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BEGIN:VEVENT
SUMMARY:Mikhail Zaicev (Moscow State University)
DTSTART:20201204T110000Z
DTEND:20201204T120000Z
DTSTAMP:20260404T095425Z
UID:AlgAndLogic/1
DESCRIPTION:Title: Polynomial identities:anomalies of codimension growth\nby M
ikhail Zaicev (Moscow State University) as part of Algebra and Logic Semin
ar\n\n\nAbstract\nWe consider numerical invariants associated with polynom
ial identities of algebras over a field of characteristic zero. Given an a
lgebra $A$\, one can construct a sequence of non-negative integers ${c_n(A
)}\, n = 1\, 2\, . . .$ \, called the codimensions of $A$\, which is an im
portant numerical characteristic of identical relations of $A$. In the pre
sent talk we discuss asymptotic behavior of codimension sequence in differ
ent classes of algebras.\n
LOCATION:https://stable.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:20260404T095425Z
UID:AlgAndLogic/2
DESCRIPTION:Title: Margarete Wolf\, Symmetric Polynomials in Noncommuting Variable
s and Noncommutative Invariant Theory\nby Silvia Boumova (Faculty of M
athematics and Informatics\,University of Sofia\, and Institute of Mathema
tics and Informatics\, Bulgarian Academy of Sciences) as part of Algebra a
nd Logic Seminar\n\n\nAbstract\nIn 1936 Margarete Caroline Wolfpublished a
paper where she proved that the symmetric polynomials in the free associa
tive algebra form a free subalgebra and described the system of free gener
ators. The purpose of the talk is to present these results from modern poi
nt of view and their relations with other results in the frames of commut
ative and noncommutative invariant theory.\n\nSatellite talk to the Webina
r Women in Mathematics in South-Eastern Europe organized by the Internatio
nal Center for Mathematical Sciences - Sofia.\n
LOCATION:https://stable.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:20260404T095425Z
UID:AlgAndLogic/3
DESCRIPTION:Title: Hagedorn transitions in Matrix Membranes\nby Denjoe O'Conno
r (School of Theoretical Physics\, Dublin Institute for Advanced Studies)
as part of Algebra and Logic Seminar\n\n\nAbstract\nMatrix models that ori
ginate in non-commutative deformations of Membranes result in models relat
ed to dimensional reductions of higher dimensional Yang-Mills theories. Th
e confining/deconfining transition becomes a Hagedorn transition in this s
etting and the models are believed to have gravitational duals. I will dis
cuss recent progress in understanding these models and their physics.\n
LOCATION:https://stable.researchseminars.org/talk/AlgAndLogic/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vesselin Drensky (Institute of Mathematics and Informatics)
DTSTART:20201218T075000Z
DTEND:20201218T082000Z
DTSTAMP:20260404T095425Z
UID:AlgAndLogic/4
DESCRIPTION:Title: New examples of fundamental algebras (joint project with Luisa
Carini\, University of Messina\, Italy)\nby Vesselin Drensky (Institut
e of Mathematics and Informatics) as part of Algebra and Logic Seminar\n\n
\nAbstract\nFundamental algebras are the building blocks used to generate
any variety of finite basic rank of associative algebras over a field of c
haracteristic 0. Our first result describes the fundamental algebras which
are tensor products of any number of finite dimensional Grassmann algebra
s. Then we show that the triangular product of two fundamental algebras is
again fundamental. The proofs are based on the recent description of fund
amental algebras in the language of cocharacter sequences due to Giambruno
\, Polcino Milies and Zaicev combined with other techniques from the theor
y of PI-algebras.\n
LOCATION:https://stable.researchseminars.org/talk/AlgAndLogic/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vassil Kanev (Institute of Mathematics and Informatics)
DTSTART:20201218T082000Z
DTEND:20201218T085000Z
DTSTAMP:20260404T095425Z
UID:AlgAndLogic/5
DESCRIPTION:Title: Hurwitz modular varieties parametrizing coverings with fixed mo
nodromy group\nby Vassil Kanev (Institute of Mathematics and Informati
cs) 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 na
tural number $n$ the talk is devoted to smooth families of coverings of $Y
$ of degree $d$ branched in $n$ points whose monodromy group is $G$. These
families form a category whose morphisms correspond to the pullback by mo
rphisms of the bases of the families. Under certain restrictions on the gr
oup $G$ we construct a universal family in this category. We discuss how t
o change the category\, so that the universal family exists without any re
strictions on $G$.\n
LOCATION:https://stable.researchseminars.org/talk/AlgAndLogic/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ivan Chipchakov (Institute of Mathematics and Informatics)
DTSTART:20201218T085500Z
DTEND:20201218T092000Z
DTSTAMP:20260404T095425Z
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 Algebra and Logic Seminar\n\n\nAbstract\nLet $E$ be a normal extension
