME:20201015T143000Z DTEND;VALUE=DATE-TIME:20201015T150000Z DTSTAMP;VALUE=DATE-TIME:20240222T215347Z UID:GaTO/31 DESCRIPTION:Title: Ge neration of unbounded derived categories of modules over groups in Krophol ler's hierarchy\nby Rudradip Biswas (Manchester) as part of Geometry a nd topology online\n\n\nAbstract\n\n For a group $G$ in Kropholler's h ierarchy and\n a commutative ring $R$\, we will go through some recently\ n discovered generation properties of $D(\\rm{Mod}(RG))$ in terms of\n l ocalising and colocalising subcategories. If time permits\, we\n will try to include a few comments on how these generation\n properties shed some light on some deep properties of\n $D(\\rm{Mod}(RG))$ as a triangulated category.\n

\n LOCATION:https://researchseminars.org/talk/GaTO/31/ END:VEVENT BEGIN:VEVENT SUMMARY:Yair Minsky (Yale) DTSTART;VALUE=DATE-TIME:20201022T140000Z DTEND;VALUE=DATE-TIME:20201022T143000Z DTSTAMP;VALUE=DATE-TIME:20240222T215347Z UID:GaTO/32 DESCRIPTION:Title: Ve ering triangulations and their polynomials\nby Yair Minsky (Yale) as p art of Geometry and topology online\n\n\nAbstract\n\n This is an introduction to Sam's talk.\n McMullen introduced certain polynomi als associated to fibered\n three-manifolds\, which package togethe r the dynamical data\n associated to all the fibrations in a given fibered face of\n Thurston's norm ball. Agol's veering triangulati ons provide a\n good setting in which similar invariants can be def ined. I\n will review this background\, explain the definition of the\n "veering Polynomial" and the "taut Polynomial"\, the\n relationship between them\, and how they recover McMullen's\n poly nomial in the fibered face.\n

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

\n LOCATION:https://researchseminars.org/talk/GaTO/32/ END:VEVENT BEGIN:VEVENT SUMMARY:Sam Taylor (Temple) DTSTART;VALUE=DATE-TIME:20201022T143000Z DTEND;VALUE=DATE-TIME:20201022T150000Z DTSTAMP;VALUE=DATE-TIME:20240222T215347Z UID:GaTO/33 DESCRIPTION:Title: Th e veering polynomial\, the flow graph\, and the Thurston norm\nby Sam Taylor (Temple) as part of Geometry and topology online\n\n\nAbstract\n
\n This is a continuation of Yair’s talk on the\n veering
polynomial. Here we show how the veering polynomial\n can be const
ructed as the Perron polynomial of a certain\n combinatorially defi
ned directed graph\, which we call\n the *flow graph*. This pe
rspective will allows us to\n relate our polynomial to a face \\(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 triang
ulation. We’ll also discuss\n criteria for when the face \\(F\\)
is fibered.\n

\n This is joint work with Micha el Landry and Yair Minsky.\n

\n LOCATION:https://researchseminars.org/talk/GaTO/33/ END:VEVENT BEGIN:VEVENT SUMMARY:Mark Bell (Independent) DTSTART;VALUE=DATE-TIME:20201029T150000Z DTEND;VALUE=DATE-TIME:20201029T153000Z DTSTAMP;VALUE=DATE-TIME:20240222T215347Z UID:GaTO/34 DESCRIPTION:Title: Co mputations in big mapping class groups\nby Mark Bell (Independent) as part of Geometry and topology online\n\n\nAbstract\n\n We will t ake a brief look at some of the\n computations that are possible in big mapping class groups. In\n particular we will discuss the impl ementation\n of Bigger\n - a Python package which allows you to study and manipulat e\n laminations and mapping classes on infinite-type surfaces.\n

\n LOCATION:https://researchseminars.org/talk/GaTO/34/ END:VEVENT BEGIN:VEVENT SUMMARY:Chenxi Wu (Rutgers) DTSTART;VALUE=DATE-TIME:20201105T150000Z DTEND;VALUE=DATE-TIME:20201105T153000Z DTSTAMP;VALUE=DATE-TIME:20240222T215347Z UID:GaTO/35 DESCRIPTION:Title: Bo unds on asymptotic translation length on free factor and free splitting co mplexes\nby Chenxi Wu (Rutgers) as part of Geometry and topology onlin e\n\n\nAbstract\n\n The free factor and free splitting complexes \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 setting of curve complexes.\n

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

\n LOCATION:https://researchseminars.org/talk/GaTO/35/ END:VEVENT BEGIN:VEVENT SUMMARY:Ivan Dynnikov (Steklov) DTSTART;VALUE=DATE-TIME:20201105T153000Z DTEND;VALUE=DATE-TIME:20201105T160000Z DTSTAMP;VALUE=DATE-TIME:20240222T215347Z UID:GaTO/36 DESCRIPTION:Title: An algorithm to compare Legendrian knots\nby Ivan Dynnikov (Steklov) as part of Geometry and topology online\n\n\nAbstract\n\n We have w orked out a general method to decide\n whether two given Legendrian knots are Legendrian\n equivalent. The method yields a formal algo rithmic solution to\n the problem (with very high algorithmic compl exity) and\, in\n certain circumstances\, allows one to distinguish Legendrian\n knots practically\, including some cases in which the \n computation of any known algebraic invariant except for the\n two classical ones (Thurston--Bennequin's and Maslov's) is\n i nfeasible. We use this\, in particular\, to provide an example\n of an annulus embedded in the three-sphere and tangent to the\n conta ct structure along the whole boundary\, such that the two\n connect ed components of the boundary are not equivalent as\n Legendrian kn ots.\n

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

\n LOCATION:https://researchseminars.org/talk/GaTO/36/ END:VEVENT BEGIN:VEVENT SUMMARY:Tara Brendle (Glasgow) DTSTART;VALUE=DATE-TIME:20201203T150000Z DTEND;VALUE=DATE-TIME:20201203T153000Z DTSTAMP;VALUE=DATE-TIME:20240222T215347Z UID:GaTO/37 DESCRIPTION:Title: Th e mapping class group of connect sums of \\(S^2 \\times S^1\\)\nby Tar a Brendle (Glasgow) as part of Geometry and topology online\n\n\nAbstract\ n\n Let \\(M_n\\) denote the connect sum of \\(n\\)\n cop ies of \\(S^2 \\times S^1\\). Laudenbach showed that the\n mapping class group \\(\\Mod(M_n)\\) is an extension of the group\n \\(\\O ut(F_n)\\) by \\((\\ZZ/2)^n\\)\, where the latter group is the\n "s phere twist" subgroup of \\(\\Mod(M_n)\\).\n

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

\n\n This is joint work with N. Broaddus and A. Putman.\n

\n LOCATION:https://researchseminars.org/talk/GaTO/37/ END:VEVENT BEGIN:VEVENT SUMMARY:Ying Hu (UNO) DTSTART;VALUE=DATE-TIME:20201203T153000Z DTEND;VALUE=DATE-TIME:20201203T160000Z DTSTAMP;VALUE=DATE-TIME:20240222T215347Z UID:GaTO/38 DESCRIPTION:Title: Eu ler class of taut foliations on Q-homology spheres and Dehn fillings\n by Ying Hu (UNO) as part of Geometry and topology online\n\n\nAbstract\n\n The Euler class of an oriented plane field\n over a thre e-manifold is a second cohomology class\, which\n determines the pl ane field up to isomorphism. In this talk\,\n we will discuss the Euler class of taut foliations on a\n \\(\\QQ\\)-homology sphere. W e view \\(\\QQ\\)-homology spheres as\n Dehn fillings on knot manif olds and give necessary and\n sufficient conditions for the Euler c lass of taut foliations\n on such manifolds to vanish. We will also apply these results\n to study the orderability of three-manifold groups.\n

\n LOCATION:https://researchseminars.org/talk/GaTO/38/ END:VEVENT BEGIN:VEVENT SUMMARY:Ruth Charney (Brandeis) DTSTART;VALUE=DATE-TIME:20201210T150000Z DTEND;VALUE=DATE-TIME:20201210T153000Z DTSTAMP;VALUE=DATE-TIME:20240222T215347Z UID:GaTO/39 DESCRIPTION:Title: Ou ter space for right-angled Artin groups\nby Ruth Charney (Brandeis) as part of Geometry and topology online\n\n\nAbstract\n\n Right-an gled 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)\\). Automorphism group s of RAAGs have been well-studied\n over the past decade from a pur ely algebraic viewpoint. To\n allow for a more geometric approach\ , one needs to construct a\n contractible space with a proper actio n of the group.\n

\n\n In this pair of talks we w ill construct such a space\, namely an\n analogue of Culler-Vogtman n’s Outer Space for arbitrary RAAGs.\n

