BEGIN:VCALENDAR
VERSION:2.0
PRODID:researchseminars.org
CALSCALE:GREGORIAN
X-WR-CALNAME:researchseminars.org
BEGIN:VEVENT
SUMMARY:Toke Carlsen (Faroe Islands)
DTSTART:20200514T100000Z
DTEND:20200514T110000Z
DTSTAMP:20260404T111215Z
UID:CRMDS/1
DESCRIPTION:Title: Graph algebras\, groupoids\, and symbolic dynamics\nby Toke Carls
en (Faroe Islands) as part of Western Sydney University Abend Seminars\n\n
\nAbstract\nI will give an overview of some recent results that link diago
nal-preserving isomorphism of graph algebras and isomorphism and equivalen
ce of graph groupoids with continuous orbit equivalence\, (eventual) conju
gacy\, and flow equivalence of symbolic dynamical systems constructed from
directed graphs.\n
LOCATION:https://stable.researchseminars.org/talk/CRMDS/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mark Lawson (Heriot-Watt University)
DTSTART:20200521T100000Z
DTEND:20200521T110000Z
DTSTAMP:20260404T111215Z
UID:CRMDS/2
DESCRIPTION:Title: Non-commutative Stone dualities\nby Mark Lawson (Heriot-Watt Univ
ersity) as part of Western Sydney University Abend Seminars\n\n\nAbstract\
nThe classical Stone dualities for lattices such as frames\, distributive
lattices and generalized Boolean algebras can be generalized to a non-comm
utative setting to pseudogroups\, distributive inverse semigroups and Bool
ean inverse semigroups\, respectively.\nThe goal of this talk is to sketch
out the how and to motivate the why.\nI shall not assume any background f
rom inverse semigroups or \\'etale groupoids.\n
LOCATION:https://stable.researchseminars.org/talk/CRMDS/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Enrique Pardo Espino (Cadiz)
DTSTART:20200528T100000Z
DTEND:20200528T110000Z
DTSTAMP:20260404T111215Z
UID:CRMDS/3
DESCRIPTION:Title: Self-similar graphs and their algebras\nby Enrique Pardo Espino (
Cadiz) as part of Western Sydney University Abend Seminars\n\n\nAbstract\n
In this talk\, we will explain the origins of the notion of self-similar g
raph. We\ngive a groupoid model of the algebra associated to a self-simila
r graph and we provide a characterization of simplicity for these algebras
. We briefly talk about further developments on this construction.\nThe co
ntents of this talk are part of a joint paper with R. Exel.\n
LOCATION:https://stable.researchseminars.org/talk/CRMDS/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mike Whittaker (Glasgow)
DTSTART:20200604T100000Z
DTEND:20200604T110000Z
DTSTAMP:20260404T111215Z
UID:CRMDS/4
DESCRIPTION:Title: Aperiodic tilings: from the Domino problem to aperiodic monotiles
\nby Mike Whittaker (Glasgow) as part of Western Sydney University Abend S
eminars\n\n\nAbstract\nAlmost 60 years ago\, Hao Wang posed the Domino Pro
blem: is there an algorithm that determines whether a given set of square
prototiles\, with specified matching rules\, can tile the plane? Robert Be
rger proved the undecidability of the Domino Problem by producing a set of
20\,426 prototiles that tile the plane\, but any such tiling is nonperiod
ic (lacks any translational symmetry). This remarkable discovery began the
search for other (not necessarily square) aperiodic prototile sets\, a fi
nite collection of prototiles that tile the plane but only nonperiodically
. In the 1970s\, Roger Penrose reduced this number to two. Penrose's disco
very led to the planar einstein (one-stone) problem: is there a single ape
riodic prototile? In a crowning achievement of tiling theory\, the existen
ce of an aperiodic monotile was resolved almost a decade ago by Joshua Soc
olar and Joan Taylor. My talk will be somewhat expository\, and culminate
in both a new direction in aperiodic tiling theory and a new aperiodic mon
otile.\n
LOCATION:https://stable.researchseminars.org/talk/CRMDS/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kevin Brix (Wollongong/Copenhagen)
DTSTART:20200611T100000Z
DTEND:20200611T110000Z
DTSTAMP:20260404T111215Z
UID:CRMDS/5
DESCRIPTION:Title: Fine structure of C*-algebras associated to topological dynamics\
nby Kevin Brix (Wollongong/Copenhagen) as part of Western Sydney Universit
y Abend Seminars\n\n\nAbstract\nI will report on the story of associating
C*-algebras to symbolic dynamical systems (e.g. shift spaces or directed g
