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BEGIN:VEVENT
SUMMARY:Erhard Aichinger (JKU Linz\, Austria)
DTSTART:20210216T200000Z
DTEND:20210216T210000Z
DTSTAMP:20260404T094340Z
UID:PALS/1
DESCRIPTION:Title: The degree as a measure of complexity of functions on a universal alge
bra\nby Erhard Aichinger (JKU Linz\, Austria) as part of PALS Pangloba
l Algebra and Logic Seminar\n\n\nAbstract\nThe degree of a function $f$ be
tween two abelian groups has been\ndefined as the smallest natural number
$d$ such that\n$f$ vanishes after $d+1$ applications\nof any of the differ
ence operators $\\Delta_a$ defined by\n$\\Delta_a * f \\\,\\\, (x) = f(x+a
) - f(x)$.\nFunctions of finite degree have also been called\ngeneralized
polynomials or solutions to Frechet's functional\n equations. A pivotal r
esult by A. Leibman (2002) is that $\\deg (f \\circ g) \\le \\deg(f) \\cdo
t\n\\deg (g)$.\nWe show how results on the degree can be used\n(i) to get
lower bounds on the number of solutions of equations\, and\n(ii) to connec
t nilpotency and supernilpotency.\nThis leads to generalizations of the Ch
evalley-Warning Theorems\nto abelian groups\, a group version of the Ax-Ka
tz Theorem on\nthe number of zeros of polynomial functions\, and a computa
ble\n$f$ such that all finite $k$-nilpotent algebras of prime power order\
nin congruence modular varieties are $f(k\, .)$-supernilpotent.\n
LOCATION:https://stable.researchseminars.org/talk/PALS/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kristina Asimi (Charles University Prague)
DTSTART:20210223T200000Z
DTEND:20210223T210000Z
DTSTAMP:20260404T094340Z
UID:PALS/2
DESCRIPTION:Title: Finitely tractable PCSPs\nby Kristina Asimi (Charles University Pr
ague) as part of PALS Panglobal Algebra and Logic Seminar\n\n\nAbstract\nT
he Promise Constraint Satisfaction Problem (PCSP) is a generalization of t
he Constraint Satisfaction Problem (CSP). In a [LICS '19] paper it was sho
wn that a specific PCSP\, the problem to find a valid Not-All-Equal soluti
on 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 neces
sarily over an infinite domain (unless P=NP). We further explore this phen
omenon: we give a general necessary condition for finite tractability and
characterize finite tractability within a class of templates - the "basic"
tractable cases in the dichotomy theorem for symmetric Boolean PCSPs allo
wing negations by Brakensiek and Guruswami [SODA'18]. This is a joint work
with Libor Barto.\n
LOCATION:https://stable.researchseminars.org/talk/PALS/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrei Bulatov (Simon Fraser University)
DTSTART:20210302T200000Z
DTEND:20210302T210000Z
DTSTAMP:20260404T094340Z
UID:PALS/3
DESCRIPTION:Title: Isomorphisms\, homomorphisms\, and some algebra\nby Andrei Bulatov
(Simon Fraser University) as part of PALS Panglobal Algebra and Logic Sem
inar\n\n\nAbstract\nWe give a survey on connections between Graph Isomorph
ism\, the CSP\, and counting homomorphisms. In the first part we give a br
ief review of the main approaches to solving the Graph Isomorphism problem
and make some observations on how the CSP techniques can be helpful. In t
he second part we focus on relaxations of graph isomorphisms and how they
can be characterized using the numbers of homomorphisms from various graph
classes.\n
LOCATION:https://stable.researchseminars.org/talk/PALS/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lexi V. Pasi (Baylor University)
DTSTART:20210309T200000Z
DTEND:20210309T210000Z
DTSTAMP:20260404T094340Z
UID:PALS/4
DESCRIPTION:Title: Forcing $\\aleph_1$-Free Groups to Be Free\nby Lexi V. Pasi (Baylo
r University) as part of PALS Panglobal Algebra and Logic Seminar\n\n\nAbs
tract\n$\\aleph_1$-free groups\, abelian groups whose countable subgroups
are free\, are objects of both algebraic and set-theoretic interest. Illus
trating this\, we note that $\\aleph_1$-free groups\, and in particular th
e question of when $\\aleph_1$-free groups are free\, were central to the
resolution of the Whitehead problem as undecidable. In elucidating the rel
ationship between $\\aleph_1$-freeness and freeness\, we prove the followi
ng result: an abelian group $G$ is $\\aleph_1$-free in a countable transit
ive model of $\\operatorname{ZFC}$ (and thus by absoluteness\, in every tr
ansitive model of $\\operatorname{ZFC}$) if and only if it is free in some
generic model extension. We would like to answer the more specific questi
on of when an $\\aleph_1$-free group can be forced to be free while preser
ving the cardinality of the group. For groups of size $\\aleph_1$\, we est
ablish a necessary and sufficient condition for when such forcings are pos
sible. We also identify a number of existing and novel forcings which forc
e such $\\aleph_1$-free groups of size $\\aleph_1$ to become free with car
dinal preservation. These forcings lay the groundwork for a larger project
which uses forcing to explore various algebraic properties of $\\aleph_1$
-free groups and develops new set-theoretical tools for working with them.
