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BEGIN:VEVENT
SUMMARY:Mikhail Zaicev (Moscow State University)
DTSTART;VALUE=DATE-TIME:20201204T110000Z
DTEND;VALUE=DATE-TIME:20201204T120000Z
DTSTAMP;VALUE=DATE-TIME:20210612T223746Z
UID:AlgAndLogic/1
DESCRIPTION:Title: Polynomial identities:anomalies of codimension growth\nby Mikhail
Zaicev (Moscow State University) as part of Algebra and Logic Seminar\n\n\
nAbstract\nWe consider numerical invariants associated with polynomial ide
ntities of algebras over a field of characteristic zero. Given an algebra
$A$\, one can construct a sequence of non-negative integers ${c_n(A)}\, n
= 1\, 2\, . . .$ \, called the codimensions of $A$\, which is an important
numerical characteristic of identical relations of $A$. In the present ta
lk we discuss asymptotic behavior of codimension sequence in different cla
sses of algebras.\n
LOCATION:https://researchseminars.org/talk/AlgAndLogic/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Silvia Boumova (Faculty of Mathematics and Informatics\,University
of Sofia\, and Institute of Mathematics and Informatics\, Bulgarian Acade
my of Sciences)
DTSTART;VALUE=DATE-TIME:20201211T110000Z
DTEND;VALUE=DATE-TIME:20201211T120000Z
DTSTAMP;VALUE=DATE-TIME:20210612T223746Z
UID:AlgAndLogic/2
DESCRIPTION:Title: Margarete Wolf\, Symmetric Polynomials in Noncommuting Variables and N
oncommutative Invariant Theory\nby Silvia Boumova (Faculty of Mathemat
ics and Informatics\,University of Sofia\, and Institute of Mathematics an
d Informatics\, Bulgarian Academy of Sciences) as part of Algebra and Logi
c Seminar\n\n\nAbstract\nIn 1936 Margarete Caroline Wolfpublished a paper
where she proved that the symmetric polynomials in the free associative al
gebra form a free subalgebra and described the system of free generators.
The purpose of the talk is to present these results from modern point of v
iew and their relations with other results in the frames of commutative a
nd noncommutative invariant theory.\n\nSatellite talk to the Webinar Women
in Mathematics in South-Eastern Europe organized by the International Cen
ter for Mathematical Sciences - Sofia.\n
LOCATION:https://researchseminars.org/talk/AlgAndLogic/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Denjoe O'Connor (School of Theoretical Physics\, Dublin Institute
for Advanced Studies)
DTSTART;VALUE=DATE-TIME:20201215T130000Z
DTEND;VALUE=DATE-TIME:20201215T140000Z
DTSTAMP;VALUE=DATE-TIME:20210612T223746Z
UID:AlgAndLogic/3
DESCRIPTION:Title: Hagedorn transitions in Matrix Membranes\nby Denjoe O'Connor (Scho
ol of Theoretical Physics\, Dublin Institute for Advanced Studies) as part
of Algebra and Logic Seminar\n\n\nAbstract\nMatrix models that originate
in non-commutative deformations of Membranes result in models related to d
imensional reductions of higher dimensional Yang-Mills theories. The confi
ning/deconfining transition becomes a Hagedorn transition in this setting
and the models are believed to have gravitational duals. I will discuss re
cent progress in understanding these models and their physics.\n
LOCATION:https://researchseminars.org/talk/AlgAndLogic/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vesselin Drensky (Institute of Mathematics and Informatics)
DTSTART;VALUE=DATE-TIME:20201218T075000Z
DTEND;VALUE=DATE-TIME:20201218T082000Z
DTSTAMP;VALUE=DATE-TIME:20210612T223746Z
UID:AlgAndLogic/4
DESCRIPTION:Title: New examples of fundamental algebras (joint project with Luisa Carini\
, University of Messina\, Italy)\nby Vesselin Drensky (Institute of Ma
thematics and Informatics) as part of Algebra and Logic Seminar\n\n\nAbstr
act\nFundamental algebras are the building blocks used to generate any var
iety of finite basic rank of associative algebras over a field of characte
ristic 0. Our first result describes the fundamental algebras which are te
nsor products of any number of finite dimensional Grassmann algebras. Then
we show that the triangular product of two fundamental algebras is again
fundamental. The proofs are based on the recent description of fundamental
algebras in the language of cocharacter sequences due to Giambruno\, Polc
ino Milies and Zaicev combined with other techniques from the theory of PI
-algebras.\n
LOCATION:https://researchseminars.org/talk/AlgAndLogic/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vassil Kanev (Institute of Mathematics and Informatics)
DTSTART;VALUE=DATE-TIME:20201218T082000Z
DTEND;VALUE=DATE-TIME:20201218T085000Z
DTSTAMP;VALUE=DATE-TIME:20210612T223746Z
UID:AlgAndLogic/5
DESCRIPTION:Title: Hurwitz modular varieties parametrizing coverings with fixed monodromy
group\nby Vassil Kanev (Institute of Mathematics and Informatics) as
part of Algebra and Logic Seminar\n\n\nAbstract\nGiven a projective curve
$Y$\, a transitive subgroup G of the symmetric group $S_d$ and a natural n
umber $n$ the talk is devoted to smooth families of coverings of $Y$ of de
gree $d$ branched in $n$ points whose monodromy group is $G$. These famili
es form a category whose morphisms correspond to the pullback by morphisms
of the bases of the families. Under certain restrictions on the group $G$
we construct a universal family in this category. We discuss how to chang
e the category\, so that the universal family exists without any restricti
ons on $G$.\n
LOCATION:https://researchseminars.org/talk/AlgAndLogic/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ivan Chipchakov (Institute of Mathematics and Informatics)
DTSTART;VALUE=DATE-TIME:20201218T085500Z
DTEND;VALUE=DATE-TIME:20201218T092000Z
DTSTAMP;VALUE=DATE-TIME:20210612T223746Z
UID:AlgAndLogic/6
DESCRIPTION:Title: Fields of dimension one\, normal over a global or local field\nby
Ivan Chipchakov (Institute of Mathematics and Informatics) as part of Alge
bra and Logic Seminar\n\n\nAbstract\nLet $E$ be a normal extension of a gl
obal or local field $K$. We show that if $K$ is a local field\, $v$ is its
(natural) discrete valuation\, and $q$ is the characteristic of the resid
ue field of $(K\, v)$\, then $E$ is a field of dimension $dim(E) ≤ 1$ if
and only if the following conditions hold: for each prime number $p ≠ q
$\, $E$ contains as a subfield an unramified $ℤ_p$-extension $K_p$ of $K
$\; the restriction $p ≠ q$ is dropped in case the value group $v’(E)$
is $q$-indivisible\, where $v’$ is the unique\, up-to equivalence\, val
uation of E extending $v$. When $K$ is a global field and $E/K$ is abelian
and tamely ramified\, nontrivial Krull valuations of $E$ are discrete\; a
lso\, $dim(E) ≤ 1$ if and only if $E$ is a nonreal field and the residue
fields of these valuations are algebraically closed. Under the hypothesis
that $K$ is a global field\, $E/K$ is abelian and $dim(E) ≤ 1$\, this i
s used for proving the existence\, for each $n \\in ℕ$\, of n-variate ho
mogeneous polynomials of degree $n$ with coefficients in $E$\, which viola
te the local-to global principle over $E$.\n
LOCATION:https://researchseminars.org/talk/AlgAndLogic/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tatiana Gateva-Ivanova (Institute of Mathematics and Informatics)
DTSTART;VALUE=DATE-TIME:20201218T092000Z
DTEND;VALUE=DATE-TIME:20201218T095000Z
DTSTAMP;VALUE=DATE-TIME:20210612T223746Z
UID:AlgAndLogic/7
DESCRIPTION:Title: Associative algebras and Lie algebras defined by Lyndon words\nby
Tatiana Gateva-Ivanova (Institute of Mathematics and Informatics) as part
of Algebra and Logic Seminar\n\n\nAbstract\nAssume that $X = {x1\,…\, xg
}$ is a finite alphabet and $\\bf{k}$ is a field. We study the class $C(X
\;W)$ of associative graded $\\bf{k}$-algebras $A$ generated by $X$ and wi
th a fixed obstructions set $W$ consisting of Lyndon words in the alphabet
$X$. Important examples are the monomial algebras $A = \\bf{k}⟨X⟩/(W)
$\, where $W$ is an antichain of Lyndon words of arbitrary cardinality and
the enveloping algebra $Ug$ of any $X$-generated Lie $\\bf{k}$-algebra $g
= {Lie}(X)=([W])$\, whenever the set of standard bracketings $[W] = {[w]
| w \\in W}$ is a Gröbner-Shirshov Lie basis. We prove that all algebras
$A$ in $C(X\;W)$ share the same Poincare-Birkhoff-Witt type $\\bf{k}$-basi
s built out of the so called Lyndon atoms $N$ (determined uniquely by $W$)
but\, in general\, $N$ may be infinite. Moreover\, $A$ has polynomial gro
wth if and only if the set of Lyndon atoms $N$ is finite. In this case $A$
has a $\\bf{k}$-basis $N = {l_1^{α1} l_1^{α2}… l_1^{αd}| α_i ≥ 0\
, 1≤ i ≤ d}$\, where $N = {l_1\,…\,l_d}$. Surprisingly\, in the case
when $A$ has polynomial growth its global dimension does not depend on th
e shape of its defining relations but only on the set of obstructions $W$:
We prove that if $A$ has polynomial growth of degree $d$ then $A$ has glo
bal dimension $d$ and is standard finitely presented\, with $d-1 ≤|W|≤
d(d - 1)/2$. We study when the set of standard $[W] = {[w] | w ∊ W}$ is
a Gröbner-Shirshov Lie basis. We use our general results to classify the
Artin-Schelter regular algebras $A$ generated by two elements\, with defi
ning relations $[W]$ and global dimension $≤ 7$.\n\nReferences\n\n[1] Ta
tiana Gateva-Ivanova\, Algebras defined by Lyndon words and Artin-Schelter
regularity\, To appear in The Transactions AMS arXiv preprint arXiv:1905.