raphs) and the recently articulated program of understanding dynamical rel
ations (such as conjugacy or flow equivalence) in terms of structure-prese
rving *-isomorphisms of the corresponding C*-algebras. A large body of rig
idity results have successfully been obtained for graphs and more general
systems. There will be an emphasis on open questions and problems yet to b
e solved!\n
LOCATION:https://stable.researchseminars.org/talk/CRMDS/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Joan Bosa (Barcelona)
DTSTART:20200618T100000Z
DTEND:20200618T110000Z
DTSTAMP:20260404T111215Z
UID:CRMDS/6
DESCRIPTION:Title: The realization problem for von Neumann regular rings\nby Joan Bo
sa (Barcelona) as part of Western Sydney University Abend Seminars\n\n\nAb
stract\nThe realization problem for von Neumann (vN) regular rings asks wh
ether all conical refinement monoids arise from monoids induced by the pro
jective modules over a vN regular ring? We will quickly overview this prob
lem and show the last developments on it? This is joint work with PAra\, E
.Pardo and \nA.Sims.\n
LOCATION:https://stable.researchseminars.org/talk/CRMDS/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Aidan Sims (Wollongong)
DTSTART:20200702T100000Z
DTEND:20200702T110000Z
DTSTAMP:20260404T111215Z
UID:CRMDS/7
DESCRIPTION:Title: Graded K-theory for Z_2-graded graph C*-algebras\nby Aidan Sims (
Wollongong) as part of Western Sydney University Abend Seminars\n\n\nAbstr
act\nWhile there is no universally agreed-upon definition of Z_2-graded K-
theory for C*-algebras\, a very natural way to define it is using Kasparov
's celebrated KK-bifunctor: KK is naturally a Z_2-graded theory\, and Kasp
arov proved that if applied to trivially-graded C*-algebras A\, the groups
KK_*(\\mathbb{C}\, A) are the K-groups of A. So it is natural to define K
^{gr}_*(A) as KK_*(\\mathbb{C}\, A) for Z_2-graded C*-algebras A in genera
l. I will discuss recent work with Adam Sierakowski and with honours stude
nts Quinn Patterson and Jonathan Taylor\, building on previous work with K
umjian and Pask\, that uses deep ideas of Pimsner to compute the graded K-
theory\, defined in this way\, of relative graph C*-algebras carrying Z_2-
gradings determined by binary labellings of the edges of the graph: the fo
rmulas that emerge strongly suggest that this notion of graded K-theory ca
ptures the right sort of information.\n
LOCATION:https://stable.researchseminars.org/talk/CRMDS/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Xiao-Wu Chen (Hefei)
DTSTART:20200709T100000Z
DTEND:20200709T110000Z
DTSTAMP:20260404T111215Z
UID:CRMDS/8
DESCRIPTION:Title: Leavitt path algebra via the singularity category of a radical-square
-zero algebra\nby Xiao-Wu Chen (Hefei) as part of Western Sydney Unive
rsity Abend Seminars\n\n\nAbstract\nWe will recall some previous work prim
arily by Paul Smith\, and show that the Leavitt path algebra \nis closely
related to the singularity category of a finite dimensional radical-square
-zero algebra. Recently\, we apply such a link to confirm Keller's conject
ure for a radical-square-zero algebra. More precisely\, we prove that for
such an algebra\, the singular Hochschild cochain complex is B_\\infinity-
isomorphic to the Hochschild cochain complex of the dg singularity categor
y. This is based on a joint work with Huanhuan Li and Zhengfang Wang.\n
LOCATION:https://stable.researchseminars.org/talk/CRMDS/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jean Renault (d'Orleans)
DTSTART:20200716T100000Z
DTEND:20200716T110000Z
DTSTAMP:20260404T111215Z
UID:CRMDS/9
DESCRIPTION:Title: Groupoids Extensions\nby Jean Renault (d'Orleans) as part of West
ern Sydney University Abend Seminars\n\n\nAbstract\nI shall present a grou
poid version of the Mackey normal subgroup analysis in a C*-algebraic fram
ework. More precisely\, the main result is a description of the C*-algebra
of a locally compact groupoid with Haar system\, possibly endowed with a
twist\, which is an extension by a group bundle. The natural expression of
this result uses Fell bundles over groupoids. When the group bundle is ab
elian\, one obtains a twisted groupoid C*-algebra. I will give some applic
ations. This talk is based on a joint work with M.Ionescu\, A.Kumjian\, A.