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

\n LOCATION:https://researchseminars.org/talk/GaTO/39/ END:VEVENT BEGIN:VEVENT SUMMARY:Corey Bregman (Brandeis) DTSTART;VALUE=DATE-TIME:20201210T153000Z DTEND;VALUE=DATE-TIME:20201210T160000Z DTSTAMP;VALUE=DATE-TIME:20240222T215347Z UID:GaTO/40 DESCRIPTION:Title: Ou ter space for right-angled Artin groups\nby Corey Bregman (Brandeis) a s part of Geometry and topology online\n\n\nAbstract\n\n Right-a ngled Artin groups (RAAGs) span a\n range of groups from free group s to free abelian groups.\n Thus\, their (outer) automorphism groups range from \\(\\Out(F_n)\\) to\n \\(\\GL(n\,\\ZZ)\\). Automorphism grou ps of RAAGs have been well-studied\n over the past decade from a pu rely algebraic viewpoint. To\n allow for a more geometric approach \, one needs to construct a\n contractible space with a proper acti on of the group.\n

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

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

\n LOCATION:https://researchseminars.org/talk/GaTO/40/ END:VEVENT BEGIN:VEVENT SUMMARY:Robert Kropholler (University of Warwick) DTSTART;VALUE=DATE-TIME:20211007T140500Z DTEND;VALUE=DATE-TIME:20211007T145500Z DTSTAMP;VALUE=DATE-TIME:20240222T215347Z UID:GaTO/41 DESCRIPTION:Title: Co arse embeddings and homological filling functions\nby Robert Kropholle r (University of Warwick) as part of Geometry and topology online\n\n\nAbs tract\n\n The homological filling function of a\n finitel y presented group \\(G\\) measures the difficulty of\n filling loop s with surfaces in a classifying space. The\n behaviour of this fun ction when passing to finitely presented\n subgroups is rather wild . If one adds assumptions on the\n dimension of \\(G\\)\, then one can bound the homological filling\n function of the subgroup by th at of \\(G\\). I will discuss how\n to generalise these results fr om subgroups to coarse\n embeddings and also to higher dimensional filling functions.\n

\n\n This is joint work with Mark Pengitore.\n

\n\nWe start five minutes after the hour.\n LOCATION:https://researchseminars.org/talk/GaTO/41/ END:VEVENT BEGIN:VEVENT SUMMARY:Ian Leary (Southampton) DTSTART;VALUE=DATE-TIME:20211014T140500Z DTEND;VALUE=DATE-TIME:20211014T145500Z DTSTAMP;VALUE=DATE-TIME:20240222T215347Z UID:GaTO/42 DESCRIPTION:Title: Gr aphical small cancellation and groups of type \\(\\mathrm{FP}\\)\nby I an Leary (Southampton) as part of Geometry and topology online\n\n\nAbstra ct\n\n Graphical small cancellation was introduced\n by G
romov to embed an expanding family inside the Cayley graph\n of a f
initely generated group. We use this technique to\n construct a la
rge family of groups of type \\(\\mathrm{FP}\\)\, most of\n which a
re not finitely presented. This is the first time\n non-finitely p
resented groups of type \\(\\mathrm{FP}\\) have been\n constructed
*without* using Bestvina-Brady Morse theory.\n I will give an
idea of how graphical small cancellation works\n and how we use it.
\n

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

\n LOCATION:https://researchseminars.org/talk/GaTO/42/ END:VEVENT BEGIN:VEVENT SUMMARY:Giles Gardam (Münster) DTSTART;VALUE=DATE-TIME:20211125T150500Z DTEND;VALUE=DATE-TIME:20211125T155500Z DTSTAMP;VALUE=DATE-TIME:20240222T215347Z UID:GaTO/43 DESCRIPTION:Title: Th e Kaplansky conjectures\nby Giles Gardam (Münster) as part of Geometr y and topology online\n\n\nAbstract\nThree conjectures on group rings of t orsion-free groups are commonly attributed to Kaplansky\, namely the unit\ , zero divisor and idempotent conjectures. For example\, the zero divisor conjecture predicts that if $K$ is a field and $G$ is a torsion-free group \, then the group ring $K[G]$ has no zero divisors. I will discuss these c onjectures and their relationship to other conjectures and properties of g roups. I will then explain how modern solvers for Boolean satisfiability c an be applied to them\, producing the first counterexample to the unit con jecture.\n LOCATION:https://researchseminars.org/talk/GaTO/43/ END:VEVENT BEGIN:VEVENT SUMMARY:Sam Kim (KIAS) DTSTART;VALUE=DATE-TIME:20211118T150500Z DTEND;VALUE=DATE-TIME:20211118T155500Z DTSTAMP;VALUE=DATE-TIME:20240222T215347Z UID:GaTO/44 DESCRIPTION:Title: Op timal regularity of mapping class group actions on the circle\nby Sam Kim (KIAS) as part of Geometry and topology online\n\n\nAbstract\nWe prove that for each finite index subgroup $H$ of the mapping class group of a c losed hyperbolic surface\, and for each real number $r>1$ there does not e xist a faithful $C^r$-action (in Hölder's sense) of $H$ on a circle. For this\, we partially determine the optimal regularity of faithful actions b y right-angled Artin groups on a circle. (Joint with Thomas Koberda and Cr istobal Rivas)\n LOCATION:https://researchseminars.org/talk/GaTO/44/ END:VEVENT BEGIN:VEVENT SUMMARY:Camille Horbez (Orsay) DTSTART;VALUE=DATE-TIME:20211021T140500Z DTEND;VALUE=DATE-TIME:20211021T145500Z DTSTAMP;VALUE=DATE-TIME:20240222T215347Z UID:GaTO/45 DESCRIPTION:Title: Or bit equivalence rigidity of irreducible actions of right-angled Artin grou ps\nby Camille Horbez (Orsay) as part of Geometry and topology online\ n\n\nAbstract\nA central goal in measured group theory is to classify f ree\, ergodic\, measure-preserving actions of countable groups on probabil ity spaces up to orbit equivalence: that is\, up to the existence of a mea sure space isomorphism sending orbits to orbits. Rigidity occurs when orbi t equivalence of two actions forces them to be conjugate through a group i somorphism. In this talk\, I will present orbit equivalence rigidity pheno mena for actions of (centerless\, one-ended) right-angled Artin groups\, u pon imposing that every standard generator acts ergodically on the space.\ n\n

This is joint work with Jingyin Huang.\n LOCATION:https://researchseminars.org/talk/GaTO/45/ END:VEVENT BEGIN:VEVENT SUMMARY:Rachel Skipper (OSU) DTSTART;VALUE=DATE-TIME:20211104T150500Z DTEND;VALUE=DATE-TIME:20211104T155500Z DTSTAMP;VALUE=DATE-TIME:20240222T215347Z UID:GaTO/46 DESCRIPTION:Title: Br aiding groups of homeomorphisms of Cantor sets\nby Rachel Skipper (OSU ) as part of Geometry and topology online\n\n\nAbstract\n

\n We w ill discuss some ways in which one can\n braid some classical subgr oups of the homeomorphism group of\n the Cantor set. This includes 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 with Xiaol ei Wu and\n Matthew Zaremsky.\n

