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BEGIN:VEVENT
SUMMARY:Kane Townsend (University of Technology Sydney)
DTSTART:20220901T230000Z
DTEND:20220901T233000Z
DTSTAMP:20260411T132833Z
UID:GroupCraft2/1
DESCRIPTION:Title: Hyperbolic groups with $k$-geodetic Cayley graph\nby Kane Townsend
(University of Technology Sydney) as part of World of GroupCraft II\n\n\n
Abstract\nA locally-finite simple connected graph is said to be \\emph{$k$
-geodetic} for some $k\\geq 1$\, if there is at most $k$ geodesic paths be
tween any two vertices. We investigate the properties of hyperbolic groups
that have $k$-geodetic Cayley graphs. We start by showing that a $k$-geod
etic graph cannot have a ``ladder-like structure" with unbounded length. A
dding the assumption that the $k$-geodetic graph is the Cayley graph of a
hyperbolic group we generalise a well-known result\, proven by Papasoglu\,
from $k=1$ to all $k\\geq 1$. We conjecture that groups with $k$-geodetic
Cayley graph are exactly the same class of groups as those with $1$-geode
tic Cayley graph.\n
LOCATION:https://researchseminars.org/talk/GroupCraft2/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Donggyun Seo (Korea Advanced Institute of Science & Technology)
DTSTART:20220901T233000Z
DTEND:20220902T000000Z
DTSTAMP:20260411T132833Z
UID:GroupCraft2/2
DESCRIPTION:Title: Outer automorphism groups of RAAGs and regular graph covers\nby Do
nggyun Seo (Korea Advanced Institute of Science & Technology) as part of W
orld of GroupCraft II\n\n\nAbstract\nRight-angled Artin groups (briefly\,
RAAGs) are finitely presented groups defined by finite simplicial graphs.
They form a huge collection that contains all finitely generated free grou
ps and free-abelian groups. Servatius and Laurence first looked into outer
automorphism groups of RAAGs\, denoted by Out(A(G))\, to study the rigidi
ty of RAAGs. This talk will focus on Out(A(G))’s rather than RAAGs. All
Out(A(G))’s share common properties: they are finitely presented\, resid
ually finite and of finite virtual cohomological dimension. In this talk\,
we are going to see how a finite normal cover of a simplicial graph induc
es a subgroup of Out(A(G)) and to introduce several properties of these su
bgroups using Birman—Hilden theory. \n\nThis is joint work with Sangrok
Oh and Philippe Tranchida.\n
LOCATION:https://researchseminars.org/talk/GroupCraft2/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:KyeongRo Kim (Korea Advanced Institute of Science & Technology)
DTSTART:20220902T000000Z
DTEND:20220902T003000Z
DTSTAMP:20260411T132833Z
UID:GroupCraft2/3
DESCRIPTION:Title: Invitation to laminar group theory\nby KyeongRo Kim (Korea Advance
d Institute of Science & Technology) as part of World of GroupCraft II\n\n
\nAbstract\nA laminar group is a subgroup of orientation preserving circle
homeomorphisms preserving circle laminations. Laminar group theory is mot
ivated by Thurston’s universal circle theorem. The theorem says that a t
autly foliated three manifold group acts on the (universal) circle preserv
ing a pair of circle laminations. Laminar group theory studies the convers
e of this theorem. In this talk\, I introduce some basic notions and recen
t progress.\n
LOCATION:https://researchseminars.org/talk/GroupCraft2/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Matt Conder (University of Auckland)
DTSTART:20220902T010000Z
DTEND:20220902T013000Z
DTSTAMP:20260411T132833Z
UID:GroupCraft2/4
DESCRIPTION:Title: Discrete two-generator subgroups of $\\mathop{PSL}_2$ over non-archime
dean local fields\nby Matt Conder (University of Auckland) as part of
World of GroupCraft II\n\n\nAbstract\nLet K be a non-archimedean local fie
ld with residue field of characteristic p. We give a complete classificati
on of all discrete two-generator subgroups G of PSL(2\,K)\, provided that
either K is the field of p-adic numbers or G contains no elements of order
p. This relies on a general structure theorem for two-generator groups ac
ting by isometries on a tree\, obtained by applying Klein-Maskit combinati
on theorems.\n\nThis is joint work with Jeroen Schillewaert.\n
LOCATION:https://researchseminars.org/talk/GroupCraft2/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Roman Gorazd (University of Newcastle)
DTSTART:20220902T013000Z
DTEND:20220902T020000Z
DTSTAMP:20260411T132833Z
UID:GroupCraft2/5
DESCRIPTION:Title: Unfolding Trees and their Higman-Thompson Groups\nby Roman Gorazd
(University of Newcastle) as part of World of GroupCraft II\n\n\nAbstract\
nIn the context of almost automrphisms\, unfolding trees were introduced b
y Waltraud Lederle a few years ago. I will present a slight generalization
of her definition and explore their structure and there almost automorphi
sm group. For the first point we will determine which graphs produce isomo
rphic and which produce almost isomorphic unfolding trees. This will be do
ne by introducing non-edge collapsing equivalence relation and drawing the
connection between the graph monoid and the almost structure of the unfol
ding tree. If we look at the almost automorphism group of these trees we c
an see since there is a natural ordering on these trees we can introduce a
n analogue of the Higman-Thompson group. We can then see that there is a s
trong connection between the connectivity of the graphs with the propertie
s of the action of the Higman-Thompson group on the boundary of the tree.
