BEGIN:VCALENDAR
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BEGIN:VEVENT
SUMMARY:Erhard Aichinger (JKU Linz\, Austria)
DTSTART:20210216T200000Z
DTEND:20210216T210000Z
DTSTAMP:20260422T212710Z
UID:PALS/1
DESCRIPTION:Title: The
degree as a measure of complexity of functions on a universal algebra
\nby Erhard Aichinger (JKU Linz\, Austria) as part of PALS Panglobal Algeb
ra and Logic Seminar\n\n\nAbstract\nThe degree of a function $f$ between t
wo abelian groups has been\ndefined as the smallest natural number $d$ suc
h that\n$f$ vanishes after $d+1$ applications\nof any of the difference op
erators $\\Delta_a$ defined by\n$\\Delta_a * f \\\,\\\, (x) = f(x+a) - f(x
)$.\nFunctions of finite degree have also been called\ngeneralized polynom
ials or solutions to Frechet's functional\n equations. A pivotal result b
y A. Leibman (2002) is that $\\deg (f \\circ g) \\le \\deg(f) \\cdot\n\\de
g (g)$.\nWe show how results on the degree can be used\n(i) to get lower b
ounds on the number of solutions of equations\, and\n(ii) to connect nilpo
tency and supernilpotency.\nThis leads to generalizations of the Chevalley
-Warning Theorems\nto abelian groups\, a group version of the Ax-Katz Theo
rem on\nthe number of zeros of polynomial functions\, and a computable\n$f
$ such that all finite $k$-nilpotent algebras of prime power order\nin con
gruence modular varieties are $f(k\, .)$-supernilpotent.\n
LOCATION:https://researchseminars.org/talk/PALS/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kristina Asimi (Charles University Prague)
DTSTART:20210223T200000Z
DTEND:20210223T210000Z
DTSTAMP:20260422T212710Z
UID:PALS/2
DESCRIPTION:Title: Fin
itely tractable PCSPs\nby Kristina Asimi (Charles University Prague) a
s part of PALS Panglobal Algebra and Logic Seminar\n\n\nAbstract\nThe Prom
ise Constraint Satisfaction Problem (PCSP) is a generalization of the Cons
traint Satisfaction Problem (CSP). In a [LICS '19] paper it was shown that
a specific PCSP\, the problem to find a valid Not-All-Equal solution to a
1-in-3-SAT instance\, is not finitely tractable in that it can be solved
by a trivial reduction to a tractable CSP\, but such a CSP is necessarily
over an infinite domain (unless P=NP). We further explore this phenomenon:
we give a general necessary condition for finite tractability and charact
erize finite tractability within a class of templates - the "basic" tracta
ble cases in the dichotomy theorem for symmetric Boolean PCSPs allowing ne
gations by Brakensiek and Guruswami [SODA'18]. This is a joint work with L
ibor Barto.\n
LOCATION:https://researchseminars.org/talk/PALS/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrei Bulatov (Simon Fraser University)
DTSTART:20210302T200000Z
DTEND:20210302T210000Z
DTSTAMP:20260422T212710Z
UID:PALS/3
DESCRIPTION:Title: Iso
morphisms\, homomorphisms\, and some algebra\nby Andrei Bulatov (Simon
Fraser University) as part of PALS Panglobal Algebra and Logic Seminar\n\
n\nAbstract\nWe give a survey on connections between Graph Isomorphism\, t
he CSP\, and counting homomorphisms. In the first part we give a brief rev
iew of the main approaches to solving the Graph Isomorphism problem and ma
ke some observations on how the CSP techniques can be helpful. In the seco
nd part we focus on relaxations of graph isomorphisms and how they can be
characterized using the numbers of homomorphisms from various graph classe
s.\n
LOCATION:https://researchseminars.org/talk/PALS/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lexi V. Pasi (Baylor University)
DTSTART:20210309T200000Z
DTEND:20210309T210000Z
DTSTAMP:20260422T212710Z
UID:PALS/4
DESCRIPTION:Title: For
cing $\\aleph_1$-Free Groups to Be Free\nby Lexi V. Pasi (Baylor Unive
rsity) as part of PALS Panglobal Algebra and Logic Seminar\n\n\nAbstract\n
$\\aleph_1$-free groups\, abelian groups whose countable subgroups are fre
e\, are objects of both algebraic and set-theoretic interest. Illustrating
this\, we note that $\\aleph_1$-free groups\, and in particular the quest
ion of when $\\aleph_1$-free groups are free\, were central to the resolut
ion of the Whitehead problem as undecidable. In elucidating the relationsh
ip between $\\aleph_1$-freeness and freeness\, we prove the following resu
lt: an abelian group $G$ is $\\aleph_1$-free in a countable transitive mod
el of $\\operatorname{ZFC}$ (and thus by absoluteness\, in every transitiv
e model of $\\operatorname{ZFC}$) if and only if it is free in some generi
c model extension. We would like to answer the more specific question of w
hen an $\\aleph_1$-free group can be forced to be free while preserving th
e cardinality of the group. For groups of size $\\aleph_1$\, we establish
a necessary and sufficient condition for when such forcings are possible.