11281\n(2019).\n\n[2] Tatiana Gateva-Ivanova\, Gunnar Floystad\, Monomial
algebras defined by Lyndon words\, Journal of Algebra 403 (2014)\, 470{496
.\n\n[3] Tatiana Gateva-Ivanova\, Quadratic algebras\, Yang-Baxter equatio
n\, and Artin-Schelter regularity\, Advances in Mathematics 230 (2012)\, 2
152{2175.\n\n[4] Tatiana Gateva-Ivanova\, Global dimension of associative
algebras\, Applied Algebra\, Algebraic Algorithms and Error-Correcting Cod
es\, Lecture Notes in Computer Science\, 357 (1989)\, 213-229.\n
LOCATION:https://researchseminars.org/talk/AlgAndLogic/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jörg Koppitz (Institute of Mathematics and Informatics)
DTSTART;VALUE=DATE-TIME:20201218T095500Z
DTEND;VALUE=DATE-TIME:20201218T101500Z
DTSTAMP;VALUE=DATE-TIME:20210612T223746Z
UID:AlgAndLogic/8
DESCRIPTION:Title: The generators of the semigroup of all transformations preserving a cr
own\nby Jörg Koppitz (Institute of Mathematics and Informatics) as pa
rt of Algebra and Logic Seminar\n\n\nAbstract\nIn this presentation\, we w
ill give a survey about the status of the study of monoids of transformati
ons preserving a fence and a crown\, respectively. In particular\, we will
consider the monoid of automorphisms preserving fence and crown\, respect
ively. Finally we will give an idea of the current status of study of the
rank of the monoid of all partial transformations preserving a finite crow
n.\n
LOCATION:https://researchseminars.org/talk/AlgAndLogic/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dimitrinka Vladeva (University of Forestry\, Sofia)
DTSTART;VALUE=DATE-TIME:20201218T101500Z
DTEND;VALUE=DATE-TIME:20201218T103000Z
DTSTAMP;VALUE=DATE-TIME:20210612T223746Z
UID:AlgAndLogic/9
DESCRIPTION:Title: Derivations of skew Ore polynomial semirings\nby Dimitrinka Vladev
a (University of Forestry\, Sofia) as part of Algebra and Logic Seminar\n\
n\nAbstract\nIn this project we investigate derivations in the semiring of
skew Ore polynomials over an additively idempotent semiring. We show that
multiplying each polynomial by $x$ on left is a derivation and construct
commutative idempotent semiring consisting of derivations of a skew polyno
mial semiring. We introduce hereditary derivations and generalized heredit
ary derivations defined as derivations acting only over the coefficients o
f the polynomial and also construct an $S$-derivation in the classical sen
se of Jacobson. Finally we give a description of the derivations in a skew
polynomial semiring $S[x]$\, assuming that $S$ is an additively idempoten
t semiring and show that an arbitrary derivation can be represented by a g
eneralized hereditary derivation and an $S$-derivation.\n
LOCATION:https://researchseminars.org/talk/AlgAndLogic/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vladimir S. Gerdjikov (Institute of Mathematics and Informatics)
DTSTART;VALUE=DATE-TIME:20201218T110000Z
DTEND;VALUE=DATE-TIME:20201218T113000Z
DTSTAMP;VALUE=DATE-TIME:20210612T223746Z
UID:AlgAndLogic/10
DESCRIPTION:Title: Recursion operators and the hierarchies of MKdV equations related to
$D_4^{(1)}$\, $D_4^{(2)}$ and $D_4^{(3)}$ Kac-Moody algebras\nby Vladi
mir S. Gerdjikov (Institute of Mathematics and Informatics) as part of Alg
ebra and Logic Seminar\n\n\nAbstract\nReference:\n\nV. S. Gerdjikov\, A.A.
Stefanov\, I. D. Iliev\, G. P. Boyadjiev et al. Recursion operators and
the hierarchies of MKdV equations related to $D_4^{(1)}$\, $D_4^{(2)}$
and $D_4^{(3)}$ Kac-Moody algebras. \nTheoretical and Mathematical Physics
\, 204 (3): 1110–1129 (2020)\, ArXiv:2006.16323 [nlin.SI]\n
LOCATION:https://researchseminars.org/talk/AlgAndLogic/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Elitza Hristova (Institute of Mathematics and Informatics)
DTSTART;VALUE=DATE-TIME:20201218T113000Z
DTEND;VALUE=DATE-TIME:20201218T115000Z
DTSTAMP;VALUE=DATE-TIME:20210612T223746Z
UID:AlgAndLogic/11
DESCRIPTION:Title: Regularity of algebras of $O(n)$-invariants using Hilbert series\
nby Elitza Hristova (Institute of Mathematics and Informatics) as part of
Algebra and Logic Seminar\n\n\nAbstract\nLet $W$ be a polynomial represent
ation of the complex general linear group $GL(n)$. In this talk\, we discu
ss the question when the algebra of invariants $ℂ[W]^{O(n)}$ is regular\
, i.e. isomorphic to a polynomial algebra. For $n=2$\, we give a list of p
olynomial $GL(2)$-representations\, so that if $ℂ[W]^{O(2)}$ is regular\
, then up to an $O(2)$-isomorphism $W$ is in this list. For general $n$\,
we prove regularity in particular cases. The talk is based on a joint work
with Vesselin Drensky.\n
LOCATION:https://researchseminars.org/talk/AlgAndLogic/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Veselin Filev (Institute of Mathematics and Informatics)
DTSTART;VALUE=DATE-TIME:20201218T115500Z
DTEND;VALUE=DATE-TIME:20201218T122500Z
DTSTAMP;VALUE=DATE-TIME:20210612T223746Z
UID:AlgAndLogic/12
DESCRIPTION:Title: Holographic Berkooz-Douglas Matrix Model at Finite Temperature\nb
y Veselin Filev (Institute of Mathematics and Informatics) as part of Alge
bra and Logic Seminar\n\n\nAbstract\nI will report on ongoing work to cons
truct the holographic dual supergravity background of the Berkooz-Douglas
matrix model at finite temperature.\n
LOCATION:https://researchseminars.org/talk/AlgAndLogic/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hristo Iliev (Institute of Mathematics and Informatics)
DTSTART;VALUE=DATE-TIME:20201218T122500Z
DTEND;VALUE=DATE-TIME:20201218T124500Z
DTSTAMP;VALUE=DATE-TIME:20210612T223746Z
UID:AlgAndLogic/13
DESCRIPTION:Title: Families of curves on ruled surfaces and applications to the Hilbert
scheme of curves\nby Hristo Iliev (Institute of Mathematics and Inform
atics) as part of Algebra and Logic Seminar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/AlgAndLogic/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vilislav Buchackchiev (Institute of Mathematics and Informatics)
DTSTART;VALUE=DATE-TIME:20201218T125000Z
DTEND;VALUE=DATE-TIME:20201218T130500Z
DTSTAMP;VALUE=DATE-TIME:20210612T223746Z
UID:AlgAndLogic/14
DESCRIPTION:Title: Forecasting of the Bulgarian House price index using some macroeconom
ic indicators\nby Vilislav Buchackchiev (Institute of Mathematics and
Informatics) as part of Algebra and Logic Seminar\n\n\nAbstract\nWith the
introduction of IFRS9 accounting standard in 2018 many banks were required
to use statistical models for forecasting the liquidation values of house
s used as collateral for mortgages. The nature of estimation of the expect
ed credit loss requires the evaluation of levels of House Price Index from
available statistical data which is\, usually\, one year old. Several spe
cifications of the models were studied to confirm that HPI is correlated w
ith various indicators\, including RE market demand\, construction industr
y business cycle and general macroeconomic environment. The general conclu
sion was\, however\, that the two most prominent drivers of HPI remain the
interest rates and the internal inertia of the RE market.\n
LOCATION:https://researchseminars.org/talk/AlgAndLogic/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dimiter Dobrev (Institute of Mathematics and Informatics)
DTSTART;VALUE=DATE-TIME:20201218T130500Z
DTEND;VALUE=DATE-TIME:20201218T133500Z
DTSTAMP;VALUE=DATE-TIME:20210612T223746Z
UID:AlgAndLogic/15
DESCRIPTION:Title: Language for Description of Worlds\nby Dimiter Dobrev (Institute
of Mathematics and Informatics) as part of Algebra and Logic Seminar\n\n\n
Abstract\nWe will reduce the task of creating AI to the task of finding an
appropriate language for description of the world. This will not be a pro
graming language because programing languages describe only computable fun
ctions\, while our language will describe a somewhat broader class of func
tions. Another specificity of this language will be that the description w
ill consist of separate modules. This will enable us look for the descript
ion of the world automatically such that we discover it module after modul
e. Our approach to the creation of this new language will be to start with
a particular world and write the description of that particular world. Th
e point is that the language which can describe this particular world will
be appropriate for describing any world.\n
LOCATION:https://researchseminars.org/talk/AlgAndLogic/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Valentin Iliev (Institute of Mathematics and Informatics)
DTSTART;VALUE=DATE-TIME:20201218T140000Z
DTEND;VALUE=DATE-TIME:20201218T143000Z
DTSTAMP;VALUE=DATE-TIME:20210612T223746Z
UID:AlgAndLogic/16
DESCRIPTION:Title: The Uncertainty Principle for Screening Tests\nby Valentin Iliev
(Institute of Mathematics and Informatics) as part of Algebra and Logic Se
minar\n\n\nAbstract\nThe aim of this elementary note is to describe the re
lation between the conditional probabilities of a false positive and a fal
se negative screening test. Non-formally\, we can state the main result of
the paper as an Uncertainty Principle: In general\, if one has better kno
wledge that the test is really positive (the probability F_+ of false posi
tive test is small)\, then for one is hard to know that the test is really
negative (the probability F_- of false negative test is large). And the b
etter one knows that the test is really negative (F_- is small)\, the hard
er it is to know that the test is really positive (F_+ is large).\n
LOCATION:https://researchseminars.org/talk/AlgAndLogic/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tatyana Ivanova (Institute of Mathematics and Informatics)
DTSTART;VALUE=DATE-TIME:20201218T143000Z
DTEND;VALUE=DATE-TIME:20201218T145000Z
DTSTAMP;VALUE=DATE-TIME:20210612T223746Z
UID:AlgAndLogic/17
DESCRIPTION:Title: Contact join-semilattices\nby Tatyana Ivanova (Institute of Mathe
matics and Informatics) as part of Algebra and Logic Seminar\n\nAbstract:
TBA\n
LOCATION:https://researchseminars.org/talk/AlgAndLogic/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Roussanka Loukanova (Institute of Mathematics and Informatics)
DTSTART;VALUE=DATE-TIME:20201218T145500Z
DTEND;VALUE=DATE-TIME:20201218T151500Z
DTSTAMP;VALUE=DATE-TIME:20210612T223746Z
UID:AlgAndLogic/18
DESCRIPTION:Title: Type-Theory of Parametric Algorithms\nby Roussanka Loukanova (Ins
titute of Mathematics and Informatics) as part of Algebra and Logic Semina
r\n\n\nAbstract\nI shall present a class of Moschovakis type-theories of r
ecursion. My focus is on an overview from the perspective of existing and
potential applications. I shall point to some of my contributions on these
topics.\n
LOCATION:https://researchseminars.org/talk/AlgAndLogic/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dimitar Guelev (Institute of Mathematics and Informatics)
DTSTART;VALUE=DATE-TIME:20201218T154500Z
DTEND;VALUE=DATE-TIME:20201218T160000Z
DTSTAMP;VALUE=DATE-TIME:20210612T223746Z
UID:AlgAndLogic/19
DESCRIPTION:Title: Strategy Profiles and a Vocabulary for Solving Infinite Concurrent Ga
mes with Temporary Coalitions in QCTL*\nby Dimitar Guelev (Institute o
f Mathematics and Informatics) as part of Algebra and Logic Seminar\n\n\nA
bstract\nThis is a short version of my seminar talk from October 30. It hi
ghlights the key notion and notations proposed in that talk. The key notio
n is a straightforward extension of the notion of strategy profile for reg
istering varying partitionings of the totality of the players into disjoin
t coalitions. The notation is a vocabulary for the propositionally quantif
ied branching time temporal logic QCTL* which augments the encoding of str
ategy profiles into this logic as known from the literature\, including my
previous work\, with symbols for specifying shifting coalition structure.
