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BEGIN:VEVENT
SUMMARY:Toke Carlsen (Faroe Islands)
DTSTART:20200514T100000Z
DTEND:20200514T110000Z
DTSTAMP:20260419T023046Z
UID:CRMDS/1
DESCRIPTION:Title: Gr
aph algebras\, groupoids\, and symbolic dynamics\nby Toke Carlsen (Far
oe Islands) as part of Western Sydney University Abend Seminars\n\n\nAbstr
act\nI will give an overview of some recent results that link diagonal-pre
serving isomorphism of graph algebras and isomorphism and equivalence of g
raph groupoids with continuous orbit equivalence\, (eventual) conjugacy\,
and flow equivalence of symbolic dynamical systems constructed from direct
ed graphs.\n
LOCATION:https://researchseminars.org/talk/CRMDS/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mark Lawson (Heriot-Watt University)
DTSTART:20200521T100000Z
DTEND:20200521T110000Z
DTSTAMP:20260419T023046Z
UID:CRMDS/2
DESCRIPTION:Title: No
n-commutative Stone dualities\nby Mark Lawson (Heriot-Watt University)
as part of Western Sydney University Abend Seminars\n\n\nAbstract\nThe cl
assical Stone dualities for lattices such as frames\, distributive lattice
s and generalized Boolean algebras can be generalized to a non-commutative
setting to pseudogroups\, distributive inverse semigroups and Boolean inv
erse semigroups\, respectively.\nThe goal of this talk is to sketch out th
e how and to motivate the why.\nI shall not assume any background from inv
erse semigroups or \\'etale groupoids.\n
LOCATION:https://researchseminars.org/talk/CRMDS/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Enrique Pardo Espino (Cadiz)
DTSTART:20200528T100000Z
DTEND:20200528T110000Z
DTSTAMP:20260419T023046Z
UID:CRMDS/3
DESCRIPTION:Title: Se
lf-similar graphs and their algebras\nby Enrique Pardo Espino (Cadiz)
as part of Western Sydney University Abend Seminars\n\n\nAbstract\nIn this
talk\, we will explain the origins of the notion of self-similar graph. W
e\ngive a groupoid model of the algebra associated to a self-similar graph
and we provide a characterization of simplicity for these algebras. We br
iefly talk about further developments on this construction.\nThe contents
of this talk are part of a joint paper with R. Exel.\n
LOCATION:https://researchseminars.org/talk/CRMDS/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mike Whittaker (Glasgow)
DTSTART:20200604T100000Z
DTEND:20200604T110000Z
DTSTAMP:20260419T023046Z
UID:CRMDS/4
DESCRIPTION:Title: Ap
eriodic tilings: from the Domino problem to aperiodic monotiles\nby Mi
ke Whittaker (Glasgow) as part of Western Sydney University Abend Seminars
\n\n\nAbstract\nAlmost 60 years ago\, Hao Wang posed the Domino Problem: i
s there an algorithm that determines whether a given set of square prototi
les\, with specified matching rules\, can tile the plane? Robert Berger pr
oved the undecidability of the Domino Problem by producing a set of 20\,42
6 prototiles that tile the plane\, but any such tiling is nonperiodic (lac
ks any translational symmetry). This remarkable discovery began the search
for other (not necessarily square) aperiodic prototile sets\, a finite co
llection of prototiles that tile the plane but only nonperiodically. In th
e 1970s\, Roger Penrose reduced this number to two. Penrose's discovery le
d to the planar einstein (one-stone) problem: is there a single aperiodic
prototile? In a crowning achievement of tiling theory\, the existence of a
n aperiodic monotile was resolved almost a decade ago by Joshua Socolar an
d Joan Taylor. My talk will be somewhat expository\, and culminate in both
a new direction in aperiodic tiling theory and a new aperiodic monotile.\
n
LOCATION:https://researchseminars.org/talk/CRMDS/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kevin Brix (Wollongong/Copenhagen)
DTSTART:20200611T100000Z
DTEND:20200611T110000Z
DTSTAMP:20260419T023046Z
UID:CRMDS/5
DESCRIPTION:Title: Fi
ne structure of C*-algebras associated to topological dynamics\nby Kev
in Brix (Wollongong/Copenhagen) as part of Western Sydney University Abend