\n LOCATION:https://researchseminars.org/talk/GaTO/46/ END:VEVENT BEGIN:VEVENT SUMMARY:Emily Stark (Wesleyan University) DTSTART;VALUE=DATE-TIME:20211202T150500Z DTEND;VALUE=DATE-TIME:20211202T155500Z DTSTAMP;VALUE=DATE-TIME:20240222T215347Z UID:GaTO/47 DESCRIPTION:Title: Gr aphically discrete groups and rigidity\nby Emily Stark (Wesleyan Unive rsity) as part of Geometry and topology online\n\n\nAbstract\nRigidity the orems prove that a group's geometry determines its algebra\, typically up to virtual isomorphism. Motivated by rigidity problems\, we study graphica lly discrete groups\, which impose a discreteness criterion on the automor phism group of any graph the group acts on geometrically. Classic examples of graphically discrete groups include virtually nilpotent groups and fun damental groups of closed hyperbolic manifolds. We will present new exampl es\, proving this property is not a quasi-isometry invariant. We will disc uss action rigidity for free products of residually finite graphically dis crete groups. This is joint work with Alex Margolis\, Sam Shepherd\, and D aniel Woodhouse.\n LOCATION:https://researchseminars.org/talk/GaTO/47/ END:VEVENT BEGIN:VEVENT SUMMARY:Arnaud de Mesmay (Laboratoire d'Informatique Gaspard-Monge) DTSTART;VALUE=DATE-TIME:20211209T150500Z DTEND;VALUE=DATE-TIME:20211209T155500Z DTSTAMP;VALUE=DATE-TIME:20240222T215347Z UID:GaTO/48 DESCRIPTION:Title: Sh ort canonical decompositions of non-orientable surfaces\nby Arnaud de Mesmay (Laboratoire d'Informatique Gaspard-Monge) as part of Geometry and topology online\n\n\nAbstract\nSuppose that $S$ is a surface and $G \\subs et S$ is an embedded graph. In many applications\, during algorithm desig n\, and even when representing the embedding\, there is a basic task: to c ut $S$ into a single disk. When $S$ is orientable\, it has long been know n how to compute a canonical cutting system that is also "short": each arc of the system runs along each edge of $G$ at most a constant number of ti mes. \n\nIn this talk we survey what is known about such cutting problems. We then explain how to obtain a short canonical system when $S$ is non-o rientable. \n\nThis is joint work with Niloufar Fuladi and Alfredo Hubard. \n LOCATION:https://researchseminars.org/talk/GaTO/48/ END:VEVENT BEGIN:VEVENT SUMMARY:Benjamin Ward (BGSU) DTSTART;VALUE=DATE-TIME:20211111T150500Z DTEND;VALUE=DATE-TIME:20211111T155500Z DTSTAMP;VALUE=DATE-TIME:20240222T215347Z UID:GaTO/49 DESCRIPTION:Title: Ma ssey Products for Graph Homology.\nby Benjamin Ward (BGSU) as part of Geometry and topology online\n\n\nAbstract\nThis talk is about graph compl exes and their homology. A graph complex can be thought of as a generaliz ation of a dg associative algebra\, but with more sophisticated compositio n operations allowing for particles to collide along any graph\, not just along a line. Is every graph complex quasi-isomorphic to its homology? C ontinuing 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 rectif y this situation. We will then discuss what these higher operations can t ell us in the particular cases of Lie and commutative graph homology.\n LOCATION:https://researchseminars.org/talk/GaTO/49/ END:VEVENT BEGIN:VEVENT SUMMARY:Kim Ruane (Tufts University) DTSTART;VALUE=DATE-TIME:20220113T150500Z DTEND;VALUE=DATE-TIME:20220113T155500Z DTSTAMP;VALUE=DATE-TIME:20240222T215347Z UID:GaTO/50 DESCRIPTION:Title: To rsion-free groups acting geometrically on the product of two trees\nby Kim Ruane (Tufts University) as part of Geometry and topology online\n\n\ nAbstract\nGiven a group acting geometrically on product of two trees\, we know that one visual boundary is the topological join of two Cantor sets. We prove that these groups are "boundary rigid": any CAT(0) space on whi ch the group acts has visual boundary homeomorphic to such a join. \n \nSi nce there is no hyperbolicity going on here\, one cannot expect that the n atural equivariant quasi-isometry between an arbitrary CAT(0) space and th e product of two trees to extend to any sort of map on boundaries\, thus t he proof requires new techniques. The proof uses work of Ricks on recogni sing product splittings from the Tits boundary as well as work of Guralnik and Swenson on general dynamics of a CAT(0) group on both the visual and Tits boundary. \n\nThis is (recent) joint work with Jankiewicz\, Karrer\, and Sathaye.\n LOCATION:https://researchseminars.org/talk/GaTO/50/ END:VEVENT BEGIN:VEVENT SUMMARY:Vladimir Vankov (Southampton) DTSTART;VALUE=DATE-TIME:20220120T150500Z DTEND;VALUE=DATE-TIME:20220120T155500Z DTSTAMP;VALUE=DATE-TIME:20240222T215347Z UID:GaTO/51 DESCRIPTION:Title: Un countably many quasi-isometric torsion-free groups\nby Vladimir Vankov (Southampton) as part of Geometry and topology online\n\n\nAbstract\nThe study of quasi-isometries between finitely generated groups has traditiona lly been one of the more common questions of geometric group theory\, whic h includes understanding the possible nature of quasi-isometry classes in general. There are several precedents for sets of uncountable cardinality to exhibit surprising behaviour differing from countable sets\, especially when it comes to subgroups. We explore generalising constructions of unco untably many torsion groups falling into the same quasi-isometry class via commensurability\, to the torsion-free setting. This is done by consideri ng bounded cohomology and appealing to algebraic concepts classically foun d in finite group theory\, in order to produce examples of a continuum of quasi-isometric and torsion-free\, but pairwise non-isomorphic finitely ge nerated groups.\n LOCATION:https://researchseminars.org/talk/GaTO/51/ END:VEVENT BEGIN:VEVENT SUMMARY:Davide Spriano (Oxford) DTSTART;VALUE=DATE-TIME:20220127T150500Z DTEND;VALUE=DATE-TIME:20220127T155500Z DTSTAMP;VALUE=DATE-TIME:20240222T215347Z UID:GaTO/52 DESCRIPTION:Title: Hy perbolic spaces for $\\mathrm{CAT}(0)$ groups\nby Davide Spriano (Oxfo rd) as part of Geometry and topology online\n\n\nAbstract\n$\\mathrm{CAT}( 0)$ spaces\, as avatars of non-positive curvature\, are both old and widel y studied. Making up an important subclass are the $\\mathrm{CAT}(0)$ cub e complexes: spaces obtained by gluing Euclidean $n$-cubes along faces and satisfying an additional combinatorial conditions. Given such a space $X $\, there are several techniques to construct associated spaces that "dete ct the hyperbolic behaviour" of $X$. All of these techniques rely on the combinatorial structure coming from the cubes. \n\nIn this talk we will pr esent a new approach to construct hyperbolic spaces on which $\\mathrm{CAT }(0)$ groups act. We thus obtain characterisations of rank-one elements a nd recover rank-rigidity results. \n\nThis is joint work with H. Petyt and A. Zalloum.\n LOCATION:https://researchseminars.org/talk/GaTO/52/ END:VEVENT BEGIN:VEVENT SUMMARY:Annette Karrer (Technion) DTSTART;VALUE=DATE-TIME:20220217T150500Z DTEND;VALUE=DATE-TIME:20220217T155500Z DTSTAMP;VALUE=DATE-TIME:20240222T215347Z UID:GaTO/53 DESCRIPTION:Title: Co nnected components of Morse boundaries of graphs of groups\nby Annette Karrer (Technion) as part of Geometry and topology online\n\n\nAbstract\nEach finitely generated group has a\n topological space associa ted to it called the Morse boundary.\n This boundary generalizes th e Gromov boundary of\n Gromov-hyperbolic groups and captures how si milar the group is\n to a Gromov-hyperbolic group.\n

\n\n In this talk\, we will study connected components of Morse \n boundaries of a graph of groups \\(G\\). We will focus on the\n case where the edge groups are undistorted and do not\n con tribute to the Morse boundary of \\(G\\). We will describe\n the c onnected components of the Morse boundary of \\(G\\) using\n the as sociated Bass-Serre tree. We will see that every\n connected compo nent of the Morse boundary with at least two\n points originates fr om the Morse boundary of a vertex group.\n

\n\n T his is joint work with Elia Fioravanti.\n

\n LOCATION:https://researchseminars.org/talk/GaTO/53/ END:VEVENT BEGIN:VEVENT SUMMARY:Luke Jeffreys (Bristol) DTSTART;VALUE=DATE-TIME:20220224T150500Z DTEND;VALUE=DATE-TIME:20220224T155500Z DTSTAMP;VALUE=DATE-TIME:20240222T215347Z UID:GaTO/54 DESCRIPTION:Title: No n-planarity of SL(2\,Z)-orbits of origamis in genus two\nby Luke Jeffr eys (Bristol) as part of Geometry and topology online\n\n\nAbstract\n* <
i>Origamis* (also known as square-tiled\n surfaces) arise natura
lly in a variety of settings in\n low-dimensional topology. They c
an be thought of as surfaces\n obtained by gluing the sides of a co
llection of unit squares.\n As such\, they generalise the torus whi
ch can be obtained by\n gluing the sides of a single square. An or
igami is said to be\n *primitive* if it is not a cover of a lo
wer genus\n origami.\n

\n In this talk\, I will describe how one can define an action of\n the matrix group \\(\\mathrm{SL}(2\,\\mathbb{Z})\\) on primitive origamis. In\n ge nus two (with one singularity)\, the orbits of this action\n were c lassified by Hubert-Lelièvre and McMullen. By\n considering a gen erating set of size two for \\(\\mathrm{SL}(2\,\\mathbb{Z})\\)\,\n we can turn these orbits into an infinite family of\n four-valent g raphs. For a specific generating set\, I will\n explain how all bu t two of these graphs are non-planar. I\n will also discuss why th is gives indirect evidence for\n McMullen's conjecture that these g raphs form a family of\n expanders.\n

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

\n LOCATION:https://researchseminars.org/talk/GaTO/54/ END:VEVENT BEGIN:VEVENT SUMMARY:Armando Martino (Southampton) DTSTART;VALUE=DATE-TIME:20220303T150500Z DTEND;VALUE=DATE-TIME:20220303T155500Z DTSTAMP;VALUE=DATE-TIME:20240222T215347Z UID:GaTO/55 DESCRIPTION:Title: On automorphisms of free groups and nearly canonical trees\nby Armando M artino (Southampton) as part of Geometry and topology online\n\n\nAbstract \n\n I will discuss some open problems for\n automorphism s of free groups\; whether centralisers are\n finitely generated\, whether their mapping tori have\n well-behaved automorphism group\, and whether the conjugacy\n problem is solvable. I will explain so me new partial results\,\n using techniques involving canonical tre es.\n