Now using the work of Nekrashevych we can determine some things about the
structure of the Higman-Thompson groups. We will also show some instances
where the Higman-Thompson groups are isomorphic. All of this is still a wo
rk in progress. There is especially much more I hope to find out about Hi
gman-Thompson groups of unfolding trees\, maybe ultimately to be able to
classify them.\n
LOCATION:https://researchseminars.org/talk/GroupCraft2/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:JV Pinto e Silva (University of Newcastle)
DTSTART:20220902T020000Z
DTEND:20220902T023000Z
DTSTAMP:20260411T132833Z
UID:GroupCraft2/6
DESCRIPTION:Title: Elementary groups with higher ranks\nby JV Pinto e Silva (Universi
ty of Newcastle) as part of World of GroupCraft II\n\n\nAbstract\nThe talk
will be focused on a class of second countable groups assembled from prof
inite and discrete by elementary operations. We focus on a rank associated
with these groups that measure their complexity. A collection of groups a
cting on trees where each vertex has $\\aleph_0$ fixing an end of the tree
is defined and used for the first construction of a group with elementary
rank $\\omega^\\omega+1$.\n
LOCATION:https://researchseminars.org/talk/GroupCraft2/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sushil Bhunia (BITS Pilani\, Hyderabad)
DTSTART:20220902T033000Z
DTEND:20220902T040000Z
DTSTAMP:20260411T132833Z
UID:GroupCraft2/7
DESCRIPTION:Title: Conjugacy and reversibility problems in groups\nby Sushil Bhunia (
BITS Pilani\, Hyderabad) as part of World of GroupCraft II\n\n\nAbstract\n
Let $G$ be a group. An element $g \\in G$ is said to be reversible (or rea
l)\nif it is conjugate to its inverse (i.e.\, $g^{−1} = x g x^{−1}$ fo
r some $x \\in G$). An element of $G$ is called strongly reversible if it
is a product of two order-two elements. In the first part of the talk we w
ill see some basic properties\, known results\, connections\nto different
branches of Mathematics\, and some open problems. The second part of the t
alk will constitute a recent work with Gangotryi Sorcar\, where we study s
elf-homeomorphisms of the plane\, and investigate when two elements are co
njugate using Haefliger-Reeb’s theory of foliations.\n
LOCATION:https://researchseminars.org/talk/GroupCraft2/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Apeksha Sanghi (IISER Bhopal)
DTSTART:20220902T040000Z
DTEND:20220902T043000Z
DTSTAMP:20260411T132833Z
UID:GroupCraft2/8
DESCRIPTION:Title: Infinite metacyclic subgroups of the mapping class group\nby Apeks
ha Sanghi (IISER Bhopal) as part of World of GroupCraft II\n\n\nAbstract\n
For $g \\ge 2$\, let $Mod(S_g)$ be the mapping class group of the closed o
rientable\nsurface $S_g$ of genus $g$. In this talk\, we discuss a complet
e characterization of\nthe infinite metacyclic subgroups of $Mod(S_g)$ up
to conjugacy. In particular\,\nwe discuss equivalent conditions under whic
h a pseudo-Anosov mapping class\ngenerates a metacyclic subgroup of $Mod(S
_g)$ with another mapping class. As\napplication to our main results\, we
describe some examples of infinite metacyclic\nsubgroups of $Mod(S_g)$. Fi
nally\, we derive bounds on the order of a periodic\ngenerator of an infin
ite metacyclic subgroup of $Mod(S_g)$.\n
LOCATION:https://researchseminars.org/talk/GroupCraft2/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Neeraj K Dhanwani (IISER Mohali)
DTSTART:20220902T043000Z
DTEND:20220902T050000Z
DTSTAMP:20260411T132833Z
UID:GroupCraft2/9
DESCRIPTION:Title: Quandles arising from surfaces\nby Neeraj K Dhanwani (IISER Mohali
) as part of World of GroupCraft II\n\n\nAbstract\nQuandles are algebraic
systems with a binary operation that encodes the three Reidemeister moves
of planar diagrams of links in the 3-space. In this talk\, we introduce qu
andles\, particularly the quandle arising from surfaces. To study surface
quandles\, we study the class of quandles which contain the surface quandl
es\, named Dehn quandle. We prove equivalent conditions for a quandle to
be a Dehn quandle and discuss the properties of enveloping groups of such
quandles. Specializing to surfaces\, we construct a generating set for the
Dehn quandle of orientable surfaces and compute their automorphism groups
. We shall end the talk by discussing two different approaches to write an
explicit presentation for Dehn quandles.\n
LOCATION:https://researchseminars.org/talk/GroupCraft2/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chandan Maity (IISER Mohali)