Seminars\n\n\nAbstract\nI will report on the story of associating C*-alge
bras to symbolic dynamical systems (e.g. shift spaces or directed graphs)
and the recently articulated program of understanding dynamical relations
(such as conjugacy or flow equivalence) in terms of structure-preserving *
-isomorphisms of the corresponding C*-algebras. A large body of rigidity r
esults have successfully been obtained for graphs and more general systems
. There will be an emphasis on open questions and problems yet to be solve
d!\n
LOCATION:https://researchseminars.org/talk/CRMDS/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Joan Bosa (Barcelona)
DTSTART:20200618T100000Z
DTEND:20200618T110000Z
DTSTAMP:20260419T023046Z
UID:CRMDS/6
DESCRIPTION:Title: Th
e realization problem for von Neumann regular rings\nby Joan Bosa (Bar
celona) as part of Western Sydney University Abend Seminars\n\n\nAbstract\
nThe realization problem for von Neumann (vN) regular rings asks whether a
ll conical refinement monoids arise from monoids induced by the projective
modules over a vN regular ring? We will quickly overview this problem and
show the last developments on it? This is joint work with PAra\, E.Pardo
and \nA.Sims.\n
LOCATION:https://researchseminars.org/talk/CRMDS/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Aidan Sims (Wollongong)
DTSTART:20200702T100000Z
DTEND:20200702T110000Z
DTSTAMP:20260419T023046Z
UID:CRMDS/7
DESCRIPTION:Title: Gr
aded K-theory for Z_2-graded graph C*-algebras\nby Aidan Sims (Wollong
ong) as part of Western Sydney University Abend Seminars\n\n\nAbstract\nWh
ile 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 cele
brated KK-bifunctor: KK is naturally a Z_2-graded theory\, and Kasparov pr
oved 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 general. I wi
ll discuss recent work with Adam Sierakowski and with honours students Qui
nn Patterson and Jonathan Taylor\, building on previous work with Kumjian
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-grading
s determined by binary labellings of the edges of the graph: the formulas
that emerge strongly suggest that this notion of graded K-theory captures
the right sort of information.\n
LOCATION:https://researchseminars.org/talk/CRMDS/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Xiao-Wu Chen (Hefei)
DTSTART:20200709T100000Z
DTEND:20200709T110000Z
DTSTAMP:20260419T023046Z
UID:CRMDS/8
DESCRIPTION:Title: Le
avitt path algebra via the singularity category of a radical-square-zero a
lgebra\nby Xiao-Wu Chen (Hefei) as part of Western Sydney University A
bend Seminars\n\n\nAbstract\nWe will recall some previous work primarily b
y Paul Smith\, and show that the Leavitt path algebra \nis closely related
to the singularity category of a finite dimensional radical-square-zero a
lgebra. Recently\, we apply such a link to confirm Keller's conjecture for
a radical-square-zero algebra. More precisely\, we prove that for such an
algebra\, the singular Hochschild cochain complex is B_\\infinity-isomorp
hic to the Hochschild cochain complex of the dg singularity category. This
is based on a joint work with Huanhuan Li and Zhengfang Wang.\n
LOCATION:https://researchseminars.org/talk/CRMDS/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jean Renault (d'Orleans)
DTSTART:20200716T100000Z
DTEND:20200716T110000Z
DTSTAMP:20260419T023046Z
UID:CRMDS/9
DESCRIPTION:Title: Gr
oupoids Extensions\nby Jean Renault (d'Orleans) as part of Western Syd
ney University Abend Seminars\n\n\nAbstract\nI shall present a groupoid ve
rsion of the Mackey normal subgroup analysis in a C*-algebraic framework.
More precisely\, the main result is a description of the C*-algebra of a l
ocally compact groupoid with Haar system\, possibly endowed with a twist\,
which is an extension by a group bundle. The natural expression of this r
esult uses Fell bundles over groupoids. When the group bundle is abelian\,
one obtains a twisted groupoid C*-algebra. I will give some applications.