Sims and D.Williams.\n
LOCATION:https://stable.researchseminars.org/talk/CRMDS/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pere Ara (Barcelona)
DTSTART:20200625T100000Z
DTEND:20200625T110000Z
DTSTAMP:20260404T111215Z
UID:CRMDS/10
DESCRIPTION:Title: Graded K-Theory\, Filtered K-theory and the classification of graph
algebras\nby Pere Ara (Barcelona) as part of Western Sydney University
Abend Seminars\n\n\nAbstract\nWe prove that an isomorphism of graded Gro
thendieck groups of two Leavitt path algebras induces an isomorphism of a
certain quotient of algebraic filtered K-theory and consequently an isomo
rphism of filtered K-theory of their associated graph C*-algebras. As an a
pplication\, we show that\, since for a finite graph E with no sinks\, the
graded Grothendieck group of L(E) coincides with Krieger's dimension grou
p of its adjacency matrix\, our result relates the shift equivalence of gr
aphs to the filtered K-theory and consequently gives that two arbitrary sh
ift equivalent matrices give stably isomorphic graph C*-algebras. This res
ult was only known for irreducible graphs. This is a joint work with Roozb
eh Hazrat and Huanhuan Li\n
LOCATION:https://stable.researchseminars.org/talk/CRMDS/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Be'eri Greenfeld (Bar Ilan)
DTSTART:20200723T100000Z
DTEND:20200723T110000Z
DTSTAMP:20260404T111215Z
UID:CRMDS/11
DESCRIPTION:Title: How do algebras grow?\nby Be'eri Greenfeld (Bar Ilan) as part of
Western Sydney University Abend Seminars\n\n\nAbstract\nThe question of `
how do algebras grow?'\, or\, which functions can be realized as growth fu
nctions of algebras (associative/Lie/etc.\, or algebras having certain add
itional algebraic properties) is a major problem in the junction of severa
l mathematical fields\, including noncommutative algebra\, combinatorics o
f (infinite) words\, symbolic dynamics\, self-similarity and more.\nWe pro
vide a novel paradigm for tackling this problem (in fact\, family of probl
ems)\, thereby resolving several open problems posed by experts regarding
possible growth types of finitely generated associative algebras and Lie a
lgebras.\nWe also consider the set of growth functions as a space\, and po
int out odd properties it admits (arbitrarily rapid holes\, and convergenc
e to outer points - with respect to some plausible notion of limits).\n
LOCATION:https://stable.researchseminars.org/talk/CRMDS/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Arun Ram (Melbourne)
DTSTART:20200730T100000Z
DTEND:20200730T110000Z
DTSTAMP:20260404T111215Z
UID:CRMDS/12
DESCRIPTION:Title: Teaching Mathematics in the next life\nby Arun Ram (Melbourne) a
s part of Western Sydney University Abend Seminars\n\n\nAbstract\nFor many
years I've been thinking about how\nto teach mathematics with honesty and
inspiration.\nThis has resulted in ideas like "reality teaching"\, "proof
machine"\, \n"marking apocalypse" and "just do it". And then a virus cam
e\, \nand the new life began\, online\, on Zoom. This will be a talk abou
t\nthe adventures of the past life and the preparations\nfor the next.\n
LOCATION:https://stable.researchseminars.org/talk/CRMDS/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bob Gray (East Anglia)
DTSTART:20200806T100000Z
DTEND:20200806T110000Z
DTSTAMP:20260404T111215Z
UID:CRMDS/13
DESCRIPTION:Title: Undecidability of the word problem for one-relator inverse monoids\nby Bob Gray (East Anglia) as part of Western Sydney University Abend S
eminars\n\n\nAbstract\nIt is a classical result of Magnus proved in the 19
30s that the word problem is decidable for one-relator groups. This result
inspired a series of investigations of the word problem in other one-rela
tor algebraic structures. For example\, in the 1960s Shirshov proved the w
ord problem is decidable in one-relator Lie algebras. In contrast\, it rem
ains a longstanding open problem whether the word problem is decidable for
one-relator monoids. An important class of algebraic structures lying in
between monoids and groups is that of inverse monoids. In this talk I will
speak about a recent result which shows that there exist one-relator inve
rse monoids of the form Inv with undecidable word problem. This ans
wers a problem originally posed by Margolis\, Meakin and Stephen in 1987.