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

\n LOCATION:https://researchseminars.org/talk/GaTO/55/ END:VEVENT BEGIN:VEVENT SUMMARY:Macarena Arenas (Cambridge) DTSTART;VALUE=DATE-TIME:20220210T150500Z DTEND;VALUE=DATE-TIME:20220210T155500Z DTSTAMP;VALUE=DATE-TIME:20240222T215347Z UID:GaTO/56 DESCRIPTION:Title: A cubical Rips construction\nby Macarena Arenas (Cambridge) as part of G eometry and topology online\n\n\nAbstract\nThe Rips exact sequence is a us eful tool for\n producing examples of groups satisfying combination s of\n properties that are not obviously compatible. It works by\n taking as an input an arbitrary finitely presented group\n \\(Q\\)\, and producing as an output a hyperbolic group \\(G\\)\n t hat maps onto \\(Q\\) with finitely generated kernel. The\n "outpu t group" \\(G\\) is crafted by adding generators and\n relations to a presentation of \\(Q\\)\, in such a way that these\n relations c reate enough "noise" in the presentation to ensure\n hyperbolicity. One can then lift pathological properties of\n \\(Q\\) to (some s ubgroup of) \\(G\\). Among other things\, Rips\n used his construc tion to produce the first examples of\n incoherent hyperbolic group s\, and of hyperbolic groups with\n unsolvable generalised word pro blem.\n\n In this talk\, I will explain Rips' result\, mention some of its\n variations\, and survey some tools and concepts related t o\n these constructions\, including small cancellation theory\,\n cubulated groups\, and asphericity. Time permitting\, I will\n describe a variation of the Rips construction that produces\n cu bulated hyperbolic groups of any desired cohomological\n dimension. \n LOCATION:https://researchseminars.org/talk/GaTO/56/ END:VEVENT BEGIN:VEVENT SUMMARY:Sam Hughes (Oxford) DTSTART;VALUE=DATE-TIME:20220310T150500Z DTEND;VALUE=DATE-TIME:20220310T155500Z DTSTAMP;VALUE=DATE-TIME:20240222T215347Z UID:GaTO/57 DESCRIPTION:Title: Ir reducible lattices fibring over the circle\nby Sam Hughes (Oxford) as part of Geometry and topology online\n\n\nAbstract\nLet \\(n \\geq 2\\) an d let \\(\\Lambda\\) be a\n lattice in a product of simple non-comp act Lie groups with\n finite centre. An application of the Marguli s normal subgroup\n theorem implies that if \\(H^1(\\Lambda)\\) is non-zer o\, then\n \\(\\Gamma\\) is reducible. In the more general\n \\(\\mathrm{CAT}(0)\\) setting there are many irreducible\n latti ces with non-vanishing first cohomology. In this case we\n can dep loy the BNSR invariants and investigate how far these\n cohomology classes are from a fibration of finite type CW\n complexes. In thi s talk we will combine the groups of Leary\n and Minasyan with the technology of Bestvina and Brady to\n construct the first examples of irreducible lattices which\n fibre over the circle.\n LOCATION:https://researchseminars.org/talk/GaTO/57/ END:VEVENT BEGIN:VEVENT SUMMARY:Rylee Lyman (Rutgers) DTSTART;VALUE=DATE-TIME:20220317T150500Z DTEND;VALUE=DATE-TIME:20220317T155500Z DTSTAMP;VALUE=DATE-TIME:20240222T215347Z UID:GaTO/58 DESCRIPTION:Title: Fo lding-like techniques for CAT(0) cube complexes\nby Rylee Lyman (Rutge rs) as part of Geometry and topology online\n\n\nAbstract\nIn a seminal pa per\, Stallings introduced folding of morphisms of graphs. One consequence of folding is the representation of finitely generated subgroups of a fin ite-rank free group as immersions of finite graphs. Stallings's methods al low one to construct this representation algorithmically\, giving effectiv e\, algorithmic answers and proofs to classical questions about subgroups of free groups. Recently Dani–Levcovitz used Stallings-like methods to s tudy subgroups of right-angled Coxeter groups\, which act geometrically on \\(\\mathrm{CAT}(0)\\) cube complexes. We extend their techniques to fund amental groups of non-positively curved cube complexes.\n LOCATION:https://researchseminars.org/talk/GaTO/58/ END:VEVENT BEGIN:VEVENT SUMMARY:Marco Linton (Warwick) DTSTART;VALUE=DATE-TIME:20220428T140500Z DTEND;VALUE=DATE-TIME:20220428T145500Z DTSTAMP;VALUE=DATE-TIME:20240222T215347Z UID:GaTO/59 DESCRIPTION:Title: Hy perbolicity of certain one-relator groups\nby Marco Linton (Warwick) a s part of Geometry and topology online\n\n\nAbstract\nThe primitivity rank of an element \\(w\\) of a free group \\(F\\) is defined as the minimal r ank of a subgroup containing w as an imprimitive element. Recent work of Louder and Wilton has shown that there is a strong connection between this quantity and the subgroup structure of the one-relator group \\(F/\\langl e \\langle w \\rangle \\rangle\\). In particular\, they show that one-rel ator groups whose defining relation has primitivity rank at least three ca nnot contain Baumslag—Solitar subgroups\, leading them to conjecture tha t such groups are hyperbolic. In this talk\, I will confirm and strengthe n this conjecture\, providing some applications.\n LOCATION:https://researchseminars.org/talk/GaTO/59/ END:VEVENT BEGIN:VEVENT SUMMARY:Susan Hermiller (Nebraska) DTSTART;VALUE=DATE-TIME:20220519T140500Z DTEND;VALUE=DATE-TIME:20220519T145500Z DTSTAMP;VALUE=DATE-TIME:20240222T215347Z UID:GaTO/60 DESCRIPTION:Title: Fo rmal conjugacy growth for graph products\nby Susan Hermiller (Nebraska ) as part of Geometry and topology online\n\n\nAbstract\n\n The conjugacy growth series of a finitely\n generated group measures th e growth of conjugacy classes\, in\n analogy with the standard grow th series that measures the\n growth of elements of the group. In contrast\, though\,\n conjugacy growth series are rarely rational\, and even for free\n groups with standard generating sets\, the ser ies are\n transcendental and their formulas are rather complicated. In\n this talk I will discuss several results on conjugacy growth \n and languages in graph products\, including a recursive formula\ n for computing the conjugacy growth series of a graph product\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 gr owth series based on a natural language of conjugacy\n representati ves.\n

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

\n LOCATION:https://researchseminars.org/talk/GaTO/60/ END:VEVENT BEGIN:VEVENT SUMMARY:Marco Barberis (Warwick) DTSTART;VALUE=DATE-TIME:20220505T140500Z DTEND;VALUE=DATE-TIME:20220505T145500Z DTSTAMP;VALUE=DATE-TIME:20240222T215347Z UID:GaTO/61 DESCRIPTION:Title: Cu rve graphs: exhaustions by rigid sets and the co-Hopfian property\nby Marco Barberis (Warwick) as part of Geometry and topology online\n\n\nAbst ract\nSince Ivanov's celebrated first result\, many rigidity theorems for various variants of the curve graph of surfaces have been proven. Among th ese\, there is a cluster of results regarding the existence of exhaustion via finite subgraphs which are rigid (that is such that every embedding is induced by an automorphism of the whole graph). From this property\, inte resting per se\, the co-Hopfian property of the graphs immediately follows . In this talk I will present the classical results in the fields\, as wel l as some new cases\, which point toward conjecturing that most curve grap hs on finite-type surfaces should admit exhaustions by rigid sets\, in lin e with Ivanov's Metaconjecture.\n LOCATION:https://researchseminars.org/talk/GaTO/61/ END:VEVENT BEGIN:VEVENT SUMMARY:Jean Pierre Mutanguha (IAS) DTSTART;VALUE=DATE-TIME:20220512T140500Z DTEND;VALUE=DATE-TIME:20220512T145500Z DTSTAMP;VALUE=DATE-TIME:20240222T215347Z UID:GaTO/62 DESCRIPTION:Title: Ca nonical forms for free group automorphisms\nby Jean Pierre Mutanguha ( IAS) as part of Geometry and topology online\n\n\nAbstract\nThe Nielsen- –Thurston theory of surface homeomorphisms can be thought of as a surfac e analogue to the Jordan canonical form. I will discuss my progress in de veloping a similar decomposition for free group automorphisms. (Un)fortun ately\, free group automorphisms can have arbitrarily complicated behaviou r. This forms a significant barrier to translating specific arguments tha t worked for surfaces into the free group setting\; nevertheless\, the ove rall ideas/strategies do translate!\n LOCATION:https://researchseminars.org/talk/GaTO/62/ END:VEVENT BEGIN:VEVENT SUMMARY:Jone Lopez de Gamiz (Warwick) DTSTART;VALUE=DATE-TIME:20220526T140500Z DTEND;VALUE=DATE-TIME:20220526T145500Z DTSTAMP;VALUE=DATE-TIME:20240222T215347Z 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 online\n\n\ nAbstract\n\n In general\, subgroups of RAAGs are known to\n have wild structure and bad algorithmic behaviour. However\,\n in this talk we will see that finitely generated normal\n subgroup s are much more tame. More precisely\, we will show\n that a finit ely generated normal subgroup of a RAAG is\n virtually co-abelian.\ n