DTSTART:20220902T053000Z
DTEND:20220902T060000Z
DTSTAMP:20260411T132833Z
UID:GroupCraft2/10
DESCRIPTION:Title: Lower dimensional cohomologies of homogeneous spaces\nby Chandan
Maity (IISER Mohali) as part of World of GroupCraft II\n\n\nAbstract\nIn t
his talk\, we will describe lower dimensional cohomologies (de Rham) of ge
neral homogeneous space. A key step is an equivariant version of the well-
known Cartan's theorem which describes the cohomology of homogeneous space
s in terms of the cohomology of a Koszul complex. As a consequence\, we sh
ow that for a large class of homogeneous spaces the difference in the dime
nsions of the third and fourth cohomologies coincides with the difference
in the number of simple factors of the Lie algebras of certain compact sub
groups associated with the homogeneous space.\n
LOCATION:https://researchseminars.org/talk/GroupCraft2/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Suman Paul (IISER Bhopal)
DTSTART:20220902T060000Z
DTEND:20220902T063000Z
DTSTAMP:20260411T132833Z
UID:GroupCraft2/11
DESCRIPTION:Title: Strongly contracting geodesics in a tree of spaces\nby Suman Paul
(IISER Bhopal) as part of World of GroupCraft II\n\n\nAbstract\nIn a metr
ic space\, 'strongly contracting Geodesics' are generalizations of geodesi
cs of a hyperbolic metric space. In short\, we call a geodesic 'strongly c
ontracting' if it satisfies the 'uniformly bounded projection property'. I
n the first part of the talk\, we will state the definition of 'strongly c
ontracting geodesic' and will give some examples of it. Also\, we will exp
lain the notion of 'tree of spaces'. Lastly\, we will state a combination
'type' result for strongly contracting geodesics of a tree of spaces. And
as a corollary\, we will prove a combination theorem for a 'tree of unifor
mly separated hyperbolic metrics spaces'. This is a joint work with Dr. Ab
hijit Pal.\n
LOCATION:https://researchseminars.org/talk/GroupCraft2/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Oorna Mitra (Chennai Mathematical Institute)
DTSTART:20220902T063000Z
DTEND:20220902T070000Z
DTSTAMP:20260411T132833Z
UID:GroupCraft2/12
DESCRIPTION:Title: The conjugacy problem and other related algorithmic questions in solv
able Baumslag Solitar groups\nby Oorna Mitra (Chennai Mathematical Ins
titute) as part of World of GroupCraft II\n\n\nAbstract\nIn this talk\, we
will introduce some algorithmic problems in groups\, namely the twisted c
onjugacy problem (TCP) and orbit decidability (OD)\, which are closely rel
ated to the classical conjugacy problem (CP) in groups. We will state some
new results towards solving the CP in certain extensions of the solvable
Baumslag Solitar groups\, using a strategy developed by Bogopolski-Martino
-Ventura (Orbit decidability and the conjugacy problem for some extensions
of groups. Trans. Amer. Math. Soc. 362 (2010)\, no. 4\, 2003–2036)\, wh
ich gives a way of solving CP in certain extensions of a group by solving
the TCP in the group. This is based on joint work with Mallika Roy and Enr
ic Ventura.\n
LOCATION:https://researchseminars.org/talk/GroupCraft2/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Corentin Bodart (University of Geneva)
DTSTART:20220902T073000Z
DTEND:20220902T080000Z
DTSTAMP:20260411T132833Z
UID:GroupCraft2/13
DESCRIPTION:Title: On the rationality of complete growth series\nby Corentin Bodart
(University of Geneva) as part of World of GroupCraft II\n\n\nAbstract\nDu
chin and Shapiro have recently proven the "numerical" growth series of the
discrete Heisenberg group is rational\, for any finite symmetric generati
ng set. I will present multiple obstructions to the rationality of complet
e growth series. As a corollary\, and in constrast with the numerical case
\, the complete growth series of the Heisenberg group is never rational. F
inally I will explain how to use those obstructions to reach the same conc
lusion in more general classes of nilpotent groups. Joint work with P. Bag
noud (Geneva)\n
LOCATION:https://researchseminars.org/talk/GroupCraft2/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Karol Duda (University of Wrocław)
DTSTART:20220902T080000Z
DTEND:20220902T083000Z
DTSTAMP:20260411T132833Z
UID:GroupCraft2/14
DESCRIPTION:Title: Torsion subgroups of small cancellation groups\nby Karol Duda (Un
iversity of Wrocław) as part of World of GroupCraft II\n\n\nAbstract\nWe
prove that torsion subgroups of groups defined by\, $C(6)$\, $C(4)$--$T(4)