of a global 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 th
e residue 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 equivale
nce\, valuation of E extending $v$. When $K$ is a global field and $E/K$ i
s abelian and tamely ramified\, nontrivial Krull valuations of $E$ are dis
crete\; also\, $dim(E) ≤ 1$ if and only if $E$ is a nonreal field and th
e residue fields of these valuations are algebraically closed. Under the h
ypothesis that $K$ is a global field\, $E/K$ is abelian and $dim(E) ≤ 1$
\, this is used for proving the existence\, for each $n \\in ℕ$\, of n-v
ariate homogeneous polynomials of degree $n$ with coefficients in $E$\, wh
ich violate the local-to global principle over $E$.\n
LOCATION:https://stable.researchseminars.org/talk/AlgAndLogic/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tatiana Gateva-Ivanova (Institute of Mathematics and Informatics)
DTSTART:20201218T092000Z
DTEND:20201218T095000Z
DTSTAMP:20260404T095425Z
UID:AlgAndLogic/7
DESCRIPTION:Title: Associative algebras and Lie algebras defined by Lyndon words\nby Tatiana Gateva-Ivanova (Institute of Mathematics and Informatics) a
s 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 cl
ass $C(X\;W)$ of associative graded $\\bf{k}$-algebras $A$ generated by $X
$ and with 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 cardina
lity and the enveloping algebra $Ug$ of any $X$-generated Lie $\\bf{k}$-al
gebra $g = {Lie}(X)=([W])$\, whenever the set of standard bracketings $[W]
= {[w] | w \\in W}$ is a Gröbner-Shirshov Lie basis. We prove that all a
lgebras $A$ in $C(X\;W)$ share the same Poincare-Birkhoff-Witt type $\\bf{
k}$-basis built out of the so called Lyndon atoms $N$ (determined uniquely
by $W$) but\, in general\, $N$ may be infinite. Moreover\, $A$ has polyno
mial growth 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 depe
nd on the shape of its defining relations but only on the set of obstructi
ons $W$: We prove that if $A$ has polynomial growth of degree $d$ then $A$
has global 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 cl
assify the Artin-Schelter regular algebras $A$ generated by two elements\,
with defining relations $[W]$ and global dimension $≤ 7$.\n\nReferences
\n\n[1] Tatiana Gateva-Ivanova\, Algebras defined by Lyndon words and Arti
n-Schelter regularity\, To appear in The Transactions AMS arXiv preprint a
rXiv: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-Baxt
er equation\, and Artin-Schelter regularity\, Advances in Mathematics 230
(2012)\, 2152{2175.\n\n[4] Tatiana Gateva-Ivanova\, Global dimension of as
sociative algebras\, Applied Algebra\, Algebraic Algorithms and Error-Corr
ecting Codes\, Lecture Notes in Computer Science\, 357 (1989)\, 213-229.\n
LOCATION:https://stable.researchseminars.org/talk/AlgAndLogic/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jörg Koppitz (Institute of Mathematics and Informatics)
DTSTART:20201218T095500Z
DTEND:20201218T101500Z
DTSTAMP:20260404T095425Z
UID:AlgAndLogic/8
DESCRIPTION:Title: The generators of the semigroup of all transformations preservi
ng a crown\nby Jörg Koppitz (Institute of Mathematics and Informatics
) as part of Algebra and Logic Seminar\n\n\nAbstract\nIn this presentation
\, we will give a survey about the status of the study of monoids of trans
formations preserving a fence and a crown\, respectively. In particular\,
we will consider the monoid of automorphisms preserving fence and crown\,
respectively. Finally we will give an idea of the current status of study
of the rank of the monoid of all partial transformations preserving a fini
te crown.\n
LOCATION:https://stable.researchseminars.org/talk/AlgAndLogic/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dimitrinka Vladeva (University of Forestry\, Sofia)
DTSTART:20201218T101500Z
DTEND:20201218T103000Z
DTSTAMP:20260404T095425Z
UID:AlgAndLogic/9
DESCRIPTION:Title: Derivations of skew Ore polynomial semirings\nby Dimitrinka
Vladeva (University of Forestry\, Sofia) as part of Algebra and Logic Sem
inar\n\n\nAbstract\nIn this project we investigate derivations in the semi
ring of skew Ore polynomials over an additively idempotent semiring. We sh
ow that multiplying each polynomial by $x$ on left is a derivation and con
struct commutative idempotent semiring consisting of derivations of a skew
polynomial semiring. We introduce hereditary derivations and generalized
hereditary derivations defined as derivations acting only over the coeffic
ients of the polynomial and also construct an $S$-derivation in the classi
cal sense of Jacobson. Finally we give a description of the derivations in
a skew polynomial semiring $S[x]$\, assuming that $S$ is an additively id
empotent semiring and show that an arbitrary derivation can be represented
by a generalized hereditary derivation and an $S$-derivation.\n