\n\n We will then discuss some algorithmic cons equences\, such as\n the decidability of the conjugacy and the memb ership problems.\n We will finally discuss residual properties\, su ch as conjugacy\n separability\, for finitely generated normal subg roups of\n RAAGs.\n

\n LOCATION:https://researchseminars.org/talk/GaTO/63/ END:VEVENT BEGIN:VEVENT SUMMARY:Naomi Andrew (Southampton) DTSTART;VALUE=DATE-TIME:20220616T140500Z DTEND;VALUE=DATE-TIME:20220616T145500Z DTSTAMP;VALUE=DATE-TIME:20240222T215347Z UID:GaTO/64 DESCRIPTION:Title: Ba umslag-Solitar groups\, automorphisms and generalisations\nby Naomi An drew (Southampton) as part of Geometry and topology online\n\n\nAbstract\n Baumslag-Solitar groups are a well known family in geometric group theory\ , providing useful (counter)examples - such as groups that are Hopfian but not residually finite. Recently\, Ian Leary and Ashot Minasyan introduced a generalisation\, finding even more counterexamples - notably groups tha t are \\(\\CAT(0)\\) but not biautomatic. Outer automorphism groups of Bau mslag-Solitar groups range from finite to not even finitely generated\, wi th proofs (and re-proofs) across several authors and years.\n\nIn this tal k I will summarise (some) of what is known about the automorphisms of Baum slag-Solitar groups\, and the more modern\, Bass-Serre theoretic technique s that can be used to prove them. I'll then discuss my work with Sam Hughe s to extend these results to the automorphisms of Leary-Minasyan groups.\n LOCATION:https://researchseminars.org/talk/GaTO/64/ END:VEVENT BEGIN:VEVENT SUMMARY:Lorenzo Ruffoni (Tufts) DTSTART;VALUE=DATE-TIME:20220623T140500Z DTEND;VALUE=DATE-TIME:20220623T145500Z DTSTAMP;VALUE=DATE-TIME:20240222T215347Z UID:GaTO/65 DESCRIPTION:Title: St rict 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 p olyhedron into a space of\n non-positive curvature. Charney and Da vis developed a refined\n "strict hyperbolisation" procedure that o utputs a space of\n strictly negative curvature. Their procedure h as been used to\n construct new examples of manifolds and groups wi th negative\n curvature\, and other prescribed features. We constru ct actions\n of the resulting groups on CAT(0) cube complexes. As an\n application\, we obtain that they are virtually special\, henc e\n linear over the integers and residually finite.\n

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

\n LOCATION:https://researchseminars.org/talk/GaTO/65/ END:VEVENT BEGIN:VEVENT SUMMARY:Gareth Wilkes (Cambridge) DTSTART;VALUE=DATE-TIME:20220630T140500Z DTEND;VALUE=DATE-TIME:20220630T145500Z DTSTAMP;VALUE=DATE-TIME:20240222T215347Z UID:GaTO/66 DESCRIPTION:Title: Re sidual properties of graphs of \\(p\\)-groups\nby Gareth Wilkes (Cambr idge) as part of Geometry and topology online\n\nLecture held in Room B3.0 3 in the Zeeman Building\, University of Warwick.\n\nAbstract\n\n When groups may be built up as graphs of\n 'simpler' groups\, it is often of interest to study how good\n residual finiteness proper ties of the simpler groups can imply\n residual properties of the w hole. The essential case of this\n theory is the study of residual properties of finite groups.\n In this talk I will discuss the que stion of when a graph of\n finite \\(p\\)-groups is residually \\(p \\)-finite\, for \\(p\\) a\n prime. I will describe the previous t heorems in this area for\n one-edge and finite graphs of groups\, a nd their method of\n proof. I will then state a generalisation of these theorems to\n potentially infinite graphs of groups\, togethe r with an\n alternative and perhaps more natural method of proof. Finally\n I will briefly describe a usage of these results in the s tudy\n of accessibility—namely the existence of a finitely genera ted\n inaccessible group which is residually \\(p\\)-finite.\n