$ or $C(3)$--$T(6)$ small cancellation presentations are finite.\nThis fol
lows from more general results about locally elliptic action on small canc
ellation complexes.\n
LOCATION:https://researchseminars.org/talk/GroupCraft2/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alex Levine (University of St Andrews)
DTSTART:20220902T083000Z
DTEND:20220902T090000Z
DTSTAMP:20260411T132833Z
UID:GroupCraft2/15
DESCRIPTION:Title: Equations in the Heisenberg group\, formal languages and quadratic eq
uations in the ring of integers\nby Alex Levine (University of St Andr
ews) as part of World of GroupCraft II\n\n\nAbstract\nIn 2016\, Ciobanu\,
Diekert and Elder showed that sets of solutions to systems of equations in
free groups can be expressed as EDT0L languages\, also giving a bound on
the space complexity in which the equations can be solved. Since then\, th
ese ideas have been extended to various other classes of groups including
hyperbolic groups\, right-angled Artin groups and virtually abelian groups
. I will discuss recent work on expressing solutions to single equations i
n the Heisenberg group as EDT0L languages\, and the relationship this prob
lem has to quadratic Diophantine equations in the ring of integers and Pel
l’s equation.\n
LOCATION:https://researchseminars.org/talk/GroupCraft2/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Islam Foniqi (University of Milano - Bicocca)
DTSTART:20220902T093000Z
DTEND:20220902T100000Z
DTSTAMP:20260411T132833Z
UID:GroupCraft2/16
DESCRIPTION:Title: Parabolic subgroups in even Artin groups of FC type\nby Islam Fon
iqi (University of Milano - Bicocca) as part of World of GroupCraft II\n\n
\nAbstract\nWe present a study of parabolic subgroups in even Artin groups
through combinatorial and geometric means. The main result states that th
e collection of parabolic subgroups of a finitely generated even Artin gro
up of FC type is closed under intersections.\n
LOCATION:https://researchseminars.org/talk/GroupCraft2/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sahana Balasubramanya (University of Münster)
DTSTART:20220902T100000Z
DTEND:20220902T103000Z
DTSTAMP:20260411T132833Z
UID:GroupCraft2/17
DESCRIPTION:Title: Property (NL) for groups\nby Sahana Balasubramanya (University of
Münster) as part of World of GroupCraft II\n\n\nAbstract\nWe introduce t
he Property (NL)\, which indicates that a group does not act on a hyperbol
ic space with any loxodromic elements. It turns out many groups satisfy th
is property\, such as many Thompson-like groups and twisted Brin--Thompson
groups. In this talk\, I shall speak about the motivation to study this p
roperty\, give examples and talk about results pertaining to this property
and its relation to other fixed point properties. This is joint work with
Anthony Genevois and Francesco Fourier.\n
LOCATION:https://researchseminars.org/talk/GroupCraft2/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yassine Guerch (Université Paris-Saclay)
DTSTART:20220902T103000Z
DTEND:20220902T110000Z
DTSTAMP:20260411T132833Z
UID:GroupCraft2/18
DESCRIPTION:Title: Growth and subgroups of $Out(F_n)$\nby Yassine Guerch (Universit
é Paris-Saclay) as part of World of GroupCraft II\n\n\nAbstract\nLet $n$
be an integer and let $Out(F_n)$ be the outer automorphism group of a nona
belian free group of rank $n$. Let $[g]$ be a conjugacy class of $F_n$ and
$F \\in Out(F_n)$. The class $[g]$ has exponential growth under iteration
of $F$ if the word length (for a given basis of $F_n$) of $F^m([g])$ grow
s exponentially fast with $m$. We will present a structure result for subg
roups of $Out(F_n)$ which shows that\, given a subgroup $H$ of $Out(F_n)$\
, there exist generic elements of $H$ which encapture the exponential grow
th of every element of $H$.\n
LOCATION:https://researchseminars.org/talk/GroupCraft2/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Macarena Arenas (U. Cambridge)
DTSTART:20220902T120000Z
DTEND:20220902T123000Z
DTSTAMP:20260411T132833Z
UID:GroupCraft2/19
DESCRIPTION:Title: A cubical Rips construction\nby Macarena Arenas (U. Cambridge) as
part of World of GroupCraft II\n\n\nAbstract\nThe Rips exact sequence is
a useful tool for producing examples of groups satisfying combinations of
properties that are not obviously compatible. It works by taking as an in
put an arbitrary finitely presented group $Q$\, and producing as an output
a hyperbolic group $G$ that maps onto $Q$ with finitely generated kernel.
