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BEGIN:VEVENT
SUMMARY:Mikhail Zaicev (Moscow State University)
DTSTART:20201204T110000Z
DTEND:20201204T120000Z
DTSTAMP:20260422T225658Z
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:20201211T110000Z
DTEND:20201211T120000Z
DTSTAMP:20260422T225658Z
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:20201215T130000Z
DTEND:20201215T140000Z
DTSTAMP:20260422T225658Z
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:20201218T075000Z
DTEND:20201218T082000Z
DTSTAMP:20260422T225658Z
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:20201218T082000Z
DTEND:20201218T085000Z
DTSTAMP:20260422T225658Z
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:20201218T085500Z
DTEND:20201218T092000Z
DTSTAMP:20260422T225658Z
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:20201218T092000Z
DTEND:20201218T095000Z
DTSTAMP:20260422T225658Z
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:20201218T095500Z
DTEND:20201218T101500Z
DTSTAMP:20260422T225658Z
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:20201218T101500Z
DTEND:20201218T103000Z
DTSTAMP:20260422T225658Z
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:20201218T110000Z
DTEND:20201218T113000Z
DTSTAMP:20260422T225658Z
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:20201218T113000Z
DTEND:20201218T115000Z
DTSTAMP:20260422T225658Z
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:20201218T115500Z
DTEND:20201218T122500Z
DTSTAMP:20260422T225658Z
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:20201218T122500Z
DTEND:20201218T124500Z
DTSTAMP:20260422T225658Z
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:20201218T125000Z
DTEND:20201218T130500Z
DTSTAMP:20260422T225658Z
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:20201218T130500Z
DTEND:20201218T133500Z
DTSTAMP:20260422T225658Z
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:20201218T140000Z
DTEND:20201218T143000Z
DTSTAMP:20260422T225658Z
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:20201218T143000Z
DTEND:20201218T145000Z
DTSTAMP:20260422T225658Z
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:20201218T145500Z
DTEND:20201218T151500Z
DTSTAMP:20260422T225658Z
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:20201218T154500Z
DTEND:20201218T160000Z
DTSTAMP:20260422T225658Z
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:20201218T151500Z
DTEND:20201218T154500Z
DTSTAMP:20260422T225658Z
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:20210108T110000Z
DTEND:20210108T120000Z
DTSTAMP:20260422T225658Z
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:20210115T080000Z
DTEND:20210115T083000Z
DTSTAMP:20260422T225658Z
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:20210115T083000Z
DTEND:20210115T090000Z
DTSTAMP:20260422T225658Z
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:20210115T090000Z
DTEND:20210115T093000Z
DTSTAMP:20260422T225658Z
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:20210115T094000Z
DTEND:20210115T101000Z
DTSTAMP:20260422T225658Z
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:20210115T101000Z
DTEND:20210115T104000Z
DTSTAMP:20260422T225658Z
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:20210115T112500Z
DTEND:20210115T114000Z
DTSTAMP:20260422T225658Z
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:20210115T114000Z
DTEND:20210115T124000Z
DTSTAMP:20260422T225658Z
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:20210115T125000Z
DTEND:20210115T133000Z
DTSTAMP:20260422T225658Z
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:20210115T133000Z
DTEND:20210115T140000Z
DTSTAMP:20260422T225658Z
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:20210115T141000Z
DTEND:20210115T144000Z
DTSTAMP:20260422T225658Z
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:20210115T144000Z
DTEND:20210115T151000Z
DTSTAMP:20260422T225658Z
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:20210129T110000Z
DTEND:20210129T120000Z
DTSTAMP:20260422T225658Z
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:20210205T110000Z
DTEND:20210205T120000Z
DTSTAMP:20260422T225658Z
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:20210212T140000Z
DTEND:20210212T150000Z
DTSTAMP:20260422T225658Z
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:20210219T110000Z
DTEND:20210219T120000Z
DTSTAMP:20260422T225658Z
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:20210226T110000Z
DTEND:20210226T120000Z
DTSTAMP:20260422T225658Z
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:20210305T140000Z
DTEND:20210305T150000Z
DTSTAMP:20260422T225658Z
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:20210312T143000Z
DTEND:20210312T160000Z
DTSTAMP:20260422T225658Z
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:20210319T140000Z
DTEND:20210319T153000Z
DTSTAMP:20260422T225658Z
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:20210326T110000Z
DTEND:20210326T123000Z
DTSTAMP:20260422T225658Z
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:20210409T100000Z
DTEND:20210409T113000Z
DTSTAMP:20260422T225658Z
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:20210416T130000Z
DTEND:20210416T143000Z
DTSTAMP:20260422T225658Z
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:20210423T130000Z
DTEND:20210423T143000Z
DTSTAMP:20260422T225658Z
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:20210429T120000Z
DTEND:20210429T130000Z
DTSTAMP:20260422T225658Z
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:20210507T100000Z
DTEND:20210507T113000Z
DTSTAMP:20260422T225658Z
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:20210514T100000Z
DTEND:20210514T113000Z
DTSTAMP:20260422T225658Z
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:20210521T130000Z
DTEND:20210521T143000Z
DTSTAMP:20260422T225658Z
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:20210528T100000Z
DTEND:20210528T113000Z
DTSTAMP:20260422T225658Z
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:20210604T100000Z
DTEND:20210604T113000Z
DTSTAMP:20260422T225658Z
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:20210611T100000Z
DTEND:20210611T113000Z
DTSTAMP:20260422T225658Z
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
tics\, vol. 133 (1992)\, pp. 81-102.\n\n[5] \nD. Wan\, "Minimal polynomial
s and distinctness of Kloosterman sums"\, Finite Fields Appl.\, 1 (1995)\,
pp. 189-203.\n
LOCATION:https://researchseminars.org/talk/AlgAndLogic/51/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bogdana Oliynik (National University of Kyiv-Mohyla Academy\, Kyiv
\, Ukraine)
DTSTART:20210618T100000Z
DTEND:20210618T113000Z
DTSTAMP:20260422T225658Z
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/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Arkadii Slinko (University of Auckland\, New Zealand)
DTSTART:20210625T080000Z
DTEND:20210625T093000Z
DTSTAMP:20260422T225658Z
UID:AlgAndLogic/53
DESCRIPTION:Title: Framing in secret sharing\nby Arkadii Slinko (University of Auckl
and\, New Zealand) as part of Algebra and Logic Seminar\n\n\nAbstract\nSec
ret sharing\, a well-known cryptographic technique\, introduced 40 years a
go as a private and reliable variant of classical storage\, has now become
a major cryptographic primitive with numerous real-world applications.\n\
nIn this paper we consider the digital forensics aspects of secret sharing
. We investigate the problem of framing which occurs when a coalition of p
articipants is able to calculate the share of a participant who does not b
elong to it. In the extreme case one authorized coalition can calculate sh
ares of another authorized coalition\, obtain the secret and use it in som
e way blaming another authorized coalition for their action. Our work show
s that in an ideal secret sharing scheme an authorized coalition cannot fr
ame participants who are less senior than all members of the coalition and
is able to frame a participant who is more senior than at least one membe
r of the coalition.\n\nThis is a joint paper with Yvo Desmedt and Songbao
Mo. It has just been published in\n\nDesmedt\, Y.\, Mo\, S.\, & Slinko\, A
. M. (2021). Framing in Secret Sharing. IEEE Transactions on Information F
orensics and Security\, 16\, 2836-2842.\n
LOCATION:https://researchseminars.org/talk/AlgAndLogic/53/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Natalia Iyudu (Lancaster University\, UK)
DTSTART:20210702T100000Z
DTEND:20210702T113000Z
DTSTAMP:20260422T225658Z
UID:AlgAndLogic/54
DESCRIPTION:Title: Noncommutative Poisson structures\, Hochschild type complexes and Gr
öbner bases theory\nby Natalia Iyudu (Lancaster University\, UK) as p
art of Algebra and Logic Seminar\n\n\nAbstract\nI will discuss Calabi-Yau
type conditions\, such as pre-Calabi-Yau and exact Calabi-Yau. We show tha
t pre-Calabi-Yau structures give rise to double Poisson brackets of Van de
n Bergh. The homological formulation of pre-Calabi-Yau structure can be de
alt with using Gröbner bases theory to prove purity in case of free graph
path algebras.\n\nThis technique is common for our study of such exact Ca
labi-Yau algebras as 3-Sklyanin. Here we are able\, for example\, to impro
ve the statement in Artin-Schelter classical paper\, based on arguments of
topological nature\, that there is a finite group action on Sklyanin alge
bras $S_{p\,q}$\, for which the orbits are exactly isomorphism classes. We
can say that this group is $SL_2(Z_3)$.\n
LOCATION:https://researchseminars.org/talk/AlgAndLogic/54/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Greta Panova (University of Southern California\, USA)
DTSTART:20210709T100000Z
DTEND:20210709T113000Z
DTSTAMP:20260422T225658Z
UID:AlgAndLogic/55
DESCRIPTION:Title: The mysterious Kronecker coefficients of the Symmetric group\nby
Greta Panova (University of Southern California\, USA) as part of Algebra
and Logic Seminar\n\n\nAbstract\nAlgebraic Combinatorics is a field of mat
hematics which studies discrete objects often originating in Representatio
n Theory\, Algebra\, Algebraic Geometry\, Number Theory via combinatorial
methods. One of its oldest problems concerns the Kronecker coefficients of
the Symmetric Group. They are originally defined by Murnaghan more than 8
0 years ago as the multiplicities of the irreducible modules in the factor
ization of the tensor product of two other irreducible modules. They actua
lly generalize the Littlewood-Richardson coefficients in the analogous pro
blem for the general linear group. Despite their algebraic nature as nonne
gative integers\, no combinatorial formula or interpretation is known. Kro
necker coefficients have recently played a role in Computational Complexit
y Theory both as a problem and as a solution.\n\nIn this talk I will give
a brief overview of the developments over the past 10 years. I will show h
ow despite our very limited knowledge we can still use the Kronecker coeff
icients to solve other\, seemingly unrelated problems\, related to enumera
tion of integer partitions (Sylvester’s unimodality theorem). I will als
o discuss some of their computational complexity aspects.\n
LOCATION:https://researchseminars.org/talk/AlgAndLogic/55/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Stefan Dantchev (Durham University\, United Kingdom)
DTSTART:20210716T100000Z
DTEND:20210716T113000Z
DTSTAMP:20260422T225658Z
UID:AlgAndLogic/56
DESCRIPTION:Title: Proof Complexity of Resolution over linear inequalities\nby Stefa
n Dantchev (Durham University\, United Kingdom) as part of Algebra and Log
ic Seminar\n\n\nAbstract\nI will start by giving a brief and non-comprehen
sive introduction to the general research area\, Propositional Proof Compl
exity.\n\nI will then focus on a specific proof system that operates on li
near inequalities with integral coefficients\, called Stabbing Planes (SP)
. Next\, a general method for proving depth lower bounds in SP will be int
roduced\, which allows us to prove logarithmic depth lower bounds for seve
ral well-studied propositional contradictions\, such as the Pigeon-Hole Pr
inciple and the Ordering Principle. Finally\, possible extensions and gene
ralisations of SP will be discussed\, plus some open questions.\n
LOCATION:https://researchseminars.org/talk/AlgAndLogic/56/
END:VEVENT
BEGIN:VEVENT
SUMMARY:George Shabat (Russian State University for the Humanities and Ind
ependent University of Moscow\, Russia)
DTSTART:20210917T080000Z
DTEND:20210917T093000Z
DTSTAMP:20260422T225658Z
UID:AlgAndLogic/57
DESCRIPTION:Title: Dessins d’enfants and moduli spaces of curves\nby George Shabat
(Russian State University for the Humanities and Independent University o
f Moscow\, Russia) as part of Algebra and Logic Seminar\n\n\nAbstract\nDes
sins d'enfants theory\, initiated by Alexander Grothendieck in\n1970's\, e
stablishes an equivalence between the category of certain\ngraphs on topol
ogical surfaces and some arithmetic-geometric category\n(of $\\text{\\it B
elyi pairs}$\, i.e. $(\\text{\\bf X}\,\\beta)$'s\, where $\\text{\\bf X}$
is a curve and \n$\\beta \\rightarrow:\\text{\\bf X}\\to\\text{\\bf P}_1({
\\mathbb C})$ is\na covering with 3 branch points). We are going to discus
s two relations\nof this equivalence with the moduli spaces of curves.\n\n
(1) It turned out (Mumford-Penner-Kontsevich-$\\cdots$) \nthat the $\\text
{\\it decorated moduli spaces of curves}$ ${\\mathcal M}_{g\,N}({\\mathbb
C})\\times {\\mathbb R}^N_{>0}$ \nadmit the orbifold cell decomposition in
which the cells are parametrized by certain\ndessins d'enfants. (In 1992
Kontsevich has applied this construction\nto the proof of the famous Witte
n conjecture). The relation of\nthis decomposition with the Grothendieck-B
elyi construction will be\nexplained.\n\n\n(2) For any triple of natural n
umbers $(b\, d\, g)$ \nand for any algebraically closed ground field $\\ma
thbb K$ we consider the $\\text{\\it critical filtration}$ of the\nmoduli
space ${\\mathcal M}_g({\\mathbb K})$ by the subvarieties \n\\[\n\\text{\\
tt Cr}_{g\;d\,b}({\\mathbb K}) :=\\{\\text{\\bf X}\\in{\\mathcal M}_g({\\m
athbb K})\\mid \\exists f\\in{\\mathbb K}(\\text{\\bf X})\,\\deg f = d\; \
\sharp \\text{\\rm CritVal}(f) \\leq b\\}\n\\]\n(the set of curves of genu
s $g$ carrying rational functions of degree $d$\nwith no more than $b$ cri
tical values -- or\, alternatively\, admitting a\ndegree-$d$ covering of t
he projective line with no more than $b$ branch\npoints).\n\nAccording to
Grothendieck-Belyi\, the zero-dimensional stratum\n$\\text{\\tt Cr}_{g\;d\
,3}({\\mathbb C}) =\\text{\\tt Cr}_{g\;d\,3}(\\overline{{\\mathbb Q}})$ co
rresponds to dessins d'enfants. \nThe combinatorial\, algebro-geometrical
and arithmetical problems\, related to the\nhigher-dimensional strata of t
he critical filtration\, will be discussed.\n
LOCATION:https://researchseminars.org/talk/AlgAndLogic/57/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Peter Danchev (Institute of Mathematics and Informatics\, Bulgaria
n Academy of Sciences)
DTSTART:20211022T110000Z
DTEND:20211022T123000Z
DTSTAMP:20260422T225658Z
UID:AlgAndLogic/58
DESCRIPTION:Title: On Some Special Decompositions of Matrices over Fields and Finite Com
mutative Rings\nby Peter Danchev (Institute of Mathematics and Informa
tics\, Bulgarian Academy of Sciences) as part of Algebra and Logic Seminar
\n\n\nAbstract\nIn order to find a suitable expression of an arbitrary squ
are matrix over an arbitrary field\, we prove that every square matrix ove
r an infinite field is always representable as a sum of a diagonalizable m
atrix and a square-zero nilpotent matrix. In addition\, each 2 x 2 matrix
over any field admits such a representation. We also show that\, for all n
atural numbers n > 2\, every n x n matrix over a finite field having no le
ss than n + 1 elements also admits such a decomposition. As a consequence
of these decompositions\, we show that every matrix over a finite field ca
n be expressed as the sum of a potent matrix and a square-zero nilpotent m
atrix. Moreover\, we prove that every matrix over a finite commutative rin
g is always representable as a sum of a potent matrix and a square-zero ni
lpotent matrix\, provided the Jacobson radical of the former ring has zero
-square. Our main theorems substantially improve on recent results due to
Abyzov et al. in Mat. Zametki (2017)\, Ster in Lin. Algebra & Appl. (2018)
\, Breaz in Lin. Algebra & Appl. (2018) and Shitov in Indag. Math. (2019).