\n LOCATION:https://researchseminars.org/talk/GaTO/66/ END:VEVENT BEGIN:VEVENT SUMMARY:Grace Garden (University of Sydney) DTSTART;VALUE=DATE-TIME:20221006T130500Z DTEND;VALUE=DATE-TIME:20221006T140000Z DTSTAMP;VALUE=DATE-TIME:20240222T215347Z UID:GaTO/67 DESCRIPTION:Title: Ea rthquakes on the once-punctured torus\nby Grace Garden (University of Sydney) as part of Geometry and topology online\n\n\nAbstract\nWe study ea rthquake deformations on Teichmüller space associated with simple closed curves of the once-punctured torus. We describe two methods to get an expl icit form of the earthquake deformation for any simple closed curve. The f irst method is rooted in hyperbolic geometry\, the second representation t heory. The two methods align\, providing both a geometric and an algebraic interpretation of the earthquake deformations. Pictures are given for ear thquakes across multiple coordinate systems for Teichmüller space. Two fa milies of curves are used as examples. Examining the limiting behaviour of each gives insight into earthquakes about measured geodesic laminations\, of which simple closed curves are a special case.\n LOCATION:https://researchseminars.org/talk/GaTO/67/ END:VEVENT BEGIN:VEVENT SUMMARY:Claudio Llosa Isenrich (KIT) DTSTART;VALUE=DATE-TIME:20221013T130500Z DTEND;VALUE=DATE-TIME:20221013T140000Z DTSTAMP;VALUE=DATE-TIME:20240222T215347Z UID:GaTO/68 DESCRIPTION:Title: Fi niteness properties\, subgroups of hyperbolic groups\, and complex hyperbo lic lattices\nby Claudio Llosa Isenrich (KIT) as part of Geometry and topology online\n\nLecture held in Room B3.02 in the Zeeman Building\, Uni versity of Warwick.\n\nAbstract\nHyperbolic groups form an important class of finitely generated groups that has attracted much attention in geometr ic 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 type \\(F_ 2\\). Hyperbolic groups are of type \\(F_n\\) for all \\(n\\). It is natu ral to ask if subgroups of hyperbolic groups inherit these strong finitene ss properties. We use methods from complex geometry to show that every un iform arithmetic lattice with positive first Betti number in \\(\\mathrm{P U}(n\, 1)\\) admits a finite index subgroup\, which maps onto the integers with kernel of type \\(F_{n−1}\\) but not \\(F_n\\). This answers an ol d question of Brady and produces many finitely presented non-hyperbolic su bgroups of hyperbolic groups. This is joint work with Pierre Py.\n LOCATION:https://researchseminars.org/talk/GaTO/68/ END:VEVENT BEGIN:VEVENT SUMMARY:Henry Bradford (Cambridge) DTSTART;VALUE=DATE-TIME:20221020T130500Z DTEND;VALUE=DATE-TIME:20221020T140000Z DTSTAMP;VALUE=DATE-TIME:20240222T215347Z UID:GaTO/69 DESCRIPTION:Title: Lo cal permutation stability\nby Henry Bradford (Cambridge) 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\nA group \\(\\Gamma\\) is sofic if elements of \\(\\Gamma\\) can be distinguished by almost-actions on fi nite sets. It is a major unsolved problem to determine whether all groups are sofic. One approach to this problem which has gained much recent atten tion is that of “permutation stability”\, that is\, showing that almos t-actions of a group are controlled by its actions. We introduce a “loca l” generalization of permutation stability\, under which actions are rep laced by partial actions. We exhibit an uncountable family of groups which are locally permutation stable but not permutation stable\, coming from t opological dynamics. The proof is based on a criterion for local stability of amenable groups\, in terms of invariant random subgroups.\n LOCATION:https://researchseminars.org/talk/GaTO/69/ END:VEVENT BEGIN:VEVENT SUMMARY:Becca Winarski (College of the Holy Cross) DTSTART;VALUE=DATE-TIME:20221103T140500Z DTEND;VALUE=DATE-TIME:20221103T150000Z DTSTAMP;VALUE=DATE-TIME:20240222T215347Z UID:GaTO/70 DESCRIPTION:Title: Po lynomials\, branched covers\, and trees\nby Becca Winarski (College of the Holy Cross) 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 Thurston proved that a post-critically finite branched cover of the plane is either equivalent to a polynomial (that is: conjugate via a mapping cla ss) or it has a topological obstruction. We use topological techniques – adapting tools used to study mapping class groups – to produce an algor ithm that determines when a branched cover is equivalent to a polynomial. 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://researchseminars.org/talk/GaTO/70/ END:VEVENT BEGIN:VEVENT SUMMARY:Bradley Zykoski (Michigan) DTSTART;VALUE=DATE-TIME:20221117T140500Z DTEND;VALUE=DATE-TIME:20221117T150000Z DTSTAMP;VALUE=DATE-TIME:20240222T215347Z UID:GaTO/71 DESCRIPTION:Title: A polytopal decomposition of strata of translation surfaces\nby Bradley Zykoski (Michigan) as part of Geometry and topology online\n\nLecture held in Room B3.02 in the Zeeman Building\, University of Warwick.\n\nAbstract \nA closed surface can be endowed with a certain locally Euclidean metric structure called a translation surface. Moduli spaces that parametrize su ch structures are called strata. There is a GL(2\,R)-action on strata\, a nd orbit closures of this action are rare gems\, the classification of whi ch has been given a huge boost in the past decade by landmark results such as the "Magic Wand" theorem of Eskin-Mirzakhani-Mohammadi and the Cylinde r Deformation theorem of Wright. Investigation of the topology of strata is still in its nascency\, although recent work of Calderon-Salter and Cos tantini-Möller-Zachhuber indicate that this field is rapidly blossoming. \n\nIn this talk\, I will discuss a way of decomposing strata into finite ly many higher-dimensional polytopes. I will discuss how I have used this decomposition to study the topology of strata\, and my ongoing work using this decomposition to study the orbit closures of the GL(2\,R)-action.\n LOCATION:https://researchseminars.org/talk/GaTO/71/ END:VEVENT BEGIN:VEVENT SUMMARY:Koji Fujiwara (Kyoto) DTSTART;VALUE=DATE-TIME:20221201T140500Z DTEND;VALUE=DATE-TIME:20221201T150000Z DTSTAMP;VALUE=DATE-TIME:20240222T215347Z UID:GaTO/73 DESCRIPTION:Title: Gr owth rates in a hyperbolic group\nby Koji Fujiwara (Kyoto) as part of Geometry and topology online\n\nLecture held in Room B3.02 in the Zeeman B uilding\, University of Warwick.\n\nAbstract\nI discuss the set of rates o f growth of a finitely generated group with respect to all its finite gene rating sets. In a joint work with Sela\, for a hyperbolic group\, we showe d that the set is well-ordered\, and that each number can be the rate of g rowth of at most finitely many generating sets up to automorphism of the g roup. If there is time\, I may also discuss generalisation to acylindrical ly hyperbolic groups.\n LOCATION:https://researchseminars.org/talk/GaTO/73/ END:VEVENT BEGIN:VEVENT SUMMARY:Daniel Berlyne (Bristol) DTSTART;VALUE=DATE-TIME:20221027T130500Z DTEND;VALUE=DATE-TIME:20221027T140000Z DTSTAMP;VALUE=DATE-TIME:20240222T215347Z UID:GaTO/74 DESCRIPTION:Title: Br aid groups of graphs\nby Daniel Berlyne (Bristol) as part of Geometry and topology online\n\nLecture held in Room B3.02 in the Zeeman Building\, University of Warwick.\n\nAbstract\nThe braid group of a space \\(X\\) is the fundamental group of its configuration space\, which tracks the motio n of some number of particles as they travel through \\(X\\). When \\(X\\) is a graph\, the configuration space turns out to be a special cube compl ex\, in the sense of Haglund and Wise. I show how these cube complexes are constructed and use graph of groups decompositions to provide methods for computing braid groups of various graphs\, as well as criteria for a grap h braid group to split as a free product. This has various applications\, such as characterising various forms of hyperbolicity in graph braid group s and determining when a graph braid group is isomorphic to a right-angled Artin group.\n LOCATION:https://researchseminars.org/talk/GaTO/74/ END:VEVENT BEGIN:VEVENT SUMMARY:Ric Wade (Oxford) DTSTART;VALUE=DATE-TIME:20221208T140500Z DTEND;VALUE=DATE-TIME:20221208T150000Z DTSTAMP;VALUE=DATE-TIME:20240222T215347Z UID:GaTO/75 DESCRIPTION:Title: Au t-invariant quasimorphisms on groups\nby Ric Wade (Oxford) as part of Geometry and topology online\n\nLecture held in Room B3.02 in the Zeeman B uilding\, University of Warwick.\n\nAbstract\n\nFor a large class of gr oups\, we exhibit an infinite-dimensional space of homogeneous quasi-morph isms that are invariant under the action of the automorphism group. This c lass includes non-elementary hyperbolic groups\, infinitely-ended finitely generated groups\, some relatively hyperbolic groups\, and a class of gra ph products of groups that includes all right-angled Artin and Coxeter gro ups that are not virtually abelian.\n