In this short presentation\, we focus on the notation and sideline the ke
y technical results of the work\, which show that complete information con
current multiplayer infinite games with LTL-definable partially ordered ob
jectives are solvable wrt whatever solution concepts happen to be expressi
ble in the proposed vocabulary. That includes temporary coalition generali
sations of some established solution concepts. The work is available from
the 8th International Workshop on Strategic Reasoning and arXiv.\n
LOCATION:https://researchseminars.org/talk/AlgAndLogic/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Valentin Goranko (Institute of Mathematics and Informatics)
DTSTART;VALUE=DATE-TIME:20201218T151500Z
DTEND;VALUE=DATE-TIME:20201218T154500Z
DTSTAMP;VALUE=DATE-TIME:20210612T223746Z
UID:AlgAndLogic/20
DESCRIPTION:Title: Rational coordination in Pure Win-Lose Coordination Games\nby Val
entin Goranko (Institute of Mathematics and Informatics) as part of Algebr
a and Logic Seminar\n\n\nAbstract\nThe main question I will address is: wh
en and how can rational agents coordinate without any prior communication
or conventions? I will consider this question in the abstract framework of
multi-player pure coordination games\, where each player has a number of
possible choices\, every choice profile determines a unique outcome\, and
in every outcome all players have identical payoffs\, `win’ or `lose’.
\n\nI will formally introduce pure win/lose coordination games and will p
resent and discuss a hierarchy of ‘rationality principles' that can be a
pplied by rational players in such games to determine their choices of act
ion. Then I will compare the strength of some of these principles in terms
of the classes of coordination games that can be solved by them by using
only pure reasoning\, without any preplay communication and conventions. I
will argue that the boundaries between pure rationality principles and ot
her rational decision methods used for solving coordination games are quit
e debatable and there is apparently no clear distinction between these. \n
\nLastly\, time permitting\, I will discuss briefly how pure coordination
games can be solved with the use of `structural’ conventions (only based
on structural properties of the games)\, agreed in a preplay communicatio
n\, and will describe precisely the scope of purely rational coordination.
\n\nThe talk is based on this recent joint paper with Antti Kuusisto and R
aine Rönnholm:\nhttps://academic.oup.com/logcom/article/30/6/1183/5869758
?guestAccessKey=374b9c38-2900-4302-\n91c6-8c8c1eac6ac4.\n
LOCATION:https://researchseminars.org/talk/AlgAndLogic/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dimitrinka Vladeva (University of Forestry\, Sofia)
DTSTART;VALUE=DATE-TIME:20210108T110000Z
DTEND;VALUE=DATE-TIME:20210108T120000Z
DTSTAMP;VALUE=DATE-TIME:20210612T223746Z
UID:AlgAndLogic/21
DESCRIPTION:Title: Derivations in matrix semirings\nby Dimitrinka Vladeva (Universit
y of Forestry\, Sofia) as part of Algebra and Logic Seminar\n\n\nAbstract\
nIn the first part of this topic we give a description of the derivations
in the semiring $UTM_n(S)$ of upper triangular matrices over an additivel
y idempotent semiring $S$. We consider the matrices $\\overline{D}_{k} = E
_{11} + \\cdots + E_{kk}$\, $1 \\leq k \\leq n$ and $\\underline{D}_{\\\
,m} = E_{n-m+1\\\,n-m+1} + \\cdots + E_{nn}$\, $1 \\leq m \\leq n$ and pr
ove that $\\delta_k(A) = \\overline{D}_{k}A$ and $d_m(A) = A\\underline{D
}_{\\\,m}$\, where\n $A \\in UTM_n(S)$\, are derivations in $UTM_n(S)$. Th
e set $\\overline{\\mathcal{D}}$ of derivations $\\delta_k$\, $k = 1\, \\
ldots\, n$ and the set $\\underline{\\mathcal{D}}$ of derivations $d_m$\,
$m = 1\, \\ldots\, n$\, are additively and multiplicatively idempotent se
mirings. Denote by ${\\mathcal{D}}$ the semiring generated by the set $\\
overline{\\mathcal{D}} \\cup \\underline{\\mathcal{D}}$. For $\\delta_k +
d_m \\in {\\mathcal{D}}$ and $A \\in UTM_n(S)$ we describe the matrix $(\
\delta_k + d_m)(A)$ and prove that $\\delta_kd_m \\in {\\mathcal{D}}$ if a
nd only $\\delta_k + d_m$ is an identiy map. In ${\\mathcal{D}}$ we constr
uct a basis $\\mathcal{B}$ consisting of derivations $\\delta_1\, \\delta
_2\\\,d_{n-1}\, \\ldots\, \\delta_{n-1}\\\,d_{2}\, d_1$ and\n $\\delta_1
\\\,d_{n-1}$\, $\\delta_2\\\,d_{n-2}$\, $\\\;\\ldots\\\;$\, $\\delta_{n-2}
\\\,d_2$\, $\\delta_{n-1}\\\,d_1$.\n The main result states that an arbitr
ary derivation in the semiring $UTM_n(S)$ is a linear combination of eleme
nts of the basis $\\mathcal{B}$ of the $S$-semimodule $\\mathcal{D}$ with
coefficients from $S$.\n\n\nIn the second part we study the derivations i
n the semiring of $n \\times n$ matrices over additively idempotent semir
ing $S$.\nIt is well-known that if $\\delta : S \\rightarrow S$ is a deriv
ation in semiring $S$ then in the semiring $M_n(S)$ of $n \\times n$ matri
ces over $S$ the map $\\delta_{\\rm her}$ such that $\\delta_{\\rm her}(A
) = (\\delta(a_{ij}))$ for any matrix $A = (a_{ij}) \\in M_n(S)$ is a der
ivation. These derivations are used in matrix calculus\, differential equa
tions\, statistics\, physics and engineering and are called hereditary der
ivations. On the other hand\n$S$-derivation in matrix semiring $M_n(S)$ (i
n sense of N. Jacobson) is a $S$ - linear map $D : M_n(S) \\rightarrow M_
n(S)$ such that $D(AB) = AD(B) + D(A)B$ where $A\, B \\in M_n(S)$. We prov
e that if $S$ is a commutative additively idempotent semiring any $S$-deri
vation is a hereditary derivation. For a noncommutative semiring $S$ is
introduced a concept of left (right) Ore elements in $S$. Then we extend
the center $C(S)$ to the semiring $LO(S)$ of left Ore elements or to the
semiring $RO(S)$ of right Ore elements in $S$. We construct left (right) d
erivations in these semirings and generalize the result from the commutati
ve case.\n\n\nhttps://math.bas.bg/wp-content/uploads/2021/01/Algebra_Logik
a_seminar_08-01-2021-abstract-EN.pdf\n
LOCATION:https://researchseminars.org/talk/AlgAndLogic/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Martin Tabakov (Institute of Philosophy and Sociology\, Bulg.Acad.
Sci.)
DTSTART;VALUE=DATE-TIME:20210115T080000Z
DTEND;VALUE=DATE-TIME:20210115T083000Z
DTSTAMP;VALUE=DATE-TIME:20210612T223746Z
UID:AlgAndLogic/22
DESCRIPTION:Title: Challenges of Contemporary Logic to Philosophy\nby Martin Tabakov
(Institute of Philosophy and Sociology\, Bulg.Acad. Sci.) as part of Alge
bra and Logic Seminar\n\n\nAbstract\nThe development of Logic will be disc
ussing in the light of the popular conceptions of Philosophy of science -
of Kuhn about the scientific revolutions and Lacatos - about the prolifera
tion. In my opinion in modern logic there are two revolutions - the transi
tion from traditional to classical logic and the transition from classical
to non-classical logic. In both revolutions the new paradigm has almost c
ompletely replaced the old one. The reason for both revolutions is that th
e development of the logical empirical sphere has gone considerably ahead
of the logical theory. My position is that logic does have „empirics‟
and this is basically the language and methods of reasoning in scientific
theories. Revolution' corresponds to the scale of change and re-evaluation
of values in modern logic\, comparable to important moments in the develo
pment of other fields: quantum mechanics\, the transition from Newtonian p
hysics to Einstein's theory of relativity\, non-Euclidean geometry.\n\nThe
main problem prior to philosophy of logic\, raised by second revolution i
s the proliferation. And respectively the questions about the monism and p
luralism of logic. After the second revolution Logic has been subdivided i
nto a number of logics\; so which one now is “proper Logic”? And can w
e talk about “proper Logic” at all?\n\nIn modern logic the term “phi
losophical logic” has become established. I will discuss questions “Wh
at they call and what must be named with It\, and is it possible and relev
ant”. Are there a significant field of study for what there is no suitab
le term? Where is this field of study named “philosophical logic”\,
“Is it a (kind of) logic\, or it is philosophy but not logic? And about
main reasons for the term – “Scientific and Theoretical”\, and “So
cial and practical”.\n\nJoint seminar dedicated to the World Logic Day w
ith the Seminar of the Department of Mathematical Logic and Its Applicatio
ns of the Faculty of Mathematics and Informatics\, Sofia University\, and
the Seminar of Logic at the Institute of Philosophy and Sociology\, Bulgar
ian Academy of Sciences\n
LOCATION:https://researchseminars.org/talk/AlgAndLogic/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Doroteya Angelova (Institute of Philosophy and Sociology\, Bulg.Ac
ad. Sci.)
DTSTART;VALUE=DATE-TIME:20210115T083000Z
DTEND;VALUE=DATE-TIME:20210115T090000Z
DTSTAMP;VALUE=DATE-TIME:20210612T223746Z
UID:AlgAndLogic/23
DESCRIPTION:Title: Some Solutions of Sorites Paradoxes\nby Doroteya Angelova (Instit
ute of Philosophy and Sociology\, Bulg.Acad. Sci.) as part of Algebra and
Logic Seminar\n\n\nAbstract\nIn the talk\, I will present the role of some
non-classical logics in resolving sorites paradoxes. I will analyze the s
pecific characteristics of these logics\, their advantages and shortcoming
s in regard to the problem of vagueness and respectively I will give argum
ents which of them are suitable for overcoming the sorites paradoxes. I wi
ll propose two own approaches through which\, according to me\, it is poss
ible to interpret and resolve the sorites paradoxes: the first one is hete
rogeneous and the second one – based on three-valued logic.\n\nKeywords:
sorites paradoxes\, vagueness\, fuzzy relevant logic\, heterogeneous appr
oach\n\nJoint seminar dedicated to the World Logic Day with the Seminar of
the Department of Mathematical Logic and Its Applications of the Faculty
of Mathematics and Informatics\, Sofia University\, and the Seminar of Log
ic at the Institute of Philosophy and Sociology\, Bulgarian Academy of Sci
ences\n
LOCATION:https://researchseminars.org/talk/AlgAndLogic/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Elena Tsvetkova (Institute of Philosophy and Sociology\, Bulg.Acad
. Sci.)