LOCATION:https://stable.researchseminars.org/talk/AlgAndLogic/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vladimir S. Gerdjikov (Institute of Mathematics and Informatics)
DTSTART:20201218T110000Z
DTEND:20201218T113000Z
DTSTAMP:20260404T095425Z
UID:AlgAndLogic/10
DESCRIPTION:Title: Recursion operators and the hierarchies of MKdV equations rela
ted to $D_4^{(1)}$\, $D_4^{(2)}$ and $D_4^{(3)}$ Kac-Moody algebras\nb
y Vladimir S. Gerdjikov (Institute of Mathematics and Informatics) as part
of Algebra and Logic Seminar\n\n\nAbstract\nReference:\n\nV. S. Gerdjikov
\, A.A. Stefanov\, I. D. Iliev\, G. P. Boyadjiev et al. Recursion operat
ors 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://stable.researchseminars.org/talk/AlgAndLogic/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Elitza Hristova (Institute of Mathematics and Informatics)
DTSTART:20201218T113000Z
DTEND:20201218T115000Z
DTSTAMP:20260404T095425Z
UID:AlgAndLogic/11
DESCRIPTION:Title: Regularity of algebras of $O(n)$-invariants using Hilbert seri
es\nby Elitza Hristova (Institute of Mathematics and Informatics) as p
art of Algebra and Logic Seminar\n\n\nAbstract\nLet $W$ be a polynomial re
presentation of the complex general linear group $GL(n)$. In this talk\, w
e discuss the question when the algebra of invariants $ℂ[W]^{O(n)}$ is r
egular\, i.e. isomorphic to a polynomial algebra. For $n=2$\, we give a li
st of polynomial $GL(2)$-representations\, so that if $ℂ[W]^{O(2)}$ is r
egular\, 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 joi
nt work with Vesselin Drensky.\n
LOCATION:https://stable.researchseminars.org/talk/AlgAndLogic/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Veselin Filev (Institute of Mathematics and Informatics)
DTSTART:20201218T115500Z
DTEND:20201218T122500Z
DTSTAMP:20260404T095425Z
UID:AlgAndLogic/12
DESCRIPTION:Title: Holographic Berkooz-Douglas Matrix Model at Finite Temperature
\nby Veselin Filev (Institute of Mathematics and Informatics) as part
of Algebra and Logic Seminar\n\n\nAbstract\nI will report on ongoing work
to construct the holographic dual supergravity background of the Berkooz-D
ouglas matrix model at finite temperature.\n
LOCATION:https://stable.researchseminars.org/talk/AlgAndLogic/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hristo Iliev (Institute of Mathematics and Informatics)
DTSTART:20201218T122500Z
DTEND:20201218T124500Z
DTSTAMP:20260404T095425Z
UID:AlgAndLogic/13
DESCRIPTION:Title: Families of curves on ruled surfaces and applications to the H
ilbert scheme of curves\nby Hristo Iliev (Institute of Mathematics and
Informatics) as part of Algebra and Logic Seminar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/AlgAndLogic/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vilislav Buchackchiev (Institute of Mathematics and Informatics)
DTSTART:20201218T125000Z
DTEND:20201218T130500Z
DTSTAMP:20260404T095425Z
UID:AlgAndLogic/14
DESCRIPTION:Title: Forecasting of the Bulgarian House price index using some macr
oeconomic indicators\nby Vilislav Buchackchiev (Institute of Mathemati
cs and Informatics) as part of Algebra and Logic Seminar\n\n\nAbstract\nWi
th the introduction of IFRS9 accounting standard in 2018 many banks were r
equired to use statistical models for forecasting the liquidation values o
f houses used as collateral for mortgages. The nature of estimation of the
expected credit loss requires the evaluation of levels of House Price Ind
ex from available statistical data which is\, usually\, one year old. Seve
ral specifications of the models were studied to confirm that HPI is corre
lated with various indicators\, including RE market demand\, construction
industry business cycle and general macroeconomic environment. The general
conclusion was\, however\, that the two most prominent drivers of HPI rem
ain the interest rates and the internal inertia of the RE market.\n
LOCATION:https://stable.researchseminars.org/talk/AlgAndLogic/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dimiter Dobrev (Institute of Mathematics and Informatics)
DTSTART:20201218T130500Z
DTEND:20201218T133500Z
DTSTAMP:20260404T095425Z
UID:AlgAndLogic/15
DESCRIPTION:Title: Language for Description of Worlds\nby Dimiter Dobrev (Ins
titute of Mathematics and Informatics) as part of Algebra and Logic Semina
r\n\n\nAbstract\nWe will reduce the task of creating AI to the task of fin
ding an appropriate language for description of the world. This will not b
e a programing language because programing languages describe only computa
ble functions\, while our language will describe a somewhat broader class
of functions. Another specificity of this language will be that the descri
ption will consist of separate modules. This will enable us look for the d
escription of the world automatically such that we discover it module afte
r module. Our approach to the creation of this new language will be to sta
rt with a particular world and write the description of that particular wo