\n
LOCATION:https://stable.researchseminars.org/talk/PALS/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Matthew Moore (University of Kansas)
DTSTART:20210316T190000Z
DTEND:20210316T200000Z
DTSTAMP:20260404T094340Z
UID:PALS/5
DESCRIPTION:Title: The Hidden Subgroup Problem for universal algebras\nby Matthew Moo
re (University of Kansas) as part of PALS Panglobal Algebra and Logic Semi
nar\n\n\nAbstract\nThe Hidden Subgroup Problem (HSP) is a computational pr
oblem which includes as\nspecial cases integer factorization\, the discret
e logarithm problem\, graph\nisomorphism\, and the shortest vector problem
. The celebrated polynomial-time\nquantum algorithms for factorization and
the discrete logarithm are restricted\nversions of a generic polynomial-t
ime quantum solution to the HSP for abelian\ngroups\, but despite focused
research no polynomial-time solution for general\ngroups has yet been foun
d. We propose a generalization of the HSP to include\narbitrary algebraic
structures and analyze this new problem on powers of\n2-element algebras.
We prove a complete classification of every such power as\nquantum tractab
le (i.e. polynomial-time)\, classically tractable\, quantum\nintractable\,
or classically intractable. In particular\, we identify a class of\nalgeb
ras for which the generalized HSP exhibits super-polynomial speedup on a\n
quantum computer compared to a classical one.\n
LOCATION:https://stable.researchseminars.org/talk/PALS/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrew Moorhead (University of Kansas)
DTSTART:20210323T190000Z
DTEND:20210323T200000Z
DTSTAMP:20260404T094340Z
UID:PALS/6
DESCRIPTION:Title: Higher Kiss terms for modular varieties\nby Andrew Moorhead (Unive
rsity of Kansas) as part of PALS Panglobal Algebra and Logic Seminar\n\n\n
Abstract\nWe explain how the 4-ary Kiss term for a modular variety can be
composed with itself to produce an infinite sequence of terms\, each havin
g a connection to a particular arity higher commutator that mimics the con
nection that the Kiss term has to the binary modular commutator. We will t
hen discuss how these terms can be used to show that there is a greatest c
lone among those that share a sequence of Day terms\, congruences\, and hi
gher commutator operations.\n
LOCATION:https://stable.researchseminars.org/talk/PALS/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexander Hulpke (Colorado State)
DTSTART:20210427T190000Z
DTEND:20210427T200000Z
DTSTAMP:20260404T094340Z
UID:PALS/7
DESCRIPTION:Title: Rewriting systems and group extensions\nby Alexander Hulpke (Color
ado State) as part of PALS Panglobal Algebra and Logic Seminar\n\n\nAbstra
ct\nThe first examples of groups in a textbook are often as words in gener
ators\, subject to some easy rules. This seems nice and natural\, but gets
quickly abandoned once the groups involved become more complicated. A sim
ilar disappointment happens when introducing group extensions: Examples in
textbooks never go beyond easy cases such as cyclic groups or split exten
sions.\nBut this is not intended to whine about textbooks. Instead I want
to show how a systematic approach to normal form words (namely confluent r
ewriting systems) can be used to describe group extension (and explicitly
compute 2-cohomology)\, resulting in practically useful (and implemented!)
algorithms.\n
LOCATION:https://stable.researchseminars.org/talk/PALS/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marcin Kozik (University of Krakow)
DTSTART:20210330T190000Z
DTEND:20210330T200000Z
DTSTAMP:20260404T094340Z
UID:PALS/8
DESCRIPTION:Title: Minimal (clones with a Taylor term)\nby Marcin Kozik (University o
f Krakow) as part of PALS Panglobal Algebra and Logic Seminar\n\n\nAbstrac
t\nWe are working with clones\, on finite sets\, which contain a Taylor op
eration. Ordering all of them by inclusion\, we focus on the elements mini
mal in that order. We show that the class is robust and provide a few exam
ples of very strong properties holding in these clones.\n\nJoint work with
L. Barto\, Z. Brady\, A. Bulatov\, D. Zhuk.\n
LOCATION:https://stable.researchseminars.org/talk/PALS/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nick Galatos (University of Denver)
DTSTART:20210406T190000Z
DTEND:20210406T200000Z
DTSTAMP:20260404T094340Z
UID:PALS/9
DESCRIPTION:Title: Amalgamation for certain conic idempotent residuated lattices\nby
Nick Galatos (University of Denver) as part of PALS Panglobal Algebra and
Logic Seminar\n\n\nAbstract\nResiduated lattices were introduced by Ward a
nd Dilworth as tools in the study of ideal lattices of rings. Residuated l
attices have a monoid and a lattice reduct\, as well as division-like oper
ations\; examples include Boolean algebras\, lattice-ordered groups and re
lation algebras. Also\, they form algebraic semantics for substructural lo
gics and are connected to mathematical linguistics and computer science (f
or example pointer management and memory allocation). We focus on a class
of residuated lattices that have an idempotent multiplication and all elem
ents are comparable to the monoid identity\; these are related to algebrai
c models of relevance logic. After establishing a decomposition result for
this class\, we show that it has the strong amalgamation property\, and e
xtend the result to the variety generated by this class\; this implies tha
t the corresponding logic has the interpolation property and Beth definabi
lity.\n
LOCATION:https://stable.researchseminars.org/talk/PALS/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marcos Mazari-Armida (Carnegie Mellon University)
DTSTART:20210413T190000Z
DTEND:20210413T200000Z
DTSTAMP:20260404T094340Z
UID:PALS/10
DESCRIPTION:Title: Stability in abstract elementary classes of modules\nby Marcos Ma
zari-Armida (Carnegie Mellon University) as part of PALS Panglobal Algebra
and Logic Seminar\n\n\nAbstract\nAbstract elementary classes (AECs for sh
ort) were introduced by Shelah in the seventies to study those classes of