We also identify a number of existing and novel forcings which force such
$\\aleph_1$-free groups of size $\\aleph_1$ to become free with cardinal p
reservation. These forcings lay the groundwork for a larger project which
uses forcing to explore various algebraic properties of $\\aleph_1$-free g
roups and develops new set-theoretical tools for working with them.\n
LOCATION:https://researchseminars.org/talk/PALS/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Matthew Moore (University of Kansas)
DTSTART:20210316T190000Z
DTEND:20210316T200000Z
DTSTAMP:20260422T212710Z
UID:PALS/5
DESCRIPTION:Title: The
Hidden Subgroup Problem for universal algebras\nby Matthew Moore (Uni
versity of Kansas) as part of PALS Panglobal Algebra and Logic Seminar\n\n
\nAbstract\nThe Hidden Subgroup Problem (HSP) is a computational problem w
hich includes as\nspecial cases integer factorization\, the discrete logar
ithm problem\, graph\nisomorphism\, and the shortest vector problem. The c
elebrated polynomial-time\nquantum algorithms for factorization and the di
screte logarithm are restricted\nversions of a generic polynomial-time qua
ntum solution to the HSP for abelian\ngroups\, but despite focused researc
h no polynomial-time solution for general\ngroups has yet been found. We p
ropose a generalization of the HSP to include\narbitrary algebraic structu
res and analyze this new problem on powers of\n2-element algebras. We prov
e a complete classification of every such power as\nquantum tractable (i.e
. polynomial-time)\, classically tractable\, quantum\nintractable\, or cla
ssically intractable. In particular\, we identify a class of\nalgebras for
which the generalized HSP exhibits super-polynomial speedup on a\nquantum
computer compared to a classical one.\n
LOCATION:https://researchseminars.org/talk/PALS/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrew Moorhead (University of Kansas)
DTSTART:20210323T190000Z
DTEND:20210323T200000Z
DTSTAMP:20260422T212710Z
UID:PALS/6
DESCRIPTION:Title: Hig
her Kiss terms for modular varieties\nby Andrew Moorhead (University o
f Kansas) as part of PALS Panglobal Algebra and Logic Seminar\n\n\nAbstrac
t\nWe explain how the 4-ary Kiss term for a modular variety can be compose
d with itself to produce an infinite sequence of terms\, each having a con
nection to a particular arity higher commutator that mimics the connection
that the Kiss term has to the binary modular commutator. We will then dis
cuss how these terms can be used to show that there is a greatest clone am
ong those that share a sequence of Day terms\, congruences\, and higher co
mmutator operations.\n
LOCATION:https://researchseminars.org/talk/PALS/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexander Hulpke (Colorado State)
DTSTART:20210427T190000Z
DTEND:20210427T200000Z
DTSTAMP:20260422T212710Z
UID:PALS/7
DESCRIPTION:Title: Rew
riting systems and group extensions\nby Alexander Hulpke (Colorado Sta
te) as part of PALS Panglobal Algebra and Logic Seminar\n\n\nAbstract\nThe
first examples of groups in a textbook are often as words in generators\,
subject to some easy rules. This seems nice and natural\, but gets quickl
y abandoned once the groups involved become more complicated. A similar di
sappointment happens when introducing group extensions: Examples in textbo
oks never go beyond easy cases such as cyclic groups or split extensions.\
nBut this is not intended to whine about textbooks. Instead I want to show
how a systematic approach to normal form words (namely confluent rewritin
g systems) can be used to describe group extension (and explicitly compute
2-cohomology)\, resulting in practically useful (and implemented!) algori
thms.\n
LOCATION:https://researchseminars.org/talk/PALS/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marcin Kozik (University of Krakow)
DTSTART:20210330T190000Z
DTEND:20210330T200000Z
DTSTAMP:20260422T212710Z
UID:PALS/8
DESCRIPTION:Title: Min
imal (clones with a Taylor term)\nby Marcin Kozik (University of Krako
w) as part of PALS Panglobal Algebra and Logic Seminar\n\n\nAbstract\nWe a
re working with clones\, on finite sets\, which contain a Taylor operation
. Ordering all of them by inclusion\, we focus on the elements minimal in
that order. We show that the class is robust and provide a few examples of
very strong properties holding in these clones.\n\nJoint work with L. Bar
to\, Z. Brady\, A. Bulatov\, D. Zhuk.\n
LOCATION:https://researchseminars.org/talk/PALS/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nick Galatos (University of Denver)
DTSTART:20210406T190000Z
DTEND:20210406T200000Z
DTSTAMP:20260422T212710Z
UID:PALS/9
DESCRIPTION:Title: Ama
lgamation for certain conic idempotent residuated lattices\nby Nick Ga
latos (University of Denver) as part of PALS Panglobal Algebra and Logic S
eminar\n\n\nAbstract\nResiduated lattices were introduced by Ward and Dilw
orth as tools in the study of ideal lattices of rings. Residuated lattices
have a monoid and a lattice reduct\, as well as division-like operations\
; examples include Boolean algebras\, lattice-ordered groups and relation
algebras. Also\, they form algebraic semantics for substructural logics an
d are connected to mathematical linguistics and computer science (for exam
ple pointer management and memory allocation). We focus on a class of resi
duated lattices that have an idempotent multiplication and all elements ar
e comparable to the monoid identity\; these are related to algebraic model
s of relevance logic. After establishing a decomposition result for this c
lass\, we show that it has the strong amalgamation property\, and extend t
he result to the variety generated by this class\; this implies that the c
orresponding logic has the interpolation property and Beth definability.\n
LOCATION:https://researchseminars.org/talk/PALS/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marcos Mazari-Armida (Carnegie Mellon University)
DTSTART:20210413T190000Z
DTEND:20210413T200000Z
DTSTAMP:20260422T212710Z
UID:PALS/10
DESCRIPTION:Title: St
ability in abstract elementary classes of modules\nby Marcos Mazari-Ar
mida (Carnegie Mellon University) as part of PALS Panglobal Algebra and Lo
gic Seminar\n\n\nAbstract\nAbstract elementary classes (AECs for short) we
re introduced by Shelah in the seventies to study those classes of structu
res that can not be axiomatized by a first-order theory. In this talk\, we
will introduce the basic notions of AECs and showcase them in classes of
modules. In particular\, we will explore if every AEC of modules with pure
embeddings is stable. Using that the class of p-groups with pure embeddin
gs is a stable AEC\, we will present a solution to a problem of László F
uchs.\n
LOCATION:https://researchseminars.org/talk/PALS/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ross Willard (University of Waterloo)
DTSTART:20210420T190000Z
DTEND:20210420T200000Z
DTSTAMP:20260422T212710Z
UID:PALS/11
DESCRIPTION:Title: In
herently nonfinitely based nonassociative algebras\nby Ross Willard (U