I will explain how this result relates to the word problem for one-relator
monoids\, the submonoid membership problem for one-relator groups\, and t
o the question of which right-angled Artin groups arise as subgroups of on
e-relator groups.\n
LOCATION:https://stable.researchseminars.org/talk/CRMDS/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jose Burillo (Barcelona)
DTSTART:20200820T100000Z
DTEND:20200820T110000Z
DTSTAMP:20260404T111215Z
UID:CRMDS/14
DESCRIPTION:Title: The irrational-slope Thompson's groups\nby Jose Burillo (Barcelo
na) as part of Western Sydney University Abend Seminars\n\n\nAbstract\nJos
é Burillo (Universitat Politècnica de Catalunya)\n\nTitle: The irrationa
l-slope Thompson's groups\n\nAbstract: Irrational-slope Thompson's groups
were introduced by Cleary in two papers in 1995 and 2000\, where he proved
they are FP_\\infty. These are groups of PL maps of [0\,1] whose breakpoi
nts are in some irrational subring of R and the slopes are also irrational
numbers. Interest in these groups grew recently when it was asked whether
they can be obtained as subgroups of Thompson's group F. In this paper we
will introduce the golden ratio group F_\\tau\, describe how to work with
it in terms of binary trees and also algebraically. We will show a presen
tation for F_\\tau and show that elements admit a unique normal form\, in
similar fashion as F. We will study its metric properties and undistorted
copies of F inside\, and finally\, if time permits\, we will say a few wor
ds about the irrational versions of Thompson's groups T and V. This is joi
nt work with Brita Nucinkis and Lawrence Reeves.\n
LOCATION:https://stable.researchseminars.org/talk/CRMDS/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Cristobal Gil Canto (Malaga)
DTSTART:20200813T100000Z
DTEND:20200813T110000Z
DTSTAMP:20260404T111215Z
UID:CRMDS/15
DESCRIPTION:Title: Invariant ideals in Leavitt path algebras\nby Cristobal Gil Cant
o (Malaga) as part of Western Sydney University Abend Seminars\n\n\nAbstra
ct\nAs well-known examples of Leavitt path algebras arise the so-called pr
imary colours: they respectively correspond to the ideal generated by the
set of line points\, the vertices that lie on cycles without exits and the
one generated by the set in extreme cycles. It is known that these ideals
are invariant under isomorphism. In this talk we will analyze the invaria
nce of another key piece of a Leavitt path algebra. We will see that thoug
h the ideal generated by the vertices whose tree contains infinitely many
bifurcation vertices or at least one infinite emitter is not invariant\, w
e will find its natural replacement (which is indeed invariant). We will a
lso give some procedures to construct invariant ideals from previous known
invariant ideals. In order to do that\, on the one hand\, we will introdu
ce a topology in the set of vertices of a graph. And on the other hand\, v
ia category theory\, we will think of the saturated and hereditary set of
a graph as a functor. This a joint work together with Dolores Martín Barq
uero and Cándido Martín González.\n
LOCATION:https://stable.researchseminars.org/talk/CRMDS/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ralf Meyer (Goettingen)
DTSTART:20200827T100000Z
DTEND:20200827T110000Z
DTSTAMP:20260404T111215Z
UID:CRMDS/16
DESCRIPTION:Title: Aperiodicity and related properties for crossed product inclusions\nby Ralf Meyer (Goettingen) as part of Western Sydney University Abend
Seminars\n\n\nAbstract\nIn recent work with Bartosz Kwa?niewski\, we have
vastly generalised the condition that was introduced by Kishimoto in order
to prove that reduced crossed products for outer group actions on simple
C*-algebras are again simple. We call this condition aperiodicity\, and i
t applies to arbitrary inclusions of C*-algebras\, without requiring a cro
ssed product structure. We relate this to topological non-triviality cond
itions in the special case of actions of inverse semigroups or étale grou
poids (which are possibly non-Hausdorff). In that generality\, we define