structures that can not be axiomatized by a first-order theory. In this ta
lk\, we will introduce the basic notions of AECs and showcase them in clas
ses of modules. In particular\, we will explore if every AEC of modules wi
th pure embeddings is stable. Using that the class of p-groups with pure e
mbeddings is a stable AEC\, we will present a solution to a problem of Lá
szló Fuchs.\n
LOCATION:https://stable.researchseminars.org/talk/PALS/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ross Willard (University of Waterloo)
DTSTART:20210420T190000Z
DTEND:20210420T200000Z
DTSTAMP:20260404T094340Z
UID:PALS/11
DESCRIPTION:Title: Inherently nonfinitely based nonassociative algebras\nby Ross Wil
lard (University of Waterloo) as part of PALS Panglobal Algebra and Logic
Seminar\n\n\nAbstract\nThis is a progress report on an exploration of Isae
v's algebras and their cousins. Isaev's algebras were the first\, and rema
in the only\, known examples of inherently nonfinitely based finite algebr
as in Maltsev varieties. In this talk I will describe a class of finite al
gebras containing Isaev's algebras\, and explain some basic tools that we
have developed to help determine which of these algebras are inherently no
nfinitely based. At the moment we are only able to apply these tools to Is
aev's algebras themselves\, but that won’t stop me from filling the 50-m
inute time slot which I have been offered! This is joint work with Emily C
arlson\, Mehul Gupta and George McNulty.\n
LOCATION:https://stable.researchseminars.org/talk/PALS/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Peter Mayr (CU Boulder)
DTSTART:20210928T190000Z
DTEND:20210928T200000Z
DTSTAMP:20260404T094340Z
UID:PALS/12
DESCRIPTION:Title: Solving small PCSPs via large CSPs\nby Peter Mayr (CU Boulder) as
part of PALS Panglobal Algebra and Logic Seminar\n\n\nAbstract\nFor relat
ional structures A\, B\, the Promise Constraint Satisfaction Problem PCSP(
A\, B) asks whether a given input structure maps homomorphically to A or d
oes not even map to B. We are promised that the input satisfies exactly on
e of these two cases.\nNote that if there exists C with homomorphisms A
→ C → B\, then PCSP(A\, B) reduces to CSP(C). All known tractable PCSP
s seem to reduce to tractable CSPs in this way. However Barto (2019) showe
d that some PCSPs over finite structures require solving CSPs over infinit
e C. We provide examples showing that even when a reduction to finite C is
possible\, this structure may become arbitrarily large.\nThis is joint wo
rk with Alexandr Kazda and Dmitriy Zhuk.\n
LOCATION:https://stable.researchseminars.org/talk/PALS/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Philipp Rothmaler (CUNY)
DTSTART:20211005T190000Z
DTEND:20211005T200000Z
DTSTAMP:20260404T094340Z
UID:PALS/13
DESCRIPTION:Title: High and low formulas\nby Philipp Rothmaler (CUNY) as part of PAL
S Panglobal Algebra and Logic Seminar\n\n\nAbstract\nA partition of the se
t of unary positive primitive (pp) formulas for modules over an associativ
e ring into four regions will be presented. These four types of formula ha
ve a bearing on various structural properties of modules\, a few instances
of which will be discussed in the talk. Domains\, specifically Ore domain
s\, turn out to play a prominent role.\n\nOne of the four types of formula
are called high. These are used to define Ulm submodules and Ulm length o
f modules over an arbitrary associative ring. Pure injective modules turn
out to have Ulm length at most 1 (just as in abelian groups). As a consequ
ence\, pure injective modules over RD domains (in particular\, pure inject
ive modules over the first Weyl algebra over a field of characteristic 0)
decompose into a largest injective and a reduced submodule.\n
LOCATION:https://stable.researchseminars.org/talk/PALS/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marcel Jackson (La Trobe University Melbourne\, Australia)
DTSTART:20211019T190000Z
DTEND:20211019T200000Z
DTSTAMP:20260404T094340Z
UID:PALS/14
DESCRIPTION:Title: Undecidability of representability as binary relations\nby Marcel
Jackson (La Trobe University Melbourne\, Australia) as part of PALS Pangl
obal Algebra and Logic Seminar\n\n\nAbstract\nIt is well-known and easy to
prove that the variety of groups abstractly captures algebras of permutat
ions under composition and inverse\, that the variety of inverse semigroup
s capture algebras of partial injective functions under composition and in
verse\, and that the variety of semigroups abstractly capture the algebras
of any of total functions\, partial functions or binary relations under t
he operation of composition. In contrast to this\, a landmark result of H
irsch and Hodkinson showing the undecidability of determining when a finit
e algebra is isomorphic to an algebra of binary relations under Tarski’s
signature: the usual set theoretic Boolean operations\, composition\, con
verse and identity. This is a very rich signature\, and it has subsequent
ly been discovered that undecidability of representability begins in weake
r signatures.\n\nThis talk will survey some of the very extensive literatu
re in this area\, and an overview of the approaches to undecidability\, po
ssibly touching on some new results for one of the weakest known algebraic
signature to experience undecidability of representability as binary rela
tions.\n
LOCATION:https://stable.researchseminars.org/talk/PALS/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michael Pinsker (Technical University Vienna\, Austria)
DTSTART:20211026T190000Z
DTEND:20211026T200000Z
DTSTAMP:20260404T094340Z
UID:PALS/15
DESCRIPTION:Title: Uniqueness of Polish topologies on endomorphism monoids of countable
structures\nby Michael Pinsker (Technical University Vienna\, Austria)
as part of PALS Panglobal Algebra and Logic Seminar\n\n\nAbstract\nMany m
athematical objects are naturally equipped with both an algebraic and a\nt