This talk is based on a joint work with M.Ionescu\, A.Kumjian\, A.Sims an
d D.Williams.\n
LOCATION:https://researchseminars.org/talk/CRMDS/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pere Ara (Barcelona)
DTSTART:20200625T100000Z
DTEND:20200625T110000Z
DTSTAMP:20260419T023046Z
UID:CRMDS/10
DESCRIPTION:Title: G
raded K-Theory\, Filtered K-theory and the classification of graph algebra
s\nby Pere Ara (Barcelona) as part of Western Sydney University Abend
Seminars\n\n\nAbstract\nWe prove that an isomorphism of graded Grothendie
ck groups of two Leavitt path algebras induces an isomorphism of a certai
n quotient of algebraic filtered K-theory and consequently an isomorphism
of filtered K-theory of their associated graph C*-algebras. As an applicat
ion\, we show that\, since for a finite graph E with no sinks\, the graded
Grothendieck group of L(E) coincides with Krieger's dimension group of it
s adjacency matrix\, our result relates the shift equivalence of graphs to
the filtered K-theory and consequently gives that two arbitrary shift equ
ivalent matrices give stably isomorphic graph C*-algebras. This result was
only known for irreducible graphs. This is a joint work with Roozbeh Hazr
at and Huanhuan Li\n
LOCATION:https://researchseminars.org/talk/CRMDS/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Be'eri Greenfeld (Bar Ilan)
DTSTART:20200723T100000Z
DTEND:20200723T110000Z
DTSTAMP:20260419T023046Z
UID:CRMDS/11
DESCRIPTION:Title: H
ow do algebras grow?\nby Be'eri Greenfeld (Bar Ilan) as part of Wester
n Sydney University Abend Seminars\n\n\nAbstract\nThe question of `how do
algebras grow?'\, or\, which functions can be realized as growth functions
of algebras (associative/Lie/etc.\, or algebras having certain additional
algebraic properties) is a major problem in the junction of several mathe
matical fields\, including noncommutative algebra\, combinatorics of (infi
nite) words\, symbolic dynamics\, self-similarity and more.\nWe provide a
novel paradigm for tackling this problem (in fact\, family of problems)\,
thereby resolving several open problems posed by experts regarding possibl
e growth types of finitely generated associative algebras and Lie algebras
.\nWe also consider the set of growth functions as a space\, and point out
odd properties it admits (arbitrarily rapid holes\, and convergence to ou
ter points - with respect to some plausible notion of limits).\n
LOCATION:https://researchseminars.org/talk/CRMDS/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Arun Ram (Melbourne)
DTSTART:20200730T100000Z
DTEND:20200730T110000Z
DTSTAMP:20260419T023046Z
UID:CRMDS/12
DESCRIPTION:Title: T
eaching Mathematics in the next life\nby Arun Ram (Melbourne) as 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 inspir
ation.\nThis has resulted in ideas like "reality teaching"\, "proof machin
e"\, \n"marking apocalypse" and "just do it". And then a virus came\, \na
nd the new life began\, online\, on Zoom. This will be a talk about\nthe
adventures of the past life and the preparations\nfor the next.\n
LOCATION:https://researchseminars.org/talk/CRMDS/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bob Gray (East Anglia)
DTSTART:20200806T100000Z
DTEND:20200806T110000Z
DTSTAMP:20260419T023046Z
UID:CRMDS/13
DESCRIPTION:Title: U
ndecidability of the word problem for one-relator inverse monoids\nby
Bob Gray (East Anglia) as part of Western Sydney University Abend Seminars
\n\n\nAbstract\nIt is a classical result of Magnus proved in the 1930s tha
t the word problem is decidable for one-relator groups. This result inspir
ed a series of investigations of the word problem in other one-relator alg
ebraic structures. For example\, in the 1960s Shirshov proved the word pro
blem is decidable in one-relator Lie algebras. In contrast\, it remains a
longstanding open problem whether the word problem is decidable for one-re
lator 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 inverse mon
oids of the form Inv with undecidable word problem. This answers 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 monoid
s\, the submonoid membership problem for one-relator groups\, and to the q
uestion of which right-angled Artin groups arise as subgroups of one-relat
or groups.\n
LOCATION:https://researchseminars.org/talk/CRMDS/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jose Burillo (Barcelona)
DTSTART:20200820T100000Z
DTEND:20200820T110000Z
DTSTAMP:20260419T023046Z
UID:CRMDS/14
DESCRIPTION:Title: T
he irrational-slope Thompson's groups\nby Jose Burillo (Barcelona) as
part of Western Sydney University Abend Seminars\n\n\nAbstract\nJosé Buri
llo (Universitat Politècnica de Catalunya)\n\nTitle: The irrational-slope
Thompson's groups\n\nAbstract: Irrational-slope Thompson's groups were in