DTSTART;VALUE=DATE-TIME:20210115T090000Z
DTEND;VALUE=DATE-TIME:20210115T093000Z
DTSTAMP;VALUE=DATE-TIME:20210612T223746Z
UID:AlgAndLogic/24
DESCRIPTION:Title: Explanation of the Conversation Implicatures with the Graded Salience
Hypothesis\nby Elena Tsvetkova (Institute of Philosophy and Sociology
\, Bulg.Acad. Sci.) as part of Algebra and Logic Seminar\n\n\nAbstract\nGr
ice’s theory of conversational implicature is viewed in this paper with
an accent to the transition between the literal meaning of an expression a
nd the implicated meaning. Assuming the position expressed in the graded s
alience hypothesis\, it is explained that in some cases the transition fro
m what the speaker says to what he wants the listener to under-stand is ba
sed on the salient meaning of the used expressions. Special attention is p
aid to ex-pressions that have more than one obvious meaning\, in order to
show that even when the con-text plays a role in the understanding of an e
xpression\, this meaning can still be perceived as a result of socio-lingu
istic conventions.\n\nKeywords: Grice\, pragmatics\, graded salience hypot
hesis\, conversational implicature.\n\nJoint seminar dedicated to the Worl
d Logic Day with the Seminar of the Department of Mathematical Logic and I
ts Applications of the Faculty of Mathematics and Informatics\, Sofia Univ
ersity\, and the Seminar of Logic at the Institute of Philosophy and Socio
logy\, Bulgarian Academy of Sciences\n
LOCATION:https://researchseminars.org/talk/AlgAndLogic/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rosen Lutskanov (Institute of Philosophy and Sociology\, Bulg.Acad
. Sci.)
DTSTART;VALUE=DATE-TIME:20210115T094000Z
DTEND;VALUE=DATE-TIME:20210115T101000Z
DTSTAMP;VALUE=DATE-TIME:20210612T223746Z
UID:AlgAndLogic/25
DESCRIPTION:Title: Binary Decision Diagrams for Rational Choice\nby Rosen Lutskanov
(Institute of Philosophy and Sociology\, Bulg.Acad. Sci.) as part of Algeb
ra and Logic Seminar\n\n\nAbstract\nRational choice theory is built on thr
ee fundamental insights: 1. rational choice is (expected) utility maximiza
tion\; 2. utilities allow the measurement of preferences on ordinal scale\
, hence can be represented by weak orders\; 3. preference relations can be
generated from axiomatically defined classes of choice operators. In the
last 60 years enormous amount of axiomatizations of rational choice were p
resented\, but virtually all of them (a) turn out to be incompatible with
robust intuitions concerning the meaning of “rational choice”\; (b) fa
ll prey to counterexamples which show that these definitions are not exten
sionally correct. The present approach proposes to dispense with the recei
ved view (“choice is rational when it generates an ordering of alternati
ves”) and sketches and alternative account (“choice is rational when t
he choice procedure fits the choice setting”). It is based on a re-inter
pretation of binary decision diagrams – rooted directed acyclic graphs r
epresenting Boolean functions (by substituting the labels “true”/“fa
lse” with “chosen”/”rejected”). It is shown that this analogy sh
eds light on some idealizations left implicit by the classic approach.\n\n
Joint seminar dedicated to the World Logic Day with the Seminar of the Dep
artment of Mathematical Logic and Its Applications of the Faculty of Mathe
matics and Informatics\, Sofia University\, and the Seminar of Logic at th
e Institute of Philosophy and Sociology\, Bulgarian Academy of Sciences\n
LOCATION:https://researchseminars.org/talk/AlgAndLogic/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexandra Soskova (Faculty of Mathematics and Informatics\, Sofia
University)
DTSTART;VALUE=DATE-TIME:20210115T101000Z
DTEND;VALUE=DATE-TIME:20210115T104000Z
DTSTAMP;VALUE=DATE-TIME:20210612T223746Z
UID:AlgAndLogic/26
DESCRIPTION:Title: Effective Coding and Decoding in Classes of Structures\nby Alexan
dra Soskova (Faculty of Mathematics and Informatics\, Sofia University) as
part of Algebra and Logic Seminar\n\n\nAbstract\nFriedman and Stanley int
roduced Borel embeddings as a way of comparing classi\ncation\nproblems fo
r di\nerent classes of structures. Many Borel embeddings are actually Turi
ng\ncomputable. The e\nective decoding is given by a uniform e\nective int
erpretation. Part\nof the e\nective interpretation is Medvedev reduction.
The class of undirected graphs and\nthe class of linear orderings both lie
on top under Turing computable embeddings. We\ngive examples of graphs th
at are not Medvedev reducible to any linear ordering\, or to the\njump of
any linear ordering. For any graph there is a linear ordering\, that the g
raph is\nMedvedev reducible to the second jump of the linear ordering. For
the Turing computable\nembedding $L$ of Friedman and Stanley of directed
graphs in linear orderings. We show\nthat there do not exist $L_{w_1w}$-fo
rmulas that uniformly interpret the input graph $G$ in the output linear o
rdering $L(G)$. This is joint work with Knight\, and Vatev.\n\nWe have als
o one positive result -- we prove that the class of fields is uniformly ef
fectively interpreted without parameters in the class of Heisenberg groups
. The second part is a joint work with Alvir\, Calvert\, Goodman\, Harizan
ov\, Knight\, Miller\, Morozov\, and\nWeisshaar.\n\nJoint seminar dedicate
d to the World Logic Day with the Seminar of the Department of Mathematica
l Logic and Its Applications of the Faculty of Mathematics and Informatics
\, Sofia University\, and the Seminar of Logic at the Institute of Philoso
phy and Sociology\, Bulgarian Academy of Sciences\n
LOCATION:https://researchseminars.org/talk/AlgAndLogic/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jean-Yves Beziau
DTSTART;VALUE=DATE-TIME:20210115T112500Z
DTEND;VALUE=DATE-TIME:20210115T114000Z
DTSTAMP;VALUE=DATE-TIME:20210612T223746Z
UID:AlgAndLogic/27
DESCRIPTION:Title: Official Address\nby Jean-Yves Beziau as part of Algebra and Logi
c Seminar\n\n\nAbstract\nJean-Yves Beziau is the creator of the World Logi
c Day and Editor-in-Chief of Logica Universalis.\n\nJean-Yves Beziau is th
e creator of the World Logic Day and Editor-in-Chief of Logica Universalis
.\n
LOCATION:https://researchseminars.org/talk/AlgAndLogic/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dimitar Vakarelov (Faculty of Mathematics and Informatics\, Sofia
University)
DTSTART;VALUE=DATE-TIME:20210115T114000Z
DTEND;VALUE=DATE-TIME:20210115T124000Z
DTSTAMP;VALUE=DATE-TIME:20210612T223746Z
UID:AlgAndLogic/28
DESCRIPTION:Title: Point-free Theories of Space and Time\nby Dimitar Vakarelov (Facu
lty of Mathematics and Informatics\, Sofia University) as part of Algebra
and Logic Seminar\n\n\nAbstract\nTo the question ”What is space” mathe
maticians immediately answer: this is what studies geometry\, one of the o
ldest branches of mathematics. Unfortunately\, mathematics does not have s
uch a branch dedicated to time. Time and space are also basic concepts of
physics\, but as a rule physicists borrow their mathematical formalisms fr
om mathematics. Modern physics has come to the conclusion that space and t
ime must be considered as aspects of a unified theory\, which is briefly c
alled ”space-time”. But till now physicists still are not given a defi
nition of time\, rather they say how it is measured\, and time is appearin
g just as a numerical parameter in the basic equations of the theory. Ther
e has been a heated debate over the nature of space and time since the tim
e of Newton and Leibniz. Newton defends the so-called ”absolute theory o
f space and time”: ”space” is a container in which the existing thin
gs are located\, and ”time” is something that ”flows” and is indep
endent of space and material things. Leibniz is the founder of the so-call
ed ”relational theory of space and time” according to which absolute s
pace and time are fictions that have no independent existence: in reality
there are only things that are in different spatial and temporal relations
. In the early 20th century\, a successor to Leibniz’s ideas was Alfred
North Whitehead\, who argued that the theory of space and time should be b
uilt on a point-free basis. What does this mean. According to the Euclidea
n tradition\, the points of space (as well as the lines and planes) are th
e basic primary concepts that lie in the axiomatization of geometry. But t
hey do not have an independent existence in reality and are convenient fic
tions. The situation is similar to the points of time (moments)\, which me
ans that the foundations of a unified theory of space and time must be bas
ed on more realistic concepts. This does not mean that the notions of spac
e point and time moment should be disregarded - they should be introduced
later on the base of the primitive notions of the theory. The point-free a
pproach to the theory of space and time is quite important from the point
of view of physics: if a given theory is intended to describe reality\, it
s basic concepts should correspond to some things of reality. The first st
eps in constructing a point-free theory of space were made by Whitehead\,
De Laguna\, and Tarski\, and this theory is now well known as the ”regio
n-based theory of space”\, which is point-free and is based on the term
”region” as an analogue of a physical body plus some simple relations
between regions\, such as ”part-of” and ”contact”. However\, a sat
isfactory point-free axiomatic theory of a unified theory of space-time do
es not yet exist. The first steps in this direction were made by the autho
r of this lecture and its purpose is to tell about one of these attempts.\
n\nThe full text on which the lecture is based can be seen here: arXiv:200
4.14755v2 [math.LO] 30 May 2020.\n\nPublished version: Journal of Applied
Logics - IfCoLog Journal of Logics and their Applications\, Vol. 7 No. 6\,
2020\, 1243-1321.\n\nAn advice to the interested listeners of the lecture
is to see the informal Introduction of the above mentioned text.\n\nJoint
seminar dedicated to the World Logic Day with the Seminar of the Departme
nt of Mathematical Logic and Its Applications of the Faculty of Mathematic
s and Informatics\, Sofia University\, and the Seminar of Logic at the Ins
titute of Philosophy and Sociology\, Bulgarian Academy of Sciences\n
LOCATION:https://researchseminars.org/talk/AlgAndLogic/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vesselin Drensky (Institute of Mathematics and Informatics\, Bulg.
Acad. Sci.)
DTSTART;VALUE=DATE-TIME:20210115T125000Z
DTEND;VALUE=DATE-TIME:20210115T133000Z
DTSTAMP;VALUE=DATE-TIME:20210612T223746Z
UID:AlgAndLogic/29
DESCRIPTION:Title: Computational Complexity and Decision Problems in Algebra\nby Ves
selin Drensky (Institute of Mathematics and Informatics\, Bulg. Acad. Sci.