opological structure. For example\, the automorphism group of any\nfirst-o
rder structure is\, of course\,\na group\, and in fact a topological group
when equipped with the\ntopology of pointwise convergence.\n\nWhile in so
me cases\, e.g. the additive group of the reals\, the\nalgebraic structure
\nof the object alone carries strictly less information than together with
the\ntopological 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 co
nvergence topology is the only compatible separable\ntopology on the full
symmetric group on a\ncountable set. Which topologies are compatible with
a given algebraic object has\nintrigued mathematicians for decades: for ex
ample\, Ulam asked whether\nthere exists a compatible\nlocally compact Pol
ish topology 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 algebrai
c and\nthe topological structure has been pursued actively over the past
40\nyears\, and numerous results have been obtained:\nmany of the most pop
ular automorphism groups\, including that of the\norder of the rationals a
nd of the random graph\,\ndo have unique Polish topologies.\n\nThe endomor
phism monoid of a first-order structure is algebraically\nnot as rich as i
ts automorphism group\, and\noften allows many different compatible topolo
gies. We show\, however\,\nthat there is a unique compatible Polish topolo
gy on the endomorphism\nmonoids of the random graph\, the weak linear orde
r\nof the rational numbers\, the random poset\, and many more.\n\nThis is
joint work with L. Elliott\, J. Jonušas\, J. D. Mitchell\, Y.\nPéresse\,
and C. Schindler.\n
LOCATION:https://stable.researchseminars.org/talk/PALS/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Laszlo Zadori (University of Szeged\, Hungary)
DTSTART:20211102T190000Z
DTEND:20211102T200000Z
DTSTAMP:20260404T094340Z
UID:PALS/16
DESCRIPTION:Title: On the primeness of 2-permutability\nby Laszlo Zadori (University
of Szeged\, Hungary) as part of PALS Panglobal Algebra and Logic Seminar\
n\n\nAbstract\nIn the talk\, I sketch a semantical proof of the conjecture
of Garcia and Taylor that congruence permutability is a prime Maltsev con
dition in the lattice of interpretability types of varieties. The proof wa
s obtained jointly with Gyenizse and Maróti\, and it is based on a combin
atorial 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-permutability when n>4 and some other result that we obtained for 3-p
ermutability.\n
LOCATION:https://stable.researchseminars.org/talk/PALS/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Miguel Couceiro (Universite de Lorraine\, France)
DTSTART:20211109T200000Z
DTEND:20211109T210000Z
DTSTAMP:20260404T094340Z
UID:PALS/17
DESCRIPTION:Title: Impossibility theorems over median algebras and beyond\nby Miguel
Couceiro (Universite de Lorraine\, France) as part of PALS Panglobal Alge
bra and Logic Seminar\n\n\nAbstract\nIn this presentation we consider aggr
egation procedures (consensus functions) over median algebras (ternary alg
ebras that subsume several ordered structures such as distributive lattice
s as well as several combinatorial structures such as median graphs). Our
starting point is a recent Arrow type impossibility result that states tha
t any median preserving consensus function over linearly ordered sets is t
rivial in the sense that it only depends on a single argument. In view of
this result\, a natural problem is then to identify those median algebras
that lead to such impossibility results. In particular\, we will show that
such impossibility results are inevitable when the codomain contains no c
ycle\, i.e.\, it is a "tree"\, and we will provide a surprisingly simple c
ondition that completely describes the latter as median algebras. To broad
en the talk\, we will also present some recent results that answer the par
ametrized version of this problem in which dependence is restricted to k a
rguments. We will conclude by observing that the underlying property to pr
oving such results is that of congruence distributivity\, which naturally
raises the question whether these results extend to other varieties of alg
ebras\, e.g.\, congruence modular varieties.\n
LOCATION:https://stable.researchseminars.org/talk/PALS/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Peter Jipsen (Chapman University)
DTSTART:20211116T210000Z
DTEND:20211116T220000Z
DTSTAMP:20260404T094340Z
UID:PALS/18
DESCRIPTION:Title: A survey of partially ordered algebras\nby Peter Jipsen (Chapman
University) as part of PALS Panglobal Algebra and Logic Seminar\n\n\nAbstr
act\nIn June 2003 I gave a talk at the Annual Meeting of the Association f
or Symbolic Logic\, University of Illinois at Chicago\, on “An online da
tabase of classes of algebraic structures”. This list of mathematical st
ructures is still on a website at http://math.chapman.edu/~jipsen/structur
es\, but is mostly just an alphabetical list of links that point to (somet
imes incomplete) axiomatic descriptions of about 300 categories of univers
al algebras. This past summer I started a project with Bianca Newell to re
create this list of (partially-ordered) algebraic structures as a computab
le LaTeX document that can be checked for consistency and updated more rel
iably than the previous collection of webpages. In this talk I will descri
be this project and recent joint work on partially ordered universal algeb
ras with José Gil-Ferez. In this setting\, a partially ordered universal
algebra is a poset with finitary operations that are order-preserving or o
rder-reversing in each argument\, and congruences are replaced by compatib
le preorders. Our investigations are based on an unpublished paper from 20
04 by Don Pigozzi: Partially ordered varieties and quasivarieties\, availa
ble at https://orion.math.iastate.edu/dpigozzi/notes/santiago_notes.pdf\n
LOCATION:https://stable.researchseminars.org/talk/PALS/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jennifer Hyndman (University of Northern British Columbia)
DTSTART:20211130T200000Z