troduced by Cleary in two papers in 1995 and 2000\, where he proved they a
re FP_\\infty. These are groups of PL maps of [0\,1] whose breakpoints are
in some irrational subring of R and the slopes are also irrational number
s. Interest in these groups grew recently when it was asked whether they c
an be obtained as subgroups of Thompson's group F. In this paper we will i
ntroduce the golden ratio group F_\\tau\, describe how to work with it in
terms of binary trees and also algebraically. We will show a presentation
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 words abou
t the irrational versions of Thompson's groups T and V. This is joint work
with Brita Nucinkis and Lawrence Reeves.\n
LOCATION:https://researchseminars.org/talk/CRMDS/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Cristobal Gil Canto (Malaga)
DTSTART:20200813T100000Z
DTEND:20200813T110000Z
DTSTAMP:20260419T023046Z
UID:CRMDS/15
DESCRIPTION:Title: I
nvariant ideals in Leavitt path algebras\nby Cristobal Gil Canto (Mala
ga) as part of Western Sydney University Abend Seminars\n\n\nAbstract\nAs
well-known examples of Leavitt path algebras arise the so-called primary c
olours: they respectively correspond to the ideal generated by the set of
line points\, the vertices that lie on cycles without exits and the one ge
nerated by the set in extreme cycles. It is known that these ideals are in
variant under isomorphism. In this talk we will analyze the invariance of
another key piece of a Leavitt path algebra. We will see that though the i
deal generated by the vertices whose tree contains infinitely many bifurca
tion vertices or at least one infinite emitter is not invariant\, we will
find its natural replacement (which is indeed invariant). We will also giv
e some procedures to construct invariant ideals from previous known invari
ant ideals. In order to do that\, on the one hand\, we will introduce a to
pology in the set of vertices of a graph. And on the other hand\, via cate
gory theory\, we will think of the saturated and hereditary set of a graph
as a functor. This a joint work together with Dolores Martín Barquero an
d Cándido Martín González.\n
LOCATION:https://researchseminars.org/talk/CRMDS/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ralf Meyer (Goettingen)
DTSTART:20200827T100000Z
DTEND:20200827T110000Z
DTSTAMP:20260419T023046Z
UID:CRMDS/16
DESCRIPTION:Title: A
periodicity and related properties for crossed product inclusions\nby
Ralf Meyer (Goettingen) as part of Western Sydney University Abend Seminar
s\n\n\nAbstract\nIn recent work with Bartosz Kwa?niewski\, we have vastly
generalised the condition that was introduced by Kishimoto in order to pro
ve that reduced crossed products for outer group actions on simple C*-alge
bras are again simple. We call this condition aperiodicity\, and it appli
es to arbitrary inclusions of C*-algebras\, without requiring a crossed pr
oduct structure. We relate this to topological non-triviality conditions
in the special case of actions of inverse semigroups or étale groupoids (
which are possibly non-Hausdorff). In that generality\, we define an esse
ntial crossed product\, which is a quotient of the reduced crossed product
. If the action satisfies Kishimoto's condition\, then the coefficient al
gebra detects ideals in this essential crossed product. And in the simple
case\, we also get criteria for the essential crossed product to be simpl
e. We also relate aperiodicity to other properties that have been used to
study the ideal structure of crossed products. This includes unique pseu
do-expectations and the almost extension property\, which assume that the
set of pure states on the coefficient algebra that extend uniquely to the
crossed product is dense.\n
LOCATION:https://researchseminars.org/talk/CRMDS/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lia Vas (Philadelphia)
DTSTART:20200903T100000Z
DTEND:20200903T110000Z
DTSTAMP:20260419T023046Z
UID:CRMDS/17
DESCRIPTION:Title: T
he Graded Classification Conjecture for graph algebras\nby Lia Vas (Ph
iladelphia) as part of Western Sydney University Abend Seminars\n\n\nAbstr
act\nThe ordinary (pointed) K_0-group is not a complete invariant of algeb
ras typically associated to a directed graph. When these algebras are cons
idered as graded algebras and the definition of the K_0-group is adjusted
to reflect the existence of this grading\, the situation becomes more inte
resting. The Graded Classification Conjecture states that this adjusted ve
rsion of the (pointed) K_0-group is a complete invariant of a Leavitt path
algebra over a field (and this statement can be adapted for other graph a
lgebras). We shall discuss the context in which this conjecture has been f