niversity of Waterloo) as part of PALS Panglobal Algebra and Logic Seminar
\n\n\nAbstract\nThis is a progress report on an exploration of Isaev's alg
ebras and their cousins. Isaev's algebras were the first\, and remain the
only\, known examples of inherently nonfinitely based finite algebras in M
altsev varieties. In this talk I will describe a class of finite algebras
containing Isaev's algebras\, and explain some basic tools that we have de
veloped to help determine which of these algebras are inherently nonfinite
ly based. At the moment we are only able to apply these tools to Isaev's a
lgebras themselves\, but that won’t stop me from filling the 50-minute t
ime slot which I have been offered! This is joint work with Emily Carlson\
, Mehul Gupta and George McNulty.\n
LOCATION:https://researchseminars.org/talk/PALS/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Peter Mayr (CU Boulder)
DTSTART:20210928T190000Z
DTEND:20210928T200000Z
DTSTAMP:20260422T212710Z
UID:PALS/12
DESCRIPTION:Title: So
lving small PCSPs via large CSPs\nby Peter Mayr (CU Boulder) as part o
f PALS Panglobal Algebra and Logic Seminar\n\n\nAbstract\nFor relational s
tructures A\, B\, the Promise Constraint Satisfaction Problem PCSP(A\, B)
asks whether a given input structure maps homomorphically to A or does not
even map to B. We are promised that the input satisfies exactly one of th
ese two cases.\nNote that if there exists C with homomorphisms A → C →
B\, then PCSP(A\, B) reduces to CSP(C). All known tractable PCSPs seem to
reduce to tractable CSPs in this way. However Barto (2019) showed that so
me PCSPs over finite structures require solving CSPs over infinite C. We p
rovide examples showing that even when a reduction to finite C is possible
\, this structure may become arbitrarily large.\nThis is joint work with A
lexandr Kazda and Dmitriy Zhuk.\n
LOCATION:https://researchseminars.org/talk/PALS/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Philipp Rothmaler (CUNY)
DTSTART:20211005T190000Z
DTEND:20211005T200000Z
DTSTAMP:20260422T212710Z
UID:PALS/13
DESCRIPTION:Title: Hi
gh and low formulas\nby Philipp Rothmaler (CUNY) as part of PALS Pangl
obal Algebra and Logic Seminar\n\n\nAbstract\nA partition of the set of un
ary positive primitive (pp) formulas for modules over an associative ring
into four regions will be presented. These four types of formula have a be
aring on various structural properties of modules\, a few instances of whi
ch will be discussed in the talk. Domains\, specifically Ore domains\, tur
n out to play a prominent role.\n\nOne of the four types of formula are ca
lled high. These are used to define Ulm submodules and Ulm length of modul
es over an arbitrary associative ring. Pure injective modules turn out to
have Ulm length at most 1 (just as in abelian groups). As a consequence\,
pure injective modules over RD domains (in particular\, pure injective mod
ules over the first Weyl algebra over a field of characteristic 0) decompo
se into a largest injective and a reduced submodule.\n
LOCATION:https://researchseminars.org/talk/PALS/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marcel Jackson (La Trobe University Melbourne\, Australia)
DTSTART:20211019T190000Z
DTEND:20211019T200000Z
DTSTAMP:20260422T212710Z
UID:PALS/14
DESCRIPTION:Title: Un
decidability of representability as binary relations\nby Marcel Jackso
n (La Trobe University Melbourne\, Australia) as part of PALS Panglobal Al
gebra and Logic Seminar\n\n\nAbstract\nIt is well-known and easy to prove
that the variety of groups abstractly captures algebras of permutations un
der composition and inverse\, that the variety of inverse semigroups captu
re algebras of partial injective functions under composition and inverse\,
and that the variety of semigroups abstractly capture the algebras of any
of total functions\, partial functions or binary relations under the oper
ation of composition. In contrast to this\, a landmark result of Hirsch a
nd Hodkinson showing the undecidability of determining when a finite algeb
ra is isomorphic to an algebra of binary relations under Tarski’s signat
ure: the usual set theoretic Boolean operations\, composition\, converse a
nd identity. This is a very rich signature\, and it has subsequently been
discovered that undecidability of representability begins in weaker signa
tures.\n\nThis talk will survey some of the very extensive literature in t
his area\, and an overview of the approaches to undecidability\, possibly
touching on some new results for one of the weakest known algebraic signat
ure to experience undecidability of representability as binary relations.\
n
LOCATION:https://researchseminars.org/talk/PALS/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michael Pinsker (Technical University Vienna\, Austria)
DTSTART:20211026T190000Z
DTEND:20211026T200000Z
DTSTAMP:20260422T212710Z
UID:PALS/15
DESCRIPTION:Title: Un
iqueness of Polish topologies on endomorphism monoids of countable structu
res\nby Michael Pinsker (Technical University Vienna\, Austria) as par
t of PALS Panglobal Algebra and Logic Seminar\n\n\nAbstract\nMany mathemat
ical objects are naturally equipped with both an algebraic and a\ntopologi
cal structure. For example\, the automorphism group of any\nfirst-order st
ructure is\, of course\,\na group\, and in fact a topological group when e
quipped with the\ntopology of pointwise convergence.\n\nWhile in some case
s\, e.g. the additive group of the reals\, the\nalgebraic structure\nof th
e object alone carries strictly less information than together with the\nt
opological structure\, in other cases its algebraic structure is so\nrich
that it actually determines\nthe topology (under some requirements for the
topology): by a result\nof Kechris and Solecki\,\nthe pointwise convergen
ce topology is the only compatible separable\ntopology on the full symmetr
ic group on a\ncountable set. Which topologies are compatible with a given
algebraic object has\nintrigued mathematicians for decades: for example\,
Ulam asked whether\nthere exists a compatible\nlocally compact Polish top
ology on the full symmetric group on a\ncountable set (by the above\, the
answer is negative).\n\nIn the case of automorphism groups of first-order
structures\, the\nquestion of the relationship between the algebraic and\n
the topological structure has been pursued actively over the past 40\nyea
rs\, and numerous results have been obtained:\nmany of the most popular au
tomorphism groups\, including that of the\norder of the rationals and of t
he random graph\,\ndo have unique Polish topologies.\n\nThe endomorphism m
onoid of a first-order structure is algebraically\nnot as rich as its auto
morphism group\, and\noften allows many different compatible topologies. W
e show\, however\,\nthat there is a unique compatible Polish topology on t
he endomorphism\nmonoids of the random graph\, the weak linear order\nof t
he rational numbers\, the random poset\, and many more.\n\nThis is joint w
ork with L. Elliott\, J. Jonušas\, J. D. Mitchell\, Y.\nPéresse\, and C.