DTEND:20211130T210000Z
DTSTAMP:20260404T094340Z
UID:PALS/19
DESCRIPTION:Title: A Reader's Guide to A Primer of Subquasivariety Lattices\nby Jenn
ifer Hyndman (University of Northern British Columbia) as part of PALS Pan
global Algebra and Logic Seminar\n\n\nAbstract\nBirkhoff and Mal'cev indep
endently posed the problem: Describe all\nsubquasivariety lattices. Nuraku
nov in 2009 showed that there are many\nunreasonable subquasivariety latti
ces where unreasonable means there is\nno algorithm to determine if a part
icular finite lattice is a\nsublattice. This sugests refinements of the o
riginal question are needed.\n\nA subquasvariety lattice has a natural equ
aclosure operator. Adaricheva\nand Gorbunov in 1989 defined an equaclosure
operator abstractly as\nhaving the properties that are known to hold in a
natural equaclosure\noperator.\n\nThe soon-to-be-published book\, A Prime
r of Quasivariety Lattices by Kira\nAdaricheva\, Jennifer Hyndman\, JB Nat
ion\, and Joy Nishida\, refines the\nabstract definition of equaclosure op
erator and provides some answers to\nthe refined question: When is a latti
ce with an equaclosure operator\nrepresentable by a subquasivariety lattic
e and the natural equaclosure\noperator. This presentation explores some o
f this new approach.\n
LOCATION:https://stable.researchseminars.org/talk/PALS/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Martin Goldstern (Technical University Vienna\, Austria)
DTSTART:20211207T200000Z
DTEND:20211207T210000Z
DTSTAMP:20260404T094340Z
UID:PALS/20
DESCRIPTION:Title: Cardinals below the continuum\nby Martin Goldstern (Technical Uni
versity Vienna\, Austria) as part of PALS Panglobal Algebra and Logic Semi
nar\n\n\nAbstract\nGeorg Cantor's "Continuum Hypothesis" (CH) postulates t
hat every\ninfinite set S of reals is either countable or equinumerous wit
h\nthe set of all reals. Using the axiom of choice this means that\nthe "
continuum" (the cardinality of the set of reals) is equal\nto aleph1\, the
smallest uncountable cardinal.\n\nDavid Hilbert's first problem asked if
CH is true\; we know now that\nneither CH nor non-CH can be proved from th
e usual axioms of\nset theory (ZFC). Paul Cohen's method of forcing allow
s us\nto build universes (structures satisfying ZFC) where the continuum\n
is arbitrarily large. \n\nThere are many relatives of the continuum\, suc
h as the answers\nto these questions: How many nulls sets (Lebesgue measur
e zero)\ndo we need to cover the real line? How many points do we need\nt
o get a non-null set? How many sequences (or convergent series)\ndo we nee
d to eventually dominate all sequences (convergent series)?\netc.\nAll the
se cardinals are located in the closed interval\nbetween aleph1 and the co
ntinuum.\n\nIn my talk I will present some of these cardinals and hint\nat
the methods used to construct universes where these cardinals\nhave presc
ribed values\, or satisfy strict inequalities.\n
LOCATION:https://stable.researchseminars.org/talk/PALS/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anna Zamojska-Dzienio (Warsaw University of Technology\, Poland)
DTSTART:20211012T190000Z
DTEND:20211012T200000Z
DTSTAMP:20260404T094340Z
UID:PALS/21
DESCRIPTION:Title: Biracks and solutions of the Yang-Baxter equation\nby Anna Zamojs
ka-Dzienio (Warsaw University of Technology\, Poland) as part of PALS Pang
lobal Algebra and Logic Seminar\n\n\nAbstract\nThe Yang-Baxter equation is
a fundamental equation occurring in integrable models in statistical mech
anics and quantum field theory. Description of all possible solutions seem
s to be extremely difficult and therefore there were some simplifications
introduced (V.G. Drinfeld 1992).\n\nBiracks are algebras studied in low-di
mensional topology which are in a one-to-one correspondence with set-theor
etical\, non-degenerate solutions to the Yang-Baxter equation. The use of
the language of biracks allows us to apply universal algebra tools. In thi
s talk\, we describe the generalized retraction relation on a birack which
gives new classes of solutions.\n\nThis is joint work with Premysl Jedlic
ka and Agata Pilitowska.\n
LOCATION:https://stable.researchseminars.org/talk/PALS/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michael Kompatscher (Charles University Prague)
DTSTART:20211130T190000Z
DTEND:20211130T200000Z
DTSTAMP:20260404T094340Z
UID:PALS/22
DESCRIPTION:Title: G-terms and the local-global property\nby Michael Kompatscher (Ch
arles University Prague) as part of PALS Panglobal Algebra and Logic Semin
ar\n\n\nAbstract\nLet $G$ be a permutation group on a $n$-element set. We
then say 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. $\\mathbf A \\models t(x_1\,\\ldots\,x_n) \\approx t(x_{\\pi(1)}\,\\ld
ots\,x_{\\pi(n)})$ for all $\\pi \\in G$. Since $G$-terms appear in the st
udy of constraint satisfaction problems and elsewhere\, it is natural to a
sk for their classification up to interpretability. In the first part of m
y talk I would like to share a few partial results on this problem.\n\nIn
the second 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 s
howing that deciding a given Maltsev condition is in P\, is to show that i
t suffices to check the condition locally (i.e. on subsets of bounded size
). We show that this „local-global“ approach works for all $G$-terms i
nduced by regular permutation groups $G$ (and direct products of them)\, b
ut fails 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://stable.researchseminars.org/talk/PALS/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Charlotte Aten (University of Rochester)
DTSTART:20220125T200000Z
DTEND:20220125T210000Z
DTSTAMP:20260404T094340Z
UID:PALS/23
DESCRIPTION:Title: Orientable smooth manifolds are essentially quasigroups\nby Charl
otte Aten (University of Rochester) as part of PALS Panglobal Algebra and
Logic Seminar\n\n\nAbstract\nIn my recent work with Semin Yoo we produced
a generalization of a construction of Herman and Pakianathan which assigns