an essential crossed product\, which is a quotient of the reduced crossed
product. If the action satisfies Kishimoto's condition\, then the coeffic
ient algebra detects ideals in this essential crossed product. And in the
simple case\, we also get criteria for the essential crossed product to b
e simple. We also relate aperiodicity to other properties that have been
used to study the ideal structure of crossed products. This includes uniq
ue pseudo-expectations and the almost extension property\, which assume th
at the set of pure states on the coefficient algebra that extend uniquely
to the crossed product is dense.\n
LOCATION:https://stable.researchseminars.org/talk/CRMDS/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lia Vas (Philadelphia)
DTSTART:20200903T100000Z
DTEND:20200903T110000Z
DTSTAMP:20260404T111215Z
UID:CRMDS/17
DESCRIPTION:Title: The Graded Classification Conjecture for graph algebras\nby Lia
Vas (Philadelphia) as part of Western Sydney University Abend Seminars\n\n
\nAbstract\nThe ordinary (pointed) K_0-group is not a complete invariant o
f algebras typically associated to a directed graph. When these algebras a
re considered as graded algebras and the definition of the K_0-group is ad
justed to reflect the existence of this grading\, the situation becomes mo
re interesting. The Graded Classification Conjecture states that this adju
sted version of the (pointed) K_0-group is a complete invariant of a Leavi
tt path algebra over a field (and this statement can be adapted for other
graph algebras). We shall discuss the context in which this conjecture has
been formulated\, the current status of the conjecture\, and some ongoing
research.\n
LOCATION:https://stable.researchseminars.org/talk/CRMDS/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Volodymyr Mazorchuk (Uppsala)
DTSTART:20200910T100000Z
DTEND:20200910T110000Z
DTSTAMP:20260404T111215Z
UID:CRMDS/18
DESCRIPTION:Title: Adjunction in the absence of identity\nby Volodymyr Mazorchuk (U
ppsala) as part of Western Sydney University Abend Seminars\n\n\nAbstract\
nIn this talk I plan to present and discuss a rather\nweak bicategorical s
etup in which one can talk about\ngenuine adjunctions. I will roughly desc
ribe the\nmain motivation coming from representation theory of\nfinitary 2
-categories (or bicategories) and make some parallells with the structure
theory of finite\nsemigroups. I will try to explain how this approach\nsim
plifies some results but also makes some other\nresults much more difficul
t. This is a joint work with Hankyung Ko and Xiaoting Zhang.\n
LOCATION:https://stable.researchseminars.org/talk/CRMDS/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Murray Elder (Sydney)
DTSTART:20200917T100000Z
DTEND:20200917T110000Z
DTSTAMP:20260404T111215Z
UID:CRMDS/19
DESCRIPTION:Title: Some new kinds of automatic groups\nby Murray Elder (Sydney) as
part of Western Sydney University Abend Seminars\n\n\nAbstract\nI will des
cribe some generalisations of the notion of an automatic group\, and how f
ar they are away from automatic (in a precise sense). Relevant papers are
\nhttps://arxiv.org/abs/2008.02381 and https://arxiv.org/abs/2008.02511\n
LOCATION:https://stable.researchseminars.org/talk/CRMDS/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jason Bell (Waterloo)
DTSTART:20200924T100000Z
DTEND:20200924T110000Z
DTSTAMP:20260404T111215Z
UID:CRMDS/20
DESCRIPTION:Title: The growth of algebras\nby Jason Bell (Waterloo) as part of West
ern Sydney University Abend Seminars\n\n\nAbstract\nWe give an overview of
the theory of growth functions for associative algebras and explain their
significance when trying to understand algebras from a combinatorial poin
t of view. We then give a classification for which functions can occur as
the growth function of a finitely generated associative algebra up to asy
mptotic equivalence. This is joint work with Efim Zelmanov.\n
LOCATION:https://stable.researchseminars.org/talk/CRMDS/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Itamar Stein (Ashdod)
DTSTART:20201015T090000Z