Schindler.\n
LOCATION:https://researchseminars.org/talk/PALS/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Laszlo Zadori (University of Szeged\, Hungary)
DTSTART:20211102T190000Z
DTEND:20211102T200000Z
DTSTAMP:20260422T212710Z
UID:PALS/16
DESCRIPTION:Title: On
the primeness of 2-permutability\nby Laszlo Zadori (University of Sze
ged\, Hungary) as part of PALS Panglobal Algebra and Logic Seminar\n\n\nAb
stract\nIn the talk\, I sketch a semantical proof of the conjecture of Gar
cia and Taylor that congruence permutability is a prime Maltsev condition
in the lattice of interpretability types of varieties. The proof was obtai
ned jointly with Gyenizse and Maróti\, and it is based on a combinatorial
property of certain digraph powers. I also discuss how the present proof
is related to the proof of our earlier result on the non-primeness of n-pe
rmutability when n>4 and some other result that we obtained for 3-permutab
ility.\n
LOCATION:https://researchseminars.org/talk/PALS/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Miguel Couceiro (Universite de Lorraine\, France)
DTSTART:20211109T200000Z
DTEND:20211109T210000Z
DTSTAMP:20260422T212710Z
UID:PALS/17
DESCRIPTION:Title: Im
possibility theorems over median algebras and beyond\nby Miguel Coucei
ro (Universite de Lorraine\, France) as part of PALS Panglobal Algebra and
Logic Seminar\n\n\nAbstract\nIn this presentation we consider aggregation
procedures (consensus functions) over median algebras (ternary algebras t
hat subsume several ordered structures such as distributive lattices as we
ll as several combinatorial structures such as median graphs). Our startin
g point is a recent Arrow type impossibility result that states that any m
edian preserving consensus function over linearly ordered sets is trivial
in the sense that it only depends on a single argument. In view of this re
sult\, a natural problem is then to identify those median algebras that le
ad to such impossibility results. In particular\, we will show that such i
mpossibility results are inevitable when the codomain contains no cycle\,
i.e.\, it is a "tree"\, and we will provide a surprisingly simple conditio
n that completely describes the latter as median algebras. To broaden the
talk\, we will also present some recent results that answer the parametriz
ed version of this problem in which dependence is restricted to k argument
s. We will conclude by observing that the underlying property to proving s
uch results is that of congruence distributivity\, which naturally raises
the question whether these results extend to other varieties of algebras\,
e.g.\, congruence modular varieties.\n
LOCATION:https://researchseminars.org/talk/PALS/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Peter Jipsen (Chapman University)
DTSTART:20211116T210000Z
DTEND:20211116T220000Z
DTSTAMP:20260422T212710Z
UID:PALS/18
DESCRIPTION:Title: A
survey of partially ordered algebras\nby Peter Jipsen (Chapman Univers
ity) as part of PALS Panglobal Algebra and Logic Seminar\n\n\nAbstract\nIn
June 2003 I gave a talk at the Annual Meeting of the Association for Symb
olic Logic\, University of Illinois at Chicago\, on “An online database
of classes of algebraic structures”. This list of mathematical structure
s is still on a website at http://math.chapman.edu/~jipsen/structures\, bu
t is mostly just an alphabetical list of links that point to (sometimes in
complete) axiomatic descriptions of about 300 categories of universal alge
bras. This past summer I started a project with Bianca Newell to recreate
this list of (partially-ordered) algebraic structures as a computable LaTe
X document that can be checked for consistency and updated more reliably t
han the previous collection of webpages. In this talk I will describe this
project and recent joint work on partially ordered universal algebras wit
h José Gil-Ferez. In this setting\, a partially ordered universal algebra
is a poset with finitary operations that are order-preserving or order-re
versing in each argument\, and congruences are replaced by compatible preo
rders. Our investigations are based on an unpublished paper from 2004 by D
on Pigozzi: Partially ordered varieties and quasivarieties\, available at
https://orion.math.iastate.edu/dpigozzi/notes/santiago_notes.pdf\n
LOCATION:https://researchseminars.org/talk/PALS/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jennifer Hyndman (University of Northern British Columbia)
DTSTART:20211130T200000Z
DTEND:20211130T210000Z
DTSTAMP:20260422T212710Z
UID:PALS/19
DESCRIPTION:Title: A
Reader's Guide to A Primer of Subquasivariety Lattices\nby Jennifer Hy
ndman (University of Northern British Columbia) as part of PALS Panglobal
Algebra and Logic Seminar\n\n\nAbstract\nBirkhoff and Mal'cev independentl
y posed the problem: Describe all\nsubquasivariety lattices. Nurakunov in
2009 showed that there are many\nunreasonable subquasivariety lattices whe
re unreasonable means there is\nno algorithm to determine if a particular
finite lattice is a\nsublattice. This sugests refinements of the original
question are needed.\n\nA subquasvariety lattice has a natural equaclosur
e operator. Adaricheva\nand Gorbunov in 1989 defined an equaclosure operat
or abstractly as\nhaving the properties that are known to hold in a natura
l equaclosure\noperator.\n\nThe soon-to-be-published book\, A Primer of Qu
asivariety Lattices by Kira\nAdaricheva\, Jennifer Hyndman\, JB Nation\, a
nd Joy Nishida\, refines the\nabstract definition of equaclosure operator
and provides some answers to\nthe refined question: When is a lattice with
an equaclosure operator\nrepresentable by a subquasivariety lattice and t