to each finite noncommutative group a closed surface in a functorial mann
er. We give a pair of functors whose domain is a subcategory of a variety
of n-ary quasigroups. The first of these functors assigns to each such qua
sigroup a smooth\, flat Riemannian manifold while the second assigns to ea
ch quasigroup a topological manifold which is a subspace of the metric com
pletion of the aforementioned Riemannian manifold. I will give examples of
these constructions\, draw some pictures\, and argue that all homeomorphi
sm classes of smooth orientable manifolds arise from this construction. I
will then discuss a connection with the Evans Conjecture on partial Latin
squares\, give its implication for orientable surfaces\, and state a relat
ed problem applicable to our construction for compact n-manifolds.\n
LOCATION:https://stable.researchseminars.org/talk/PALS/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ross Willard (University of Waterloo)
DTSTART:20220201T200000Z
DTEND:20220201T210000Z
DTSTAMP:20260404T094340Z
UID:PALS/24
DESCRIPTION:Title: Characterizing [alpha\,beta]=0 using Kiss terms\nby Ross Willard
(University of Waterloo) as part of PALS Panglobal Algebra and Logic Semin
ar\n\n\nAbstract\nMany years ago\, Kiss proved that the commutator relatio
n [alpha\,beta]=0 can be characterized in congruence modular varieties by
a simple condition involving a certain kind of 4-ary term\, which is now c
alled a Kiss term. Seven years ago\, Kearnes\, Szendrei and I claimed to
extend this characterization to varieties having a difference term\, and w
e used this at a key step in proving our finite basis theorem for finite a
lgebras 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
question the validity of our finite basis theorem. In this talk I will s
ketch a new (correct) proof of this extension. This is joint work with K
eith Kearnes and Agnes Szendrei.\n
LOCATION:https://stable.researchseminars.org/talk/PALS/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dragan Masulovic (University of Novi Sad)
DTSTART:20220208T200000Z
DTEND:20220208T210000Z
DTSTAMP:20260404T094340Z
UID:PALS/25
DESCRIPTION:Title: Dual Ramsey properties for classes of algebras\nby Dragan Masulov
ic (University of Novi Sad) as part of PALS Panglobal Algebra and Logic Se
minar\n\n\nAbstract\nAlmost any reasonable class of finite relational stru
ctures has the Ramsey property or a precompact Ramsey expansion. In contra
st to that\, the list of classes of finite algebras with the precompact Ra
msey expansion is surprisingly short. In this talk we show that any nontri
vial variety (that is\, equationally defined class of algebras) enjoys var
ious dual Ramsey properties. We develop a completely new set of strategies
that rely on the fact that left adjoints preserve the dual Ramsey propert
y\, 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 small Ramsey degrees\, and that every finite algebra has finite dual
big Ramsey degree in the free algebra on countably many free generators.
As usual\, these come as consequences of ordered versions of the statement
s.\n
LOCATION:https://stable.researchseminars.org/talk/PALS/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bill De Witt (University of St Andrews)
DTSTART:20220215T200000Z
DTEND:20220215T210000Z
DTSTAMP:20260404T094340Z
UID:PALS/26
DESCRIPTION:Title: The number of countable subdirect powers of finite unary algebras
\nby Bill De Witt (University of St Andrews) as part of PALS Panglobal Alg
ebra and Logic Seminar\n\n\nAbstract\nThe number of subdirect powers of an
finite algebraic structure is a question that has appeared at various poi
nts in recent history. The situation is known in full for groups\, and to
some extent in semigroups. We answer the question for unary algebras\, and
look at how the situation is more complicated for infinite algebras. We t
hen discuss what these results can tell us about the general question\, an
d how it ties into other topics such as boolean separation.\n
LOCATION:https://stable.researchseminars.org/talk/PALS/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jordan DuBeau (CU Boulder)
DTSTART:20220222T200000Z
DTEND:20220222T210000Z
DTSTAMP:20260404T094340Z
UID:PALS/27
DESCRIPTION:Title: Jónsson Jónsson-Tarski algebras\nby Jordan DuBeau (CU Boulder)
as part of PALS Panglobal Algebra and Logic Seminar\n\n\nAbstract\nFor an
infinite algebra J in a countable algebraic language\, we say J is Jónsso
n if it has no proper subalgebra of the same cardinality as J. This talk e
xplores Jónsson algebras in a particular variety: the variety of Jónsson
-Tarski algebras. When a Jónsson algebra of size $\\aleph_1$ was construc
ted in this variety\, it showed that minimal varieties can contain uncount
able Jónsson algebras. We will describe that construction and two further
results\, demonstrating exactly which cardinalities are possible for Jón
sson Jónsson-Tarski algebras\, and how many pairwise nonisomorphic Jónss
on Jónsson-Tarski algebras exist. We discuss implications for other varie
ties and Jónsson algebras in general.\n
LOCATION:https://stable.researchseminars.org/talk/PALS/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Paolo Lipparini (Universita' di Tor Vergata\, Rome\, Italy)
DTSTART:20220329T190000Z
DTEND:20220329T200000Z
DTSTAMP:20260404T094340Z
UID:PALS/28
DESCRIPTION:Title: Relative lengths of Maltsev conditions\nby Paolo Lipparini (Unive
rsita' di Tor Vergata\, Rome\, Italy) as part of PALS Panglobal Algebra an
d Logic Seminar\n\n\nAbstract\nThe study of Maltsev conditions is a signif
icant part of universal algebra\, with classical characterizations of fami
lies of varieties (congruence permutable\, distributive\, modular...) and
recent advanced results by Hobby\, McKenzie\, Kearnes\, Kiss\, among other
s. In particular\, the interplay between distinct Maltsev conditions for c
ongruence modular varieties has led to a refined theory for such varieties