rld. The point is that the language which can describe this particular wor
ld will be appropriate for describing any world.\n
LOCATION:https://stable.researchseminars.org/talk/AlgAndLogic/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Valentin Iliev (Institute of Mathematics and Informatics)
DTSTART:20201218T140000Z
DTEND:20201218T143000Z
DTSTAMP:20260404T095425Z
UID:AlgAndLogic/16
DESCRIPTION:Title: The Uncertainty Principle for Screening Tests\nby Valentin
Iliev (Institute of Mathematics and Informatics) as part of Algebra and L
ogic Seminar\n\n\nAbstract\nThe aim of this elementary note is to describe
the relation between the conditional probabilities of a false positive an
d a false negative screening test. Non-formally\, we can state the main re
sult of the paper as an Uncertainty Principle: In general\, if one has bet
ter knowledge that the test is really positive (the probability F_+ of fal
se positive 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). An
d the better one knows that the test is really negative (F_- is small)\, t
he harder it is to know that the test is really positive (F_+ is large).\n
LOCATION:https://stable.researchseminars.org/talk/AlgAndLogic/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tatyana Ivanova (Institute of Mathematics and Informatics)
DTSTART:20201218T143000Z
DTEND:20201218T145000Z
DTSTAMP:20260404T095425Z
UID:AlgAndLogic/17
DESCRIPTION:Title: Contact join-semilattices\nby Tatyana Ivanova (Institute o
f Mathematics and Informatics) as part of Algebra and Logic Seminar\n\nAbs
tract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/AlgAndLogic/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Roussanka Loukanova (Institute of Mathematics and Informatics)
DTSTART:20201218T145500Z
DTEND:20201218T151500Z
DTSTAMP:20260404T095425Z
UID:AlgAndLogic/18
DESCRIPTION:Title: Type-Theory of Parametric Algorithms\nby Roussanka Loukano
va (Institute of Mathematics and Informatics) as part of Algebra and Logic
Seminar\n\n\nAbstract\nI shall present a class of Moschovakis type-theori
es of recursion. My focus is on an overview from the perspective of existi
ng and potential applications. I shall point to some of my contributions o
n these topics.\n
LOCATION:https://stable.researchseminars.org/talk/AlgAndLogic/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dimitar Guelev (Institute of Mathematics and Informatics)
DTSTART:20201218T154500Z
DTEND:20201218T160000Z
DTSTAMP:20260404T095425Z
UID:AlgAndLogic/19
DESCRIPTION:Title: Strategy Profiles and a Vocabulary for Solving Infinite Concur
rent Games with Temporary Coalitions in QCTL*\nby Dimitar Guelev (Inst
itute of Mathematics and Informatics) as part of Algebra and Logic Seminar
\n\n\nAbstract\nThis is a short version of my seminar talk from October 30
. It highlights the key notion and notations proposed in that talk. The ke
y notion is a straightforward extension of the notion of strategy profile
for registering varying partitionings of the totality of the players into
disjoint coalitions. The notation is a vocabulary for the propositionally
quantified branching time temporal logic QCTL* which augments the encoding
of strategy profiles into this logic as known from the literature\, inclu
ding my previous work\, with symbols for specifying shifting coalition str
ucture. In this short presentation\, we focus on the notation and sideline
the key technical results of the work\, which show that complete informat
ion concurrent multiplayer infinite games with LTL-definable partially ord
ered objectives are solvable wrt whatever solution concepts happen to be e
xpressible in the proposed vocabulary. That includes temporary coalition g
eneralisations of some established solution concepts. The work is availabl
e from the 8th International Workshop on Strategic Reasoning and arXiv.\n
LOCATION:https://stable.researchseminars.org/talk/AlgAndLogic/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Valentin Goranko (Institute of Mathematics and Informatics)
DTSTART:20201218T151500Z
DTEND:20201218T154500Z
DTSTAMP:20260404T095425Z
UID:AlgAndLogic/20
DESCRIPTION:Title: Rational coordination in Pure Win-Lose Coordination Games\
nby Valentin Goranko (Institute of Mathematics and Informatics) as part of
Algebra and Logic Seminar\n\n\nAbstract\nThe main question I will address
is: when and how can rational agents coordinate without any prior communi
cation or conventions? I will consider this question in the abstract frame
work of multi-player pure coordination games\, where each player has a num
ber of possible choices\, every choice profile determines a unique outcome
\, and in every outcome all players have identical payoffs\, `win’ or `l
ose’. \n\nI will formally introduce pure win/lose coordination games and
will present and discuss a hierarchy of ‘rationality principles' that c
an be applied by rational players in such games to determine their choices