DTEND:20201015T100000Z
DTSTAMP:20260404T111215Z
UID:CRMDS/21
DESCRIPTION:Title: Representation theory of the monoid of all partial functions on a se
t and other Ehresmann semigroups\nby Itamar Stein (Ashdod) as part of
Western Sydney University Abend Seminars\n\n\nAbstract\nGiven a finite sem
igroup S\, we can study its linear representations (for this talk - over t
he field of complex numbers). Semigroups with natural combinatorial struct
ure are clearly of major interest. An important example of such semigroup
is the monoid of all partial functions on an n element set\, denoted PT_n.
A description of its simple modules by induced left Schützenberger modul
es was obtained in the fifties by Munn and Ponizovskii as part of a more g
eneral work on the representation theory of finite semigroups. Unlike grou
p algebras\, semigroup algebras are seldom semisimple and therefore have (
none-semisimple) projective modules. We give a description of the indecomp
osable projective modules of PT_n which is similar in spirit to the Munn-P
onizovskii construction of the simple modules. Moreover\, we generalize bo
th results and describe the simple and the indecomposable projective modul
es of a certain class of Ehresmann semigroups\, with the case of PT_n bein
g a natural example. This is a joint work with Stuart Margolis.\n
LOCATION:https://stable.researchseminars.org/talk/CRMDS/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nora Szakacs (York)
DTSTART:20201022T090000Z
DTEND:20201022T100000Z
DTSTAMP:20260404T111215Z
UID:CRMDS/22
DESCRIPTION:Title: Simplicity of Nekrashevych algebras of contracting self-similar grou
ps\nby Nora Szakacs (York) as part of Western Sydney University Abend
Seminars\n\n\nAbstract\nA self-similar group is a group G acting on the in
finite |X|-regular rooted tree by automorphisms in such a way that the sel
f-similarity of the tree is reflected in the group. The most common exampl
es are generated by the states of a finite automaton. Many famous groups
like Grigorchuk's 2-group of intermediate growth are of this form. Nekrash
evych associated C*-algebras and algebras with coefficients in a field to
self-similar groups. In the case G is trivial\, the algebra is the classic
al Leavitt algebra. Nekrashevych showed that the algebra associated to the
Grigorchuk group is not simple in characteristic 2\, but Clark\, Exel\, P
ardo\, Sims and Starling showed its Nekrashevych algebra is simple over al
l other fields. Nekrashevych then showed that the algebra associated to th
e Grigorchuk-Erschler group is not simple over any field (the first such e
xample). The Grigorchuk and Grigorchuk-Erschler groups are contracting sel
f-similar groups. This important class of self-similar groups includes Gup
ta-Sidki p-groups and many iterated monodromy groups like the Basilica gro
up. Nekrashevych proved algebras associated to contracting groups are fini
tely presented.\nIn this talk we discuss the simplicity of Nekrashevych al
gebras of contracting groups. In particular\, we give an algorithm which\,
given an automaton generating the group\, outputs the characteristics ove
r which the algebra is non-simple. We apply our results to several familie
s of contracting groups like Sunic's generalizations of Grigorchuk's group
associated to polynomials over finite fields. This work is joint with B
enjamin Steinberg (City College of New York).\n
LOCATION:https://stable.researchseminars.org/talk/CRMDS/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nikolai Vavilov (St. Petersburg)
DTSTART:20201105T090000Z
DTEND:20201105T100000Z
DTSTAMP:20260404T111215Z
UID:CRMDS/23
DESCRIPTION:Title: 50 SHADES OF PROOF\nby Nikolai Vavilov (St. Petersburg) as part
of Western Sydney University Abend Seminars\n\n\nAbstract\nQui dit Mathém
atiques\, dit démonstration. The only problem is that there is no obvious
standard of proof\, common for different areas of mathematics at differen
t times.\n \nFor vast majority of mathematicians proofs are not mere texts
\, and are intimately\nrelated to individual and collective understanding.