he natural equaclosure\noperator. This presentation explores some of this
new approach.\n
LOCATION:https://researchseminars.org/talk/PALS/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Martin Goldstern (Technical University Vienna\, Austria)
DTSTART:20211207T200000Z
DTEND:20211207T210000Z
DTSTAMP:20260422T212710Z
UID:PALS/20
DESCRIPTION:Title: Ca
rdinals below the continuum\nby Martin Goldstern (Technical University
Vienna\, Austria) as part of PALS Panglobal Algebra and Logic Seminar\n\n
\nAbstract\nGeorg Cantor's "Continuum Hypothesis" (CH) postulates that eve
ry\ninfinite set S of reals is either countable or equinumerous with\nthe
set of all reals. Using the axiom of choice this means that\nthe "continu
um" (the cardinality of the set of reals) is equal\nto aleph1\, the smalle
st uncountable cardinal.\n\nDavid Hilbert's first problem asked if CH is t
rue\; we know now that\nneither CH nor non-CH can be proved from the usual
axioms of\nset theory (ZFC). Paul Cohen's method of forcing allows us\nt
o build universes (structures satisfying ZFC) where the continuum\nis arbi
trarily large. \n\nThere are many relatives of the continuum\, such as th
e answers\nto these questions: How many nulls sets (Lebesgue measure zero)
\ndo we need to cover the real line? How many points do we need\nto get a
non-null set? How many sequences (or convergent series)\ndo we need to ev
entually dominate all sequences (convergent series)?\netc.\nAll these card
inals are located in the closed interval\nbetween aleph1 and the continuum
.\n\nIn my talk I will present some of these cardinals and hint\nat the me
thods used to construct universes where these cardinals\nhave prescribed v
alues\, or satisfy strict inequalities.\n
LOCATION:https://researchseminars.org/talk/PALS/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anna Zamojska-Dzienio (Warsaw University of Technology\, Poland)
DTSTART:20211012T190000Z
DTEND:20211012T200000Z
DTSTAMP:20260422T212710Z
UID:PALS/21
DESCRIPTION:Title: Bi
racks and solutions of the Yang-Baxter equation\nby Anna Zamojska-Dzie
nio (Warsaw University of Technology\, Poland) as part of PALS Panglobal A
lgebra and Logic Seminar\n\n\nAbstract\nThe Yang-Baxter equation is a fund
amental equation occurring in integrable models in statistical mechanics a
nd quantum field theory. Description of all possible solutions seems to be
extremely difficult and therefore there were some simplifications introdu
ced (V.G. Drinfeld 1992).\n\nBiracks are algebras studied in low-dimension
al topology which are in a one-to-one correspondence with set-theoretical\
, non-degenerate solutions to the Yang-Baxter equation. The use of the lan
guage of biracks allows us to apply universal algebra tools. In this talk\
, we describe the generalized retraction relation on a birack which gives
new classes of solutions.\n\nThis is joint work with Premysl Jedlicka and
Agata Pilitowska.\n
LOCATION:https://researchseminars.org/talk/PALS/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michael Kompatscher (Charles University Prague)
DTSTART:20211130T190000Z
DTEND:20211130T200000Z
DTSTAMP:20260422T212710Z
UID:PALS/22
DESCRIPTION:Title: G-
terms and the local-global property\nby Michael Kompatscher (Charles U
niversity Prague) as part of PALS Panglobal Algebra and Logic Seminar\n\n\
nAbstract\nLet $G$ be a permutation group on a $n$-element set. We then sa
y that an algebra $\\mathbf A$ has a $G$-term $t(x_1\,\\ldots\,x_n)$\, if
$t$ is invariant under permuting its variables according to $G$\, i.e. $\\
mathbf A \\models t(x_1\,\\ldots\,x_n) \\approx t(x_{\\pi(1)}\,\\ldots\,x_
{\\pi(n)})$ for all $\\pi \\in G$. Since $G$-terms appear in the study of
constraint satisfaction problems and elsewhere\, it is natural to ask for
their classification up to interpretability. In the first part of my talk
I would like to share a few partial results on this problem.\n\nIn the sec
ond part I am going to discuss the complexity of deciding whether a given
finite algebra has a $G$-term. The most commonly used strategy in showing
that deciding a given Maltsev condition is in P\, is to show that it suffi
ces to check the condition locally (i.e. on subsets of bounded size). We s
how that this „local-global“ approach works for all $G$-terms induced
by regular permutation groups $G$ (and direct products of them)\, but fail
s for some other „rich enough" permutation groups\, such as $Sym(n)$ for
$n \\geq 3$.\n\nThis is joint work with Alexandr Kazda.\n
LOCATION:https://researchseminars.org/talk/PALS/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Charlotte Aten (University of Rochester)
DTSTART:20220125T200000Z
DTEND:20220125T210000Z
DTSTAMP:20260422T212710Z
UID:PALS/23
DESCRIPTION:Title: Or
ientable smooth manifolds are essentially quasigroups\nby Charlotte At
en (University of Rochester) as part of PALS Panglobal Algebra and Logic S
eminar\n\n\nAbstract\nIn my recent work with Semin Yoo we produced a gener
alization of a construction of Herman and Pakianathan which assigns to eac
h finite noncommutative group a closed surface in a functorial manner. We
give a pair of functors whose domain is a subcategory of a variety of n-ar
y quasigroups. The first of these functors assigns to each such quasigroup
a smooth\, flat Riemannian manifold while the second assigns to each quas
igroup a topological manifold which is a subspace of the metric completion
of the aforementioned Riemannian manifold. I will give examples of these
constructions\, draw some pictures\, and argue that all homeomorphism clas
ses of smooth orientable manifolds arise from this construction. I will th
en discuss a connection with the Evans Conjecture on partial Latin squares