) as part of Algebra and Logic Seminar\n\n\nAbstract\nThe idea of the talk
is to show on concrete examples how classical problems in algebra and ari
thmetic can be considered from the point of view of mathematical logic\, t
heory of algorithms and computer science. The examples are taken from clas
sical number theory\, cryptography\, numerical semigroups\, commutative an
d noncommutative ring theory\, finite axiomatization\, the P versus NP pro
blem\, decision problems in the theory of groups\, semigroups and rings.\n
\nJoint seminar dedicated to the World Logic Day with the Seminar of the D
epartment of Mathematical Logic and Its Applications of the Faculty of Mat
hematics and Informatics\, Sofia University\, and the Seminar of Logic at
the Institute of Philosophy and Sociology\, Bulgarian Academy of Sciences\
n
LOCATION:https://researchseminars.org/talk/AlgAndLogic/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Petar Iliev (Institute of Philosophy and Sociology\, Bulg.Acad. Sc
i.)
DTSTART;VALUE=DATE-TIME:20210115T133000Z
DTEND;VALUE=DATE-TIME:20210115T140000Z
DTSTAMP;VALUE=DATE-TIME:20210612T223746Z
UID:AlgAndLogic/30
DESCRIPTION:Title: Why Philosophers and Logicians Should Learn More about Computational
Complexity\nby Petar Iliev (Institute of Philosophy and Sociology\, Bu
lg.Acad. Sci.) as part of Algebra and Logic Seminar\n\n\nAbstract\nOne mig
ht be tempted to assume that using computer time and memory as efficiently
as possible to perform a computational task is something that obsessive e
ngineers might find important but is of no philosophical and logical relev
ance. This is going to be a very high-level talk\, dedicated to a very sma
ll number of ideas and concepts that originated in the field of computatio
nal complexity\, whose main purpose is to convince philosophers and logici
ans unfamiliar with the area but curious to know more about it that the ab
ove assumption is wrong.\n\nJoint seminar dedicated to the World Logic Day
with the Seminar of the Department of Mathematical Logic and Its Applicat
ions of the Faculty of Mathematics and Informatics\, Sofia University\, an
d the Seminar of Logic at the Institute of Philosophy and Sociology\, Bulg
arian Academy of Sciences\n
LOCATION:https://researchseminars.org/talk/AlgAndLogic/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ivan Chipchakov (Institute of Mathematics and Informatics\, Bulg.
Acad. Sci.)
DTSTART;VALUE=DATE-TIME:20210115T141000Z
DTEND;VALUE=DATE-TIME:20210115T144000Z
DTSTAMP;VALUE=DATE-TIME:20210612T223746Z
UID:AlgAndLogic/31
DESCRIPTION:Title: Open Problems on Field Extensions of Finite Transcendency Degree and
the PAC Property\nby Ivan Chipchakov (Institute of Mathematics and Inf
ormatics\, Bulg. Acad. Sci.) as part of Algebra and Logic Seminar\n\n\nAbs
tract\nOne of the major open problems on fields of finite transcendency de
grees over their prime subfields is to understand whether an infinite fiel
d E of this kind is pseudo algebraically closed (abbr.\, PAC)\, provided t
hat its absolute Galois group is torsion-free and the Henselian closures o
f nontrivial valuations of E are separably closed. The purpose of this tal
k is to exhibit relations between the stated problem and the study of Diop
hantine properties of fields of dimension ≤ 1 that are algebraic extensi
ons of a global field K. We also present an open question posed by Koenigs
mann. It concerns the structure of absolute Galois groups and the elementa
ry characterization of fields by such groups\, an area of common research
interest to field theorists – logicians and algebraists.\n\nJoint semina
r dedicated to the World Logic Day with the Seminar of the Department of M
athematical Logic and Its Applications of the Faculty of Mathematics and I
nformatics\, Sofia University\, and the Seminar of Logic at the Institute
of Philosophy and Sociology\, Bulgarian Academy of Sciences\n
LOCATION:https://researchseminars.org/talk/AlgAndLogic/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dimitar P. Guelev (Institute of Mathematics and Informatics\, Bulg
. Acad. Sci.)
DTSTART;VALUE=DATE-TIME:20210115T144000Z
DTEND;VALUE=DATE-TIME:20210115T151000Z
DTSTAMP;VALUE=DATE-TIME:20210612T223746Z
UID:AlgAndLogic/32
DESCRIPTION:Title: Temporary Coalitions and Preference in Quantified Computation Tree Lo
gic\nby Dimitar P. Guelev (Institute of Mathematics and Informatics\,
Bulg. Acad. Sci.) as part of Algebra and Logic Seminar\n\n\nAbstract\nTemp
oral winning conditions appear in both terminating and infinite games\, wi
th terminating games corresponding to safety and reachability (guarantee)
conditions\, and arbitrary temporal conditions for non-terminating games.
In a multiplayer game\, the latter classes of winning conditions are natur
al to drive the players into forming permanent coalitions as the longevity
of a coalition needs to match the duration of the joint agenda. However\,
a lifelong joint agenda is often inconsistent with the ability of players
to change their alliances as soon as they see the benefit of doing so. Th
is ability can be regarded as inalienable within the considered game as lo
ng as forbidding players to change sides can be modeled by appropriately m
odifying the game. Therefore games with temporal winning conditions need t
o be studied with the possibility of temporary coalitioning in mind. Estab
lished logical notations for strategic behaviour such as ATLs (Alur Henzin
ger and Kupferman\, 1997\, 2002) and Strategy Logics (Chatterjee\, Henzing
er and Piterman\, 2010\, also Mogavero\, Murano and Vardi\, 2010) include
dedicated constructs which are ‘off-the-shelf’ for permanent coalition
s only.\n\nCoalitions form around concrete local agreements with each pros
pective coalition member assessing the prospective coalition with the pros
pective agreement in mind\, and assuming just rationality on behalf of the
non-signatories. With temporary coalitions this assessment is determined
by the progress on each player's individual objectives that can be made\,
if the local agreement goes ahead. The natural ambiguity of rationality an
d assessment entails that even established solution concepts such as equil
ibria and domination are liable to spawn multiple new variants yet another
time upon their generalization to temporary coalitions.\n\nIn this talk w
e propose two elements of notation for the handling of solution concepts w
ith temporary coalitions in Quantified Computation Tree Logic. QCTL is now
an established intermediate notation for strategic reasoning as it admits
embeddings from systems with more specialised constructs and is known to
have decidable validity and model-checking on trees (French\, 2001\, 2006)
. The contributed elements are a propositional vocabulary for temporary co
alitions and a temporal variant of the binary preference operator which ca
n be traced back to the work of Von Wright\, 1963. The latter construct is
not temporary-coalition-specific\, but still necessary for the handling o
f multiple objectives.\n\nKeywords: strategic ability\, temporary coalitio
ns\, rational synthesis\, preference\, concurrent multiplayer games\n\nThe
re is a related paper on arXiv: 2011.03724\n\nJoint seminar dedicated to t
he World Logic Day with the Seminar of the Department of Mathematical Logi
c and Its Applications of the Faculty of Mathematics and Informatics\, Sof
ia University\, and the Seminar of Logic at the Institute of Philosophy an
d Sociology\, Bulgarian Academy of Sciences\n
LOCATION:https://researchseminars.org/talk/AlgAndLogic/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Roussanka Loukanova (Institute of Mathematics and Informatics\, Bu
lgarian Academy of Sciences)
DTSTART;VALUE=DATE-TIME:20210129T110000Z
DTEND;VALUE=DATE-TIME:20210129T120000Z
DTSTAMP;VALUE=DATE-TIME:20210612T223746Z
UID:AlgAndLogic/33
DESCRIPTION:Title: Reduction Calculus of Type-Theory of Acyclic Algorithms\nby Rouss
anka Loukanova (Institute of Mathematics and Informatics\, Bulgarian Acade
my of Sciences) as part of Algebra and Logic Seminar\n\n\nAbstract\nIn 198
9\, Moschovakis [1] initiated a new theory of the mathematical notion of a
lgorithm\, within untyped\, full recursion. In 2006\, Moschovakis [2] intr
oduced the formal language of Type-Theory of Recursion (TTR)\, which model
s the notion of algorithm and concepts of meaning in typed semantic struct
ures. The focus of [2] is on Type-Theory of Acyclic Algorithms (TTAR) for
computations that end up after a finite number of steps. The approach\, in
its varieties\, with full and acyclic recursion\, provides for new develo
pments of type theory of computation and new applications to computational
syntax-semantics interfaces in programming and natural languages.\n\nIn t
his talk\, I present the formal language (LAR) of TTAR\, by extending it w
ith a restrictor operator that sets conditions on denotations of terms. In
addition\, the operator defines restricted memory and parameters. TTAR pr
ovides two kinds of semantics of the formal language LAR\, denotational an
d algorithmic. The reduction system of TTAR is essential for the notion of
algorithm and syntax-semantics interfaces. I shall overview the reduction
calculus and some of the theoretical results of TTAR.\n\n[1] Yiannis N Mo
schovakis. The formal language of recursion. Journal of Symbolic Logic\, 5
4(04):1216–1252\, 1989.\n\n[2] Yiannis N. Moschovakis. A Logical Calculu
s of Meaning and Synonymy. Linguistics and Philosophy\, 29(1):27–89\, 20
06.\n
LOCATION:https://researchseminars.org/talk/AlgAndLogic/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Roussanka Loukanova (Institute of Mathematics and Informatics\, Bu
lgarian Academy of Sciences)
DTSTART;VALUE=DATE-TIME:20210205T110000Z
DTEND;VALUE=DATE-TIME:20210205T120000Z
DTSTAMP;VALUE=DATE-TIME:20210612T223746Z
UID:AlgAndLogic/34
DESCRIPTION:Title: Reduction Calculus of Type-Theory of Acyclic Algorithms\, II\nby
Roussanka Loukanova (Institute of Mathematics and Informatics\, Bulgarian
Academy of Sciences) as part of Algebra and Logic Seminar\n\n\nAbstract\nI
n 1989\, Moschovakis [1] initiated a new theory of the mathematical notion
of algorithm\, within untyped\, full recursion. In 2006\, Moschovakis [2]
introduced the formal language of Type-Theory of Recursion (TTR)\, which
models the notion of algorithm and concepts of meaning in typed semantic s
tructures. The focus of [2] is on Type-Theory of Acyclic Algorithms (TTAR)
for computations that end up after a finite number of steps. The approach
\, in its varieties\, with full and acyclic recursion\, provides for new d
evelopments of type theory of computation and new applications to computat
ional syntax-semantics interfaces in programming and natural languages.\n\
nIn this talk\, I present the formal language (LAR) of TTAR\, by extending
it with a restrictor operator that sets conditions on denotations of term
s. In addition\, the operator defines restricted memory and parameters. TT
AR provides two kinds of semantics of the formal language LAR\, denotation
al and algorithmic. The reduction system of TTAR is essential for the noti
on of algorithm and syntax-semantics interfaces. I shall overview the redu
ction calculus and some of the theoretical results of TTAR.\n\n[1] Yiannis
N Moschovakis. The formal language of recursion. Journal of Symbolic Logi
c\, 54(04):1216–1252\, 1989.\n\n[2] Yiannis N. Moschovakis. A Logical Ca
lculus of Meaning and Synonymy. Linguistics and Philosophy\, 29(1):27–89
\, 2006.\n\nThis is a continuation of the talk given on January 29\, 2021.