of action. Then I will compare the strength of some of these principles i
n terms of the classes of coordination games that can be solved by them by
using only pure reasoning\, without any preplay communication and convent
ions. I will argue that the boundaries between pure rationality principles
and other rational decision methods used for solving coordination games a
re quite debatable and there is apparently no clear distinction between th
ese. \n\nLastly\, time permitting\, I will discuss briefly how pure coordi
nation games can be solved with the use of `structural’ conventions (onl
y based on structural properties of the games)\, agreed in a preplay commu
nication\, and will describe precisely the scope of purely rational coordi
nation.\n\nThe talk is based on this recent joint paper with Antti Kuusist
o and Raine Rönnholm:\nhttps://academic.oup.com/logcom/article/30/6/1183/
5869758?guestAccessKey=374b9c38-2900-4302-\n91c6-8c8c1eac6ac4.\n
LOCATION:https://stable.researchseminars.org/talk/AlgAndLogic/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dimitrinka Vladeva (University of Forestry\, Sofia)
DTSTART:20210108T110000Z
DTEND:20210108T120000Z
DTSTAMP:20260404T095425Z
UID:AlgAndLogic/21
DESCRIPTION:Title: Derivations in matrix semirings\nby Dimitrinka Vladeva (Un
iversity of Forestry\, Sofia) as part of Algebra and Logic Seminar\n\n\nAb
stract\nIn the first part of this topic we give a description of the deriv
ations in the semiring $UTM_n(S)$ of upper triangular matrices over an ad
ditively 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 prove that $\\delta_k(A) = \\overline{D}_{k}A$ and $d_m(A) = A\\unde
rline{D}_{\\\,m}$\, where\n $A \\in UTM_n(S)$\, are derivations in $UTM_n(
S)$. The 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 idempo
tent semirings. Denote by ${\\mathcal{D}}$ the semiring generated by the
set $\\overline{\\mathcal{D}} \\cup \\underline{\\mathcal{D}}$. For $\\del
ta_k + d_m \\in {\\mathcal{D}}$ and $A \\in UTM_n(S)$ we describe the mat
rix $(\\delta_k + d_m)(A)$ and prove that $\\delta_kd_m \\in {\\mathcal{D}
}$ if and only $\\delta_k + d_m$ is an identiy map. In ${\\mathcal{D}}$ we
construct a basis $\\mathcal{B}$ consisting of derivations $\\delta_1\,
\\delta_2\\\,d_{n-1}\, \\ldots\, \\delta_{n-1}\\\,d_{2}\, d_1$ and\n $\\
delta_1\\\,d_{n-1}$\, $\\delta_2\\\,d_{n-2}$\, $\\\;\\ldots\\\;$\, $\\delt
a_{n-2}\\\,d_2$\, $\\delta_{n-1}\\\,d_1$.\n The main result states that an
arbitrary derivation in the semiring $UTM_n(S)$ is a linear combination o
f elements of the basis $\\mathcal{B}$ of the $S$-semimodule $\\mathcal{D
}$ with coefficients from $S$.\n\n\nIn the second part we study the deriva
tions in the semiring of $n \\times n$ matrices over additively idempoten
t semiring $S$.\nIt is well-known that if $\\delta : S \\rightarrow S$ is
a derivation in semiring $S$ then in the semiring $M_n(S)$ of $n \\times n
$ matrices over $S$ the map $\\delta_{\\rm her}$ such that $\\delta_{\\rm
her}(A) = (\\delta(a_{ij}))$ for any matrix $A = (a_{ij}) \\in M_n(S)$ i
s a derivation. These derivations are used in matrix calculus\, differenti
al equations\, statistics\, physics and engineering and are called heredit
ary derivations. On the other hand\n$S$-derivation in matrix semiring $M_n
(S)$ (in sense of N. Jacobson) is a $S$ - linear map $D : M_n(S) \\rightar
row M_n(S)$ such that $D(AB) = AD(B) + D(A)B$ where $A\, B \\in M_n(S)$.
We prove that if $S$ is a commutative additively idempotent semiring any $
S$-derivation 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 (r
ight) derivations in these semirings and generalize the result from the co
mmutative case.\n\n\nhttps://math.bas.bg/wp-content/uploads/2021/01/Algebr
a_Logika_seminar_08-01-2021-abstract-EN.pdf\n
LOCATION:https://stable.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:20260404T095425Z
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 Algebra and Logic Seminar\n\n\nAbstract\nThe development of Logic will
be discussing in the light of the popular conceptions of Philosophy of sci
ence - of Kuhn about the scientific revolutions and Lacatos - about the pr
oliferation. In my opinion in modern logic there are two revolutions - the
transition from traditional to classical logic and the transition from cl
assical to non-classical logic. In both revolutions the new paradigm has a
lmost completely replaced the old one. The reason for both revolutions is
that the development of the logical empirical sphere has gone considerably
ahead of the logical theory. My position is that logic does have „empir
ics‟ and this is basically the language and methods of reasoning in scie
ntific theories. Revolution' corresponds to the scale of change and re-eva
luation of values in modern logic\, comparable to important moments in the
development of other fields: quantum mechanics\, the transition from Newt
onian physics to Einstein's theory of relativity\, non-Euclidean geometry.