\, give its implication for orientable surfaces\, and state a related prob
lem applicable to our construction for compact n-manifolds.\n
LOCATION:https://researchseminars.org/talk/PALS/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ross Willard (University of Waterloo)
DTSTART:20220201T200000Z
DTEND:20220201T210000Z
DTSTAMP:20260422T212710Z
UID:PALS/24
DESCRIPTION:Title: Ch
aracterizing [alpha\,beta]=0 using Kiss terms\nby Ross Willard (Univer
sity of Waterloo) as part of PALS Panglobal Algebra and Logic Seminar\n\n\
nAbstract\nMany years ago\, Kiss proved that the commutator relation [alph
a\,beta]=0 can be characterized in congruence modular varieties by a simpl
e condition involving a certain kind of 4-ary term\, which is now called a
Kiss term. Seven years ago\, Kearnes\, Szendrei and I claimed to extend
this characterization to varieties having a difference term\, and we used
this at a key step in proving our finite basis theorem for finite algebras
in varieties having a difference term and having a finite residual bound.
\nIt was recently brought to our attention that the published proof of our
extension of Kiss’s result has a significant gap\, bringing into questi
on the validity of our finite basis theorem. In this talk I will sketch a
new (correct) proof of this extension. This is joint work with Keith Ke
arnes and Agnes Szendrei.\n
LOCATION:https://researchseminars.org/talk/PALS/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dragan Masulovic (University of Novi Sad)
DTSTART:20220208T200000Z
DTEND:20220208T210000Z
DTSTAMP:20260422T212710Z
UID:PALS/25
DESCRIPTION:Title: Du
al Ramsey properties for classes of algebras\nby Dragan Masulovic (Uni
versity of Novi Sad) as part of PALS Panglobal Algebra and Logic Seminar\n
\n\nAbstract\nAlmost any reasonable class of finite relational structures
has the Ramsey property or a precompact Ramsey expansion. In contrast to t
hat\, the list of classes of finite algebras with the precompact Ramsey ex
pansion is surprisingly short. In this talk we show that any nontrivial va
riety (that is\, equationally defined class of algebras) enjoys various du
al Ramsey properties. We develop a completely new set of strategies that r
ely on the fact that left adjoints preserve the dual Ramsey property\, and
then treat classes of algebras as Eilenberg-Moore categories for a monad.
We show that finite algebras in any nontrivial variety have finite dual s
mall Ramsey degrees\, and that every finite algebra has finite dual big Ra
msey degree in the free algebra on countably many free generators. As usua
l\, these come as consequences of ordered versions of the statements.\n
LOCATION:https://researchseminars.org/talk/PALS/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bill De Witt (University of St Andrews)
DTSTART:20220215T200000Z
DTEND:20220215T210000Z
DTSTAMP:20260422T212710Z
UID:PALS/26
DESCRIPTION:Title: Th
e number of countable subdirect powers of finite unary algebras\nby Bi
ll De Witt (University of St Andrews) as part of PALS Panglobal Algebra an
d Logic Seminar\n\n\nAbstract\nThe number of subdirect powers of an finite
algebraic structure is a question that has appeared at various points in
recent history. The situation is known in full for groups\, and to some ex
tent in semigroups. We answer the question for unary algebras\, and look a
t how the situation is more complicated for infinite algebras. We then dis
cuss what these results can tell us about the general question\, and how i
t ties into other topics such as boolean separation.\n
LOCATION:https://researchseminars.org/talk/PALS/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jordan DuBeau (CU Boulder)
DTSTART:20220222T200000Z
DTEND:20220222T210000Z
DTSTAMP:20260422T212710Z
UID:PALS/27
DESCRIPTION:Title: J
ónsson Jónsson-Tarski algebras\nby Jordan DuBeau (CU Boulder) as par
t of PALS Panglobal Algebra and Logic Seminar\n\n\nAbstract\nFor an infini
te algebra J in a countable algebraic language\, we say J is Jónsson if i
t has no proper subalgebra of the same cardinality as J. This talk explore
s Jónsson algebras in a particular variety: the variety of Jónsson-Tarsk
i algebras. When a Jónsson algebra of size $\\aleph_1$ was constructed in
this variety\, it showed that minimal varieties can contain uncountable J
ónsson algebras. We will describe that construction and two further resul
ts\, demonstrating exactly which cardinalities are possible for Jónsson J
ónsson-Tarski algebras\, and how many pairwise nonisomorphic Jónsson Jó
nsson-Tarski algebras exist. We discuss implications for other varieties a
nd Jónsson algebras in general.\n
LOCATION:https://researchseminars.org/talk/PALS/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Paolo Lipparini (Universita' di Tor Vergata\, Rome\, Italy)
DTSTART:20220329T190000Z
DTEND:20220329T200000Z
DTSTAMP:20260422T212710Z
UID:PALS/28
DESCRIPTION:Title: Re
lative lengths of Maltsev conditions\nby Paolo Lipparini (Universita'
di Tor Vergata\, Rome\, Italy) as part of PALS Panglobal Algebra and Logic
Seminar\n\n\nAbstract\nThe study of Maltsev conditions is a significant p
art of universal algebra\, with classical characterizations of families of
varieties (congruence permutable\, distributive\, modular...) and recent
advanced results by Hobby\, McKenzie\, Kearnes\, Kiss\, among others. In p
articular\, the interplay between distinct Maltsev conditions for congruen
ce modular varieties has led to a refined theory for such varieties.\n\nRe
call that a Maltsev condition is\, roughly\, a statement of the form "ther
e are some n and terms t1\,...\,tn such that a certain finite set of equat
ions hold". As we mentioned\, many deep and sophisticated results are know