ormulated\, the current status of the conjecture\, and some ongoing resear
ch.\n
LOCATION:https://researchseminars.org/talk/CRMDS/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Volodymyr Mazorchuk (Uppsala)
DTSTART:20200910T100000Z
DTEND:20200910T110000Z
DTSTAMP:20260419T023046Z
UID:CRMDS/18
DESCRIPTION:Title: A
djunction in the absence of identity\nby Volodymyr Mazorchuk (Uppsala)
as part of Western Sydney University Abend Seminars\n\n\nAbstract\nIn thi
s talk I plan to present and discuss a rather\nweak bicategorical setup in
which one can talk about\ngenuine adjunctions. I will roughly describe th
e\nmain motivation coming from representation theory of\nfinitary 2-catego
ries (or bicategories) and make some parallells with the structure theory
of finite\nsemigroups. I will try to explain how this approach\nsimplifies
some results but also makes some other\nresults much more difficult. This
is a joint work with Hankyung Ko and Xiaoting Zhang.\n
LOCATION:https://researchseminars.org/talk/CRMDS/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Murray Elder (Sydney)
DTSTART:20200917T100000Z
DTEND:20200917T110000Z
DTSTAMP:20260419T023046Z
UID:CRMDS/19
DESCRIPTION:Title: S
ome new kinds of automatic groups\nby Murray Elder (Sydney) as part of
Western Sydney University Abend Seminars\n\n\nAbstract\nI will describe s
ome generalisations of the notion of an automatic group\, and how far 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://researchseminars.org/talk/CRMDS/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jason Bell (Waterloo)
DTSTART:20200924T100000Z
DTEND:20200924T110000Z
DTSTAMP:20260419T023046Z
UID:CRMDS/20
DESCRIPTION:Title: T
he growth of algebras\nby Jason Bell (Waterloo) as part of Western Syd
ney University Abend Seminars\n\n\nAbstract\nWe give an overview of the th
eory of growth functions for associative algebras and explain their signif
icance when trying to understand algebras from a combinatorial point of vi
ew. We then give a classification for which functions can occur as the gr
owth function of a finitely generated associative algebra up to asymptotic
equivalence. This is joint work with Efim Zelmanov.\n
LOCATION:https://researchseminars.org/talk/CRMDS/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Itamar Stein (Ashdod)
DTSTART:20201015T090000Z
DTEND:20201015T100000Z
DTSTAMP:20260419T023046Z
UID:CRMDS/21
DESCRIPTION:Title: R
epresentation theory of the monoid of all partial functions on a set and o
ther Ehresmann semigroups\nby Itamar Stein (Ashdod) as part of Western
Sydney University Abend Seminars\n\n\nAbstract\nGiven a finite semigroup
S\, we can study its linear representations (for this talk - over the fiel
d of complex numbers). Semigroups with natural combinatorial structure 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 desc
ription of its simple modules by induced left Schützenberger modules was
obtained in the fifties by Munn and Ponizovskii as part of a more general
work on the representation theory of finite semigroups. Unlike group algeb
ras\, semigroup algebras are seldom semisimple and therefore have (none-se
misimple) projective modules. We give a description of the indecomposable
projective modules of PT_n which is similar in spirit to the Munn-Ponizovs
kii construction of the simple modules. Moreover\, we generalize both resu
lts and describe the simple and the indecomposable projective modules of a
certain class of Ehresmann semigroups\, with the case of PT_n being a nat
ural example. This is a joint work with Stuart Margolis.\n
LOCATION:https://researchseminars.org/talk/CRMDS/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nora Szakacs (York)
DTSTART:20201022T090000Z
DTEND:20201022T100000Z
DTSTAMP:20260419T023046Z
UID:CRMDS/22
DESCRIPTION:Title: S
implicity of Nekrashevych algebras of contracting self-similar groups\
nby Nora Szakacs (York) as part of Western Sydney University Abend Seminar
s\n\n\nAbstract\nA self-similar group is a group G acting on the infinite
|X|-regular rooted tree by automorphisms in such a way that the self-simil
arity of the tree is reflected in the group. The most common examples are
generated by the states of a finite automaton. Many famous groups like Gr
igorchuk's 2-group of intermediate growth are of this form. Nekrashevych a
ssociated C*-algebras and algebras with coefficients in a field to self-si
milar groups. In the case G is trivial\, the algebra is the classical Leav
itt algebra. Nekrashevych showed that the algebra associated to the Grigor
chuk group is not simple in characteristic 2\, but Clark\, Exel\, Pardo\,
Sims and Starling showed its Nekrashevych algebra is simple over all other
fields. Nekrashevych then showed that the algebra associated to the Grigo