The "output group" $G$ is crafted by adding generators and relations to a
presentation of $Q$\, in such a way that these relations create enough "n
oise" in the presentation to ensure hyperbolicity. One can then lift patho
logical properties of $Q$ to (some subgroup of) $G$. Among other things\,
Rips used his construction to produce the first examples of incoherent hyp
erbolic groups\, and of hyperbolic groups with unsolvable generalised word
problem.\n\nIn this talk\, I will explain Rips’ result\, and describe a
variation that produces cubulated hyperbolic groups of any desired cohomo
logical dimension.\n
LOCATION:https://researchseminars.org/talk/GroupCraft2/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:André da Cruz Carvalho (U. Porto)
DTSTART:20220902T123000Z
DTEND:20220902T130000Z
DTSTAMP:20260411T132833Z
UID:GroupCraft2/20
DESCRIPTION:Title: Dynamics of endomorphisms of free-abelian times free groups\nby A
ndré da Cruz Carvalho (U. Porto) as part of World of GroupCraft II\n\n\nA
bstract\nIn this talk\, we will discuss the dynamics at the infinity for e
ndomorphisms of free-abelian times free groups admitting a continuous exte
nsion to the infinity (in some sense). In the case of free group automorph
isms\, the dynamical notions of periodic\, recurrent and nonwandering poin
ts coincide. For free-abelian times free groups\, we will describe the end
omorphisms that admit a continuous extension to the infinity and see that
the same result can be obtained for some of these endomorphisms\, defined
in a precise way. In particular\, the result holds for all (extendable) au
tomorphisms.\n
LOCATION:https://researchseminars.org/talk/GroupCraft2/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jone Lopez de Gamiz Zearra (U. Warwick)
DTSTART:20220902T130000Z
DTEND:20220902T133000Z
DTSTAMP:20260411T132833Z
UID:GroupCraft2/21
DESCRIPTION:Title: Subgroups of right-angled Artin groups\nby Jone Lopez de Gamiz Ze
arra (U. Warwick) as part of World of GroupCraft II\n\n\nAbstract\nIn gene
ral\, subgroups of RAAGs are known to have wild structure and bad algorith
mic behaviour. However\, in this talk\, we will center on properties of su
bgroups and specific families of RAAGs that assure a tame structure and go
od algorithmic behaviour.\n\nIn particular\, we will discuss finitely gene
rated normal subgroups of RAAGs. A classical result of Schreier states tha
t nontrivial finitely generated normal subgroups of free groups are of fin
ite index. We will see a generalisation of this result and show that the q
uotient of a RAAG by a finitely generated normal subgroup is abelian-by-fi
nite and finite-by-abelian.\n\nWe will then talk about some algorithmic co
nsequences\, such as the decidability of the conjugacy and the membership
problems. We will finally discuss residual properties\, such as conjugacy
separability\, for finitely generated normal subgroups of RAAGs.\n
LOCATION:https://researchseminars.org/talk/GroupCraft2/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Monika Kudlinska (U. Oxford)
DTSTART:20220902T140000Z
DTEND:20220902T143000Z
DTSTAMP:20260411T132833Z
UID:GroupCraft2/22
DESCRIPTION:Title: Quasi-isometries of free-by-cyclic groups\nby Monika Kudlinska (U
. Oxford) as part of World of GroupCraft II\n\n\nAbstract\nA group is free
-by-cyclic if it admits an epimorphism onto the infinite cyclic group with
kernel isomorphic to a free group of finite rank. The study of free-by-cy
clic groups is largely motivated by the case of 3-manifolds which fiber ov