.\n\nRecall that a Maltsev condition is\, roughly\, a statement of the for
m "there are some n and terms t1\,...\,tn such that a certain finite set o
f equations hold". As we mentioned\, many deep and sophisticated results a
re known about Maltsev conditions. On the other hand\, when two conditions
are compared\, really little is known about the exact value of the smalle
st n as above. For example\, a simple observation by A. Day asserts that i
f 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 b
est of our knowledge\, an exact solution is not yet known.\n\nA deeper pro
blem (asked by Lakser\, Taylor\, Tschantz in 1985) concerns the relative l
engths of sequences of Day and Gumm terms characterizing congruence modula
rity. More recently\, Kazda\, Kozik\, McKenzie\, Moore provided still anot
her characterization of congruence distributive and modular varieties by m
eans of "directed" terms. Again\, the exact relationships between the leng
ths of the sequences of terms is not known. A solution of the above proble
ms is supposed to provide either interesting exotic examples of congruence
modular and distributive varieties\, or more refined structure theorems.\
n\nWe shall present recent results about the above Day\, LTT and KKMM prob
lems\, with an unexpected application to congruence distributive varieties
.\n
LOCATION:https://stable.researchseminars.org/talk/PALS/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michael Levet (CU Boulder)
DTSTART:20220419T190000Z
DTEND:20220419T200000Z
DTSTAMP:20260404T094340Z
UID:PALS/29
DESCRIPTION:Title: Weisfeiler—Leman for Group Isomorphism: Action Compatibility\nb
y Michael Levet (CU Boulder) as part of PALS Panglobal Algebra and Logic S
eminar\n\n\nAbstract\nThe Weisfeiler—Leman (WL) algorithm is a key combi
natorial subroutine in Graph Isomorphism\, that (for fixed $k \\geq 2$) co
mputes an isomorphism invariant coloring of the k-tuples of vertices. Brac
hter & Schweitzer (LICS 2020) recently adapted WL to the setting of groups
. Using a classical Ehrenfeucht-Fra\\"iss\\'e pebble game\, we will show t
hat Weisfeiler—Leman serves as a polynomial-time isomorphism test for se
veral families of groups previously shown to be in $\\textsf{P}$ by multip
le methods. These families of groups include:\n\n(1) Coprime extensions $H
\\ltimes N$\, where $H$ is $O(1)$-generated and the normal Hall subgroup
$N$ is Abelian (Qiao\, Sarma\, & Tang\, STACS 2011).\n\n(2) Groups without
Abelian normal subgroups (Babai\, Codenotti\, & Qiao\, ICALP 2012). \n\n
\nIn both of these cases\, the previous strategy involved identifying key
group-theoretic structure that could then be leveraged algorithmically\, r
esulting in different algorithms for each family. A common theme among the
se is that the group-theoretic structure is mostly about the action of one
group on another. Our main contribution is to show that a single\, combin
atorial algorithm (Weisfeiler-Leman) can identify those same group-theoret
ic structures in polynomial time.\n\n \n\nWe also show that Weisfeiler—L
eman requires only a constant number of rounds to identify groups from eac
h of these families. Combining this result with the parallel WL implementa
tion due to Grohe & Verbitsky (ICALP 2006)\, this improves the upper bound
for isomorphism testing in each of these families from $\\textsf{P}$ to $
\\textsf{TC}^0$.\n\n \n\nThis is joint work with Joshua A. Grochow.\n
LOCATION:https://stable.researchseminars.org/talk/PALS/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:James Rooney (McMaster University\, Canada)
DTSTART:20220301T200000Z
DTEND:20220301T210000Z
DTSTAMP:20260404T094340Z
UID:PALS/30
DESCRIPTION:Title: Nonlinear idempotent Mal'tsev Condition Satisfaction Problems: why se
milattices are hard and lattices are easier\nby James Rooney (McMaster
University\, Canada) as part of PALS Panglobal Algebra and Logic Seminar\
n\n\nAbstract\nIn their 2020 article "Deciding some Mal'tsev conditions in
finite idempotent algebras" Kazda and Valeriote conjecture that for a lin
ear strong Mal'tsev condition the associated idempotent Mal'tsev condition
satisfaction problem (MCSP) will always be polynomial-time decidable. In
an earlier-published 2019 article Freese\, Nation and Valeriote showed tha
t testing for a semilattice term (a nonlinear condition) is EXPTIME-comple
te even for idempotent algebras. \n\nWhile preparing my PhD thesis I inves
tigated the hypothesis that nonlinear Mal'tsev conditions might always be
EXPTIME-complete to detect. I was able to prove that there are nonlinear M
al'tsev conditions whose related idempotent MCSPs are in the class NP. Ass
uming that NP is not EXPTIME this provides the first examples of nonlinear
Mal'tsev conditions whose idempotent MCSPs are not EXPTIME-complete. The
existence of lattice terms is one such example.\n\nIn this talk we briefly
revisit the 2019 result of Freese\, Nation and Valeriote before sketching
the details of my proof that detection of lattice terms in an idempotent
algebra is an NP problem.\n
LOCATION:https://stable.researchseminars.org/talk/PALS/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Monica VanDieren (Robert Morris University)
DTSTART:20220308T200000Z
DTEND:20220308T210000Z
DTSTAMP:20260404T094340Z
UID:PALS/31
DESCRIPTION:Title: Twenty years of tameness\nby Monica VanDieren (Robert Morris Univ
ersity) 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 abstract elementary classes. For over three decades\, limited progres
s was made\, most of which required additional set theoretic axioms. In 20
01\, Rami Grossberg and I introduced the model theoretic concept of tamene
ss which opened the door for stability results in abstract elementary clas
ses in ZFC. During the following 20 years\, tameness along with limit mod
els have been used by several mathematicians to prove categoricity theorem
s and to develop non-first order analogs to forking calculus and stability
theory\, solving a very large number of problems posed by Shelah in ZFC.