\n\nThe results have been published partially in the following articles:\n
\n(1) P. Danchev\, E. Garcia\, M. G. Lozano\, Decompositions of matrices i
nto diagonalizable and square-zero matrices\, Linear & Multilinear Algebra
(in press 2022)\, published online https://doi.org/10.1080/03081087.2020.
1862742 .\n\n(2) P. Danchev\, E. Garcia\, M. G. Lozano\, Decompositions of
matrices into potent and square-zero matrices\, submitted to a scientific
journal.\n\n(3) P. Danchev\, E. Garcia\, M. G. Lozano\, On some special m
atrix decompositions over fields and finite commutative rings\, Proceeding
s of the Fiftieth Spring Conference of the Union of Bulgarian Mathematicia
ns\, 95-101\, 2021.\n
LOCATION:https://researchseminars.org/talk/AlgAndLogic/58/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kalina Mincheva (Tulane University\, New Orleans\, USA)
DTSTART:20211029T140000Z
DTEND:20211029T153000Z
DTSTAMP:20260422T225658Z
UID:AlgAndLogic/59
DESCRIPTION:Title: Tropical Geometry and the Commutative Algebra of Semirings\nby Ka
lina Mincheva (Tulane University\, New Orleans\, USA) as part of Algebra a
nd Logic Seminar\n\n\nAbstract\nTropical geometry provides a new set of pu
rely combinatorial tools\, which has been used to approach classical probl
ems. In tropical geometry most algebraic computations are done on the clas
sical side - using the algebra of the original variety. The theory develop
ed so far has explored the geometric aspect of tropical varieties as oppos
ed to the underlying (semiring) algebra and there are still many commutati
ve algebra tools and notions without a tropical analogue. In the recent ye
ars\, there has been a lot of effort dedicated to developing the necessary
tools for commutative algebra using different frameworks\, among which pr
ime congruences\, tropical ideals\, tropical schemes. These approaches all
ows for the exploration of the properties of tropicalized spaces without
tying them up to the original varieties and working with geometric structu
res inherently defined in characteristic one (that is\, additively idempot
ent) semifields. In this talk we explore the relationship between tropical
ideals and congruences and what they remember about the geometry of a tro
pical variety.\n
LOCATION:https://researchseminars.org/talk/AlgAndLogic/59/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Erkko Lehtonen (Universidade Nova de Lisboa\, Portugal)
DTSTART:20211105T110000Z
DTEND:20211105T123000Z
DTSTAMP:20260422T225658Z
UID:AlgAndLogic/60
DESCRIPTION:Title: Permutation groups and permutation patterns\nby Erkko Lehtonen (U
niversidade Nova de Lisboa\, Portugal) as part of Algebra and Logic Semina
r\n\n\nAbstract\nWe approach permutations from two different points of vie
w: the algebraic one of permutation groups and the combinatorial one of pe
rmutation patterns. While these two well-established notions do not seem t
o have much in common\, there is a perhaps surprising connection that will
be explained in this talk. Namely\, the class of permutations avoiding th
e complement of a permutation group is comprised of levels that are permut
ation groups.\n\nWith the help of invariant relations\, we describe the pe
rmutation groups that arise in this way from pattern avoidance. Furthermor
e\, we propose refinements to the work by Atkinson and Beals on permutatio
n classes in which all levels are groups.\n\nThis talk is partly based on
joint work with Reinhard Pöschel (Technische Universität Dresden).\n
LOCATION:https://researchseminars.org/talk/AlgAndLogic/60/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexey V. Kislitsin (Altai State Pedagogical University\, Barnaul\
, Russia)
DTSTART:20211119T110000Z
DTEND:20211119T123000Z
DTSTAMP:20260422T225658Z
UID:AlgAndLogic/61
DESCRIPTION:Title: Identities of Vector Spaces and Nonassociative Linear Algebras\nb
y Alexey V. Kislitsin (Altai State Pedagogical University\, Barnaul\, Russ
ia) as part of Algebra and Logic Seminar\n\n\nAbstract\nIn this talk\, we
study the concept of the identity of the $L$-space as a weak identity of t
he pair $(A\, E)$\, where $A$ is the associative $F$-algebra generated by
the vector space $E$ over the field $F$. We study the properties of the $L
$-spaces and their identities. Corollaries of some of the results proved a
re also obtained for non-associative linear algebras satisfying the identi
ty $x(yz) = 0$.\n\nThis is a joint talk with Ismail M. Isaev (Altai State
Pedagogical University\, Barnaul\, Russia).\nThe talk will be delivered in
Russian\, the slides will be in English.\n
LOCATION:https://researchseminars.org/talk/AlgAndLogic/61/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Petar Iliev (Institute of Philosophy and Sociology and Institute o
f Mathematics and Informatics\, Bulgarian Academy of Sciences)
DTSTART:20211126T110000Z
DTEND:20211126T123000Z
DTSTAMP:20260422T225658Z
UID:AlgAndLogic/62
DESCRIPTION:Title: On a method of proving the non-existence of modal formulae satisfying
certain syntactic properties and defining a given class of frames\nby
Petar Iliev (Institute of Philosophy and Sociology and Institute of Mathe
matics and Informatics\, Bulgarian Academy of Sciences) as part of Algebra
and Logic Seminar\n\n\nAbstract\nWe elaborate on semantically labeled syn
tax trees\, which provide a method of proving the non-existence of modal f
ormulae satisfying certain syntactic properties and defining a given class
of either models or frames\, and use them to show that there are classes
of Kripke frames that are definable by both non-Sahlqvist and Sahlqvist fo
rmulae but the latter require more propositional variables.\n\nThe talk is
based on the following articles.\n\nP. Iliev. On a method of proving the
non-existence of modal formulae\nsatisfying certain syntactic properties a
nd defining a given class of frames (submitted).\n\nP. Balbiani\, D. Ferna
ndez-Duque\, A. Herzig\, and P. Iliev. Frame validity Games and Lower Boun
ds on the Complexity of Modal Axioms. Logic Journal of the IGPL (2020).\n
LOCATION:https://researchseminars.org/talk/AlgAndLogic/62/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dimitar Guelev (Institute of Mathematics and Informatics\, Bulgari
an Academy of Sciences)
DTSTART:20211203T110000Z
DTEND:20211203T113000Z
DTSTAMP:20260422T225658Z
UID:AlgAndLogic/63
DESCRIPTION:Title: A Separation Theorem for Discrete Time Interval Temporal Logic\nb
y Dimitar Guelev (Institute of Mathematics and Informatics\, Bulgarian Aca
demy of Sciences) as part of Algebra and Logic Seminar\n\n\nAbstract\nGabb
ay’s separation theorem about linear temporal logic with past is admitte
dly one of the most useful theoretical results in temporal logic. In this
talk\, we establish an analogous statement about Moszkowski’s discrete t
ime propositional Interval Temporal Logic (ITL) with two sets of expanding
modalities\, namely the unary neighbourhood modalities and the binary wea
k inverses of ITL’s chop operator. (The two pairs of expanding modalitie
s are interexpressible.) We prove that separation holds for ITL both with
and without its loop construct chop-star. A considerable share of these ap
plications can be upgraded to the new case of ITL. We give brief prelimina
ries on ITL and LTL\, and the relevance of separation to applications as k
nown about LTL first.\n\nThe talk is based on a joint work with Ben Moszko
wski.\n\nThe talk will be delivered in Bulgarian with presentation in Engl
ish.\n
LOCATION:https://researchseminars.org/talk/AlgAndLogic/63/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Roussanka Loukanova (Institute of Mathematics and Informatics\, Bu
lgarian Academy of Sciences)
DTSTART:20211203T113000Z
DTEND:20211203T120000Z
DTSTAMP:20260422T225658Z
UID:AlgAndLogic/64
DESCRIPTION:Title: Restricted Quantification in New Type-Theory of Algorithms\nby Ro
ussanka Loukanova (Institute of Mathematics and Informatics\, Bulgarian Ac
ademy of Sciences) as part of Algebra and Logic Seminar\n\n\nAbstract\nIn
this talk\, I present an extended Type-Theory of Algorithms for restricted
computations. The restrictor operator supports algorithmic rules of intro
duction and elimination\, for each of the existential and universal quanti
fiers. I define and discuss new rules of existential quantification.\n\nMy
focus is on development of mathematics of Type Theory\, from the perspect
ive of new\, advanced technological applications. I shall point to one of
its most important applications for representing semantic underspecificati
on of quantifier scope.\n
LOCATION:https://researchseminars.org/talk/AlgAndLogic/64/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Antoni Rangachev (Institute of Mathematics and Informatics\, Bulga
rian Academy of Sciences)
DTSTART:20220107T110000Z
DTEND:20220107T123000Z
DTSTAMP:20260422T225658Z
UID:AlgAndLogic/65
DESCRIPTION:Title: A valuation theorem for Noetherian rings\nby Antoni Rangachev (In
stitute of Mathematics and Informatics\, Bulgarian Academy of Sciences) as
part of Algebra and Logic Seminar\n\n\nAbstract\nA classical result due t
o Krull says that a normal domain R is equal to the intersection of the va
luation rings in its field of fractions that contain R. If in addition R i
s Noetherian\, then one can restrict the intersection to the discrete valu
ation rings that contain R. Now consider the following relative setting. L
et A and B be integral domains. Suppose A is Noetherian and B is a finitel
y generated A-algebra that contains A. Denote by A’ the integral closure
of A in B. In this talk I will show that A’ is determined by finitely m
any unique discrete valuation rings. This result generalizes Rees’ class
ical valuation theorem for ideals. If time permits I will obtain a variant
of Zariski’s main theorem.\n
LOCATION:https://researchseminars.org/talk/AlgAndLogic/65/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rosen Lutskanov (Institute of Philosophy and Sociology\, Bulgarian
Academy of Sciences)
DTSTART:20220114T083000Z
DTEND:20220114T090000Z
DTSTAMP:20260422T225658Z
UID:AlgAndLogic/66
DESCRIPTION:Title: Defeasible Preference Logic\nby Rosen Lutskanov (Institute of Phi
losophy and Sociology\, Bulgarian Academy of Sciences) as part of Algebra
and Logic Seminar\n\n\nAbstract\nThe talk explores a formal framework for
reasoning about preferences that employs\ntwo types of preference: defeasi
ble and fixed. Preference learning is modeled as a process of\ngradual sub
stitution of defeasible preferences with fixed preferences. It is shown th
at\, under\nsome natural axiomatic conditions\, this logic admits a semant
ics with partially ordered truth\nvalues. The partial order belongs to the
family of series-parallel semiorders whose properties\nare further discus
sed.\n\nThe talk is part of a seminar dedicated to the Fourth World Logic
Day 2022\, January 14th.\n
LOCATION:https://researchseminars.org/talk/AlgAndLogic/66/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Elena Tsvetkova (Institute of Philosophy and Sociology\, Bulgarian
Academy of Sciences)
DTSTART:20220114T090000Z
DTEND:20220114T093000Z
DTSTAMP:20260422T225658Z
UID:AlgAndLogic/67
DESCRIPTION:Title: Difference between material and behavioral implicatures\nby Elena
Tsvetkova (Institute of Philosophy and Sociology\, Bulgarian Academy of S
ciences) as part of Algebra and Logic Seminar\n\n\nAbstract\nIn Grice’s
theory of conversational implicatures a difference can be drawn between\nm
aterial and behavioral implicatures. This distinction has been proposed by
Mark Jary and\nsuggests that by material implicatures there is a link bet
ween the explicit content of an\nutterance and the implicature that is bas
ed on the conceptual content of the utterance\, while by behavioral implic
atures inference is drawn based on understanding the speaker’s behavior
and reasons for uttering a sentence. Considering this distinction\, Grice
’s definition of non-natural meaning is interpreted as a case of behavio
ral implicature. In this talk I will consider a way of keeping the distinc
tion between material and behavioral implicatures and at the same time def
end Grice’s notion of non-natural meaning.\n\nThe talk is part of a semi
nar dedicated to the Fourth World Logic Day 2022\, January 14th.\n
LOCATION:https://researchseminars.org/talk/AlgAndLogic/67/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lukasz T. Stepien (The Pedagogical University of Cracow)
DTSTART:20220114T093000Z
DTEND:20220114T101000Z
DTSTAMP:20260422T225658Z
UID:AlgAndLogic/68
DESCRIPTION:Title: On a proof of consistency of Arithmetic System\nby Lukasz T. Step
ien (The Pedagogical University of Cracow) as part of Algebra and Logic Se
minar\n\n\nAbstract\nA sketch of a proof of consistency of Arithmetic Syst
em will be presented. This\nproof has been done within this Arithmetic Sys
tem.\n\nThe talk is part of a seminar dedicated to the Fourth World Logic
Day 2022\, January 14th.\n
LOCATION:https://researchseminars.org/talk/AlgAndLogic/68/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Stoyan Mihov and Stefan Gerdzhikov (IICT-BAS and FMI-Sofia Univers
ity)
DTSTART:20220114T111000Z
DTEND:20220114T114000Z
DTSTAMP:20260422T225658Z
UID:AlgAndLogic/69
DESCRIPTION:Title: On Space Bounds for Bimachine Constructions\nby Stoyan Mihov and
Stefan Gerdzhikov (IICT-BAS and FMI-Sofia University) as part of Algebra a
nd Logic Seminar\n\n\nAbstract\nBimachines are deterministic finite-state
devices which have the same expressive\npower as the class of regular (rat
ional) functions. The main practical advantage of the\nbimachines is the d
eterministic traversal\, which facilitates the computation of the image of
an\ninput string $S$ in time $O(|S|)$. Furthermore\, the class of regular
functions and hence the\nbimachines are closed under composition. We firs
t show a direct algorithm for constructing a\nbimachine from a transducer
representing a regular function. Following this construction\nevery succes
sful run of the bimachine corresponds to a successful path in the original
\ntransducer and the outputs of the bimachine correspond to the outputs of
the transducer\ntransitions on the given path. Afterwards\, we present an
optimized algorithm which constructs\na bimachine with $O(2^N)$ states\,
where $N$ is the number of states in the original transducer. In\nthis con
struction the runs of the bimachine do not correspond to the outputs of th
e transducer\ntransitions. Finally\, we show an asymptotical lower bound o