n about Maltsev conditions. On the other hand\, when two conditions are co
mpared\, really little is known about the exact value of the smallest n as
above. For example\, a simple observation by A. Day asserts that if some
variety V has k Jónsson terms witnessing congruence distributivity\, then
V has 2k-1 Day terms witnessing congruence modularity. About fifty years
ago Day asked whether this result is best possible\, but\, to the best of
our knowledge\, an exact solution is not yet known.\n\nA deeper problem (a
sked by Lakser\, Taylor\, Tschantz in 1985) concerns the relative lengths
of sequences of Day and Gumm terms characterizing congruence modularity. M
ore recently\, Kazda\, Kozik\, McKenzie\, Moore provided still another cha
racterization of congruence distributive and modular varieties by means of
"directed" terms. Again\, the exact relationships between the lengths of
the sequences of terms is not known. A solution of the above problems is s
upposed to provide either interesting exotic examples of congruence modula
r and distributive varieties\, or more refined structure theorems.\n\nWe s
hall present recent results about the above Day\, LTT and KKMM problems\,
with an unexpected application to congruence distributive varieties.\n
LOCATION:https://researchseminars.org/talk/PALS/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michael Levet (CU Boulder)
DTSTART:20220419T190000Z
DTEND:20220419T200000Z
DTSTAMP:20260422T212710Z
UID:PALS/29
DESCRIPTION:Title: We
isfeiler—Leman for Group Isomorphism: Action Compatibility\nby Micha
el Levet (CU Boulder) as part of PALS Panglobal Algebra and Logic Seminar\
n\n\nAbstract\nThe Weisfeiler—Leman (WL) algorithm is a key combinatoria
l subroutine in Graph Isomorphism\, that (for fixed $k \\geq 2$) computes
an isomorphism invariant coloring of the k-tuples of vertices. Brachter &
Schweitzer (LICS 2020) recently adapted WL to the setting of groups. Using
a classical Ehrenfeucht-Fra\\"iss\\'e pebble game\, we will show that Wei
sfeiler—Leman serves as a polynomial-time isomorphism test for several f
amilies of groups previously shown to be in $\\textsf{P}$ by multiple meth
ods. These families of groups include:\n\n(1) Coprime extensions $H \\ltim
es N$\, where $H$ is $O(1)$-generated and the normal Hall subgroup $N$ is
Abelian (Qiao\, Sarma\, & Tang\, STACS 2011).\n\n(2) Groups without Abelia
n normal subgroups (Babai\, Codenotti\, & Qiao\, ICALP 2012). \n\n \nIn bo
th of these cases\, the previous strategy involved identifying key group-t
heoretic structure that could then be leveraged algorithmically\, resultin
g in different algorithms for each family. A common theme among these is t
hat the group-theoretic structure is mostly about the action of one group
on another. Our main contribution is to show that a single\, combinatorial
algorithm (Weisfeiler-Leman) can identify those same group-theoretic stru
ctures in polynomial time.\n\n \n\nWe also show that Weisfeiler—Leman re
quires only a constant number of rounds to identify groups from each of th
ese families. Combining this result with the parallel WL implementation du
e to Grohe & Verbitsky (ICALP 2006)\, this improves the upper bound for is
omorphism testing in each of these families from $\\textsf{P}$ to $\\texts
f{TC}^0$.\n\n \n\nThis is joint work with Joshua A. Grochow.\n
LOCATION:https://researchseminars.org/talk/PALS/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:James Rooney (McMaster University\, Canada)
DTSTART:20220301T200000Z
DTEND:20220301T210000Z
DTSTAMP:20260422T212710Z
UID:PALS/30
DESCRIPTION:Title: No
nlinear idempotent Mal'tsev Condition Satisfaction Problems: why semilatti
ces are hard and lattices are easier\nby James Rooney (McMaster Univer
sity\, Canada) as part of PALS Panglobal Algebra and Logic Seminar\n\n\nAb
stract\nIn their 2020 article "Deciding some Mal'tsev conditions in finite
idempotent algebras" Kazda and Valeriote conjecture that for a linear str
ong Mal'tsev condition the associated idempotent Mal'tsev condition satisf
action problem (MCSP) will always be polynomial-time decidable. In an earl
ier-published 2019 article Freese\, Nation and Valeriote showed that testi
ng for a semilattice term (a nonlinear condition) is EXPTIME-complete even
for idempotent algebras. \n\nWhile preparing my PhD thesis I investigated
the hypothesis that nonlinear Mal'tsev conditions might always be EXPTIME
-complete to detect. I was able to prove that there are nonlinear Mal'tsev
conditions whose related idempotent MCSPs are in the class NP. Assuming t
hat NP is not EXPTIME this provides the first examples of nonlinear Mal'ts
ev conditions whose idempotent MCSPs are not EXPTIME-complete. The existen
ce of lattice terms is one such example.\n\nIn this talk we briefly revisi
t the 2019 result of Freese\, Nation and Valeriote before sketching the de
tails of my proof that detection of lattice terms in an idempotent algebra
is an NP problem.\n
LOCATION:https://researchseminars.org/talk/PALS/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Monica VanDieren (Robert Morris University)
DTSTART:20220308T200000Z
DTEND:20220308T210000Z
DTSTAMP:20260422T212710Z
UID:PALS/31
DESCRIPTION:Title: Tw
enty years of tameness\nby Monica VanDieren (Robert Morris University)
as part of PALS Panglobal Algebra and Logic Seminar\n\n\nAbstract\nIn the
1970s Saharon Shelah initiated a program to develop classification theory
for non-elementary classes\, and eventually settled on the setting of abs
tract elementary classes. For over three decades\, limited progress was m
ade\, most of which required additional set theoretic axioms. In 2001\, Ra
mi Grossberg and I introduced the model theoretic concept of tameness whic