er the circle. In this talk we will show that the class of free-by-cyclic
groups is quasi-isometrically rigid amongst all groups of finite cohomolog
ical dimension which admit the property of being residually finite rationa
lly solvable.\n
LOCATION:https://researchseminars.org/talk/GroupCraft2/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alan McLeay (U. Madrid)
DTSTART:20220902T143000Z
DTEND:20220902T150000Z
DTSTAMP:20260411T132833Z
UID:GroupCraft2/23
DESCRIPTION:Title: Small covers of big surfaces\nby Alan McLeay (U. Madrid) as part
of World of GroupCraft II\n\n\nAbstract\nCovering spaces are ubiquitous in
topology. This talk will be about finite-sheeted covers of surfaces. In
particular\, one can ask\; given two surfaces\, when does one admit such
a cover over the other.\n\nA result of Massey provides the answer when the
surfaces are finite-type. In joint work with Ty Ghaswala\, we look at wha
t can be said about the remaining (uncountably many) cases.\n
LOCATION:https://researchseminars.org/talk/GroupCraft2/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mallika Roy (U. Basque Country)
DTSTART:20220902T150000Z
DTEND:20220902T153000Z
DTSTAMP:20260411T132833Z
UID:GroupCraft2/24
DESCRIPTION:Title: Computation of auto-fixed closure and endo-fixed closure in free and
extension of free groups\nby Mallika Roy (U. Basque Country) as part o
f World of GroupCraft II\n\n\nAbstract\nThe classical result by Dyer–Sco
tt about fixed subgroups of finite order automorphisms of being free facto
rs of free groups is no longer true in $\\Z^m \\times F_n$. Within this mo
re general context\, in this talk we will prove a relaxed version in the s
pirit of Bestvina–Handel Theorem: the rank of fixed subgroups of finite
order automorphisms is uniformly bounded in terms of $m\,n$. We will give
an algorithm to compute auto-fixed closures and endo-fixed closures of fin
itely generated subgroups of $\\Z^m \\times F_n$. \n\n\nOn the way\, we wi
ll prove the analog of Day's Theorem for real elements in $\\Z^m \\times F
_n$\, contributing a modest step into the project of doing so for any righ
t angled Artin group (as McCool did with respect to Whitehead's Theorem in
the free context).\n
LOCATION:https://researchseminars.org/talk/GroupCraft2/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sam Shepherd (Vanderbilt University)
DTSTART:20220902T163000Z
DTEND:20220902T170000Z
DTSTAMP:20260411T132833Z
UID:GroupCraft2/25
DESCRIPTION:Title: Semistability of cubulated groups\nby Sam Shepherd (Vanderbilt Un
iversity) as part of World of GroupCraft II\n\n\nAbstract\nI will discuss
my theorem that cubulated groups are semistable at infinity\, together wit
h background on these two concepts. I will also present a result about mod
ifying the cubulation of a group to achieve certain geometric features\, w
hich is needed to prove the semistability theorem.\n\nPassword: size of th
e smallest non-abelian finite simple group\n
LOCATION:https://researchseminars.org/talk/GroupCraft2/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Francis Wagner (The Ohio State University)
DTSTART:20220902T170000Z
DTEND:20220902T173000Z
DTSTAMP:20260411T132833Z
UID:GroupCraft2/26
DESCRIPTION:Title: Torsion Subgroups of Groups with Quadratic Dehn Function\nby Fran
cis Wagner (The Ohio State University) as part of World of GroupCraft II\n
\n\nAbstract\nThe Dehn function of a finitely presented group is a useful
invariant closely related to the solvability of the group's word problem.