Recently\, Marcos Mazari-Armida found applications to Abelian group theory
and ring theory. In this presentation I will highlight some of the more
surprising results involving tameness and limit models from the past 20 ye
ars.\n
LOCATION:https://stable.researchseminars.org/talk/PALS/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andres Villaveces (Universidad Nacional de Colombia – Bogotá)
DTSTART:20220315T190000Z
DTEND:20220315T200000Z
DTSTAMP:20260404T094340Z
UID:PALS/32
DESCRIPTION:Title: On the small index property for AECs with strong amalgamation propert
ies\nby Andres Villaveces (Universidad Nacional de Colombia – Bogot
á) as part of PALS Panglobal Algebra and Logic Seminar\n\n\nAbstract\nWe
first revisit notions of interpretability and internality in a category-th
eoretical language (for first order theories)\, reframing work of Hrushovs
ki and Kamensky in a formalism derived from Makkai's early work. We then d
escribe the issue of recovering the bi-intepretability class of a theory i
n terms of the automorphism group of a saturated model\, and the role of t
he "Small Index Property" (SIP) - a way of recovering the topology of a gr
oup action from purely algebraic information.\n\nWe then turn to abstract
elementary classes\, and discuss the same notions\, in the opposite order:
first\, two situations where a Small Index Property holds (joint work wit
h Ghadernezhad)\, and then some applications to the problem of interpretat
ion and reconstruction\, adapted to abstract elementary classes.\n
LOCATION:https://stable.researchseminars.org/talk/PALS/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Thomas Kucera (University of Manitoba)
DTSTART:20220412T190000Z
DTEND:20220412T200000Z
DTSTAMP:20260404T094340Z
UID:PALS/33
DESCRIPTION:Title: Saturated free algebras and almost indiscernible theories: an overvie
w\nby Thomas Kucera (University of Manitoba) as part of PALS Panglobal
Algebra and Logic Seminar\n\n\nAbstract\nThis is work motivated by questi
ons at the intersection of algebra and model theory\, and using advanced t
echniques of model theory.\nBaldwin and Shelah (Algebra Universalis\, 1983
) studied saturated free algebras. Pillay and Sklinos (Bull. Symb. Logic 2
015)\, following the lead of this paper\, studied "almost indiscernible th
eories"\, taking the opportunity to refine the statements of the major res
ults and improve the proofs. We extend these results to large infinite con
texts\, both in the size of the language and the kinds of tuples allowed i
n a "basis"\; and return to examples and applications in algebra\, in part
icular in the theory of modules.\nThe theory develops by noting various an
alogies. The model-theoretic concept 'indiscernible sequence' generalizes
'linearly independent set' in a vector space\, 'free (generating) set' of
an algebra\, 'algebraic independence' in an algebraically closed field\, a
nd similar concepts. 'Saturated model' generalizes concepts such as 'injec
tive envelope of a module'\, 'algebraic closure of a field'\, and similar
constructions. 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 cons
traints\, but nonetheless there are natural motivating examples.\nI start
with some history and motivation from algebra\, then I will give an overvi
ew of the main model theoretic concepts and techniques\, motivating them a
s much as possible by examples from algebra. I'll state the new technical
structural results for almost indiscernible theories in our more general c
ontext\, with no more than informal 'hand-waving' about the proof techniqu
es. Then I will present some consequences for free algebras and for theori
es of modules\, including structure theorems and some examples. I conclude
with a list of open questions.\nThis is joint work with Anand Pillay.\n
LOCATION:https://stable.researchseminars.org/talk/PALS/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nik Ruskuc (University of St Andrews)
DTSTART:20220405T190000Z
DTEND:20220405T200000Z
DTSTAMP:20260404T094340Z
UID:PALS/34
DESCRIPTION:Title: Direct and subdirect products in combinatorial algebra\, groups and s
emigroups\nby Nik Ruskuc (University of St Andrews) as part of PALS Pa
nglobal Algebra and Logic Seminar\n\n\nAbstract\nFor a while now\, Peter M
ayr and I have been looking at properties of direct and\nsubdirect product
s in algebra\, often motivated by some well known or particularly\nnice re
sults from combinatorial group theory. The topics include finite generatio
n\,\nfinite presentability\, residual finiteness\, infinite subdirect powe
rs\, etc. A fairly\nrich landscape has emerged over the years. Perhaps uns
urprisingly the most general\nresults can be obtained in the context of co
ngruence permutable or modular varieties.\nThis then leaves semigroups out
side\, 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\nstran
ds\, results and comparisons.\n
LOCATION:https://stable.researchseminars.org/talk/PALS/34/
END:VEVENT
END:VCALENDAR