\n\nThis is joint work with Fr ancesco Fournier-Facio.\n

\n LOCATION:https://researchseminars.org/talk/GaTO/75/ END:VEVENT BEGIN:VEVENT SUMMARY:Davide Spriano (Oxford) DTSTART;VALUE=DATE-TIME:20230126T140500Z DTEND;VALUE=DATE-TIME:20230126T150000Z DTSTAMP;VALUE=DATE-TIME:20240222T215347Z UID:GaTO/76 DESCRIPTION:Title: Co mbinatorial criteria for hyperbolicity\nby Davide Spriano (Oxford) 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 of the m ost fascinating properties of hyperbolic groups is that they admit equival ent definitions coming from different areas of mathematics. In this talk\, we will survey some interesting definitions\, and discuss a new one that\ , perhaps surprisingly\, was previously unknown\, namely that fact that hy perbolicity can be detected by the language of quasi-geodesics in the Cayl ey graph. As an application\, we will discuss some progress towards a conj ecture of Shapiro concerning groups with uniquely geodesic Cayley graphs.\ n LOCATION:https://researchseminars.org/talk/GaTO/76/ END:VEVENT BEGIN:VEVENT SUMMARY:Saul Schleimer (Warwick) DTSTART;VALUE=DATE-TIME:20230223T140500Z DTEND;VALUE=DATE-TIME:20230223T150000Z DTSTAMP;VALUE=DATE-TIME:20240222T215347Z UID:GaTO/77 DESCRIPTION:Title: Fr om loom spaces to veering triangulations\nby Saul Schleimer (Warwick) as part of Geometry and topology online\n\nLecture held in Room B3.02 in t he Zeeman Building\, University of Warwick.\n\nAbstract\nA ``loom space'' is a copy of $\\mathbb{R}^2$ equipped with a pair of transverse foliations satisfying certain axioms. These arise as the link spaces associated to veering triangulations and also as the flow spaces of (drilled) pseudo-Ano sov flows without perfect fits. Following work of Guéritaud\, we prove a converse: namely\, every loom space gives rise\, canonically\, to a local ly veering triangulation. Furthermore\, the realisation of this triangulat ion (minus the vertices) is homeomorphic to $\\mathbb{R}^3$. I will sketc h the proof\, giving many pictures.\n\nThis is joint work with Henry Seger man.\n LOCATION:https://researchseminars.org/talk/GaTO/77/ END:VEVENT BEGIN:VEVENT SUMMARY:Malavika Mukundan (Michigan) DTSTART;VALUE=DATE-TIME:20230302T140500Z DTEND;VALUE=DATE-TIME:20230302T150000Z DTSTAMP;VALUE=DATE-TIME:20240222T215347Z UID:GaTO/78 DESCRIPTION:Title: Dy namical approximation of entire functions\nby Malavika Mukundan (Michi gan) as part of Geometry and topology online\n\nLecture held in Room B3.02 in the Zeeman Building\, University of Warwick.\n\nAbstract\nPostsingular ly finite holomorphic functions are entire functions for which the forward orbit of the set of critical and asymptotic values is finite. Motivated b y previous work on approximating entire functions dynamically by polynomia ls\, we ask the following question: given a postsingularly finite entire f unction $f$\, can $f$ be realised as the locally uniform limit of a sequen ce of postcritically finite polynomials?\n\nIn joint work with Nikolai Pro chorov and Bernhard Reinke\, we show how we may answer this question in th e affirmative.\n LOCATION:https://researchseminars.org/talk/GaTO/78/ END:VEVENT BEGIN:VEVENT SUMMARY:Elia Fioravanti (MPIM Bonn) DTSTART;VALUE=DATE-TIME:20230309T140500Z DTEND;VALUE=DATE-TIME:20230309T150000Z DTSTAMP;VALUE=DATE-TIME:20240222T215347Z UID:GaTO/79 DESCRIPTION:Title: Co arse cubical rigidity\nby Elia Fioravanti (MPIM Bonn) as part of Geome try and topology online\n\nLecture held in Room D1.07 in the Zeeman Buildi ng\, University of Warwick.\n\nAbstract\nWhen a group $G$ admits nice acti ons on $\\mathrm{CAT}(0)$ cube complexes\, understanding the space of all such actions can provide useful information on the outer automorphism grou p $\\mathrm{Out}(G)$. As a classical example\, the Culler-Vogtmann outer s pace is (roughly) the space of all geometric actions of the free group $F_ n$ on a $1$-dimensional cube complex (a tree). In general\, however\, spac es of cubulations tend to be awkwardly vast\, even for otherwise rigid gro ups 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 coarse ly look the same\, in a strong sense: they all induce the same coarse medi an structure on the group. \n\nThis is joint work with Ivan Levcovitz and Michah Sageev.\n LOCATION:https://researchseminars.org/talk/GaTO/79/ END:VEVENT BEGIN:VEVENT SUMMARY:Nansen Petrosyan (Southampton) DTSTART;VALUE=DATE-TIME:20230309T150500Z DTEND;VALUE=DATE-TIME:20230309T160000Z DTSTAMP;VALUE=DATE-TIME:20240222T215347Z UID:GaTO/80 DESCRIPTION:Title: Hy perbolicity and $L$-infinity cohomology\nby Nansen Petrosyan (Southamp ton) as part of Geometry and topology online\n\nLecture held in Room D1.07 in the Zeeman Building\, University of Warwick.\n\nAbstract\n$L$-infinity cohomology is a quasi-isometry invariant of finitely generated groups. It was introduced by Gersten as a tool to find lower bounds for the Dehn fun ction of some finitely presented groups. I will discuss a generalisation o f a theorem of Gersten on surjectivity of the restriction map in $L$-infin ity cohomology of groups. This leads to applications on subgroups of hyper bolic groups\, quasi-isometric distinction of finitely generated groups an d $L$-infinity cohomology calculations for some well-known classes of grou ps such as RAAGs\, Bestvina-Brady groups and $\\mathrm{Out}(F_n)$. Along t he way\, we obtain hyperbolicity criteria for groups of type $FP_2(Q)$ and for those satisfying a rational homological linear isoperimetric inequali ty.\n\nI will first define L-infinity cohomology and discuss some of its p roperties. I will then sketch some of the main ideas behind the proofs. Th is is joint work with Vladimir Vankov.\n LOCATION:https://researchseminars.org/talk/GaTO/80/ END:VEVENT BEGIN:VEVENT SUMMARY:Alan Logan (Heriot-Watt University) DTSTART;VALUE=DATE-TIME:20230427T130500Z DTEND;VALUE=DATE-TIME:20230427T140000Z DTSTAMP;VALUE=DATE-TIME:20240222T215347Z UID:GaTO/81 DESCRIPTION:Title: Dy namics and algorithms for endomorphisms of free groups\nby Alan Logan (Heriot-Watt University) 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\nRecent work of Mutanguha has given a topological insight into endo morphisms of free groups and their dynamics. The purpose of this talk is t o sketch this theory\, and to explain how it can be applied to resolve the conjugacy problem for ascending HNN-extensions of free groups.\n LOCATION:https://researchseminars.org/talk/GaTO/81/ END:VEVENT BEGIN:VEVENT SUMMARY:Michael Borinsky (ETH-ITS) DTSTART;VALUE=DATE-TIME:20230525T130500Z DTEND;VALUE=DATE-TIME:20230525T140000Z DTSTAMP;VALUE=DATE-TIME:20240222T215347Z UID:GaTO/82 DESCRIPTION:Title: Th e commutative graph complex and the amount of top-weight cohomology in the moduli space of curves\nby Michael Borinsky (ETH-ITS) as part of Geom etry and topology online\n\nLecture held in Room B3.02 in the Zeeman Build ing\, University of Warwick.\n\nAbstract\nI will present new results on th e asymptotic growth rate of\nthe Euler characteristic of Kontsevich's comm utative graph complex. By\nwork of Chan\, Galatius and Payne\, these resul ts imply the same\nasymptotic growth rate for the top-weight Euler charact eristic of M_g\,\nthe moduli space of curves\, and establish the existence of a large amount\nof unexplained top-weight cohomology in this space.\n LOCATION:https://researchseminars.org/talk/GaTO/82/ END:VEVENT BEGIN:VEVENT SUMMARY:Raphael Zentner (Durham University) DTSTART;VALUE=DATE-TIME:20231005T130500Z DTEND;VALUE=DATE-TIME:20231005T140000Z DTSTAMP;VALUE=DATE-TIME:20240222T215347Z UID:GaTO/83 DESCRIPTION:Title: Ra tional homology ribbon cobordism is a partial order\nby Raphael Zentne r (Durham University) as part of Geometry and topology online\n\nLecture h eld in Room B3.02 in the Zeeman Building\, University of Warwick.\n\nAbstr act\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 t han three decades. His proof is beautiful and surprisingly simple. There i s an analogous notion of ribbon cobordism for closed 3-manifolds. We use A gol's method to show that this is also a partial order within the class of irreducible 3-manifolds. \n\nThis is joint work with Stefan Friedl and Fi lip Misev.\n LOCATION:https://researchseminars.org/talk/GaTO/83/ END:VEVENT BEGIN:VEVENT SUMMARY:Mark Pengitore (University of Virginia) DTSTART;VALUE=DATE-TIME:20231012T130500Z DTEND;VALUE=DATE-TIME:20231012T140000Z DTSTAMP;VALUE=DATE-TIME:20240222T215347Z UID:GaTO/84 DESCRIPTION:Title: Re sidual finiteness growth functions of surface groups with respect to chara cteristic quotients\nby Mark Pengitore (University of Virginia) 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\nResidual finiteness gro wth functions of groups have attracted much interest in recent years. \nTh ese are functions that roughly measure the complexity of the finite quotie nts needed to separate particular group elements from the identity in term s of word length. In this talk\, we study the growth rate of these functio ns adapted to finite characteristic quotients. One potential application o f this result is towards linearity of the mapping class group.\n LOCATION:https://researchseminars.org/talk/GaTO/84/ END:VEVENT BEGIN:VEVENT SUMMARY:Clement Legrand (University of Bordeaux) DTSTART;VALUE=DATE-TIME:20231019T130500Z DTEND;VALUE=DATE-TIME:20231019T140000Z DTSTAMP;VALUE=DATE-TIME:20240222T215347Z UID:GaTO/85 DESCRIPTION:Title: Re configuration of square-tiled surfaces\nby Clement Legrand (University of Bordeaux) as part of Geometry and topology online\n\nLecture held in R oom B3.02 in the Zeeman Building\, University of Warwick.\n\nAbstract\nA s quare-tiled surface is a special case of a quadrangulation of a surface\, that can be encoded as a pair of permutations in \\(S_n \\times S_n\\) tha t generates a transitive subgroup of \\(S_n\\). Square-tiled surfaces can be classified into different strata according to the total angles around their conical singularities. Among other parameters\, strata fix the genu s and the size of the quadrangulation. Generating a random square-tiled s urface in a fixed stratum is a widely open question. We propose a Markov c hain approach using "shearing moves": \na natural reconfiguration operatio n 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 quadrangulation.