It is well-known that a finitely presented group is word hyperbolic if an
d only if it has a sub-quadratic (and thus linear) Dehn function. A resul
t of Ghys and de la Harpe states that no hyperbolic group can contain a (f
initely generated) infinite torsion subgroup. We show that this property
does not carry over to classes of groups of larger Dehn function. In part
icular\, for every m>1 and n sufficiently large (and satisfying some weak
restrictions)\, there exists a quasi-isometric embedding of the infinite f
ree Burnside group B(m\,n) into a finitely presented group with quadratic
Dehn function.\n
LOCATION:https://researchseminars.org/talk/GroupCraft2/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Elizabeth Field (University of Utah)
DTSTART:20220902T180000Z
DTEND:20220902T183000Z
DTSTAMP:20260411T132833Z
UID:GroupCraft2/27
DESCRIPTION:Title: Stable commutator length on big mapping class groups\nby Elizabet
h Field (University of Utah) as part of World of GroupCraft II\n\n\nAbstra
ct\nIn this talk\, we will discuss the stable commutator length function o
n the\nmapping class groups of infinite-type surfaces which satisfy a cert
ain\ntopological characterization. In particular\, we will show that stabl
e\ncommutator length is a continuous function on these big mapping class\n
groups\, as well as that the commutator subgroups of these big mapping\ncl
ass groups are both open and closed. We will also discuss certain\ntopolog
ical properties of a class of infinite-type surfaces and their end\nspaces
which may be of independent interest. This talk represents joint\nwork wi
th Priyam Patel and Alexander Rasmussen.\n
LOCATION:https://researchseminars.org/talk/GroupCraft2/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hannah Hoganson (University of Maryland)
DTSTART:20220902T183000Z
DTEND:20220902T190000Z
DTSTAMP:20260411T132833Z
UID:GroupCraft2/28
DESCRIPTION:Title: Big Out(F_n)" and its Coarse Geometry\nby Hannah Hoganson (Univer
sity of Maryland) as part of World of GroupCraft II\n\n\nAbstract\nRecentl
y\, Algom-Kfir and Bestvina introduced mapping class groups of locally fin
ite graphs as a proposed analog of Out(F_n) in the infinite-type setting.
In this talk\, we will introduce the classification of infinite-type graph
s\, their mapping class groups\, and some important types of elements in t
hese groups. Using a framework established by Rosendal\, we will then dis
cuss the coarse geometry of the pure mapping class groups. This is joint w
ork with George Domat and Sanghoon Kwak.\n
LOCATION:https://researchseminars.org/talk/GroupCraft2/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jean Pierre Mutanguha (Institute for Advanced Study)
DTSTART:20220902T190000Z
DTEND:20220902T193000Z
DTSTAMP:20260411T132833Z
UID:GroupCraft2/29
DESCRIPTION:Title: Canonical forms for free group automorphisms\nby Jean Pierre Muta
nguha (Institute for Advanced Study) as part of World of GroupCraft II\n\n
\nAbstract\nThe Nielsen–Thurston theory of surface homeomorphisms can be
thought of as a surface analogue to the Jordan Canonical Form. I will dis
cuss my progress in developing a similar canonical form for free group aut
omorphisms. (Un)Fortunately\, free group automorphisms can have arbitraril
y complicated behaviour. This is a significant barrier to translating argu
ments that worked for surfaces into the free group setting\; nevertheless\
, the overall ideas/strategies do translate!\n
LOCATION:https://researchseminars.org/talk/GroupCraft2/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lorenzo Ruffoni (Tufts University)
DTSTART:20220902T200000Z
DTEND:20220902T203000Z
DTSTAMP:20260411T132833Z
UID:GroupCraft2/30
DESCRIPTION:Title: Special cubulation of strict hyperbolization\nby Lorenzo Ruffoni
(Tufts University) as part of World of GroupCraft II\n\n\nAbstract\nGromov
introduced some “hyperbolization” procedures\, i.e. some procedures t
hat turn a given polyhedron into a space of non-positive curvature. Charne
y and Davis then developed a refined “strict hyperbolization” procedur
e that outputs a space of strictly negative curvature. Their procedure has
been used to construct examples of manifolds and groups that exhibit vari
ous pathologies\, despite having negative curvature. We construct actions
of the resulting groups on CAT(0) cube complexes. As an application\, we o
btain that they are virtually special\, hence linear over the integers and
residually finite. This is joint work with J. Lafont.\n
LOCATION:https://researchseminars.org/talk/GroupCraft2/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anschel Shaffer-Cohen (National Autonomous University of Mexico)
DTSTART:20220902T203000Z
DTEND:20220902T210000Z
DTSTAMP:20260411T132833Z
UID:GroupCraft2/31