\n\nThe main problem prior to philosophy of logic\, raised by second revol
ution is the proliferation. And respectively the questions about the monis
m and pluralism of logic. After the second revolution Logic has been subdi
vided into a number of logics\; so which one now is “proper Logic”? An
d can we talk about “proper Logic” at all?\n\nIn modern logic the term
“philosophical logic” has become established. I will discuss question
s “What they call and what must be named with It\, and is it possible an
d relevant”. Are there a significant field of study for what there is no
suitable 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
“Social and practical”.\n\nJoint seminar dedicated to the World Logic
Day with the Seminar of the Department of Mathematical Logic and Its Appl
ications of the Faculty of Mathematics and Informatics\, Sofia University\
, and the Seminar of Logic at the Institute of Philosophy and Sociology\,
Bulgarian Academy of Sciences\n
LOCATION:https://stable.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:20260404T095425Z
UID:AlgAndLogic/23
DESCRIPTION:Title: Some Solutions of Sorites Paradoxes\nby Doroteya Angelova
(Institute of Philosophy and Sociology\, Bulg.Acad. Sci.) as part of Algeb
ra 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 analyz
e the specific characteristics of these logics\, their advantages and shor
tcomings in regard to the problem of vagueness and respectively I will giv
e arguments which of them are suitable for overcoming the sorites paradoxe
s. I will propose two own approaches through which\, according to me\, it
is possible to interpret and resolve the sorites paradoxes: the first one
is heterogeneous and the second one – based on three-valued logic.\n\nKe
ywords: sorites paradoxes\, vagueness\, fuzzy relevant logic\, heterogeneo
us approach\n\nJoint seminar dedicated to the World Logic Day with the Sem
inar of the Department of Mathematical Logic and Its Applications of the F
aculty of Mathematics and Informatics\, Sofia University\, and the Seminar
of Logic at the Institute of Philosophy and Sociology\, Bulgarian Academy
of Sciences\n
LOCATION:https://stable.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:20260404T095425Z
UID:AlgAndLogic/24
DESCRIPTION:Title: Explanation of the Conversation Implicatures with the Graded S
alience Hypothesis\nby Elena Tsvetkova (Institute of Philosophy and So
ciology\, Bulg.Acad. Sci.) as part of Algebra and Logic Seminar\n\n\nAbstr
act\nGrice’s theory of conversational implicature is viewed in this pape
r with an accent to the transition between the literal meaning of an expre
ssion and the implicated meaning. Assuming the position expressed in the g
raded salience hypothesis\, it is explained that in some cases the transit
ion from what the speaker says to what he wants the listener to under-stan
d is based on the salient meaning of the used expressions. Special attenti
on is paid to ex-pressions that have more than one obvious meaning\, in or
der to show that even when the con-text plays a role in the understanding
of an expression\, this meaning can still be perceived as a result of soci
o-linguistic conventions.\n\nKeywords: Grice\, pragmatics\, graded salienc
e hypothesis\, conversational implicature.\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://stable.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:20260404T095425Z
UID:AlgAndLogic/25
DESCRIPTION:Title: Binary Decision Diagrams for Rational Choice\nby Rosen Lut
skanov (Institute of Philosophy and Sociology\, Bulg.Acad. Sci.) as part o
f Algebra and Logic Seminar\n\n\nAbstract\nRational choice theory is built
on three fundamental insights: 1. rational choice is (expected) utility m
aximization\; 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 presented\, but virtually all of them (a) turn out to be incompatibl
e with robust intuitions concerning the meaning of “rational choice”\;
(b) fall prey to counterexamples which show that these definitions are no
t extensionally correct. The present approach proposes to dispense with th
e received view (“choice is rational when it generates an ordering of al
ternatives”) and sketches and alternative account (“choice is rational
when the choice procedure fits the choice setting”). It is based on a r
e-interpretation of binary decision diagrams – rooted directed acyclic g
raphs representing Boolean functions (by substituting the labels “true
”/“false” with “chosen”/”rejected”). It is shown that this a
nalogy sheds light on some idealizations left implicit by the classic appr
oach.\n\nJoint seminar dedicated to the World Logic Day with the Seminar o
f the Department of Mathematical Logic and Its Applications of the Faculty
of Mathematics and Informatics\, Sofia University\, and the Seminar of Lo
gic at the Institute of Philosophy and Sociology\, Bulgarian Academy of Sc
iences\n
LOCATION:https://stable.researchseminars.org/talk/AlgAndLogic/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexandra Soskova (Faculty of Mathematics and Informatics\, Sofia
University)
DTSTART:20210115T101000Z
DTEND:20210115T104000Z
DTSTAMP:20260404T095425Z
UID:AlgAndLogic/26
DESCRIPTION:Title: Effective Coding and Decoding in Classes of Structures\nby
Alexandra Soskova (Faculty of Mathematics and Informatics\, Sofia Univers
ity) as part of Algebra and Logic Seminar\n\n\nAbstract\nFriedman and Stan
ley introduced Borel embeddings as a way of comparing classi\ncation\nprob
lems for di\nerent classes of structures. Many Borel embeddings are actual
ly Turing\ncomputable. The e\nective decoding is given by a uniform e\nect
ive interpretation. Part\nof the e\nective interpretation is Medvedev redu
ction. The class of undirected graphs and\nthe class of linear orderings b
oth lie on top under Turing computable embeddings. We\ngive examples of gr
aphs that are not Medvedev reducible to any linear ordering\, or to the\nj
ump of any linear ordering. For any graph there is a linear ordering\, tha
t the graph is\nMedvedev reducible to the second jump of the linear orderi