\n LOCATION:https://researchseminars.org/talk/GaTO/85/ END:VEVENT BEGIN:VEVENT SUMMARY:Adele Jackson (University of Oxford) DTSTART;VALUE=DATE-TIME:20231102T140500Z DTEND;VALUE=DATE-TIME:20231102T150000Z DTSTAMP;VALUE=DATE-TIME:20240222T215347Z UID:GaTO/86 DESCRIPTION:Title: Al gorithms for Seifert fibered spaces\nby Adele Jackson (University of O xford) as part of Geometry and topology online\n\nLecture held in Room B3. 02 in the Zeeman Building\, University of Warwick.\n\nAbstract\nGiven two mathematical objects\, the most basic question is whether they are the sam e. We will discuss this question for triangulations of three-manifolds. In practice there is fast software to answer this question and theoretical ly the problem is known to be decidable. However\, our understanding is l imited and known theoretical algorithms could have extremely long run-time s. I will describe a programme to show that the three-manifold homeomorph ism problem is in the complexity class NP\, and discuss the important sub- case of Seifert fibered spaces.\n LOCATION:https://researchseminars.org/talk/GaTO/86/ END:VEVENT BEGIN:VEVENT SUMMARY:Monika Kudlinska (University of Oxford) DTSTART;VALUE=DATE-TIME:20231109T140500Z DTEND;VALUE=DATE-TIME:20231109T150000Z DTSTAMP;VALUE=DATE-TIME:20240222T215347Z UID:GaTO/87 DESCRIPTION:Title: Su bgroup 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 of Warwi ck.\n\nAbstract\nA group \\(G\\) is said to be subgroup separable if every finitely generated subgroup of \\(G\\) is the intersection of finite inde x subgroups. It is known that a fundamental group of a compact\, irreducib le\, closed 3-manifold \\(M\\) is subgroup separable if and only if \\(M\\ ) is geometric. We will discuss the problem of subgroup separability in fr ee-by-cyclic groups by drawing a parallel between free-by-cyclic and 3-man ifold groups. Time permitting\, we will discuss how to extend these ideas to find non-separable subgroups in random groups.\n LOCATION:https://researchseminars.org/talk/GaTO/87/ END:VEVENT BEGIN:VEVENT SUMMARY:Rob Kropholler (University of Warwick) DTSTART;VALUE=DATE-TIME:20231116T140500Z DTEND;VALUE=DATE-TIME:20231116T150000Z DTSTAMP;VALUE=DATE-TIME:20240222T215347Z UID:GaTO/88 DESCRIPTION:Title: Th e landscape of Dehn functions\nby Rob Kropholler (University of Warwic k) as part of Geometry and topology online\n\nLecture held in Room B3.02 i n the Zeeman Building\, University of Warwick.\n\nAbstract\nThe Dehn funct ion of a finitely presented group \\(G\\) can be used to measure the compl exity of its word problem. Specifically the Dehn function measures the min imal area required to fill loops in the Cayley graph of \\(G\\). There 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 various Deh n functions can be used to prove interesting results. I will be particular ly interested in the case of subgroups of hyperbolic groups.\n LOCATION:https://researchseminars.org/talk/GaTO/88/ END:VEVENT BEGIN:VEVENT SUMMARY:Jeffrey Giansiracusa (Durham University) DTSTART;VALUE=DATE-TIME:20231123T140500Z DTEND;VALUE=DATE-TIME:20231123T150000Z DTSTAMP;VALUE=DATE-TIME:20240222T215347Z UID:GaTO/89 DESCRIPTION:Title: To pology of the matroid Grassmannian\nby Jeffrey Giansiracusa (Durham Un iversity) as part of Geometry and topology online\n\nLecture held in Room B3.02 in the Zeeman Building\, University of Warwick.\n\nAbstract\nThe mat roid Grassmannian is the moduli space of oriented matroids\; this is an im portant combinatorial analogue of the ordinary oriented real Grassmannian. Thirty years ago MacPherson showed us that understanding the homotopy ty pe of this space can have significant implications in manifold topology\, such as providing combinatorial formulae for the Pontrjagin classes. In s ome easy cases\, the matroid Grassmannian is homotopy equivalent to the or iented real Grassmannian\, but in most cases we have no idea whether or no t they are equivalent. This question is known as MacPherson's conjecture. I'll show that one of the important homotopical structures of the orient ed Grassmannians has an analogue on the matroid Grassmannian: the direct s um monoidal product (which gives rise to topological K-theory) is E-infini ty.\n LOCATION:https://researchseminars.org/talk/GaTO/89/ END:VEVENT BEGIN:VEVENT SUMMARY:Cameron Gates Rudd (MPI Bonn) DTSTART;VALUE=DATE-TIME:20231130T140500Z DTEND;VALUE=DATE-TIME:20231130T150000Z DTSTAMP;VALUE=DATE-TIME:20240222T215347Z UID:GaTO/90 DESCRIPTION:Title: St retch laminations and hyperbolic Dehn surgery\nby Cameron Gates Rudd ( MPI Bonn) as part of Geometry and topology online\n\nLecture held in Room B3.02 in the Zeeman Building\, University of Warwick.\n\nAbstract\nGiven a hyperbolic manifold \\(M\\) and a homotopy class of maps from \\(M\\) to the circle\, there is an associated geodesic "stretch" lamination encoding at which points in \\(M\\) the Lipschitz constant of any map in the homot opy class must be large. Recently\, Farre-Landesberg-Minsky related these laminations to horocycle orbit closures in infinite cyclic covers and when \\(M\\) is a surface\, they analyzed the possible structure of these lami nations. I will discuss the case where \\(M\\) is a 3-manifold and give th e first 3-dimensional examples where these laminations can be identified. The argument uses the Thurston norm and tools from quantitative Dehn surge ry.\n LOCATION:https://researchseminars.org/talk/GaTO/90/ END:VEVENT BEGIN:VEVENT SUMMARY:Francesco Fournier-Facio (University of Cambridge) DTSTART;VALUE=DATE-TIME:20240125T140500Z DTEND;VALUE=DATE-TIME:20240125T150000Z DTSTAMP;VALUE=DATE-TIME:20240222T215347Z UID:GaTO/92 DESCRIPTION:Title: In finite simple characteristic quotients\nby Francesco Fournier-Facio (U niversity of Cambridge) as part of Geometry and topology online\n\nLecture held in Room B3.02 in the Zeeman Building\, University of Warwick.\n\nAbs tract\nThe rank of a finitely generated group is the minimal size of a gen erating set. Several questions that received a lot of attention around 50 years ago ask about the rank of finitely generated groups\, and how this r elates to the rank of their direct powers. In this context\, Wiegold asked about the existence of infinite simple characteristic quotients of free g roups. I will review this framework\, present several open questions - old and new - and present a solution to Wiegold's problem. \n\nThis is joint with Remi Coulon.\n LOCATION:https://researchseminars.org/talk/GaTO/92/ END:VEVENT BEGIN:VEVENT SUMMARY:Sam Hughes (University of Oxford) DTSTART;VALUE=DATE-TIME:20231207T140500Z DTEND;VALUE=DATE-TIME:20231207T150000Z DTSTAMP;VALUE=DATE-TIME:20240222T215347Z UID:GaTO/93 DESCRIPTION:Title: Ce ntralisers and classifying spaces for $\\mathrm{Out}(F_N)$\nby Sam Hug hes (University of Oxford) 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\nIn this talk I will outline reduction theory for mapping classes and explain various attempts to construct similar machinery for elements of $\\mathrm{Out}(F_N)$. I will then present a new reduction theory for s tudying centralisers of elements in $\\mathrm{IA}_3(N)$\, the finite index level three congruence subgroup of $\\mathrm{Out}(F_N)$. Using this I wi ll explain an application to the classifying space for virtually cyclic su bgroups\, a space notable for its appearance in the Farrell--Jones Conject ure. \n\nBased on joint work with Yassine Guerch and Luis Jorge Sanchez Sa ldana.\n LOCATION:https://researchseminars.org/talk/GaTO/93/ END:VEVENT BEGIN:VEVENT SUMMARY:Richard Wade (University of Oxford) DTSTART;VALUE=DATE-TIME:20240111T140500Z DTEND;VALUE=DATE-TIME:20240111T150000Z DTSTAMP;VALUE=DATE-TIME:20240222T215347Z UID:GaTO/94 DESCRIPTION:Title: Qu asi-flats in the Aut free factor complex\nby Richard Wade (University 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 wil l describe families of quasi-flats in the "$\\mathrm{Aut}(F_n)$ version" o f the free factor complex. This shows that\, unlike its more popular "Oute r" cousin\, the $\\mathrm{Aut}$ free factor complex is not hyperbolic. The flats are reasonably simple to describe and are shown to be q.i. embedded via the construction of a coarse Lipschitz retraction. This leaves many o pen problems about the coarse geometry of this space\, and I hope to talk about a few of them. \n\nThis is joint work with Mladen Bestvina and Marti n Bridson.\n LOCATION:https://researchseminars.org/talk/GaTO/94/ END:VEVENT BEGIN:VEVENT SUMMARY:Ian Leary (University of Southampton) DTSTART;VALUE=DATE-TIME:20240118T140500Z DTEND;VALUE=DATE-TIME:20240118T150000Z DTSTAMP;VALUE=DATE-TIME:20240222T215347Z UID:GaTO/95 DESCRIPTION:Title: Re sidual finiteness of generalized Bestvina-Brady groups\nby Ian Leary ( University of Southampton) 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\nI discovered/created generalized Bestvina-Brady groups to give a n uncountable family of groups with surprising homological properties. In this talk\, I will introduce the groups and address the following questio ns: when are they virtually torsion-free? when are they residually finite? This leads naturally to a third question: when do they virtually embed in right-angled Artin groups? There are nice conjectural answers to all thre e questions\, which we have proved in some cases.\n\nThis is joint work wi th Vladimir Vankov.\n LOCATION:https://researchseminars.org/talk/GaTO/95/ END:VEVENT BEGIN:VEVENT SUMMARY:Samuel Shepherd (Vanderbilt University) DTSTART;VALUE=DATE-TIME:20240201T140500Z DTEND;VALUE=DATE-TIME:20240201T150000Z DTSTAMP;VALUE=DATE-TIME:20240222T215347Z UID:GaTO/96 DESCRIPTION:Title: On e-ended halfspaces in group splittings\nby Samuel Shepherd (Vanderbilt University) as part of Geometry and topology online\n\nLecture held in Ro om B3.02 in the Zeeman Building\, University of Warwick.\n\nAbstract\nI wi ll introduce the notion of halfspaces in group splittings and discuss the problem of when these halfspaces are one-ended. I will also discuss connec tions to JSJ splittings of groups\, and to determining whether groups are simply connected at infinity. \n\nThis is joint work with Michael Mihalik. \n LOCATION:https://researchseminars.org/talk/GaTO/96/ END:VEVENT END:VCALENDAR