DESCRIPTION:Title: What does a "typical" (i.e. random) infinite-type surface look like?<
/a>\nby Anschel Shaffer-Cohen (National Autonomous University of Mexico) a
s part of World of GroupCraft II\n\n\nAbstract\nThe study of big mapping c
lass groups has introduced a plethora of properties that an infinite type
surface might or might not have. But in most cases\, it is not at all obvi
ous how common these properties are. For instance\, are most surfaces tame
? Doubly pointed? Infinite-genus? I will present some ideas of how we migh
t tackle these questions\, and explain why some obvious solutions don't se
em to pan out.\n
LOCATION:https://researchseminars.org/talk/GroupCraft2/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Israel Morales Jiménez (National Autonomous University of Mexico)
DTSTART:20220902T210000Z
DTEND:20220902T213000Z
DTSTAMP:20260411T132833Z
UID:GroupCraft2/32
DESCRIPTION:Title: Big mapping class groups from a GGT perspective\nby Israel Morale
s Jiménez (National Autonomous University of Mexico) as part of World of
GroupCraft II\n\n\nAbstract\nThe mapping class group\, Map(S)\, of a surfa
ce S\, is the group of all isotopy classes of homeomorphisms of S to itsel
f. A mapping class group is a topological group with the quotient topology
inherited from the quotient map of Homeo(S) with the compact-open topolog
y.\n\nFor surfaces of finite type\, Map(S) is countable and discrete. Surp
risingly\, the topology of Map(S) is more interesting if S is an infinite-
type surface\; it is uncountable\, topologically perfect\, totally disconn
ected\, and more importantly\, has the structure of a Polish group. In rec
ent literature\, this last class of groups is called “big mapping class
groups” (big MCG’s). \n\nIn this talk\, I will very\, very briefly int
roduce Rosendal's framework for studying Polish groups from the GGT perspe
ctive and\, I will present you a countable graph with the same type of qua
si-isometry as a big MCG and ask open questions about it.\n
LOCATION:https://researchseminars.org/talk/GroupCraft2/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Keegan Boyle (University of British Columbia)
DTSTART:20220902T220000Z
DTEND:20220902T223000Z
DTSTAMP:20260411T132833Z
UID:GroupCraft2/33
DESCRIPTION:Title: Involutions on the 4-ball and strongly negative amphichiral knots
\nby Keegan Boyle (University of British Columbia) as part of World of Gro
upCraft II\n\n\nAbstract\nA natural step in studying the diffeomorphism gr
oup of a manifold is understanding the conjugacy classes of involutions. E
ven in the case of the 4-ball\, it is not known what the order 2 conjugacy
classes are. In this talk\, I will discuss how to use symmetric knots to
study this question\, and state some results in this direction with Wenzha
o Chen.\n
LOCATION:https://researchseminars.org/talk/GroupCraft2/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jacob Garcia (University of California\, Riverside)
DTSTART:20220902T223000Z
DTEND:20220902T230000Z
DTSTAMP:20260411T132833Z
UID:GroupCraft2/34
DESCRIPTION:Title: Stability and the Morse Boundary\nby Jacob Garcia (University of
California\, Riverside) as part of World of GroupCraft II\n\n\nAbstract\nG
iven a subgroup of a finitely generated group\, a natural question is to a
sk if the geometry of the subgroup is nicely encoded in the geometry of th
e ambient group. For a hyperbolic group\, this is classified exactly by th
e concept of a quasi-convex subgroup. These subgroups have several nice eq
uivalent characterizations with respect to the Gromov boundary\, in partic
ular\, they admit nice actions on the weak convex hulls of their limit set
s\, and all of their limit points are conical. In this talk\, we'll be des
cribing a generalization of the Gromov boundary introduced by Cordes calle
d the Morse boundary\, and exploring its relationship with a generalizatio
n of quasi-convexity called subgroup stability.\n
LOCATION:https://researchseminars.org/talk/GroupCraft2/34/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daxun Wang (University at Buffalo)
DTSTART:20220902T230000Z
DTEND:20220902T233000Z
DTSTAMP:20260411T132833Z
UID:GroupCraft2/35
DESCRIPTION:Title: On the classification of generalized Baumslag-Solitar groups\nby
Daxun Wang (University at Buffalo) as part of World of GroupCraft II\n\n\n
Abstract\nA generalized Baumslag-Solitar (GBS) group is a group that acts
on a tree with infinite cyclic edge and vertex stabilizers. Equivalently\,
it is the fundamental group of a graph of infinite cyclic groups. These g
roups have arisen in the study of splitting of groups. In this talk\, we w
ill discuss how to approach the group-theoretic classification of GBS grou
ps and the current results of this problem.\n
LOCATION:https://researchseminars.org/talk/GroupCraft2/35/
END:VEVENT
END:VCALENDAR