ng. For the Turing computable\nembedding $L$ of Friedman and Stanley of di
rected graphs in linear orderings. We show\nthat there do not exist $L_{w_
1w}$-formulas that uniformly interpret the input graph $G$ in the output l
inear ordering $L(G)$. This is joint work with Knight\, and Vatev.\n\nWe h
ave also one positive result -- we prove that the class of fields is unifo
rmly effectively interpreted without parameters in the class of Heisenberg
groups. The second part is a joint work with Alvir\, Calvert\, Goodman\,
Harizanov\, Knight\, Miller\, Morozov\, and\nWeisshaar.\n\nJoint seminar d
edicated to the World Logic Day with the Seminar of the Department of Math
ematical Logic and Its Applications of the Faculty of Mathematics and Info
rmatics\, Sofia University\, and the Seminar of Logic at the Institute of
Philosophy and Sociology\, Bulgarian Academy of Sciences\n
LOCATION:https://stable.researchseminars.org/talk/AlgAndLogic/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jean-Yves Beziau
DTSTART:20210115T112500Z
DTEND:20210115T114000Z
DTSTAMP:20260404T095425Z
UID:AlgAndLogic/27
DESCRIPTION:Title: Official Address\nby Jean-Yves Beziau as part of Algebra a
nd Logic Seminar\n\n\nAbstract\nJean-Yves Beziau is the creator of the Wor
ld Logic Day and Editor-in-Chief of Logica Universalis.\n\nJean-Yves Bezia
u is the creator of the World Logic Day and Editor-in-Chief of Logica Univ
ersalis.\n
LOCATION:https://stable.researchseminars.org/talk/AlgAndLogic/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dimitar Vakarelov (Faculty of Mathematics and Informatics\, Sofia
University)
DTSTART:20210115T114000Z
DTEND:20210115T124000Z
DTSTAMP:20260404T095425Z
UID:AlgAndLogic/28
DESCRIPTION:Title: Point-free Theories of Space and Time\nby Dimitar Vakarelo
v (Faculty of Mathematics and Informatics\, Sofia University) as part of A
lgebra and Logic Seminar\n\n\nAbstract\nTo the question ”What is space
” mathematicians immediately answer: this is what studies geometry\, one
of the oldest branches of mathematics. Unfortunately\, mathematics does n
ot have such a branch dedicated to time. Time and space are also basic con
cepts of physics\, but as a rule physicists borrow their mathematical form
alisms from mathematics. Modern physics has come to the conclusion that sp
ace and time must be considered as aspects of a unified theory\, which is
briefly called ”space-time”. But till now physicists still are not giv
en a definition of time\, rather they say how it is measured\, and time is
appearing just as a numerical parameter in the basic equations of the the
ory. There has been a heated debate over the nature of space and time sinc
e the time of Newton and Leibniz. Newton defends the so-called ”absolute
theory of space and time”: ”space” is a container in which the exis
ting things are located\, and ”time” is something that ”flows” and
is independent of space and material things. Leibniz is the founder of th
e so-called ”relational theory of space and time” according to which a
bsolute space 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 wa
s Alfred North Whitehead\, who argued that the theory of space and time sh
ould be built on a point-free basis. What does this mean. According to the
Euclidean tradition\, the points of space (as well as the lines and plane
s) are the basic primary concepts that lie in the axiomatization of geomet
ry. But they do not have an independent existence in reality and are conve
nient fictions. The situation is similar to the points of time (moments)\,
which means that the foundations of a unified theory of space and time mu
st be based on more realistic concepts. This does not mean that the notion
s of space point and time moment should be disregarded - they should be in
troduced later on the base of the primitive notions of the theory. The poi
nt-free approach to the theory of space and time is quite important from t
he point of view of physics: if a given theory is intended to describe rea
lity\, its basic concepts should correspond to some things of reality. The
first steps in constructing a point-free theory of space were made by Whi
tehead\, De Laguna\, and Tarski\, and this theory is now well known as the
”region-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 r
elations between regions\, such as ”part-of” and ”contact”. Howeve
r\, a satisfactory point-free axiomatic theory of a unified theory of spac
e-time does not yet exist. The first steps in this direction were made by
the author of this lecture and its purpose is to tell about one of these a
ttempts.\n\nThe full text on which the lecture is based can be seen here:
arXiv:2004.14755v2 [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 th
e 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
Department of Mathematical Logic and Its Applications of the Faculty of M
athematics and Informatics\, Sofia University\, and the Seminar of Logic a
t the Institute of Philosophy and Sociology\, Bulgarian Academy of Science
s\n
LOCATION:https://stable.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:20260404T095425Z
UID:AlgAndLogic/29
DESCRIPTION:Title: Computational Complexity and Decision Problems in Algebra\
nby Vesselin Drensky (Institute of Mathematics and Informatics\, Bulg. Aca
d. Sci.) as part of Algebra and Logic Seminar\n\n\nAbstract\nThe idea of t
he talk is to show on concrete examples how classical problems in algebra
and arithmetic can be considered from the point of view of mathematical lo
gic\, theory of algorithms and computer science. The examples are taken fr
om classical number theory\, cryptography\, numerical semigroups\, commuta
tive and noncommutative ring theory\, finite axiomatization\, the P versus
NP problem\, decision problems in the theory of groups\, semigroups and r
ings.\n\nJoint seminar dedicated to the World Logic Day with the Seminar o
f the Department of Mathematical Logic and Its Applications of the Faculty
of Mathematics and Informatics\, Sofia University\, and the Seminar of Lo
gic at the Institute of Philosophy and Sociology\, Bulgarian Academy of Sc
iences\n