f $O(2^{N/2})$ for any construction that\nproduces a bimachine equivalent
to a given functional transducer with N states.\n\nThe talk is part of a s
eminar dedicated to the Fourth World Logic Day 2022\, January 14th.\n
LOCATION:https://researchseminars.org/talk/AlgAndLogic/69/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yana Rumenova and Tinko Tinchev (FMI-Sofia University)
DTSTART:20220114T123000Z
DTEND:20220114T130000Z
DTSTAMP:20260422T225658Z
UID:AlgAndLogic/70
DESCRIPTION:Title: Modal definability of some classes of modal products\nby Yana Rum
enova and Tinko Tinchev (FMI-Sofia University) as part of Algebra and Logi
c Seminar\n\n\nAbstract\nhttps://math.bas.bg/wp-content/uploads/2022/01/Ru
menovaTinchev.pdf\n\nThe talk is part of a seminar dedicated to the Fourth
World Logic Day 2022\, January 14th.\n
LOCATION:https://researchseminars.org/talk/AlgAndLogic/70/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Petar Iliev (IPS-BAS and IMI-BAS)
DTSTART:20220114T114000Z
DTEND:20220114T121000Z
DTSTAMP:20260422T225658Z
UID:AlgAndLogic/71
DESCRIPTION:Title: On the formula-size of the parity function\nby Petar Iliev (IPS-B
AS and IMI-BAS) as part of Algebra and Logic Seminar\n\n\nAbstract\nOn the
formula-size of the parity function. Subbotovskaya'\;s and Khrapchenko
'\;s\ntheorems\, both providing lower bounds on the formula-size of the
parity function\, are\ncornerstones of Boolean function complexity. We ar
e going to give a slow-paced introduction\nto these results and some relat
ed open problems.\n\nThe talk is part of a seminar dedicated to the Fourth
World Logic Day 2022\, January 14th.\n
LOCATION:https://researchseminars.org/talk/AlgAndLogic/71/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ivan Georgiev (FMI-Sofia University)
DTSTART:20220114T130000Z
DTEND:20220114T133000Z
DTSTAMP:20260422T225658Z
UID:AlgAndLogic/72
DESCRIPTION:Title: On the computational complexity of some representations of irrational
numbers\nby Ivan Georgiev (FMI-Sofia University) as part of Algebra a
nd Logic Seminar\n\n\nAbstract\nIn this talk we consider different represe
ntations of irrational numbers: Cauchy\nsequences\, Dedekind cuts\, contin
ued fractions and Hurwitz characteristics. All of them are\ncomputationall
y equivalent when using full Turing computability. However\, this is not t
he\ncase for restricted notions of computability. We make a survey of some
known results\,\nleading to an open problem on graphs of continued fracti
ons. In the end of the talk\, we take a\nglimpse of an unexplored directio
n concerning the small Grzegorczyk classes.\n\nThe talk is part of a semin
ar dedicated to the Fourth World Logic Day 2022\, January 14th.\n
LOCATION:https://researchseminars.org/talk/AlgAndLogic/72/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tatyana Todorova (FMI\, Sofia University\, Bulgaria)
DTSTART:20220121T110000Z
DTEND:20220121T123000Z
DTSTAMP:20260422T225658Z
UID:AlgAndLogic/73
DESCRIPTION:Title: On the distribution of αp modulo one for primes p=aq^2+1 with prime
q\nby Tatyana Todorova (FMI\, Sofia University\, Bulgaria) as part of
Algebra and Logic Seminar\n\n\nAbstract\nIt is a long-standing conjecture
that there are infinitely many primes of the form $n^2+1$. Several approxi
mations to this problem have been made. Baier and Zhao showed that for any
$ε > 0$\, there are infinitely many primes of the form $p = aq^2 + 1$\,
where $a ≤ p^{5/9+ε}$. The best known result\, due to Matomäki is that
there are infinitely many primes of the form $p = aq^2 + 1$\, where $a
≤ p^{1/2+ε}$ and $q$ is a prime.\n\nWe prove that there are infinitely
many primes of the form $p = aq^2 + 1$ with $a ≤ p^(5/9+ε)$ and $q$ is
a prime\, such that $||αp+β||< p^(-θ)$\, where $α$ is irrational\, $β
$ is real and $θ < 1/18$.\n
LOCATION:https://researchseminars.org/talk/AlgAndLogic/73/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vesselin Drensky (Institute of Mathematics and Informatics\, Bulga
rian Academy of Sciences)
DTSTART:20220128T110000Z
DTEND:20220128T123000Z
DTSTAMP:20260422T225658Z
UID:AlgAndLogic/74
DESCRIPTION:Title: Bicommutative algebras from commutative point of view\nby Vesseli
n Drensky (Institute of Mathematics and Informatics\, Bulgarian Academy of
Sciences) as part of Algebra and Logic Seminar\n\n\nAbstract\nThe nonasso
ciative algebra R is right-commutative if\n\n$(ab)c = (ac)b$ for all $a\,
b\, c$ in $R$\,\n\n$R$ is left-commutative if\n\n$a(bc) = b(ac)$ for all $
a\, b\, c$ in $R$.\n\nBicommutative algebras are algebras which are both l
eft- and right-commutative. One-sided commutative algebras appeared for th
e first time in a paper by Cayley in 1857. Their important subclass of Gel
fand-Dorfman-Novikov algebras were studied by Gelfand and Dorfman for the
needs of the Hamiltonian operator in finite-dimensional mechanics and by B
alinskii and Novikov in relation with the equations of hydrodynamics.\n\nD
zhumadil’daev\, Ismailov and Tulenbaev described the free bicommutative
algebra and in the case of characteristic 0 determined the main parameters
needed in the study of varieties of bicommutative algebras. They proved t
hat the square $F^2$ of the free bicommutative algebra $F$ is a commutativ
e associative algebra. This idea was further explored by the speaker and Z
hakhayev who applied classical methods of commutative algebra in the study
of bicommutative algebras.\n\nRecently Yuxiu Bai\, Yuqun Chen and Zerui Z
hang have established that the ideals of finitely generated free bicommuta
tive algebras have finite Gröbner-Shirshov bases. In this way they have d
emonstrated the power of the methods of Shirshov for the study of ideals o
f nonassociative algebras. Bai\, Chen and Zhang also have shown the integr
ality of the Gelfand-Kirillov dimension of finitely generated bicommutativ
e algebras.\n\nOnce results are established it is natural to search for ne
w proofs and further generalizations. The idea of the talk is to show that
many results for bicommutative algebras can be obtained with well known r
esults in commutative algebra. Additionally this approach allows the usage
of popular computer packages for calculations with bicommutative algebras
.\n
LOCATION:https://researchseminars.org/talk/AlgAndLogic/74/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yana Rumenova (FMI\, Sofia University\, Bulgaria)
DTSTART:20220211T110000Z
DTEND:20220211T123000Z
DTSTAMP:20260422T225658Z
UID:AlgAndLogic/75
DESCRIPTION:Title: Modal definability of some classes of modal products\nby Yana Rum
enova (FMI\, Sofia University\, Bulgaria) as part of Algebra and Logic Sem
inar\n\n\nAbstract\nAbstract\n\nThis is a joint
work with Tinko Tinchev (Sofia University).\n
LOCATION:https://researchseminars.org/talk/AlgAndLogic/75/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vesselin Drensky (Institute of Mathematics and Informatics\, Bulga
rian Academy of Sciences)
DTSTART:20220218T140000Z
DTEND:20220218T153000Z
DTSTAMP:20260422T225658Z
UID:AlgAndLogic/76
DESCRIPTION:Title: The Bulgarian Solitaire and Other Games on Partitions\nby Vesseli
n Drensky (Institute of Mathematics and Informatics\, Bulgarian Academy of
Sciences) as part of Algebra and Logic Seminar\n\n\nAbstract\nIn 2020 the
L.N. Gumilyov Eurasian National University (Nur-Sultan\, Kazakhstan) deci
ded to organize International Scientific Conference "Algebra and Logic" de
dicated to the 60th anniversary of Professor Ualbai Umirbaev and the 75th
anniversary of Professor Leonid Makar-Limanov. The meeting was cancelled b
ecause of the Covid-19 pandemic. The present talk is based on the talk I p
lanned to give in Nur-Sultan.\n\nThe (quite amusing) story presented in th
e talk is an example of how an elementary mathematical game can inspirit s
erious mathematical investigations in Combinatorics\, Graph theory\, Discr
ete dynamical systems\, Cellular automata\, Linear algebra\, Statistics\,
Economical models. The topic has the advantage that most of the problems c
an be stated in a form which attracts young people to mathematical researc
h.\n\nThe Bulgarian solitaire is a mathematical card game played by one pe
rson. A pack of $n$ cards is divided into several decks (or "piles"). Each
move consists of the removing of one card from each deck and collecting t
he removed cards to form a new deck. The game ends when the same position
occurs twice. It has turned out that when $n = k(k + 1)/2$ is a triangular
number\, the game reaches the same stable configuration with size of the
piles $1\, 2\, ...\, k$. In the talk we discuss mathematical problems rela
ted with the Bulgarian solitaire. The talk is based on the paper (with add
itional information collected after its publishing):\n\nV. Drensky\, The B
ulgarian solitaire and the mathematics around it\, Math. and Education in
Math.\, Proc. of the 44-th Spring Conf. of the Union of Bulgar. Mathematic
ians\, SOK-Kamchia\, April 2-6\, 2015\, 79-91\; arXiv:1503.00885v1 [math.C
O].\nhttp://www.math.bas.bg/smb/2015_PK/tom_2015/pdf/079-091.pdf\n
LOCATION:https://researchseminars.org/talk/AlgAndLogic/76/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Valentin Iliev (Institute of Mathematics and Informatics\, Bulgari
an Academy of Sciences)
DTSTART:20220225T110000Z
DTEND:20220225T123000Z
DTSTAMP:20260422T225658Z
UID:AlgAndLogic/77
DESCRIPTION:Title: On the Degree of Dependence of Two Events as a Relative Invariant of
the Dihedral Group of Order 8\nby Valentin Iliev (Institute of Mathema
tics and Informatics\, Bulgarian Academy of Sciences) as part of Algebra a
nd Logic Seminar\n\n\nAbstract\nThe joint experiment $\\mathcal{J}(A\,B)$
of two binary trials $A \\cup A^c$ and $B \\cup B^c$ in a probability spac
e can be produced not only by the ordered pair $(A\,B)$ but by a set consi
sting\, in general\, of 24 ordered pairs of events (named Yule's pairs). T
he probabilities $ξ_1$\, $ξ_2$\, $ξ_3$\, $ξ_4$ of the four results of
$\\mathcal{J}(A\,B)$ are linear functions in three variables $α = \\text{
Pr}(A)$\, $β = \\text{Pr}(B)$\, $γ = \\text{Pr}(A ∩ B)$\, and constitu
te a probability distribution. The symmetric group $S_4$ of degree four ha
s an exact representation in the affine group $\\text{Aff}(3\, R)$\, which
is constructed by using the types of the form $[α\, β\, θ]$ of those 2
4 Yule's pairs. The corresponding action of $S_4$ permutes the components
of the probability distribution $(ξ_1\, ξ_2\, ξ_3\, ξ_4)$\, and\, in p
articular\, its entropy function is $S_4$-invariant. The function of degre
e of dependence of two events\, defined via modifying the entropy function
\, turns out to be a relative invariant of the dihedral group of order 8.\
n
LOCATION:https://researchseminars.org/talk/AlgAndLogic/77/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Carsten Schneider (Research Institute for Symbolic Computation\, J
ohannes Kepler University\, Linz\, Austria)
DTSTART:20220311T120000Z
DTEND:20220311T133000Z
DTSTAMP:20260422T225658Z
UID:AlgAndLogic/78
DESCRIPTION:Title: Multi-summation in difference rings and applications\nby Carsten
Schneider (Research Institute for Symbolic Computation\, Johannes Kepler U
niversity\, Linz\, Austria) as part of Algebra and Logic Seminar\n\n\nAbst
ract\nSymbolic summation in difference fields started with Karr's summatio
n algorithm (1981) which can be considered as the discrete version of Risc
h's indefinite integration algorithm in differential fields. In the last 2
0 years this approach has been generalized and enhanced to a constructive
summation theory of difference rings.\n\nIn general\, one can represent al
gorithmically any expression in terms of indefinite nested sums defined ov
er hypergeometric products in such rings. As a crucial by-product one obta
ins optimal representations where the arising sums and products are algebr
aically independent among each other. In particular\, difference ring algo
rithms have been developed that enable one to simplify certain classes of
definite multi-sums to expressions in terms of indefinite nested sums defi
ned over hypergeometric products.\n\nWithin this machinery one can apply Z
eilberger's creative telescoping paradigm in order to compute linear recur
rences for definite multi-sums and one can find all solutions of linear re
currences that can be expressed in terms of indefinite nested sums and pro
ducts. In this talk we will present this algorithmic difference ring theor
y for symbolic summation implemented in the summation package Sigma and wi
ll illustrate its potential by non-trivial applications coming\, e.g.\, fr
om combinatorics and elementary particle physics.\n
LOCATION:https://researchseminars.org/talk/AlgAndLogic/78/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ece Yetkin Celikel (Hasan Kalyoncu University\, Turkey)
DTSTART:20220318T140000Z
DTEND:20220318T153000Z
DTSTAMP:20260422T225658Z
UID:AlgAndLogic/79
DESCRIPTION:Title: Absorbing ideal structures of commutative rings\nby Ece Yetkin Ce
likel (Hasan Kalyoncu University\, Turkey) as part of Algebra and Logic Se
minar\n\n\nAbstract\nLet R be a commutative ring with nonzero identity. As
generalizations\nof prime ideals\, the absorbing ideals were first define
d and studied by A.\nBadawi in 2007. A proper ideal I of R is said to be 2
-absorbing if\nwhenever $a\, b\, c \\in R$ with $abc \\in I$\, then either
$ab \\in I$ or $ac \\in I$ or $bc\n\\in I$. After this date\, many resear
ches have been done to introduce\nvarious extensions of this concept.\nIn
this talk\, we present some absorbing ideals of this class of ideals in\ng
eneral aspect with a number of examples\, and also we give many\ncharacter
izations for some particular rings such as quasi-local rings\,\nDedekind d
omains\, fields in terms of absorbing ideals.\n
LOCATION:https://researchseminars.org/talk/AlgAndLogic/79/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dimitar Guelev (Institute of Mathematics and Informatics\, Bulgari
an Academy of Sciences)
DTSTART:20220325T110000Z
DTEND:20220325T123000Z
DTSTAMP:20260422T225658Z
UID:AlgAndLogic/80
DESCRIPTION:Title: An Application of Separation in Discrete Time Interval Temporal Logic
to Branching Time\nby Dimitar Guelev (Institute of Mathematics and In
formatics\, Bulgarian Academy of Sciences) as part of Algebra and Logic Se
minar\n\n\nAbstract\nIn this talk we make an application of our separation
theorem for discrete time Interval Temporal Logic (ITL) to the study of I
nterval-based Computation Tree Logic (ICTL*). We prove that the expressibi