\n
LOCATION:https://researchseminars.org/talk/AlgAndLogic/34/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Leonid Makar-Limanov (Wayne State University\, Detroit\, USA and W
eizmann Institute of Science\, Rehovot\, Israel)
DTSTART;VALUE=DATE-TIME:20210212T140000Z
DTEND;VALUE=DATE-TIME:20210212T150000Z
DTSTAMP;VALUE=DATE-TIME:20210612T223746Z
UID:AlgAndLogic/35
DESCRIPTION:Title: On the Newton polytope of a Jacobian pair\nby Leonid Makar-Limano
v (Wayne State University\, Detroit\, USA and Weizmann Institute of Scienc
e\, Rehovot\, Israel) as part of Algebra and Logic Seminar\n\n\nAbstract\n
First\, I remind what is the Jacobian Conjecture and talk about some histo
ry related to it. Then I'll briefly explain what is the “shape” of a m
inimal counterexample to the conjecture. After that the Newton polytope re
lated to a “minimal” counterexample to the Jacobian conjecture will be
introduced and described. This description allows to obtain the best know
n estimate for the geometric degree of the polynomial mapping given by a J
acobian pair.\n
LOCATION:https://researchseminars.org/talk/AlgAndLogic/35/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jose Brox (Centre for Mathematics of the University of Coimbra\, P
ortugal)
DTSTART;VALUE=DATE-TIME:20210219T110000Z
DTEND;VALUE=DATE-TIME:20210219T120000Z
DTSTAMP;VALUE=DATE-TIME:20210612T223746Z
UID:AlgAndLogic/36
DESCRIPTION:Title: Identities in Prime Rings\nby Jose Brox (Centre for Mathematics o
f the University of Coimbra\, Portugal) as part of Algebra and Logic Semin
ar\n\n\nAbstract\nGiven a ring\, a generalized polynomial identity (GPI) i
s a polynomial identity in which the coefficients can be taken from the ri
ng. Prime rings are a class of rings very well suited to manage problems r
elated to identities\, as for example those coming from Herstein’s theor
y\, which is the study of nonassociative objects and structures arising fr
om associative rings. After a motivating introduction to prime rings\, wit
h some examples from Herstein’s theory\, I will show the usefulness of M
artindale’s lemma\, the key tool for solving GPIs in one variable in pri
me rings\, and I will explain a new promising approach to solve them based
on elementary algebraic geometry which avoids some shortcomings of the le
mma\, allowing to find the optimal solutions.\n
LOCATION:https://researchseminars.org/talk/AlgAndLogic/36/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hristo Ganchev (Faculty of Mathematics and Informatics\, Sofia Uni
versity)
DTSTART;VALUE=DATE-TIME:20210226T110000Z
DTEND;VALUE=DATE-TIME:20210226T120000Z
DTSTAMP;VALUE=DATE-TIME:20210612T223746Z
UID:AlgAndLogic/37
DESCRIPTION:Title: Enumeration Reducibility: 60 years of investigation\nby Hristo Ga
nchev (Faculty of Mathematics and Informatics\, Sofia University) as part
of Algebra and Logic Seminar\n\n\nAbstract\nWe will make an overview of th
e main results and problems in Еnumeration reducibility – one of the tw
o main reducibilities used to compare the complexity of the information co
ntent in sets of natural numbers.\n
LOCATION:https://researchseminars.org/talk/AlgAndLogic/37/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dessislava Kochloukova (University of Campinas\, Brazil)
DTSTART;VALUE=DATE-TIME:20210305T140000Z
DTEND;VALUE=DATE-TIME:20210305T150000Z
DTSTAMP;VALUE=DATE-TIME:20210612T223746Z
UID:AlgAndLogic/38
DESCRIPTION:Title: Finite presentability for metabelian groups\, Lie algebras and restri
cted Lie algebras\nby Dessislava Kochloukova (University of Campinas\,
Brazil) as part of Algebra and Logic Seminar\n\n\nAbstract\nIn the first
part of the talk we revisе the already known classifications of finite pr
esentability (in terms of generators and relations) for metabelian groups
and metabelian Lie algebras. The case of groups was solved by Robert Bieri
and Ralph Strebel in 1980s and that of Lie algebras was done by Roger Bry
ant and John Groves in late 1990s. In the last part of the talk we discuss
new results about the classification of finitely presented metabelian res
tricted Lie algebras based on joint work with Adriana Leon\, J. Algebra\,
560 (2020)\, 1107-1145.\n
LOCATION:https://researchseminars.org/talk/AlgAndLogic/38/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ljudmila Kamenova (Stony Brook University\, USA)
DTSTART;VALUE=DATE-TIME:20210312T143000Z
DTEND;VALUE=DATE-TIME:20210312T160000Z
DTSTAMP;VALUE=DATE-TIME:20210612T223746Z
UID:AlgAndLogic/39
DESCRIPTION:Title: Algebraic Non-hyperbolicity of Hyperkähler Manifolds\nby Ljudmil
a Kamenova (Stony Brook University\, USA) as part of Algebra and Logic Sem
inar\n\n\nAbstract\nA projective manifold is algebraically hyperbolic if t
he degree of any curve is bounded from above by its genus times a constant
\, which is independent from the curve. This is a property which follows f
rom Kobayashi hyperbolicity. We prove that hyperkahler manifolds are not a
lgebraically hyperbolic when the Picard rank is at least 3\, or if the Pic
ard rank is 2 and the SYZ conjecture on existence of Lagrangian fibrations
is true. We also prove that if the automorphism group of a hyperkahler ma
nifold is infinite\, then it is algebraically non-hyperbolic. These result
s are joint with Misha Verbitsky.\n\nThese results are joint with Misha Ve
rbitsky.\n
LOCATION:https://researchseminars.org/talk/AlgAndLogic/39/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andreas Weiermann (Ghent University\, Belgium)
DTSTART;VALUE=DATE-TIME:20210319T140000Z
DTEND;VALUE=DATE-TIME:20210319T153000Z
DTSTAMP;VALUE=DATE-TIME:20210612T223746Z
UID:AlgAndLogic/40
DESCRIPTION:Title: Some applications of transfinite numbers to algebra and some applicat
ions of number theory to transfinite numbers\nby Andreas Weiermann (Gh
ent University\, Belgium) as part of Algebra and Logic Seminar\n\n\nAbstra
ct\nIn the first part we will survey the role of transfinite numbers in th
e study of Hilbert's basis theorem and its extension by MacLagan. To this
end we associate ordinals to some natural well partial orderings related C
artesian products of the set of natural numbers and we apply this apparatu
s to monomial ideals in F[X_1\,...\,X_n] where F is a field.\n\nIn the sec
ond part we use the machinery of Tauberian theorems to prove some structur
al results about transfinite numbers regarding limit laws and phase transi
tions.\n\nThe talk will be non technical and it is aimed at a general math
ematical audience.\n
LOCATION:https://researchseminars.org/talk/AlgAndLogic/40/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dimitar Guelev (Institute of Mathematics and Informatics\, Bulgari
an Academy of Sciences)
DTSTART;VALUE=DATE-TIME:20210326T110000Z
DTEND;VALUE=DATE-TIME:20210326T123000Z
DTSTAMP;VALUE=DATE-TIME:20210612T223746Z
UID:AlgAndLogic/41
DESCRIPTION:Title: Some axioms about rationality in infinite concurrent multiplayer game
s with ordered objectives and temporary coalitions in QCTL*\nby Dimita
r Guelev (Institute of Mathematics and Informatics\, Bulgarian Academy of
Sciences) as part of Algebra and Logic Seminar\n\n\nAbstract\nTemporal win
ning conditions appear in both terminating and infinite games. Reachabilit
y (guarantee) winning conditions appear in terminating games. Safety condi
tions and conditions higher up in the (Manna & Pnueli\, 1989) hierarchy ap
pear in non-terminating games. In a multiplayer game\, the latter classes
of winning conditions are natural to drive players into forming permanent
coalitions as the longevity of a coalition needs to match the duration of
its agenda\, which may take entire infinite plays to implement. However\,
a lifelong joint agenda is often inconsistent with the ability of players
to change alliances\, especially if there are multiple objectives with pre
ference. The dedicated constructs of established logical notations for str
ategic behaviour such as Alternating-time Temporal Logic (ATL\, Alur Henzi
nger and Kupferman\, ICALP 1997\, J. of the ACM\, 2002) and Strategy Logic
(SL\, Chatterjee\, Henzinger and Piterman\, I& C\, 2010\, Mogavero\, Mura
no and Vardi\, FST TCS 2010)\, in their now many variants and extensions\,
are off-the-shelf for permanent coalitions only. To the best of our knowl
edge\, no dedicated constructs such as those of ATL and SL are available f
or temporary coalitioning.\n\nIn this talk we fall back onto Quantified Co
mputation Tree Logic\, QCTL*\, which admits embeddings of both ATL and SL\
, and is now an established intermediate notation for logics for strategic
ability\, largely because of its decidability on the unwindings of finite
models (French\, Australian AI 2001\, Ph.D. Thesis 2006\, Laroussinie and
Markey\, LMCS 2014). The embedding of ATL was introduced in (Da Costa Lop
ez et al\, CONCUR 2012)\, and independently by myself in (Guelev\, SR 2013
). Elements can be identified already in the correspondence between ATL's
2002 and 1997 semantics in (Goranko and Jamroga\, Synthese 2004).\n\nWe pr
opose a vocabulary which extends this embedding to allow temporary coaliti
ons. We illustrate its use to formulate example sufficient conditions for