rchuk-Erschler group is not simple over any field (the first such example)
. The Grigorchuk and Grigorchuk-Erschler groups are contracting self-simil
ar groups. This important class of self-similar groups includes Gupta-Sidk
i p-groups and many iterated monodromy groups like the Basilica group. Nek
rashevych proved algebras associated to contracting groups are finitely pr
esented.\nIn this talk we discuss the simplicity of Nekrashevych algebras
of contracting groups. In particular\, we give an algorithm which\, given
an automaton generating the group\, outputs the characteristics over which
the algebra is non-simple. We apply our results to several families of co
ntracting groups like Sunic's generalizations of Grigorchuk's group associ
ated to polynomials over finite fields. This work is joint with Benjamin
Steinberg (City College of New York).\n
LOCATION:https://researchseminars.org/talk/CRMDS/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nikolai Vavilov (St. Petersburg)
DTSTART:20201105T090000Z
DTEND:20201105T100000Z
DTSTAMP:20260419T023046Z
UID:CRMDS/23
DESCRIPTION:Title: 5
0 SHADES OF PROOF\nby Nikolai Vavilov (St. Petersburg) as part of West
ern Sydney University Abend Seminars\n\n\nAbstract\nQui dit Mathématiques
\, dit démonstration. The only problem is that there is no obvious standa
rd of proof\, common for different areas of mathematics at different times
.\n \nFor vast majority of mathematicians proofs are not mere texts\, and
are intimately\nrelated to individual and collective understanding. From t
his viewpoint FORMAL\nPROOFS are not higher forms of traditional proofs\,
they ARE NOT mathematical\nPROOFS at all. Rather\, they play a role of tes
timonies\, or experimental evidence\,\nurging us to find a real proof that
might give such an understanding.\n \nI plan to discuss and illustrate by
a medley of historical examples of various\nlevels\, the difference betwe
en proofs\, verifications\, and their intermediate\nforms\, as far as thei
r reliability\, transparency\, and durability.\n
LOCATION:https://researchseminars.org/talk/CRMDS/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Julius Jonusas (Vienna)
DTSTART:20201029T090000Z
DTEND:20201029T100000Z
DTSTAMP:20260419T023046Z
UID:CRMDS/24
DESCRIPTION:Title: C
anonical topologies for monoids\nby Julius Jonusas (Vienna) as part of
Western Sydney University Abend Seminars\n\n\nAbstract\nThe problem of de
termining which topologies are compatible with the multiplication and inve
rsion in a group has an extensive history that can be traced back to Marko
v. For example\, it has been shown by Gaughan in the 1960s that the symmet
ric group on a countable set has a unique Polish topology which makes comp
osition and inversion continuous. In the same way we will explore to what
extent the algebraic structure of a monoid structure determines the topolo
gies which make the multiplication of the monoid continuous\, such topolog
ies are known as semigroup topologies. In particular\, we will investigate
which monoids have a unique Polish semigroup topology and which have auto
matic continuity. If M is a monoid equipped with a semigroup topology\, th
en automatic continuity\, in this context\, means that every homomorphsim
from M to a second countable topological monoid is necessarily continuous.
\n
LOCATION:https://researchseminars.org/talk/CRMDS/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tony Bak (Bielefeld)
DTSTART:20201029T100000Z
DTEND:20201029T110000Z
DTSTAMP:20260419T023046Z
UID:CRMDS/25
DESCRIPTION:Title: S
olution to the sandwich classification problem in arbitrary groups and app
lications to classical-like groups over arbitrary rings\nby Tony Bak (
Bielefeld) as part of Western Sydney University Abend Seminars\n\n\nAbstra
ct\nLet G be an arbitrary group and F an arbitrary subgroup. For each mixe
d commutator subgroup K = [F\, H] of G\, we define the notion of an F-coco
mmutator 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 has a la
rgest 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 set
ting of arbitrary groups for the notion of full congruence subgroup in the
setting of classical-like groups over rings when F is the elementary subg
roup and the K's are replacements for the relative elementary subgroups of
a classical-like group. The MAIN THEOREM is: A subgroup H of G is F-nor
mal if and only if it belongs to a sandwich Sand(K) for some K. Moreover
K is unique. We show that the known classification of E-normal subgroups o
f 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 w
e use the Main Theorem to extend this result to classical-like groups G(R)
over an arbitrary ring R.\n
LOCATION:https://researchseminars.org/talk/CRMDS/25/
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