lity of the expanding modalities and\, most importantly\, propositional qu
antification\, carry over from linear time ITL to the branching time syste
m of ICTL*. The relevance of this follows from the fact that point-based p
ropositionally quantified CTL* (QCTL*) is the established intermediate lan
guage for temporal logics of agency as propositional quantification enable
s expressing the existence of strategies with given temporal properties. B
y moving to ITL we move a step further\, using the expressibility of propo
sitional quantification in the logic\, which is markedly more expressive t
han point-based CTL* and facilitates the compositionality of specification
s.\n
LOCATION:https://researchseminars.org/talk/AlgAndLogic/80/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Altyngul Naurazbekova (L. N. Gumilyov Eurasian National University
\, Nur-Sultan\, Kazakhstan)
DTSTART:20220401T100000Z
DTEND:20220401T113000Z
DTSTAMP:20260422T225658Z
UID:AlgAndLogic/81
DESCRIPTION:Title: Automorphisms of simple quotients of the Poisson and universal envelo
ping algebras of $\\text{sl}_2$\nby Altyngul Naurazbekova (L. N. Gumil
yov Eurasian National University\, Nur-Sultan\, Kazakhstan) as part of Alg
ebra and Logic Seminar\n\n\nAbstract\nLet $P(\\text{sl}_2(K))$ be the Pois
son enveloping algebra of the Lie algebra $\\text{sl}_2(K)$ over an algebr
aically closed field $K$ of characteristic zero. U. Umirbaev\, V. Zhelyabi
n proved that the quotient algebras $P(\\text{sl}_2(K))/(C_P – λ)$\, wh
ere $C_P$ is the standard Casimir element of $\\text{sl}_2(K)$ in $P(\\tex
t{sl}_2(K))$ and $0 ≠ λ ∈K$\, are simple. Using a result by L. Makar-
Limanov on groups of automorphisms of a class of surfaces\, we describe ge
nerators of the automorphism group of $P(\\text{sl}_2(K))/(C_P – λ)$ an
d represent this group as an amalgamated product of its subgroups. Moreove
r\, using similar results by J. Dixmier and O. Fleury for the quotient alg
ebras $U(\\text{sl}_2(K))/(C_U – λ)$\, where $C_U$ is the standard Casi
mir element of $\\text{sl}_2(K)$ in the universal enveloping algebra $U(\\
text{sl}_2(K))$\, we prove that the automorphism groups of $P(\\text{sl}_2
(K))/(C_P – λ)$ and $U(\\text{sl}_2(K))/(C_U – λ)$ are isomorphic.\n
\nThis is a joint work with professor U. Umirbaev.\n
LOCATION:https://researchseminars.org/talk/AlgAndLogic/81/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexander V. Mikhailov (University of Leeds\, UK)
DTSTART:20220415T100000Z
DTEND:20220415T113000Z
DTSTAMP:20260422T225658Z
UID:AlgAndLogic/82
DESCRIPTION:Title: Quantisation of free associative dynamical systems. Bi-quantum struct
ure of the stationary KdV hierarchy. Non-deformation quantisation of the V
olterra hierarchy\nby Alexander V. Mikhailov (University of Leeds\, UK
) as part of Algebra and Logic Seminar\n\n\nAbstract\nTraditional quantisa
tion theories start with classical Hamiltonian systems with variables taki
ng values in commutative algebras and then study their non-commutative def
ormations\, such that the commutators of observables tend to the correspon
ding Poisson brackets as the (Planck) constant of deformation goes to zero
. I am proposing to depart from dynamical systems defined on a free associ
ative algebra A. In this approach the quantisation problem is reduced to t
he problem of finding of a two-sided ideal J ⸦ A satisfying two conditio
ns: the ideal J has to be invariant with respect to the dynamics of the sy
stem and to define a complete set of commutation relations in the quotient
algebras A_J = A / J.\n\nTo illustrate this approach I’ll consider the
quantisation problem for N-th Novikov equations and the corresponding fini
te KdV hierarchy. I will show that stationary KdV equations and Novikov’
s equations admit two compatible quantisations\, i.e. two distinct commuta
tion relations between the variables\, such that a linear combination of t
he corresponding commutators is also a valid quantisation rule leading to
the Heisenberg form of quantum equations. The picture is very similar to t
he bi-Hamiltonian structure in the case of classical integrable equations.
\n\nAlso\, I am going to discuss quantisation of the Bogoyavlensky family
of integrable systems. In particular\, I will show that odd degree symmetr
ies of the Volterra chain admit two quantisations\, one of them is a well-
known quantisation of the Volterra chain\, and another one is new and not
a deformation quantisation.\n\nThe talk is partially based on:\n\nAVM\, Qu
antisation ideals of nonabelian integrable systems\, arXiv:2009.01838\, 20
20 (Published in Russ. Math. Surv. v.75:5\, pp 199-200\, 2020)\n\nV. M. Bu
chstaber and AVM\, KdV hierarchies and quantum Novikov’s equations\, arX
iv:2109.06357v2\, 2021.\n
LOCATION:https://researchseminars.org/talk/AlgAndLogic/82/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Thiago Castilho de Mello (Universidade Federal de São Paulo\, Bra
zil)
DTSTART:20220429T130000Z
DTEND:20220429T143000Z
DTSTAMP:20260422T225658Z
UID:AlgAndLogic/83
DESCRIPTION:Title: Images of multilinear polynomials on upper triangular matrices\nb
y Thiago Castilho de Mello (Universidade Federal de São Paulo\, Brazil) a
s part of Algebra and Logic Seminar\n\n\nAbstract\nLet $f(x_1\,…\,x_m)$
be a polynomial in noncommutative variables over an infinite field $K$. If
$A$ is a $K$-algebra\, it defines in a natural way a map $A^m →A$. If t
he polynomial $f$ is multilinear\, the famous Lvov-Kaplansky conjecture as
ks whether the image of a multilinear polynomial on a matrix algebra is a
vector subspace. Solutions to this problem are known only for $n=2$ or $m=
2$ with partial results for $m=3$ and $n=3$. \n\nIn this talk\, we survey
these results and discuss possible variations for this problem in the asso
ciative and nonassociative settings. \n\nIn particular\, we discuss a joi
nt work with I. Gargate about images of multilinear polynomials on upper t
riangular matrices.\n
LOCATION:https://researchseminars.org/talk/AlgAndLogic/83/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Diego García-Lucas (Universidad de Murcia\, Spain)
DTSTART:20220513T100000Z
DTEND:20220513T113000Z
DTSTAMP:20260422T225658Z
UID:AlgAndLogic/84
DESCRIPTION:Title: A counterexample to the modular isomorphism problem\nby Diego Gar
cía-Lucas (Universidad de Murcia\, Spain) as part of Algebra and Logic Se
minar\n\n\nAbstract\nThe modular isomorphism problem asks whether the isom
orphism type of the modular group algebra of a $p$-group $G$ over a field
of characteristic $p$ determines the isomorphism type of $G$. It was expli
citly mentioned in a survey by Richard Brauer in 1963\, and was the only c
lassical version of the isomorphism problem for group rings which had resi
sted a solution\, though it received considerable attention. Several parti
al positive solutions were obtained imposing very strong conditions on the
group $G$\, for instance the one of being metacyclic.\n\nIn a joint work
with Leo Margolis and Ángel del Río\, we solve the modular isomorphism p
roblem in the negative by exhibiting a series of pairs of non-isomorphic 2
-groups with isomorphic modular group algebras over every field of charact
eristic 2. These groups are two-generated with cyclic derived subgroup. We
will also discuss the (lack of) possibility of obtaining\, in a naive way
\, analogues to the counterexamples for $p > 2$ verifying this condition.\
n
LOCATION:https://researchseminars.org/talk/AlgAndLogic/84/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ivailo Hartarsky (Université Paris-Dauhpine\, PSL\, France\, visi
ting scholar at Instituto de Matemática Pura e Aplicada\, Rio de Janeiro\
, Brazil)
DTSTART:20220520T130000Z
DTEND:20220520T143000Z
DTSTAMP:20260422T225658Z
UID:AlgAndLogic/85
DESCRIPTION:Title: Bootstrap percolation: merging operations for polytopes\nby Ivail
o Hartarsky (Université Paris-Dauhpine\, PSL\, France\, visiting scholar
at Instituto de Matemática Pura e Aplicada\, Rio de Janeiro\, Brazil) as
part of Algebra and Logic Seminar\n\n\nAbstract\nBootstrap percolation is
a group of statistical physics models intensively studied since the 1970s
in mathematics\, physics\, computer science\, as well as social sciences.
They are cellular automata generalising the following paradigmatic example
. Arbitrarily declare some sites of $Z^2$ initially infected. Iteratively\
, at each discrete-time round\, additionally infect each site with at leas
t 2 infected neighbours.\n\nThe last decade has seen the accomplishment of
a full classification of all such models into `universality classes’\,
depending on their behavior when few sites are initially infected. In this
talk\, we will overview universality results\, mostly in two dimensions.
We will focus particularly on a key aspect of the proof of the lower bound
s for the `critical’ class. Thаt is a natural polygon merging procedure
to be discussed in detail.\n\nNo prerequisites (particularly in probabili
ty) are required\, as we will exclusively focus on the combinatorial side
of the subject\, which is completely elementary.\n
LOCATION:https://researchseminars.org/talk/AlgAndLogic/85/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Plamen Koev (San José State University\, USA)
DTSTART:20220610T130000Z
DTEND:20220610T143000Z
DTSTAMP:20260422T225658Z
UID:AlgAndLogic/86
DESCRIPTION:Title: Computing Eigenvectors of Symmetric Tridiagonals with the Correct Num
ber of Sign Changes\nby Plamen Koev (San José State University\, USA)
as part of Algebra and Logic Seminar\n\n\nAbstract\nThe symmetric tridiag
onal eigenvector problem has been a central research topic in numerical li
near algebra since its inception. Of the myriad of algorithms today\, none
is provably optimal and accurate at the same time. “Optimal” means\,
a subset of $k$ eigenvectors is computed in O($kn$) time. “Accurate” m
eans that the computes eigenvectors are orthogonal and satisfy the typical
relative gap error bound.\n\nIn this talk\, we focus our attention on a n
eglected oscillating property of the eigenvectors: the $i$-th eigenvector
has exactly $i-1$ changes of sign in its entries. Long considered irreleva
nt\, because the tiny entries of the eigenvectors don't seem to be of any
practical importance\, this property may hold the key to accurate eigenvec
tors computed in optimal time!\n\nSuch an approach is not without preceden
t: the preservation of the mathematical properties of the computed objects
has lead to major progress in various computations.\n\nWe present a new a
lgorithm that computes individual eigenvectors in optimal\, O($n$) time\,
each guaranteed to have the correct number of sign changes\, and satisfyin
g the conventional relative gap error bound. The numerical experiments in
this work in progress look promising in that the computed eigenvectors see
m to also be orthogonal.\n
LOCATION:https://researchseminars.org/talk/AlgAndLogic/86/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Roussanka Loukanova (Institute of Mathematics and Informatics\, Bu
lgarian Academy of Sciences)
DTSTART:20220624T100000Z
DTEND:20220624T113000Z
DTSTAMP:20260422T225658Z
UID:AlgAndLogic/87
DESCRIPTION:Title: Dependent-Type Theory of Situated Information with Context Assessment
s\nby Roussanka Loukanova (Institute of Mathematics and Informatics\,
Bulgarian Academy of Sciences) as part of Algebra and Logic Seminar\n\n\nA
bstract\nI shall introduce an enriched formal language of information that
establishes propositions dependent on situations and types. The types can
be basic or complex. Complex propositional types are defined recursively.
The language supports structured data of situated information\, which can
be partial\, parametric\, and underspecified. Information can be associat
ed with quantitative evaluations depending on situations. The formal terms
can integrate propositional types of situated information with statistica
l and other quantitative evaluations. Structured content integrated with q
uantitative data facilitates development of new techniques for amalgamatin
g logic representation of situated\, propositional content with numerical
data. Numerical data can be provided by techniques from mathematical stati
stics and probability. Furthermore\, information can be dynamically update
d by integration with techniques of machine learning.\n
LOCATION:https://researchseminars.org/talk/AlgAndLogic/87/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lyubomir Borisov (Institute of Mathematics and Informatics\, Bulga
rian Academy of Sciences)
DTSTART:20220701T100000Z
DTEND:20220701T113000Z
DTSTAMP:20260422T225658Z
UID:AlgAndLogic/88
DESCRIPTION:Title: On the parity of the coefficients of minimal polynomial of Kloosterma
n sums over F_p\nby Lyubomir Borisov (Institute of Mathematics and Inf
ormatics\, Bulgarian Academy of Sciences) as part of Algebra and Logic Sem
inar\n\n\nAbstract\nKloosterman sums over finite fields play an important
role in “Algebraic Coding Theory” and “Cryptography”. E.g.\, they
are related to some families of algebraic codes (Melas\, Kloosterman) and
(hyper-)bent functions. Particularly\, the divisibility properties of some
quantities connected with the Kloosterman sums\, e.g.\, of minimal polyno
mial coefficients and power moments\, were also investigated (see\, e.g.\,
[1]\; [2]).\nIn this talk I shall present some results about the divisibi
lity by 2 of the coefficients of minimal polynomials of the Kloosterman su
ms.\n\n[1] M. Moisio\, “On certain values of Kloosterman sums”\, IEEE
IT\, vol. 55.8 (2009)\, 3563-3564.\n\n[2] Choi H. T.\, R. Evans\, “Congr
uences for Sums of Powers of Kloosterman Sums”\, International Journal o
f Number Theory\, vol. 3(1): 105-117\, 2007.\n
LOCATION:https://researchseminars.org/talk/AlgAndLogic/88/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Petar Iliev (Institute of Philosophy and Sociology and Institute o
f Mathematics and Informatics\, Bulgarian Academy of Sciences)
DTSTART:20220729T100000Z
DTEND:20220729T113000Z
DTSTAMP:20260422T225658Z
UID:AlgAndLogic/89
DESCRIPTION:Title: Modal Descriptive Complexity\nby Petar Iliev (Institute of Philos
ophy and Sociology and Institute of Mathematics and Informatics\, Bulgaria
n Academy of Sciences) as part of Algebra and Logic Seminar\n\n\nAbstract\
nThe study of the descriptive complexity of a class of structures $S$ rela
tive to a class of formulae $F$ from a logic $L$ revolves around the quest
ion: what can we say about the definability of $S$ with formulae from $F$?