the rationality of shifting coalition structure and decisions in the exten
sion of QCTL* by a temporal form of a binary preference operator after (Vo
n Wright\, 1963) which we introduced in (Guelev\, CoRR 2020). The conditio
ns reflect naive game-theoretic reasoning and are considered to become par
t of analogons to backward induction to infinite concurrent games with ord
ered objectives. We adopt ordered objectives from the thorough study of pu
re Nash equilibria concurrent ω-regular games without coalitioning in (Bo
uyer\, Brenguier and Markey and Ummels\, FoSSaCS 2012\, LMCS 2015).\n\nKey
words: strategic ability\, temporary coalitions\, rational synthesis\, ord
ered objectives\, concurrent multiplayer games\n
LOCATION:https://researchseminars.org/talk/AlgAndLogic/41/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ivan Penkov (Jacobs University Bremen\, Germany)
DTSTART;VALUE=DATE-TIME:20210409T100000Z
DTEND;VALUE=DATE-TIME:20210409T113000Z
DTSTAMP;VALUE=DATE-TIME:20210612T223746Z
UID:AlgAndLogic/42
DESCRIPTION:Title: Universal tensor categories and “algebraic functional analysis”\nby Ivan Penkov (Jacobs University Bremen\, Germany) as part of Algebra
and Logic Seminar\n\n\nAbstract\nIn this talk I will outline the construc
tion of some tensor categories generated by two objects $X$\, $Y$ with a p
airing $X\\otimes Y$ → 1 to the monoidal unit 1. These categories are ca
tegories of representations of certain infinite-dimensional Lie algebras\,
and they turn out to be universal in a sense which will be explained in t
he talk. The interpretation of $Y$ as a dual space to $X$ allows an analog
y with functional analysis. Joint work with A. Chirvasitu\, based on earli
er joint work with V. Serganova.\n
LOCATION:https://researchseminars.org/talk/AlgAndLogic/42/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Veselin Filev (Institute of Mathematics and Informatics\, Bulgaria
n Academy of Sciences)
DTSTART;VALUE=DATE-TIME:20210416T130000Z
DTEND;VALUE=DATE-TIME:20210416T143000Z
DTSTAMP;VALUE=DATE-TIME:20210612T223746Z
UID:AlgAndLogic/43
DESCRIPTION:Title: The Holographic Principle – Motivation and Applications\nby Ves
elin Filev (Institute of Mathematics and Informatics\, Bulgarian Academy o
f Sciences) as part of Algebra and Logic Seminar\n\n\nAbstract\nI will tal
k about the arguments that lead to the formulation of the holographic prin
ciple and its realization in the framework of superstring theory via the A
dS/CFT correspondence. I will focus on the applications of the holographic
principle for the description of confinement\, chiral symmetry breaking a
nd novel phases of strongly interacting matter.\n\nThis is the inaugural l
ecture of Assoc. Prof. Veselin Filev.\n
LOCATION:https://researchseminars.org/talk/AlgAndLogic/43/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexandr Zubkov (United Arab Emirates University\, Al Ain\, UAE an
d Sobolev Institute of Mathematics (Omsk branch)\, Omsk\, Russia)
DTSTART;VALUE=DATE-TIME:20210423T130000Z
DTEND;VALUE=DATE-TIME:20210423T143000Z
DTSTAMP;VALUE=DATE-TIME:20210612T223746Z
UID:AlgAndLogic/44
DESCRIPTION:Title: On Krull dimension of Noetherian super-rings\nby Alexandr Zubkov
(United Arab Emirates University\, Al Ain\, UAE and Sobolev Institute of M
athematics (Omsk branch)\, Omsk\, Russia) as part of Algebra and Logic Sem
inar\n\n\nAbstract\nThe notion of Krull dimension plays crucial role in th
e algebraic geometry and in the theory of commutative rings. It seems quit
e natural to define such a notion for (supercommutative) super-rings in or
der to develop the algebraic supergeometry in more or less systematic way\
, similar to the classical case. This talk is partially based on the recen
t joint work with A. Masuoka (published in JPAA) and new results (yet unpu
blished).\n
LOCATION:https://researchseminars.org/talk/AlgAndLogic/44/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Peter Danchev (Institute of Mathematics and Informatics\, Bulgaria
n Academy of Sciences)
DTSTART;VALUE=DATE-TIME:20210429T120000Z
DTEND;VALUE=DATE-TIME:20210429T130000Z
DTSTAMP;VALUE=DATE-TIME:20210612T223746Z
UID:AlgAndLogic/45
DESCRIPTION:Title: Commutative Group Rings and Abelian Groups\nby Peter Danchev (Ins
titute of Mathematics and Informatics\, Bulgarian Academy of Sciences) as
part of Algebra and Logic Seminar\n\n\nAbstract\nSome specific questions f
rom the theory of commutative group rings and Abelian groups are being con
sidered as complete solutions to some of them are given\, which definitely
generalize certain classical results in these directions.\n\nInaugural le
cture of Assoc. Prof. Peter Danchev.\n
LOCATION:https://researchseminars.org/talk/AlgAndLogic/45/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Valentin Iliev (Institute of Mathematics and Informatics\, Bulgari
an Academy of Sciences)
DTSTART;VALUE=DATE-TIME:20210507T100000Z
DTEND;VALUE=DATE-TIME:20210507T113000Z
DTSTAMP;VALUE=DATE-TIME:20210612T223746Z
UID:AlgAndLogic/46
DESCRIPTION:Title: On the Degree of Dependence of Two Events\nby Valentin Iliev (Ins
titute of Mathematics and Informatics\, Bulgarian Academy of Sciences) as
part of Algebra and Logic Seminar\n\n\nAbstract\nWe define degree of depen
dence of two events A and B in a probability space by using Boltzmann-Shan
non entropy function of an appropriate distribution produced by these even
ts and depending on one parameter varying within a closed interval I. The
important particular case of discrete uniform probability space motivates
this definition in the following way. The entropy function has a global ma
ximum exactly when the events A and B are independent. It has a minimum at
the left endpoint of I exactly when A is a subset of B^c or B^c is a subs
et of A (maximal negative dependence). It has a minimum at the right endpo
int of I exactly when A is a subset of B or B is a subset of A (maximal po
sitive dependence).\n
LOCATION:https://researchseminars.org/talk/AlgAndLogic/46/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vesselin Drensky (Institute of Mathematics and Informatics\, Bulga
rian Academy of Sciences)
DTSTART;VALUE=DATE-TIME:20210514T100000Z
DTEND;VALUE=DATE-TIME:20210514T113000Z
DTSTAMP;VALUE=DATE-TIME:20210612T223746Z
UID:AlgAndLogic/47
DESCRIPTION:Title: Non-finitely based and limit varieties of algebraic systems\nby V
esselin Drensky (Institute of Mathematics and Informatics\, Bulgarian Acad
emy of Sciences) as part of Algebra and Logic Seminar\n\n\nAbstract\nA var
iety of algebraic systems is non-finitely (or infinitely) based if it does
not have a finite basis of identities. It is just-non-finitely based (or
limit) if it is non-finitely based but all its proper subvarieties are fin
itely based. By the Zorn lemma every variety without a finite basis of ide
ntities contains a just-non-finitely based subvariety.\n\nWe survey result
s on non-finitely based varieties of groups\, semigroups and on associativ
e\, Lie and nonassociative rings and algebras.\nWe also present examples o
f just-non-finitely based varieties of nonassociative algebras and varieti
es of pairs over fields of characteristic 0.\n
LOCATION:https://researchseminars.org/talk/AlgAndLogic/47/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ednei Aparecido Santulo Jr. (Universidade Estadual de Maringá\, P
araná\, Brazil)
DTSTART;VALUE=DATE-TIME:20210521T130000Z
DTEND;VALUE=DATE-TIME:20210521T143000Z
DTSTAMP;VALUE=DATE-TIME:20210612T223746Z
UID:AlgAndLogic/48
DESCRIPTION:Title: Group gradings on incidence algebras\nby Ednei Aparecido Santulo
Jr. (Universidade Estadual de Maringá\, Paraná\, Brazil) as part of Alge
bra and Logic Seminar\n\n\nAbstract\nThis is a joint work with Felipe Y. Y
asumura and Jonathan P. Souza.\n\nThe main goal of this talk is presenting
the classification of group gradings on incidence algebras as obtained in
[2]. To do so\, we start by defining incidence algebras and emphasizing t
heir resemblances and differences relative to the algebra of upper triangu
lar matrices. We recall the classification of group gradings on the algebr
a of upper triangular matrices with entries in a field obtained by Di Vin
cenzo\, Koshlukov and Valenti in [1] and generalized in [3] by Valenti and
Zaicev. Then we present some examples to show that a similar result canno
t be true in the general context of incidence algebras. Since good and ele
mentary gradings play a major role in the classification of group gradings
in the case of upper triangular matrices\, we present the natural general
ization of those concepts in the context of incidence algebras (and even i
n more general contexts than that of matrix algebras). Since it is impossi
ble\, due to time\, to present the proofs of the lemmas used to obtain the
main result in a level of details necessary to understand them completely
\, we decided to describe how we were led to those lemmas\, believing that
\, with that approach\, the attendants can get more intuition about the si
tuation we dealt with and\, consequently\, they may be more interested in
studying incidence algebras (or group gradings on algebras)\, beyond the p
roblem presented in our talk\, in the future.\n\n[1] O.M. Di Vincenzo\, P.