From this viewpoint FORMAL\nPROOFS are not higher forms of traditional pr
oofs\, they ARE NOT mathematical\nPROOFS at all. Rather\, they play a role
of testimonies\, or experimental evidence\,\nurging us to find a real pro
of that might give such an understanding.\n \nI plan to discuss and illust
rate by a medley of historical examples of various\nlevels\, the differenc
e between proofs\, verifications\, and their intermediate\nforms\, as far
as their reliability\, transparency\, and durability.\n
LOCATION:https://stable.researchseminars.org/talk/CRMDS/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Julius Jonusas (Vienna)
DTSTART:20201029T090000Z
DTEND:20201029T100000Z
DTSTAMP:20260404T111215Z
UID:CRMDS/24
DESCRIPTION:Title: Canonical topologies for monoids\nby Julius Jonusas (Vienna) as
part of Western Sydney University Abend Seminars\n\n\nAbstract\nThe proble
m of determining which topologies are compatible with the multiplication a
nd inversion in a group has an extensive history that can be traced back t
o Markov. For example\, it has been shown by Gaughan in the 1960s that the
symmetric group on a countable set has a unique Polish topology which mak
es composition and inversion continuous. In the same way we will explore t
o what extent the algebraic structure of a monoid structure determines the
topologies which make the multiplication of the monoid continuous\, such
topologies are known as semigroup topologies. In particular\, we will inve
stigate which monoids have a unique Polish semigroup topology and which ha
ve automatic continuity. If M is a monoid equipped with a semigroup topolo
gy\, then automatic continuity\, in this context\, means that every homomo
rphsim from M to a second countable topological monoid is necessarily cont
inuous.\n
LOCATION:https://stable.researchseminars.org/talk/CRMDS/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tony Bak (Bielefeld)
DTSTART:20201029T100000Z
DTEND:20201029T110000Z
DTSTAMP:20260404T111215Z
UID:CRMDS/25
DESCRIPTION:Title: Solution to the sandwich classification problem in arbitrary groups
and applications to classical-like groups over arbitrary rings\nby Ton
y Bak (Bielefeld) as part of Western Sydney University Abend Seminars\n\n\
nAbstract\nLet G be an arbitrary group and F an arbitrary subgroup. For ea
ch mixed commutator subgroup K = [F\, H] of G\, we define the notion of an
F-cocommutator subgroup over K. The set of F-cocommutator subgroups over
K forms a sandwich of subgroups of G\, which is denoted by Sand(K). It ha
s a largest member C(K) called the full cocommutator subgroup over K and
if F is perfect then K is its smallest member. C(K) is the replacement in
the setting of arbitrary groups for the notion of full congruence subgroup
in the setting of classical-like groups over rings when F is the elementa
ry subgroup and the K's are replacements for the relative elementary subgr
oups of a classical-like group. The MAIN THEOREM is: A subgroup H of G i
s F-normal if and only if it belongs to a sandwich Sand(K) for some K. Mo
reover K is unique. We show that the known classification of E-normal subg
roups of a classical-like group G(R) over a quasi-finite ring R\, where E
is the elementary subgroup of G(R)\, is a consequence of the Main Theorem
and we use the Main Theorem to extend this result to classical-like grou
ps G(R) over an arbitrary ring R.\n
LOCATION:https://stable.researchseminars.org/talk/CRMDS/25/
END:VEVENT
END:VCALENDAR