For example\, we might want to know whether there is a formula from $F$ d
efining $S$ or\, if not\, whether there is a countably infinite sequence o
f F-formulae such that each formula from the sequence defines a subset of
$S$ and the union of all these subsets is the whole $S$. If we have the fo
rmer situation\, it is natural to ask about the minimal number of variable
s in any $F$-formula defining $S$\, or its minimal length\, or the minimal
number of operators like quantifiers\, disjunctions and conjunctions\, an
d the minimal depth of their nesting. In the latter situation\, we might w
ant to know how (some of) these measures scale with the index of individua
l formulae.\n\nIn my talk\, I am going to survey several recent results\,
in some of which I have been involved\, coming from the area of the descri
ptive complexity of classes of Kripke frames (directed graphs) and classes
of Kripke models (edge-and vertex-coloured directed graphs) relative to s
ome well-known modal logics.\n
LOCATION:https://researchseminars.org/talk/AlgAndLogic/89/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hristo Iliev (American University in Bulgaria and Institute of Mat
hematics and Informatics\, Bulgarian Academy of Sciences)
DTSTART:20220819T100000Z
DTEND:20220819T113000Z
DTSTAMP:20260422T225658Z
UID:AlgAndLogic/90
DESCRIPTION:Title: Examples of non-reduced components of the Hilbert Scheme of smooth pr
ojective curves using ruled surfaces\nby Hristo Iliev (American Univer
sity in Bulgaria and Institute of Mathematics and Informatics\, Bulgarian
Academy of Sciences) as part of Algebra and Logic Seminar\n\nLecture held
in Room 578 of IMI - BAS.\n\nAbstract\nLet $I_{d\, g\, r}$ be the union of
irreducible components of the Hilbert scheme whose general points represe
nt smooth irreducible non-degenerate curves of degree $d$ and genus $g$ in
$P^r$. Using a family of curves found on ruled surfaces over smooth curve
s of genus $γ$\, we show that for $γ ≥ 7$ and $g ≥ 6γ+5$ the scheme
$I_{2g−4γ+1\,g\,g−3γ+1}$ acquires a non-reduced component $D′$ su
ch that $\\text{dim } T[X′]D′ = \\text{dim }D′ + 1$ for a general po
int $[X′] ∈ D′$.\n
LOCATION:https://researchseminars.org/talk/AlgAndLogic/90/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Naijun Zhan (Institute of Software\, Chinese Academy of Sciences I
SCAS\, China)
DTSTART:20220909T100000Z
DTEND:20220909T113000Z
DTSTAMP:20260422T225658Z
UID:AlgAndLogic/91
DESCRIPTION:Title: Timing delays in cyber-physical systems\nby Naijun Zhan (Institut
e of Software\, Chinese Academy of Sciences ISCAS\, China) as part of Alge
bra and Logic Seminar\n\n\nAbstract\nWith the rapid development of feedbac
k control\, sensor techniques and computer control\, time delay has become
an essential feature of cyber-physical systems (CPSs)\, underlying both t
he continuous evolution of physical plants and the discrete transition of
computer programs\, which may well annihilate the stability/safety certifi
cate and control performance of CPSs. In the safety-critical context\, aut
omatic verification and synthesis methods addressing time-delay in CPSs sh
ould therefore abound. However\, surprisingly\, they do not\, although tim
e-delay has been extensively studied in the literature of mathematics and
control theory from a qualitative perspective. In this talk\, we will repo
rt our recent efforts to tackle these issues\, including bounded and unbou
nded verification of delay differential equations and controller synthesis
for time-delayed systems\, and discuss remaining challenges and future tr
ends.\n
LOCATION:https://researchseminars.org/talk/AlgAndLogic/91/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alaa Abouhalaka (Çukurova University\, Adana\, Turkey)
DTSTART:20220916T110000Z
DTEND:20220916T123000Z
DTSTAMP:20260422T225658Z
UID:AlgAndLogic/92
DESCRIPTION:Title: Almost Prime Ideal and Almost Prime Radical\nby Alaa Abouhalaka (
Çukurova University\, Adana\, Turkey) as part of Algebra and Logic Semina
r\n\n\nAbstract\nIn this talk\, we introduce the concept of almost prime (
right) ideals in noncommutative rings and provide some equivalent definiti
ons and new results. Also we introduce the concept of almost prime radical
of an ideal.\n\nReferences:\n\n[1] M.S. Bhatwadekar\, P. K. Sharma\, Uniq
ue factorization and birth of almost primes\, Comm. Algebra\, 33(1)\, 43-4
9\, (2005).\n\n[2] W.D. Blair\, H. Tsutsui\, Fully prime rings\, Comm. Alg
ebra\, 22(13)\, 5389-5400\, (1994).\n
LOCATION:https://researchseminars.org/talk/AlgAndLogic/92/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hristo Iliev (American University in Bulgaria and Institute of Mat
hematics and Informatics of BAS)
DTSTART:20221014T100000Z
DTEND:20221014T113000Z
DTSTAMP:20260422T225658Z
UID:AlgAndLogic/93
DESCRIPTION:Title: Families of triple coverings of algebraic curves\nby Hristo Iliev
(American University in Bulgaria and Institute of Mathematics and Informa
tics of BAS) as part of Algebra and Logic Seminar\n\n\nAbstract\nThe talk
is a continuation of my previous talk "Examples of non-reduced components
of the Hilbert scheme of smooth projective curves using ruled surfaces" th
at I gave on August 19\, 2022. In the present talk we consider curves that
are triple covers of smooth projective curves of genus γ ≥ 0. We obtai
n families of curves on smooth surface scrolls which\, under suitable nume
rical assumptions\, yield components of the Hilbert scheme of curves.\n
LOCATION:https://researchseminars.org/talk/AlgAndLogic/93/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jörg Koppitz (Institute of Mathematics and Informatics\, Bulgaria
n Academy of Sciences)
DTSTART:20221021T100000Z
DTEND:20221021T113000Z
DTSTAMP:20260422T225658Z
UID:AlgAndLogic/94
DESCRIPTION:Title: Ranks and Presentations for Order-Preserving Transformations with One
Fixed Point\nby Jörg Koppitz (Institute of Mathematics and Informati
cs\, Bulgarian Academy of Sciences) as part of Algebra and Logic Seminar\n
\n\nAbstract\nWe consider the semigroup (no monoid) of all order-preservin
g full transformations $α$ on an $n$-element chain $X_n = \\{1 < 2 …< n
\\}$\, where $p$ is the only fixed point in $α$\, for some given $p ∈X_
n$\, denoted by $O_{n\,p}$. This semigroup is nilpotent. In particular\, t
he semigroup $O_{n\,1}$ (i.e. $p = 1$) is already well studied\, since it
is the maximal nilpotent subsemigroup of the Catalan monoid. But the semig
roup $O_{n\,p}$ is still not well studied for $p > 1$ except of $p = n$ si
nce $O_{n\,n}$ is isomorphic to $O_{n\,1}$. We determine the rank of $O_{n
\,p}$ (it is $C_{p-1}C_{n-p} – C_{p-2}C_{n-p-1}$) and give a presentatio
n of $On\,p$ in $(C_{n-1} – C_{n-2})$ generators and $(1 + C_{n-1} – C
_{n-2})(C_{n-1} – C_{n-2})$ relations. We illustrate the result for $n =
4$.\n\nThis is a joint work with S. Worawiset.\n
LOCATION:https://researchseminars.org/talk/AlgAndLogic/94/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dimitar Guelev (Institute of Mathematics and Informatics\, Bulgari
an Academy of Sciences)
DTSTART:20221028T100000Z
DTEND:20221028T113000Z
DTSTAMP:20260422T225658Z
UID:AlgAndLogic/95
DESCRIPTION:Title: Gabbay Separation for the Duration Calculus\nby Dimitar Guelev (I
nstitute of Mathematics and Informatics\, Bulgarian Academy of Sciences) a
s part of Algebra and Logic Seminar\n\n\nAbstract\nGabbay's separation the
orem about linear temporal logic (LTL) with past has proved to be one of t
he most useful theoretical results in temporal logic. Is expressive power
ultimately affected\, if past constructs are not allowed in the scope of f
uture ones\, or vice versa? Separation implies that it does not\, and also
provides a technically convenient normal form for temporal conditions.\n\
nInterval Temporal Logic (ITL) and the Duration Calculus (DC) are interval
-based logics. Unlike LTL\, they are based on modalities which allow refer
ence to subintervals of the reference intervals only. Adding the neighbour
hood modalities\, which are written $\\lt A\\gt$ and $\\lt A-1\\gt$ in the
notation stemming from Allen's system of interval relations\, enables ref
erence outside the reference interval and this way makes temporal separati
on relevant. In this talk I propose a DC analogue of a separation theorem
for discrete time ITL which I established in a joint work with Ben Moszkow
ski.\n\nBoth theorems are analogous to Gabbay's pioneering result and can
be spelled out in similar terms\, but the technical differences are signif
icant. I take the opportunity to not repeat my previous talk on separation
for ITL and instead discuss some aspects of the proofs for both the ITL a
nd the DC theorems. Interestingly\, these theorems admit proofs that are b
ased on syntactical transformations of the formulas in the respective logi
cs\, and are therefore compositional and very intuitive. I will focus on t
he common and the distinct features of the proofs\, and on some side corol
laries.\n
LOCATION:https://researchseminars.org/talk/AlgAndLogic/95/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Roussanka Loukanova (Institute of Mathematics and Informatics\, Bu
lgarian Academy of Sciences)
DTSTART:20221125T110000Z
DTEND:20221125T123000Z
DTSTAMP:20260422T225658Z
UID:AlgAndLogic/96
DESCRIPTION:Title: Logic Operators and Quantifiers in Type-Theory of Algorithms\nby
Roussanka Loukanova (Institute of Mathematics and Informatics\, Bulgarian
Academy of Sciences) as part of Algebra and Logic Seminar\n\n\nAbstract\nI
shall introduce an extension of Moschovakis Type-Theory of Algorithms (LR
) and its reduction calculus\, by adding logic operators and quantifiers.
The LR has two kinds of terms of formulae\, for designating state-independ
ent and state-dependent propositions and predications. The logic operators
include conjunction\, disjunction\, implication\, and negation. I extend
the formal language of LR by state-dependent quantifiers\, for enhancing t
he standard quantifiers of predicate logic. I provide an extended reductio
n calculus of the Type-Theory of Acyclic Algorithms\, for reductions of LR
terms to their canonical forms.\n
LOCATION:https://researchseminars.org/talk/AlgAndLogic/96/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dimitrinka Vladeva (Institute of Mathematics and Informatics\, Bul
garian Academy of Sciences)
DTSTART:20221202T110000Z
DTEND:20221202T123000Z
DTSTAMP:20260422T225658Z
UID:AlgAndLogic/97
DESCRIPTION:Title: Derivations of upper triangular matrix rings vs Derivations of upper
triangular matrix semirings\nby Dimitrinka Vladeva (Institute of Mathe
matics and Informatics\, Bulgarian Academy of Sciences) as part of Algebra
and Logic Seminar\n\n\nAbstract\nThe motivation for this talk is the prob
lem how to represent a derivation of a matrix ring and of an additively id
empotent matrix semiring as a sum of well-known derivations.\n\nThe result
s of two of my articles\, published in 2022\, will be compared and we will
draw conclusions about the advantages and disadvantages of these results.
\n\nWe begin by considering the nature of derivations of triangular matric
es over an additively idempotent semiring $R$ generated by left and right
semicentral idempotents. Then we construct a semiring $D$ of these derivat
ions and find a basis of $D$\, considered as an $R$-semimodule. The main r
esult of the first article states that an arbitrary derivation of $\\text{
UTM}_n(R)$ (the semiring of upper triangular matrices over an additively i
dempotent semiring $R$) is a linear combination of a derivations from the
basis of $R$-semimodule $D$. When $R$ is an associative ring with identity
and $\\text{UTM}_n(R)$ is the ring of upper triangular $n \\times n$ matr
ices over $R$\, we propose a basis of an additive group $D$ of derivations
of $\\text{UTM}_n(R)$ consisting of derivations $δ_i$ such that $δ_i(A)
= [e_ii\,A]$\, where $A \\in \\text{UTM}_n(R)$ and $e_{ii}$ are diagonal
matrix units for $i = 2\, …\, n$. The main result states that if $D$ is
an arbitrary derivation of the ring $\\text{UTM}_n(R)$ and $A \\in \\text{
UTM}_n(R)$\, then there are matrices\, such that the derivative $D(A)$ is
a linear combination of the values of derivations $δ_i \\in D\, i = 2\,
…\, n$\, of these matrices with coefficients the entries of the matrix $
A$.\n
LOCATION:https://researchseminars.org/talk/AlgAndLogic/97/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Veselin Filev (Institute of Mathematics and Informatics\, Bulgaria
n Academy of Sciences)
DTSTART:20221209T110000Z
DTEND:20221209T120000Z
DTSTAMP:20260422T225658Z
UID:AlgAndLogic/98
DESCRIPTION:Title: AdS/CFT Correspondence\, Metropolis-Hastings algorithm and Generative
Adversarial Networks\nby Veselin Filev (Institute of Mathematics and
Informatics\, Bulgarian Academy of Sciences) as part of Algebra and Logic
Seminar\n\n\nAbstract\nI will report on a recent publication on the constr
uction of a backreacted D0/D4 background. I will discuss the relevance of
this study in the AdS/CFT correspondence and the simulation of the Berkooz
-Douglas matrix model. In the second part of the talk\, I will review the
Metropolis-Hastings algorithm and report on possible applications of the G
enerative Adversarial Networks (GANs) in the simulation of computationally
expensive matrix models.\n
LOCATION:https://researchseminars.org/talk/AlgAndLogic/98/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Peter Dalakov (American University in Bulgaria and Institute of Ma
thematics and Informatics\, Bul. Acad. Sci.)