h opened the door for stability results in abstract elementary classes in
ZFC. During the following 20 years\, tameness along with limit models hav
e been used by several mathematicians to prove categoricity theorems and t
o develop non-first order analogs to forking calculus and stability theory
\, solving a very large number of problems posed by Shelah in ZFC. Recentl
y\, Marcos Mazari-Armida found applications to Abelian group theory and ri
ng theory. In this presentation I will highlight some of the more surpris
ing results involving tameness and limit models from the past 20 years.\n
LOCATION:https://researchseminars.org/talk/PALS/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andres Villaveces (Universidad Nacional de Colombia – Bogotá)
DTSTART:20220315T190000Z
DTEND:20220315T200000Z
DTSTAMP:20260422T212710Z
UID:PALS/32
DESCRIPTION:Title: On
the small index property for AECs with strong amalgamation properties
\nby Andres Villaveces (Universidad Nacional de Colombia – Bogotá) as p
art of PALS Panglobal Algebra and Logic Seminar\n\n\nAbstract\nWe first re
visit notions of interpretability and internality in a category-theoretica
l language (for first order theories)\, reframing work of Hrushovski and K
amensky in a formalism derived from Makkai's early work. We then describe
the issue of recovering the bi-intepretability class of a theory in terms
of the automorphism group of a saturated model\, and the role of the "Smal
l Index Property" (SIP) - a way of recovering the topology of a group acti
on from purely algebraic information.\n\nWe then turn to abstract elementa
ry classes\, and discuss the same notions\, in the opposite order: first\,
two situations where a Small Index Property holds (joint work with Ghader
nezhad)\, and then some applications to the problem of interpretation and
reconstruction\, adapted to abstract elementary classes.\n
LOCATION:https://researchseminars.org/talk/PALS/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Thomas Kucera (University of Manitoba)
DTSTART:20220412T190000Z
DTEND:20220412T200000Z
DTSTAMP:20260422T212710Z
UID:PALS/33
DESCRIPTION:Title: Sa
turated free algebras and almost indiscernible theories: an overview\n
by Thomas Kucera (University of Manitoba) as part of PALS Panglobal Algebr
a and Logic Seminar\n\n\nAbstract\nThis is work motivated by questions at
the intersection of algebra and model theory\, and using advanced techniqu
es of model theory.\nBaldwin and Shelah (Algebra Universalis\, 1983) studi
ed saturated free algebras. Pillay and Sklinos (Bull. Symb. Logic 2015)\,
following the lead of this paper\, studied "almost indiscernible theories"
\, taking the opportunity to refine the statements of the major results an
d improve the proofs. We extend these results to large infinite contexts\,
both in the size of the language and the kinds of tuples allowed in a "ba
sis"\; and return to examples and applications in algebra\, in particular
in the theory of modules.\nThe theory develops by noting various analogies
. The model-theoretic concept 'indiscernible sequence' generalizes 'linear
ly independent set' in a vector space\, 'free (generating) set' of an alge
bra\, 'algebraic independence' in an algebraically closed field\, and simi
lar concepts. 'Saturated model' generalizes concepts such as 'injective en
velope of a module'\, 'algebraic closure of a field'\, and similar constru
ctions. A complete first-order theory is "almost indiscernible" if it has
a (sufficiently large) saturated model which lies in the algebraic closure
of an indiscernible set (of sequences). Requiring that a saturated model
be generated by an indiscernible set imposes strong structural constraints
\, but nonetheless there are natural motivating examples.\nI start with so
me history and motivation from algebra\, then I will give an overview of t
he main model theoretic concepts and techniques\, motivating them as much
as possible by examples from algebra. I'll state the new technical structu
ral results for almost indiscernible theories in our more general context\
, with no more than informal 'hand-waving' about the proof techniques. The
n I will present some consequences for free algebras and for theories of m
odules\, including structure theorems and some examples. I conclude with a
list of open questions.\nThis is joint work with Anand Pillay.\n
LOCATION:https://researchseminars.org/talk/PALS/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nik Ruskuc (University of St Andrews)
DTSTART:20220405T190000Z
DTEND:20220405T200000Z
DTSTAMP:20260422T212710Z
UID:PALS/34
DESCRIPTION:Title: Di
rect and subdirect products in combinatorial algebra\, groups and semigrou
ps\nby Nik Ruskuc (University of St Andrews) as part of PALS Panglobal
Algebra and Logic Seminar\n\n\nAbstract\nFor a while now\, Peter Mayr and
I have been looking at properties of direct and\nsubdirect products in al
gebra\, often motivated by some well known or particularly\nnice results f
rom combinatorial group theory. The topics include finite generation\,\nfi
nite presentability\, residual finiteness\, infinite subdirect powers\, et
c. A fairly\nrich landscape has emerged over the years. Perhaps unsurprisi
ngly the most general\nresults can be obtained in the context of congruenc
e permutable or modular varieties.\nThis then leaves semigroups outside\,
and I have been working on such questions in\nparallel with some of my PhD
students. In this talk I will try to sketch this\nlandscape\, not so much
by means of a systematics introduction\, but a few selected\nstrands\, re
sults and comparisons.\n
LOCATION:https://researchseminars.org/talk/PALS/34/
END:VEVENT
END:VCALENDAR