Koshlukov\, A. Valenti\, Gradings on the algebra of upper triangular matr
ices and their graded identities\, J. Algebra 275(2) (2004) 550–566.\n\n
[2] E.A. Santulo Jr.\, J.P. Souza\, F.Y. Yasumura\, Group gradings on fini
te dimensional incidence algebras\, J. Algebra 544 (2) (2020) 302-328.\n\n
[3] A. Valenti\, M.V. Zaicev\, Group gradings on upper triangular matrices
\, Arch. Math. 89(1) (2007) 33–40.\n
LOCATION:https://researchseminars.org/talk/AlgAndLogic/48/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ilinka Dimitrova (South-West University “Neofit Rilski”\, Blag
oevgrad)
DTSTART;VALUE=DATE-TIME:20210528T100000Z
DTEND;VALUE=DATE-TIME:20210528T113000Z
DTSTAMP;VALUE=DATE-TIME:20210612T223746Z
UID:AlgAndLogic/49
DESCRIPTION:Title: Ranks of Monoids of Endomorphisms\, Partial Automorphisms and Injecti
ve Partial Endomorphisms of a Finite Undirected Path\nby Ilinka Dimitr
ova (South-West University “Neofit Rilski”\, Blagoevgrad) as part of A
lgebra and Logic Seminar\n\n\nAbstract\nIn the same way that automorphisms
of graphs allow to establish natural connections between Graph Theory and
Group Theory\, endomorphisms of graphs do the same between Graph Theory
and Semigroup Theory.\nFor this reason\, it is not surprising that monoids
of endomorphisms of graphs have been attracting the attention of several
authors over the last decades. In fact\, from combinatorial properties to
more algebraic concepts have been extensively studied.\n\nLet $G=(V\,E)$ b
e a simple graph (i.e. undirected graph without loops and without multiple
edges).\nLet $\\alpha$ be a partial transformation of $V$. Denote by $\\m
athop{\\mathrm{Dom}} \\alpha$ the domain of $\\alpha$ and by $\\mathop{\\m
athrm{Im}} \\alpha$ the image of $\\alpha$.\nWe say that $\\alpha$ is:\n\n
● a partial endomorphism of $G$ if $\\{u\,v\\}\\in E$ implies $\\{u\\al
pha\,v\\alpha\\}\\in E$\, for all $u\,v\\in\\mathop{\\mathrm{Dom}} \\alpha
$\;\n\n● a weak partial endomorphism of $G$ if $\\{u\,v\\}\\in E$ and $u
\\alpha\\ne v\\alpha$ imply $\\{u\\alpha\,v\\alpha\\}\\in E$\, for all $u
\,v\\in\\mathop{\\mathrm{Dom}} \\alpha$\;\n\n● a strong endomorphism of
$G$ if $\\{u\,v\\}\\in E$ if and only if $\\{u\\alpha\,v\\alpha\\}\\in E$
\, for all $u\,v\\in V$\;\n\n● a strong weak endomorphism of $G$ if $\\{
u\,v\\}\\in E$ and $u\\alpha\\ne v\\alpha$ if and only if $\\{u\\alpha\,v\
\alpha\\}\\in E$\, for all $u\,v\\in V$\;\n\n● a partial automorphism of
$G$ if $\\alpha$ is an injective mapping (i.e. a partial permutation) and
$\\alpha$ and $\\alpha^{-1}$ are both partial endomorphisms\;\n\n● if
$\\alpha$ is a full mapping (i.e. $\\alpha\\in \\mathcal{T}(V)$) then to a
partial endomorphism (respectively\, weak partial endomorphism and partia
l automorphism) we just call endomorphism (respectively\, week endomorphis
m and automorphism).\n\n\nDenote by:\n\n● $\\mathrm{End}(G)$ the set of
all endomorphisms of $G$\;\n\n● $\\mathrm{wEnd}(G)$ the set of all weak
endomorphisms of $G$\;\n\n● $\\mathrm{sEnd}(G)$ the set of all strong en
domorphisms of $G$\;\n\n● $\\mathrm{swEnd}(G)$ the set of all strong wea
k endomorphisms of $G$\;\n\n● $\\mathrm{Aut}(G)$ the set of all automorp
hisms of $G$.\n\n● $\\mathrm{wPEnd}(G)$ the set of all weak partial endo
morphisms of $G$\;\n\n● $\\mathrm{PEnd}(G)$ the set of all partial endom
orphisms of $G$\;\n\n● $\\mathrm{IEnd}(G)$ the set of all injective part
ial endomorphisms of $G$\;\n\n● $\\mathrm{PAut}(G)$ the set of all parti
al automorphisms of $G$\;\n\n\nClearly\, $\\mathrm{End}(G)$\, $\\mathrm{wE
nd}(G)$\, $\\mathrm{sEnd}(G)$\, $\\mathrm{swEnd}(G)$\, $\\Aut(G)$\, $\\mat
hrm{wPEnd}(G)$\, $\\mathrm{PEnd}(G)$\, $\\mathrm{IEnd}(G)$ and $\\mathrm{P
Aut}(G)$ are monoids under composition of maps with the identity mapping $
\\mathop{\\mathrm{id}}$ as the identity element. Moreover\, $\\mathrm{Aut}
(G)$ is also a group and $\\mathrm{PAut}(G)$ is an inverse semigroup.\n\nT
he rank of a monoid $S$\, denoted by $\\mathop{\\mathrm{rank}} S$\, is the
least number of generators of $S$. We focus our attention on this importa
nt notion of Semigroup Theory\, which has been\, in recent years\, the sub
ject of intensive research.\n\nWe study the widely considered endomorphism
s\, weak endomorphisms\, partial automorphisms and\, more generally\, inje
ctive partial endomorphisms of a finite undirected path $P_n$ with $n \\in
\\mathbb{N}$ vertices from monoid generators perspective. Our main object
ive is to give formulas for the ranks of the monoids $\\mathrm{wEnd}(P_n)$
\, $\\mathrm{End}(P_n)$\, $\\mathrm{sEnd}(P_n)$\, $\\mathrm{swEn}d(P_n)$\,
$\\mathrm{Aut}(P_n)$\, $\\mathrm{IEnd}(P_n)$ and $\\mathrm{PAut}(P_n)$. W
e also study Green's relations\, regularity\, and cardinality for some of
these monoids.\n
LOCATION:https://researchseminars.org/talk/AlgAndLogic/49/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michael Vaughan-Lee (Oxford University Mathematical Institute\, Un
ited Kingdom)
DTSTART;VALUE=DATE-TIME:20210604T100000Z
DTEND;VALUE=DATE-TIME:20210604T113000Z
DTSTAMP;VALUE=DATE-TIME:20210612T223746Z
UID:AlgAndLogic/50
DESCRIPTION:Title: Schur’s exponent conjecture\nby Michael Vaughan-Lee (Oxford Uni
versity Mathematical Institute\, United Kingdom) as part of Algebra and Lo
gic Seminar\n\n\nAbstract\nIf $G$ is a finite group and we write $G = F/R$
where $F$ is a free group\, then the Schur multiplier $M(G)$ is $(R \\cap
F')/[R\, F]$.\n\nThere is a long-standing conjecture attributed to I. Sch
ur that the exponent of $M(G)$ divides the exponent of $G$. It is easy to
show that this is true for groups $G$ of exponent 2 or exponent 3\, but it
has been known since 1974 that the conjecture fails for exponent 4. Howev
er the truth or otherwise of this conjecture has remained open up till now
for groups of odd exponent.\n\nIn my talk I describe counterexamples to t
he conjecture of exponent 5 and exponent 9.\n
LOCATION:https://researchseminars.org/talk/AlgAndLogic/50/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lyubomir Borissov (Institute of Mathematics and Informatics\, Bulg
arian Academy of Sciences)
DTSTART;VALUE=DATE-TIME:20210611T100000Z
DTEND;VALUE=DATE-TIME:20210611T113000Z
DTSTAMP;VALUE=DATE-TIME:20210612T223746Z
UID:AlgAndLogic/51
DESCRIPTION:Title: Distinctness of the “lifted” Kloosterman sums over the prime fiel
d F_p\nby Lyubomir Borissov (Institute of Mathematics and Informatics\
, Bulgarian Academy of Sciences) as part of Algebra and Logic Seminar\n\n\
nAbstract\nIn this talk I consider the Kloosterman sums over the finite fi
eld $\\mathbb F_{q}$ of characteristic $p$\, defined by\n$$K_{q} (u)= \\su
m_{x \\in \\mathbb F^{*}_{q}} \\omega^{\\ Tr(x+ u x^{-1})}\,\n$$\nwhere $\
\displaystyle\\omega=e^{\\frac{2 \\pi i}p}$ is a primitive $p-$th root of
unity\, and $Tr(a)$ is the absolute trace of $a \\in \\mathbb F_{q}$ over
$\\mathbb F_{p}$.\n\nThe focus of special attention are the so-called "li
fted" Kloosterman sums over $\\mathbb F_{q}$ (see\, [1])\, i.e.\, \n$ K_{q
^{n}} (u)\, u \\in \\mathbb F_{q}$\, where $\\mathbb F_{q^{n}}$ is the fin
ite field of order $q^{n}\, n > 1$.\n\nIt is well-known that the Kloosterm
an sums play an important role in algebraic coding theory and cryptography
(see\, e.g.\, the surveys [2]-[3]).\n\nFirstly I clashed with them in the
problem of enumerating the elements of a finite field having prescribed t
race and co-trace: \nhttps://arxiv.org/pdf/1711.08306.pdf\n\nThe issue of
their distinctness is considered and partly solved for the first time by B
enjamin Fisher in 1992 [4]. In particular\, this author has proved that fa
ct for the simplest sums\, i.e.\, over the prime fields.\n\nRecently\, in
a personal communication with us\, Daqing Wan has announced that as a co-p
roduct of his research [5] (based on deep algebraic number theory such as
Stickelberger's theorem) it follows the distinctness of \n"lifted" Klooste
rman sums over any prime field $\\mathbb F_p$ whenever the extension degre
e is not a multiple of $p$. This statement generalizes our result for the
fields whose extension degree is a power of $2$:\nhttps://link.springer.co
m/article/10.1007/s12095-020-00443-1\n\nHere I am giving a proof for the d
istinctness of the "lifted" Kloosterman sums over $\\mathbb F_3$ for any d
egree of extension thus improving Wan's result in case $p = 3$. \n\nI beli
eve that (jointly with Y. Borissov)\, we have found a proof that all "lift
ed" Kloosterman sums over each prime field of characteristic $\\geq3$ and
any extension degree\, are distinct.\nIn the final slides I present some a
rguments concerning this fact which is to be elaborated in a future work.
\n\nReferences\n\n[1] L. Carlitz\, "Kloosterman sums and finite field exte
nsions"\, Acta Arithmetika vol.~XVI.2 (1969)\, pp. 179-193.\n\n[2] \nN. E.
Hurt\, "Exponential sums and coding theory: a review"\, Acta Appl. Math.\
, vol. 46.1 (1997)\, pp. 49-91.\n\n[3] \nV. A. Zinoviev\, "On classical Kl
oosterman sums"\, Cryptogr. and Commun.\, 11.3 (2019)\, pp. 461-496.\n\n[4
] \nB. Fischer\, "Distinctness of Kloosterman sums"\, Contemporary Mathema
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LOCATION:https://researchseminars.org/talk/AlgAndLogic/51/
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BEGIN:VEVENT
SUMMARY:Bogdana Oliynik (National University of Kyiv-Mohyla Academy\, Kyiv
\, Ukraine)
DTSTART;VALUE=DATE-TIME:20210618T100000Z
DTEND;VALUE=DATE-TIME:20210618T113000Z
DTSTAMP;VALUE=DATE-TIME:20210612T223746Z
UID:AlgAndLogic/52
DESCRIPTION:Title: Primary decompositions of unital locally matrix algebras and Steinitz
numbers\nby Bogdana Oliynik (National University of Kyiv-Mohyla Acade
my\, Kyiv\, Ukraine) as part of Algebra and Logic Seminar\n\n\nAbstract\nL
et $F$ be a ground field. An $F$-algebra $A$ with unit 1 is said to be a l
ocally matrix algebra if an arbitrary finite collection of elements $a_1\,
. . . \, a_s$ from $A$ lies in a subalgebra $B$ with 1 of the algebra $A$
\, and $B$ is isomorphic to a matrix algebra $M_n(F)$\, $n ≥$. We assign
a Steinitz number $n(A)$ to an arbitrary unital locally matrix algebra A.
In this talk\, we outline the construction of a unital locally matrix alg
ebra of uncountable dimension that does not admit a primary de-composition
. It gives negative answers to the question posed in V. M. Kurochkin\, On
the theory of locally simple and locally normal algebras (Russian)\, Mat.
Sb.\, Nov. Ser. 22(64) (1948)\, no. 3\, 443–454. We also show that for a
n arbitrary infinite Steinitz number s there exists a unital locally matri
x algebra A having the Steinitz number s and being not isomorphic to a ten
sor product of finite dimensional matrix algebras.\n\nThis talk is based o
n the joint works with Oksana Bezushchak.\n
LOCATION:https://researchseminars.org/talk/AlgAndLogic/52/
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