DTSTART:20221209T120000Z
DTEND:20221209T124500Z
DTSTAMP:20260422T225658Z
UID:AlgAndLogic/99
DESCRIPTION:Title: Hitchin base: Seiberg-Witten differentials and their derivatives\
nby Peter Dalakov (American University in Bulgaria and Institute of Mathem
atics and Informatics\, Bul. Acad. Sci.) as part of Algebra and Logic Semi
nar\n\n\nAbstract\nWe consider a variation of Hodge structures of weight 1
and a Seiberg-Witten differential on the Hitchin base and discuss an expl
icit formula its Gauss-Manin derivative.\n
LOCATION:https://researchseminars.org/talk/AlgAndLogic/99/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yacine Barhoumi-Andréani (Ruhr-Universität Bochum\, Germany)
DTSTART:20230210T110000Z
DTEND:20230210T123000Z
DTSTAMP:20260422T225658Z
UID:AlgAndLogic/100
DESCRIPTION:Title: A New Approach to the Characteristic Polynomial of a Random Unitary
Matrix\nby Yacine Barhoumi-Andréani (Ruhr-Universität Bochum\, Germa
ny) as part of Algebra and Logic Seminar\n\n\nAbstract\nThe characteristic
polynomial of a random (Haar-distributed) unitary matrix is considered as
an interesting toy model for the probabilistic study of the Riemann Zeta
function. We will recall the history of the topic starting with the Montgo
mmery-Dyson correspondance\, the Keating-Snaith moments conjecture and som
e recent developments on other functionals. We will then give a conceptual
comparison of some of the techniques used in the field and a zoo of resul
ts one can achieve\, with a particular focus on a recent technique that al
lows to rederive all the results in a unified way using symmetric function
theory and local Central Limit Theorems.\n
LOCATION:https://researchseminars.org/talk/AlgAndLogic/100/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Valdemar Tsanov (Institute of Mathematics and Informatics\, Bulgar
ian Academy of Sciences)
DTSTART:20230217T110000Z
DTEND:20230217T123000Z
DTSTAMP:20260422T225658Z
UID:AlgAndLogic/101
DESCRIPTION:Title: Invariant theory for reductive subgroups of reductive groups\nby
Valdemar Tsanov (Institute of Mathematics and Informatics\, Bulgarian Aca
demy of Sciences) as part of Algebra and Logic Seminar\n\n\nAbstract\nLet
$H \\subset G$ be an embedding of connected complex reductive linear algeb
raic groups. A classical question with several important interpretations i
s: which irreducible $G$-modules contain nonzero $H$-invariant vectors? An
approach based on the Geometric Invariant Theory of Hilbert-Mumford was d
eveloped in works of Heckman\, Berenstein-Sjamaar\, Belkale-Kumar and Ress
ayre\, culminating in a description of the generalized Littlewood-Richadso
n cone - the convex hull of set of the highest weights of the $G$-modules
containing $H$-invariants. The discrepancy between the convex hull and the
actual set of weights presents the so-called saturation problem\, famousl
y solved by Knutson and Tao for diagonal embeddings of $GL_n$\, and widely
open in general. Ressayre's description of the cone demands extensive cal
culations even in relatively tame cases\, which makes applications difficu
lt. Further development of the structure theory seems desirable.\n\nIn thi
s talk\, based on joint works with Seppänen and Staneva\, I will present
some structural properties of generalized Littlewood-Richardson cones\, al
lowing to partition the subgroups of a given $G$ into types according to t
he properties of the cones. We derive a new numerical invariant of reducti
ve groups\, and use it to show that for “generic” subgroups the cone f
ills the entire Weyl chamber of $G$. This greatly reduces the difficulty o
f the saturation problem and allows it to be solved for some new cases\, e
.g. $SL_2$-subgroups of classical groups.\n
LOCATION:https://researchseminars.org/talk/AlgAndLogic/101/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vladimir Gerdjikov (Institute of Mathematics and Informatics\, Bul
garian Academy of Sciences)
DTSTART:20230224T110000Z
DTEND:20230224T123000Z
DTSTAMP:20260422T225658Z
UID:AlgAndLogic/102
DESCRIPTION:Title: Real Hamiltonian forms of affine Toda field theories: spectral aspec
ts\nby Vladimir Gerdjikov (Institute of Mathematics and Informatics\,
Bulgarian Academy of Sciences) as part of Algebra and Logic Seminar\n\n\nA
bstract\n(Joint work with G. G. Grahovski and A. A. Stefanov)\n\nThe talk
is devoted to real Hamiltonian forms of 2-dimensional Toda field theories
related to exceptional simple Lie algebras\, and to the spectral theory of
the associated Lax operators. Real Hamiltonian forms are a special type o
f reductions of Hamiltonian systems\, similar to real forms of semisimple
Lie algebras. The real Hamiltonian forms of affine Toda field theories rel
ated to exceptional complex untwisted affine Kac - Moody algebras are stud
ied. Along with the associated Lax representations\, we also formulate the
relevant Riemann - Hilbert problems and derive the minimal sets of scatte
ring data that uniquely determine the scattering matrices and the potentia
ls of the Lax operators.\n\nReferences \n\n[1] V. S. Gerdjikov\, G. G. Gra
hovski\, A. A. Stefanov. Real Hamiltonian forms of affine Toda field theor
ies: spectral aspects. Theoretical and Mathematical Physics\, 212(2): 1053
-1072 (2022)\; arXiv:2205.03844v1 [nlin.SI]\n
LOCATION:https://researchseminars.org/talk/AlgAndLogic/102/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bogdan Stankov (Institut Camille Jordan\, Université Claude Berna
rd Lyon 1\, France)
DTSTART:20230407T100000Z
DTEND:20230407T113000Z
DTSTAMP:20260422T225658Z
UID:AlgAndLogic/103
DESCRIPTION:Title: Exact values of exponential Følner functions and the Coulhon and Sa
loff-Coste inequality\nby Bogdan Stankov (Institut Camille Jordan\, Un
iversité Claude Bernard Lyon 1\, France) as part of Algebra and Logic Sem
inar\n\n\nAbstract\nFor infinite groups\, the Følner criterion states tha
t a group is amenable if and only if the isoperimetric constant of its Cay
ley graph is 0. In that case\, a more precise description of its isoperime
tric profile is given by the Følner function. It depends on the choice of
generating set\, but different functions on the same group are asymptotic
ally equivalent. Multiple results have been obtained on Følner functions\
, but only up to asymptotic equivalence class. In this talk\, we will cons
ider fixed generating sets and obtain (to our knowledge) the first results
(outside of virtually nilpotent groups) on the exact values of Følner fu
nctions – on wreath products ℤ ≀ D for a finite group D. We will con
sider possible applications. In particular\, we’re interested in the con
nections with the Coulhon and Saloff-Coste inequality. That inequality giv
es a lower bound on the Følner function. In joint work with Christophe Pi
ttet\, for groups of exponential growth we obtain a description of the opt
imal multiplicative constant in the Coulhon and Saloff-Coste inequality. W
e show that the optimal value over all groups of this constant is between
1 and 2.\n
LOCATION:https://researchseminars.org/talk/AlgAndLogic/103/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jörg Koppitz (Institute of Mathematics and Informatics\, Bulgaria
n Academy of Sciences)
DTSTART:20230505T100000Z
DTEND:20230505T113000Z
DTSTAMP:20260422T225658Z
UID:AlgAndLogic/104
DESCRIPTION:Title: Algebraic Properties of Transformation Semigroups\nby Jörg Kopp
itz (Institute of Mathematics and Informatics\, Bulgarian Academy of Scien
ces) as part of Algebra and Logic Seminar\n\n\nAbstract\nEach semigroup is
isomorphic to a semigroup of transformations on a suitable set (Cayley Th
eorem for semigroups). If we know generating sets of minimal size (rank) o
f a finitely generating semigroup then we have important information about
the algebraic structure of the semigroup itself. For not finitely generat
ed semigroups\, we consider relative generating sets of minimal size modul
o a given subset of the semigroup (relative rank). We determine the (relat
ive) rank of several semigroups of transformations. These semigroups were
already considered by other authors.\n\nBy the study of congruences on a s
emigroup\, we obtain further important information about the structure of
a given semigroup\, which are related to its ideals. We discuss the congru
ence lattice of an infinite transformation semigroup as well of the maxima
l nilpotent subsemigroups of the Catalan Monoid.\n
LOCATION:https://researchseminars.org/talk/AlgAndLogic/104/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vladimir Dotsenko (Institute for Advanced Mathematical Research (I
RMA)\, University of Strasbourg and CNRS\, France)
DTSTART:20230609T100000Z
DTEND:20230609T113000Z
DTSTAMP:20260422T225658Z
UID:AlgAndLogic/105
DESCRIPTION:Title: Old and new aspects of the Poincaré-Birkhoff-Witt theorem\nby V
ladimir Dotsenko (Institute for Advanced Mathematical Research (IRMA)\, Un
iversity of Strasbourg and CNRS\, France) as part of Algebra and Logic Sem
inar\n\n\nAbstract\nThe Poincaré-Birkhoff-Witt theorem on universal envel
oping algebras of Lie algebras is a fundamental result in many areas of ma
thematics: from differential geometry and representation theory to homolog
ical algebra and deformation quantization. I shall give a short overview o
f that result and some of its proofs that emerged in about 120 years since
Poincaré published a paper about it\, and outline a new proof which perh
aps captures its category-theoretic essence in the best way possible. The
talk is based on a joint work with Pedro Tamaroff.\n
LOCATION:https://researchseminars.org/talk/AlgAndLogic/105/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nurlan Ismailov (Astana IT University and Suleyman Demirel Univers
ity\, Kaskelen\, Kazakhstan)
DTSTART:20230616T100000Z
DTEND:20230616T113000Z
DTSTAMP:20260422T225658Z
UID:AlgAndLogic/106
DESCRIPTION:Title: Polynomial identities in Novikov algebras\nby Nurlan Ismailov (A
stana IT University and Suleyman Demirel University\, Kaskelen\, Kazakhsta
n) as part of Algebra and Logic Seminar\n\n\nAbstract\nThe talk is devoted
to Novikov algebras satisfying nontrivial identities. We show that a Novi
kov algebra over a field of zero characteristic that satisfies a nontrivia
l identity satisfies some unexpected “universal” identities\, in parti
cular\, right associator nilpotence\, and right nilpotence of the commutat
or ideal. This\, in particular\, implies that a Novikov algebra over a fie
ld of zero characteristic satisfies a nontrivial identity if and only if i
t is Lie-solvable. We also establish that any system of identities of Novi
kov algebras over a field of zero characteristic follows from finitely man
y of them\, and that the same holds over any field for multilinear Novikov
identities. Some analogous simpler statements are also proved for commuta
tive differential algebras.\n\nJoint work with V. Dotsenko and U. Umirbaev
\n
LOCATION:https://researchseminars.org/talk/AlgAndLogic/106/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Naijun Zhan (Institute of Software Chinese Academy of Sciences (IS
CAS))
DTSTART:20230929T100000Z
DTEND:20230929T113000Z
DTSTAMP:20260422T225658Z
UID:AlgAndLogic/107
DESCRIPTION:Title: Reset Controller Synthesis\nby Naijun Zhan (Institute of Softwar
e Chinese Academy of Sciences (ISCAS)) as part of Algebra and Logic Semina
r\n\n\nAbstract\nController synthesis provides a Correct-by-construction m
echanism to guarantee the correctness and reliability of hybrid systems (H
S) by design. Depending on the types of controls\, controllers can be clas
sified into reset controllers\, feedback controllers\, and switching logic
controllers. Reset controllers steer the behaviour of a HS to attain syst
em objective through restricting its initial set and redefining the reset
map associated with discrete jumps\, which is less explored in the literat
ure\, although it is of theoretical and practical significance. In this ta
lk\, I will summarize our recent work on the reset controller synthesis fo
r HS. The basic idea is to reduce the problem of guaranteeing safety and l
iveness properties to differential invariant generation and generalized re
ach-avoid problems. For polynomial hybrid systems\, those problems can be
solved by further reduced to convex optimizations.\n\nMoreover\, for reali
ty\, we discuss this issue in the context of time-delay\, as time delay is
inevitable in practice. So\, we investigate the reset controller synthesi
s problem for delay hybrid systems (dHS).\n
LOCATION:https://researchseminars.org/talk/AlgAndLogic/107/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marin Genov (Institute of Mathematics and Informatics\, Bulgarian
Academy of Sciences)
DTSTART:20231013T100000Z
DTEND:20231013T113000Z
DTSTAMP:20260422T225658Z
UID:AlgAndLogic/108
DESCRIPTION:Title: Emmy Noether’s Theorem on the Finite Generation of the Algebra of
Invariants\nby Marin Genov (Institute of Mathematics and Informatics\,
Bulgarian Academy of Sciences) as part of Algebra and Logic Seminar\n\n\n
Abstract\nI will introduce Emmy Noether’s theorem on the finite generati
on of invariants and give two proofs of it. As an example\, I will also ca
lculate the algebra of invariants of the dihedral group of order $2n$ acti
ng on $C[x\,y]$.\n
LOCATION:https://researchseminars.org/talk/AlgAndLogic/108/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alberto Fraile (Czech Technical University in Prague\, Czech Repub
lic)
DTSTART:20231020T100000Z
DTEND:20231020T113000Z
DTSTAMP:20260422T225658Z
UID:AlgAndLogic/109
DESCRIPTION:Title: Prime numbers and random walks in a square grid\nby Alberto Frai
le (Czech Technical University in Prague\, Czech Republic) as part of Alge
bra and Logic Seminar\n\nLecture held in Room 578 of IMI - BAS\, Sofia\, B
ulgaria.\n\nAbstract\nOne can argue that prime numbers present perplexing
features\, in a hybrid of local unpredictability and global regular behavi
or. It is this interplay between randomness and regularity that motivated
searches for both local and global patterns that could potentially become
signatures for certain underlying fundamental mathematical properties.In r
ecent years\, computer simulations are playing a fundamental role in unvei
ling some of the most intriguing features of prime numbers. In this work\,
we define an algorithm for a deterministic walk through a two-dimensional
grid that we refer to as Prime Walk (PW). The walk is constructed from a
sequence of steps dictated by and dependent on the sequence of last digits
of the primes. Despite the apparent randomness of this generating sequenc
e\, the resulting structure – both in 2d and 3d – created by the algor
ithm presents remarkable properties and regularities in its pattern that w
e proceed to analyze in detail [1].\n\n[1] A. Fraile\, O. Kinouchi\, P. Dw
ivedi\, R. Martínez\, T. E. Raptis\, D. Fernández\, Prime numbers and ra
ndom walks in a square grid\, Phys. Rev. E 104 (5)\, 054114-054120 (2021).
\n\nJoint work with Osame Kinouchi\, Prashant Dwivedi\, Roberto Martínez\
, Theophanes E. Raptis\, and Daniel Fernández.\n
LOCATION:https://researchseminars.org/talk/AlgAndLogic/109/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dimitar Guelev (Institute of Mathematics and Informatics\, Bulgari
an Academy of Sciences)
DTSTART:20231103T110000Z
DTEND:20231103T123000Z
DTSTAMP:20260422T225658Z
UID:AlgAndLogic/110
DESCRIPTION:Title: A Reduction of Temporary Coalitions in Infinite Multiplayer Games\nby Dimitar Guelev (Institute of Mathematics and Informatics\, Bulgarian
Academy of Sciences) as part of Algebra and Logic Seminar\n\n\nAbstract\n
We propose a transformation of Concurrent Game Models which enables the re
duction of infinite multiplayer games where players can form temporary coa
litions to games with no coalitions by extending moves to include the nego
tiation steps that lead to the formation of coalitions. We adopt condition
al promises as the building blocks of negotiation. Temporary coalitions an
d their agendas arise as the logical consequences of mutual promises. The
transformation enables the use of established solution concepts about game
s with no coalitions for the analysis of games with temporary coalitions.\
n
LOCATION:https://researchseminars.org/talk/AlgAndLogic/110/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mishel Carelli (Technion – Israel Institute of Technology\, Isra
el)
DTSTART:20231110T110000Z
DTEND:20231110T123000Z
DTSTAMP:20260422T225658Z
UID:AlgAndLogic/111
DESCRIPTION:Title: Transfinite version of the Mittag-Leffler condition for the vanishin
g of the derived limit\nby Mishel Carelli (Technion – Israel Institu
te of Technology\, Israel) as part of Algebra and Logic Seminar\n\n\nAbstr
act\nWe give a necessary and sufficient condition for an inverse sequence
$S_0 ← S_1 ← \\dots$ indexed by natural numbers to have $\\lim^1 S
= 0$. This condition can be treated as a transfinite version of the Mittag
-Leffler condition. We consider inverse sequences in the category of abeli
an groups. We also show that the class of inverse sequences S such that $
\\lim S = \\lim^1S = 0$ is the least class of inverse sequences containing
the trivial inverse sequence and closed with respect to small limits and
a certain type of extensions.\n
LOCATION:https://researchseminars.org/talk/AlgAndLogic/111/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Boyan Kostadinov (Institute of Mathematics and Informatics\, Bulga
rian Academy of Sciences)
DTSTART:20231117T110000Z
DTEND:20231117T123000Z
DTSTAMP:20260422T225658Z
UID:AlgAndLogic/112
DESCRIPTION:Title: Noncommutative invariants of dihedral groups\nby Boyan Kostadino
v (Institute of Mathematics and Informatics\, Bulgarian Academy of Science
s) as part of Algebra and Logic Seminar\n\n\nAbstract\nWe consider the 2-g
enerated free metabelian associative and Lie algebras over the complex fie
ld and the invariants of the dihedral groups of finite order acting on the
se algebras. In the associative case we find a finite set of generators of
the algebra of invariants. In the Lie case\, when the algebra of invarian
ts is not finitely generated\, we give a minimal system of generators of t
he invariants in the commutator ideal as a module of the algebra of the in
variants in the polynomial algebra in two variables. In both associative a
nd Lie cases we compute the Hilbert series of the algebras of invariants.\
n\nThe results are obtained jointly with Vesselin Drensky.\n
LOCATION:https://researchseminars.org/talk/AlgAndLogic/112/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dimitrinka Vladeva (Institute of Mathematics and Informatics\, Bul
garian Academy of Sciences)
DTSTART:20231124T110000Z
DTEND:20231124T120000Z
DTSTAMP:20260422T225658Z
UID:AlgAndLogic/113
DESCRIPTION:Title: Catalan numbers and additively idempotent semirings\nby Dimitrin
ka Vladeva (Institute of Mathematics and Informatics\, Bulgarian Academy o
f Sciences) as part of Algebra and Logic Seminar\n\n\nAbstract\nThe purpos
e of the present talk is to provide new applications of remarkable Catalan
numbers. In Richard Stanley’s book Enumerative Combinatorics\, Volume I
I (Cambridge University Press) there are many combinatorial objects that a
re counted by the Catalan numbers as well as applications in graph theory\
, Young diagrams\, lattice theory\, real matrices\, real polynomials and s
o on. We show applications of Catalan numbers in some additively idempoten
t semirings which appeared in my results in 5 papers published between 201
1 and 2023.\nThe set of nilpotent endomorphisms in the endomorphism semiri
ng of a finite chain is a semiring of order $(n - 1)$-th Catalan number an
d is an ideal in another semiring of order $n$-th Catalan number. The semi
ring of $k$-th nilpotent endomorphisms\, where $0 \\le k \\le n – 1$ is
of order a product of two Catalan numbers. By complex products of Catalan
numbers we describe the roots of arbitrary idempotent of the endomorphism
semiring of a finite chain.\nIn an additively idempotent semiring which is
a generalization of the endomorphism semiring of a finite chain considere
d as a simplex we prove that the subsimplex of nilpotent elements is of or
der $(n - 1)$-th Catalan number and it is closed under derivations which a
re projections of the simplex to some simplices.\nIn the last paper\, 2023
\, we prove that an additively idempotent semiring which is an $S0$-semial
gebra\, where $S0$ is a commutative additively idempotent semiring\, and w
ith a finite basis of a special type is isomorphic to a matrix semiring. A
s a consequence we obtain two different semirings of upper triangular matr
ices over the Boolean semiring\, which are of order $(n + 1)$-th Catalan n
umber.\n
LOCATION:https://researchseminars.org/talk/AlgAndLogic/113/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Roussanka Loukanova (Institute of Mathematics and Informatics\, Bu
lgarian Academy of Sciences)
DTSTART:20231124T120000Z
DTEND:20231124T130000Z
DTSTAMP:20260422T225658Z
UID:AlgAndLogic/114
DESCRIPTION:Title: Semantics of Propositional Attitudes in Type-Theory of Algorithms\nby Roussanka Loukanova (Institute of Mathematics and Informatics\, Bulg
arian Academy of Sciences) as part of Algebra and Logic Seminar\n\n\nAbstr
act\nNatural language (NL) is notorious for various kinds of ambiguities.
Among the most difficult ones\, for computational handling of NL\, are e
xpressions with multiple occurrences of quantifiers\, which contribute to
quantifier scope ambiguities. Far more difficult for computational linguis
tics are NL expressions having occurrences of so-called attitude component
s designating knowledge\, believes\, statements\, and similar semantic inf
ormation.\n\nOften\, the syntactic complement of an attitude lexeme is a s
entential expression. The sentential complement may have subexpressions th
at designate semantic information belonging to varying scopes. Depending
on context\, some components can be semantic parts of the attitudinal inf
ormation\, which is in the scope of the propositional attitude\, or extern
al to it.\n\nThe first formal representation of NL attitudes was by Montag
ue\, 1973\, along with the quantifier scope ambiguities\, by the notions o
f extension and intension\, and using extra-syntactic disambiguation of NL
expressions. That approach\, while unsatisfactory in important aspects\,
was adopted and adapted by some variants of Montague grammars\, for specif
ic purposes. The problem has been largely open\, due to its purely semanti
c nature and computational difficulties\, without direct syntactic appeara
nce.\n\nThe semantic phenomena of attitudes include statements in natural
language\, including in the domains of mathematical texts and proofs.\n\nI
n this presentation of a recent paper\, I extend the type-theory of algori
thms\, to cover algorithmic semantics of some of the major attitude expres
sions and their semantic underspecification. I provide reduction calculus
for deriving semantic specifications in contexts.\n
LOCATION:https://researchseminars.org/talk/AlgAndLogic/114/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jörg Koppitz (Institute of Mathematics and Informatics\, Bulgaria
n Academy of Sciences)
DTSTART:20231201T110000Z
DTEND:20231201T123000Z
DTSTAMP:20260422T225658Z
UID:AlgAndLogic/115
DESCRIPTION:Title: Characterization of Ideals of Q-algebras Related to its G-part\n
by Jörg Koppitz (Institute of Mathematics and Informatics\, Bulgarian Aca
demy of Sciences) as part of Algebra and Logic Seminar\n\n\nAbstract\nIn t
his presentation\, we study the $G$-part of $Q$-algebras $X$\, i.e. the se
t $G(X)=\\{x\\in X:0x=x\\}$. We show that $G(X)$ is an abelian group\, whe
never $G(X)$ is an ideal and characterize all $Q$-algebras $X$ such that $
G(X)$ is an ideal of $X$. Moreover\, we show that\, up to isomorphism\, th
ere is only one $Q$-algebra $X$ with $G(X)=X$\, which is only possible if
$|X|=2^{k}$ ($k\\in \\mathbb{N}$).\n
LOCATION:https://researchseminars.org/talk/AlgAndLogic/115/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Annual Scientific Session (Institute of Mathematics and Informatic
s\, Bulgarian Academy of Sciences)
DTSTART:20231215T075500Z
DTEND:20231215T123000Z
DTSTAMP:20260422T225658Z
UID:AlgAndLogic/116
DESCRIPTION:Title: Annual Scientific Session of the Algebra and Logic Department\nb
y Annual Scientific Session (Institute of Mathematics and Informatics\, Bu
lgarian Academy of Sciences) as part of Algebra and Logic Seminar\n\nLectu
re held in Room 578 of IMI - BAS\, Sofia\, Bulgaria.\n\nAbstract\nPROGRAMM
E\n\n9:55 – 10:00 Opening\n\n10:00 – 10:30 Ivan Chipchakov: Diophantin
e and cohomological dimensions of fields\n\n10:30 – 10:50 Elitza Hristov
a: Some new results on the GL(n)-module structure of relatively free alge
bras and applications to noncommutative invariant theory\n\n10:50 – 11:0
0 Break\n\n11:00 – 11:30 Hristo Iliev: On the Tschirnhausen module of mu
ltiple coverings and some applications\n\n11:30 – 11:50 Veselin Filev: A
Sampling Approach for Tackling Large-Scale Linear Optimization Problems\
n\n11:50 – 11:55 Break\n\n11:55 – 12:15 Marin Genov: Some Aspects of H
olomorphy over Finite-Dimensional Commutative Algebras\n\n12:15 – 12:35
Yacine Barhoumi-Andreani: Max-independence structures in random partitions
of an integer\n\n12:35 – 13:30 Lunch Break\n\n13:30 – 13:50 Petar Ili
ev: There are no Sahlqvist formulae containing at most a logarithmic numbe
r of variables that define the n-density or the n-width of Kripke frames\n
\n13:50 – 14:10 Tatyana Ivanova: The fragment of elementary plane Euclid
ean geometry based on perpendicularity alone - a complete axiomatization\n
\n14:10 – 14:25 Vilislav Boutchaktchiev: Methods for estimation of the I
nferred Loss Given Default of credit portfolios\n
LOCATION:https://researchseminars.org/talk/AlgAndLogic/116/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bruce Westbury (retired from University of Warwick\, UK)
DTSTART:20240108T110000Z
DTEND:20240108T123000Z
DTSTAMP:20260422T225658Z
UID:AlgAndLogic/117
DESCRIPTION:Title: On the exceptional series and its siblings\nby Bruce Westbury (r
etired from University of Warwick\, UK) as part of Algebra and Logic Semin
ar\n\n\nAbstract\nThe exceptional series is the following series of eight
simple Lie algebras: \n\n \n\nA1\, A2\, G2\, D4\, F4\, E6\, E7\, E8 \n\n \
n\nConsider each Lie algebra\, g\, as a representation of the group Aut(g)
. Then the centraliser algebras of the first five tensor powers of g have
common structure. First\, they have the same branching rules. We introduce
a parameter so that the exceptional series is a set of eight points on a
line. Then the values of the quadratic Casimir are linear functions of thi
s parameter and the dimensions are rational functions of this parameter. \
n\nThe exceptional series is one row in the Freudenthal magic square and a
ll the preferred representations for each row also have analogous common s
tructure. These series are lines. I will give a broad context for this com
mon structure. \n\nThere is a plane which contains the first and fourth ro
ws of the magic square and a three-dimensional space which contains the Vo
gel plane.\n
LOCATION:https://researchseminars.org/talk/AlgAndLogic/117/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yuri Bahturin (Memorial University of Newfoundland\, Canada)
DTSTART:20240118T110000Z
DTEND:20240118T123000Z
DTSTAMP:20260422T225658Z
UID:AlgAndLogic/118
DESCRIPTION:Title: Nilpotent algebras\, groups and beyond\nby Yuri Bahturin (Memori
al University of Newfoundland\, Canada) as part of Algebra and Logic Semin
ar\n\nLecture held in Room 403 of IMI - BAS.\n\nAbstract\nWe study various
correspondences between finite-dimensional nilpotent algebras and (quasi)
groups similar to those given by the circle product in the case of associa
tive algebras or by the Baker-Campbell-Hausdorff formulas in the the case
of Lie algebras or their generalizations. In the particular case of Malcev
's correspondence\, we obtain some new results about groups using Lie alge
bras and vice versa.\n\nJoint work with Alexander Olshanskii.\n
LOCATION:https://researchseminars.org/talk/AlgAndLogic/118/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Niall Hir (University of Glasgow\, UK)
DTSTART:20240223T110000Z
DTEND:20240223T123000Z
DTSTAMP:20260422T225658Z
UID:AlgAndLogic/119
DESCRIPTION:Title: Invariant subalgebras of the rational Cherednik algebra\nby Nial
l Hir (University of Glasgow\, UK) as part of Algebra and Logic Seminar\n\
n\nAbstract\nThe rational Cherednik algebra is a degeneration of the doubl
e affine Hecke algebra and an object of interest to many representation th
eorists\, it also has strong connections to integrable systems. In my talk
I will discuss two subalgebras that arise from considering the invariants
of the action of reductive subgroups of the special linear group. In part
icular we will examine the centres of these invariant subalgebras and comp
are with the algebra of invariants of the centre of the entire rational Ch
erednik algebra under the same groups. These subalgebras arise naturally i
n the study of rational Cherednik algebras\, one of which is the Dunkl ang
ular momentum algebra and the other is generated by all degree zero elemen
ts.\n
LOCATION:https://researchseminars.org/talk/AlgAndLogic/119/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bakhrom A. Omirov (Harbin Institute of Technologies\, Harbin\, Chi
na and Romanovskiy Institute of Mathematics\, Uzbekistan Academy of Scienc
es\, Uzbekistan)
DTSTART:20240322T110000Z
DTEND:20240322T123000Z
DTSTAMP:20260422T225658Z
UID:AlgAndLogic/120
DESCRIPTION:Title: On the uniqueness of maximal solvable extensions of nilpotent Lie al
gebras\nby Bakhrom A. Omirov (Harbin Institute of Technologies\, Harbi
n\, China and Romanovskiy Institute of Mathematics\, Uzbekistan Academy of
Sciences\, Uzbekistan) as part of Algebra and Logic Seminar\n\n\nAbstract
\nDuring the talk it will be shown that under certain condition an arbitra
ry complex finite-dimensional maximal extension of a nilpotent Lie algebra
N is isomorphic to the semidirect sum of N and its maximal torus. A crite
rion of the completeness for a finite-dimensional solvable Lie algebra is
established. Comparisons with some existing results will also be discussed
.\n
LOCATION:https://researchseminars.org/talk/AlgAndLogic/120/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dimitar Guelev (Institute of Mathematics and Informatics\, Bulgari
an Academy of Sciences)
DTSTART:20240329T110000Z
DTEND:20240329T123000Z
DTSTAMP:20260422T225658Z
UID:AlgAndLogic/121
DESCRIPTION:Title: Generalized Definability of Discrete Time Interval-based Temporal Co
nnectives\nby Dimitar Guelev (Institute of Mathematics and Informatics
\, Bulgarian Academy of Sciences) as part of Algebra and Logic Seminar\n\n
\nAbstract\nIn Linear Temporal Logic with past (PLTL)\, expressive complet
eness implies that any first-order definable connective is also definable
in the temporal language based on the Since and Until temporal operators.
This is not the case about discrete time interval-based temporal logics wi
th state-based semantics for the propositional variables. In this talk I p
rove the next best thing about the extension ITLNL of Moszkowski's discret
e time propositional Interval Temporal Logic (ITL) by the neighbourhood mo
dalities: given an interval-based connective # which admits a first-order
definition\, a star-free ITLNL defining formula for $\\#(A_1\,...\,A_m)$ c
an be produced that is built from the past\, future and introspective form
ulas appearing in some separated equivalents of the operands $A_1\,...\,A_
m$. The proof is based in an interval-based analogue of Gabbay's separatio
n theorem about PLTL that was previously established about ITLNL by the ne
ighbourhood modalities by me and Moszkowski and have now used to prove the
expressive completeness of ITLNL. As a side result I have come upon new p
roofs of expressive completeness and temporal separation for ITLNL's star-
free subset that I will briefly discuss too.\n
LOCATION:https://researchseminars.org/talk/AlgAndLogic/121/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Valentin Ilieav (Institute of Mathematics and Informatics\, Bulgar
ian Academy of Sciences)
DTSTART:20240412T100000Z
DTEND:20240412T113000Z
DTSTAMP:20260422T225658Z
UID:AlgAndLogic/122
DESCRIPTION:Title: On an Aspect of Second Quantum Revolution\nby Valentin Ilieav (I
nstitute of Mathematics and Informatics\, Bulgarian Academy of Sciences) a
s part of Algebra and Logic Seminar\n\n\nAbstract\nThe 2022 Nobel Prize in
Physics has been awarded to Alain Aspect\, John Clauser\, and Anton Zeili
nger for their work in Quantum Theory. Mass media called this event part o
f second quantum revolution which includes mainly quantum computing and ot
her super-technologies. Here we discuss Alain Aspect's version of Einstein
-Podolsky-Rosen thought experiment and show that there exists an internal
dependence of the simultaneous measurements made by the two pairs of linea
r polarizers operated in each leg of the apparatus during this experiment.
The corresponding Shannon-Kolmogorov information flow (or\, noise?) linki
ng a polarizer from one leg to a polarizer from the other leg is proportio
nal to the absolute value of this function of dependence. It turns out tha
t if Bell's inequality is violated\, then the experiment performed at one
leg is informationally dependent on the experiment at the other leg.\n
LOCATION:https://researchseminars.org/talk/AlgAndLogic/122/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Valentin Iliev (Institute of Mathematics and Informatics\, Bulgari
an Academy of Sciences)
DTSTART:20250314T110000Z
DTEND:20250314T123000Z
DTSTAMP:20260422T225658Z
UID:AlgAndLogic/123
DESCRIPTION:Title: Protection Against Noise for a Type of Quantum Computation\nby V
alentin Iliev (Institute of Mathematics and Informatics\, Bulgarian Academ
y of Sciences) as part of Algebra and Logic Seminar\n\nLecture held in Roo
m 578 of IMI - BAS.\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/AlgAndLogic/123/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Plamen Koshlukov (State University of Campinas\, Brazil)
DTSTART:20250328T110000Z
DTEND:20250328T123000Z
DTSTAMP:20260422T225658Z
UID:AlgAndLogic/124
DESCRIPTION:Title: Graded algebras that are the sum of two homogeneous subalgebras\
nby Plamen Koshlukov (State University of Campinas\, Brazil) as part of Al
gebra and Logic Seminar\n\n\nAbstract\nLet $A$ be an algebra over a field
$F$\, graded by a group $G$\, and let $B$ and $C$ be two homogeneous subal
gebras of $A$ such that $A=B+C$. We study the following problem: If $B$ an
d $C$ satisfy graded identities\, does the same also hold for $A$?\n\nThe
analogous problem for algebras without any grading was proposed in 1994 by
Beidar and Mikhalev\; in implicit form it appeared in a paper by O. Kegel
\, in 1963. Several particular cases were considered in a series of papers
by various authors. In 2016\, Kępczyk gave an affirmative answer to this
problem (without grading).\n\nWe show that if $B$ and $C$ satisfy graded
identities\, and also $B$ is a (one-sided) ideal of $A$ then $A=B+C$ also
satisfies graded identities. We also study the situation where $A$ satisfi
es specific graded semi-identities. In this case\, if $C$ satisfies some g
raded identity in neutral variables\, we show that $A$ satisfies graded id
entities. We also find upper bounds for the degrees of such identities. He
re we use methods that go back to the classical Regev theorem on the growt
h of the codimensions of an associative algebra.\n\nFinally we exhibit an
example that shows that the graded version of the Kępczyk theorem is no l
onger valid.\n\nThis is a joint work with P. S. Fagundes.\n
LOCATION:https://researchseminars.org/talk/AlgAndLogic/124/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Soowhan Yoon (American University in Bulgaria)
DTSTART:20250516T100000Z
DTEND:20250516T113000Z
DTSTAMP:20260422T225658Z
UID:AlgAndLogic/126
DESCRIPTION:Title: Grätzer-Schmidt Theorem in arithmetical transfinite recursion\n
by Soowhan Yoon (American University in Bulgaria) as part of Algebra and L
ogic Seminar\n\n\nAbstract\nWe assess the reverse mathematical strength of
the Grätzer-Schmidt theorem (GS) as a principle in second order arithmet
ic. The theorem GS was studied in an article by Katie Brodhead\, Mushfeq K
han\, Bjørn Kjos-Hanssen\, William A. Lampe\, Paul Kim Long V. Nguyen\, a
nd Richard A. Shore\, where they establish the provability of GS in Π$^1_
1$ Comprehension (Π$_1^1$-CA$_0$) and its restrictive variant GSD in arit
hmetical comprehension (ACA$_0$). It will be shown that the arithmetical t
ransfinite recursion (ATR$_0$) is sufficient to prove GS. Additionally\, o
ther variants of GS will be explored as well. Some will be proved in ACA$_
0$\, while others will be shown equivalent to ATR$_0$ over ACA$_0$. Then\,
we will discuss these results in the context of “Almost Theorems of Hyp
erarithmetic Analysis” (ATHA) by Shore in 2023.\n
LOCATION:https://researchseminars.org/talk/AlgAndLogic/126/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Veselin Filev (Institute of Mathematics and Informatics\, Bulgaria
n Academy of Sciences)
DTSTART:20250606T093000Z
DTEND:20250606T110000Z
DTSTAMP:20260422T225658Z
UID:AlgAndLogic/127
DESCRIPTION:Title: Holographic probe branes and artificial neural networks\nby Vese
lin Filev (Institute of Mathematics and Informatics\, Bulgarian Academy of
Sciences) as part of Algebra and Logic Seminar\n\n\nAbstract\nIn holograp
hy\, flavour probe branes are used to introduce fundamental matter to the
AdS/CFT correspondence. At a technical level\, the probes are described by
extremizing the DBI action and solving the Lagrange–Euler equations of
motion. I will report on applications of artificial neural networks that a
llow direct minimization of the regularized DBI action (interpreted as a f
ree energy) without the need to derive and solve the equations of motion.
I will consider\, as examples\, magnetic catalysis of chiral symmetry brea
king and the meson melting phase transition in the D3/D7 holographic set-u
p.\n
LOCATION:https://researchseminars.org/talk/AlgAndLogic/127/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hristo Iliev (American University in Bulgaria and IMI-BAS)
DTSTART:20251003T100000Z
DTEND:20251003T113000Z
DTSTAMP:20260422T225658Z
UID:AlgAndLogic/128
DESCRIPTION:Title: Decomposition of Tschirnhausen Modules for Coverings on Decomposable
P^1-Bundles\nby Hristo Iliev (American University in Bulgaria and IMI
-BAS) as part of Algebra and Logic Seminar\n\n\nAbstract\nLet $\\varphi :
X → Y$ be a finite morphism of degree $m ≥ 2$\, where $X$ and $Y$ are
smooth projective algebraic varieties. Such a covering gives rise to the
short exact sequence of vector bundles on $Y$ :\n$$0 → \\mathcal{O}_Y \\
stackrel{\\varphi^\\sharp}{\\to}\\varphi∗\\mathcal{O}X → \\mathcal{E}^
∨ → 0\,$$\nwhere $\\mathcal{E}^∨$ is known as the Tschirnhausen modu
le the covering $\\varphi$.\n\nIn the talk\, we focus on the case where $Y
$ is smooth and $X$ is a smooth $m$-multisection of the $\\mathbb{P}^1$-bu
ndle\n$$f : \\mathbb{P}(\\mathcal{O}_Y ⊕ \\mathcal O_Y (E)) \\longrighta
rrow Y\,$$\nwith $E$ an effective divisor on $Y$ such that $H^1(Y\, \\math
cal O_Y (kE)) = 0$ for all $k = 1\, . . . \, m − 1$. We show that the Ts
chirnhausen module of the induced covering $f|_X : X \\longrightarrow Y$ i
s completely decomposable\, after which we discuss applications of this re
sult.\n
LOCATION:https://researchseminars.org/talk/AlgAndLogic/128/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vladimir Gerdjikov (Institute of Mathematics and Informatics\, Bul
garian Academy of Sciences)
DTSTART:20251010T100000Z
DTEND:20251010T113000Z
DTSTAMP:20260422T225658Z
UID:AlgAndLogic/129
DESCRIPTION:Title: On Z_5 reduction of soliton equations related to sl(5) algebra\
nby Vladimir Gerdjikov (Institute of Mathematics and Informatics\, Bulgari
an Academy of Sciences) as part of Algebra and Logic Seminar\n\n\nAbstract
\nThis is joint work with B. Kostadinov (IMI-BAS)\, S. Mishev (NBU)\, and
A. Stefanov (FMU-SU).\n\nRecently a new approach to the integrable systems
\, extending and generalizing the ISM was formulated. It is based on an ef
fective parametrization of the Riemann-Hilbert problem\, which allows one
to extend the class of Lax pairs and effectively derive only the correspon
ding NLEE as compatibility condition of two linear problems. This method i
s based on the possibility to treat the solution of the RHP as a fundament
al analytic solution of the Lax pair\, and then to apply the dressing Zakh
arov-Shabat method for deriving the soliton solutions of the NLEE. The aim
of the present paper is to extend Mikhailov Z5 reduction group to the pa
rametrization of the Z5 RHP. The NLEE that we obtained are dispersionless.
\n\nPublished in Journal of Physics: Conference Series\, Vol. 3002:(1)\, i
d. 012014\, 14 pp.\n\nJoint meeting of the the Algebra and Logic Seminar a
nd the Seminar of the Department of Differential Equations and Mathematica
l Physics at the Institute of Mathematics and Informatics\, Bulgarian Acad
emy of Sciences.\n
LOCATION:https://researchseminars.org/talk/AlgAndLogic/129/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dimitar Guelev (Institute of Mathematics and Informatics\, Bulgari
an Academy of Sciences)
DTSTART:20251205T110000Z
DTEND:20251205T123000Z
DTSTAMP:20260422T225658Z
UID:AlgAndLogic/130
DESCRIPTION:Title: Classical Results in ITL with the Neighbourhood Modalities and Thei
r Short Proofs Using Separation\nby Dimitar Guelev (Institute of Mathe
matics and Informatics\, Bulgarian Academy of Sciences) as part of Algebra
and Logic Seminar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/AlgAndLogic/130/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Valentin Iliev (Institute of Mathematics and Informatics\, Bulgari
an Academy of Sciences)
DTSTART:20260403T100000Z
DTEND:20260403T113000Z
DTSTAMP:20260422T225658Z
UID:AlgAndLogic/131
DESCRIPTION:Title: On Pairs of Non-commuting Hermitian Operators on the Unitary Plane w
hich are Permutable Measurements\nby Valentin Iliev (Institute of Math
ematics and Informatics\, Bulgarian Academy of Sciences) as part of Algebr
a and Logic Seminar\n\n\nAbstract\nIn this presentation we study observabl
es with spectre {-1\,1} on quantum systems with the unitary plane as a spa
ce of states. Examples of such quantum systems are spin-1/2 particles. We
find necessary and sufficient conditions for two non-commuting observables
to be permutable measurements\, that is\, the probability of obtaining a
particular pair of results does not depend on the order of taking these me
asurements. Several examples are presented.\n
LOCATION:https://researchseminars.org/talk/AlgAndLogic/131/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kaloyan Slavov (Medical University\, Sofia\, Bulgaria)
DTSTART:20260424T100000Z
DTEND:20260424T113000Z
DTSTAMP:20260422T225658Z
UID:AlgAndLogic/132
DESCRIPTION:Title: Sets preserved by a large subgroup of the special linear group\n
by Kaloyan Slavov (Medical University\, Sofia\, Bulgaria) as part of Algeb
ra and Logic Seminar\n\n\nAbstract\nThe classical Kakeya problem in Euclid
ean space asks how “small” a set can be if it contains a unit line seg
ment in every direction. More generally\, packing sets contain all images
of a given set under a collection of transformations. Finite field analogu
es offer a combinatorial and algebraic perspective and motivate our work.\
n\nWe study sets \\(E\\) in the affine plane over a finite field that are
invariant under a large subgroup \\(R\\) of \\(SL_2\\). We prove that if \
\(|R|>c|E|^{3/2}\\)\, then \\(E\\) must be contained in a line. The expone
nt \\(3/2\\) is sharp. We conclude with a remark on a related phenomenon i
n the Euclidean setting. This is joint work with Thang Pham and Le Quang-H
ung.\n
LOCATION:https://researchseminars.org/talk/AlgAndLogic/132/
END:VEVENT
END:VCALENDAR