LOCATION:https://stable.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:20260404T095425Z
UID:AlgAndLogic/30
DESCRIPTION:Title: Why Philosophers and Logicians Should Learn More about Computa
tional Complexity\nby Petar Iliev (Institute of Philosophy and Sociolo
gy\, Bulg.Acad. Sci.) as part of Algebra and Logic Seminar\n\n\nAbstract\n
One might be tempted to assume that using computer time and memory as effi
ciently as possible to perform a computational task is something that obse
ssive engineers might find important but is of no philosophical and logica
l relevance. This is going to be a very high-level talk\, dedicated to a v
ery small number of ideas and concepts that originated in the field of com
putational complexity\, whose main purpose is to convince philosophers and
logicians unfamiliar with the area but curious to know more about it that
the above assumption is wrong.\n\nJoint seminar dedicated to the World Lo
gic Day with the Seminar of the Department of Mathematical Logic and Its A
pplications of the Faculty of Mathematics and Informatics\, Sofia Universi
ty\, and the Seminar of Logic at the Institute of Philosophy and Sociology
\, Bulgarian Academy of Sciences\n
LOCATION:https://stable.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:20260404T095425Z
UID:AlgAndLogic/31
DESCRIPTION:Title: Open Problems on Field Extensions of Finite Transcendency Degr
ee and the PAC Property\nby Ivan Chipchakov (Institute of Mathematics
and Informatics\, Bulg. Acad. Sci.) as part of Algebra and Logic Seminar\n
\n\nAbstract\nOne of the major open problems on fields of finite transcend
ency degrees over their prime subfields is to understand whether an infini
te field E of this kind is pseudo algebraically closed (abbr.\, PAC)\, pro
vided that its absolute Galois group is torsion-free and the Henselian clo
sures of nontrivial valuations of E are separably closed. The purpose of t
his talk is to exhibit relations between the stated problem and the study
of Diophantine properties of fields of dimension ≤ 1 that are algebraic
extensions of a global field K. We also present an open question posed by
Koenigsmann. It concerns the structure of absolute Galois groups and the e
lementary characterization of fields by such groups\, an area of common re
search interest to field theorists – logicians and algebraists.\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://stable.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:20260404T095425Z
UID:AlgAndLogic/32
DESCRIPTION:Title: Temporary Coalitions and Preference in Quantified Computation
Tree Logic\nby Dimitar P. Guelev (Institute of Mathematics and Informa
tics\, Bulg. Acad. Sci.) as part of Algebra and Logic Seminar\n\n\nAbstrac
t\nTemporal winning conditions appear in both terminating and infinite gam
es\, with terminating games corresponding to safety and reachability (guar
antee) conditions\, and arbitrary temporal conditions for non-terminating
games. In a multiplayer game\, the latter classes of winning conditions ar
e natural to drive the players into forming permanent coalitions as the lo
ngevity of a coalition needs to match the duration of the joint agenda. Ho
wever\, 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. This ability can be regarded as inalienable within the considered gam
e as long as forbidding players to change sides can be modeled by appropri
ately modifying the game. Therefore games with temporal winning conditions
need to be studied with the possibility of temporary coalitioning in mind
. Established logical notations for strategic behaviour such as ATLs (Alur
Henzinger and Kupferman\, 1997\, 2002) and Strategy Logics (Chatterjee\,
Henzinger and Piterman\, 2010\, also Mogavero\, Murano and Vardi\, 2010) i
nclude dedicated constructs which are ‘off-the-shelf’ for permanent co
alitions only.\n\nCoalitions form around concrete local agreements with ea
ch prospective coalition member assessing the prospective coalition with t
he prospective agreement in mind\, and assuming just rationality on behalf
of the non-signatories. With temporary coalitions this assessment is dete
rmined by the progress on each player's individual objectives that can be
made\, if the local agreement goes ahead. The natural ambiguity of rationa
lity and assessment entails that even established solution concepts such a
s equilibria and domination are liable to spawn multiple new variants yet
another time upon their generalization to temporary coalitions.\n\nIn this
talk we propose two elements of notation for the handling of solution con
cepts with 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 kn
own to have decidable validity and model-checking on trees (French\, 2001\
, 2006). The contributed elements are a propositional vocabulary for tempo
rary coalitions and a temporal variant of the binary preference operator w
hich can be traced back to the work of Von Wright\, 1963. The latter const
ruct is not temporary-coalition-specific\, but still necessary for the han
dling of multiple objectives.\n\nKeywords: strategic ability\, temporary c
oalitions\, rational synthesis\, preference\, concurrent multiplayer games
\n\nThere is a related paper on arXiv: 2011.03724\n\nJoint seminar dedicat
ed to the World Logic Day with the Seminar of the Department of Mathematic
al Logic and Its Applications of the Faculty of Mathematics and Informatic
s\, Sofia University\, and the Seminar of Logic at the Institute of Philos
ophy and Sociology\, Bulgarian Academy of Sciences\n
LOCATION:https://stable.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:20260404T095425Z
UID:AlgAndLogic/33
DESCRIPTION:Title: Reduction Calculus of Type-Theory of Acyclic Algorithms\nb
y Roussanka Loukanova (Institute of Mathematics and Informatics\, Bulgaria
n Academy of Sciences) as part of Algebra and Logic Seminar\n\n\nAbstract\
nIn 1989\, Moschovakis [1] initiated a new theory of the mathematical noti
on of algorithm\, within untyped\, full recursion. In 2006\, Moschovakis [
2] introduced the formal language of Type-Theory of Recursion (TTR)\, whic
h models the notion of algorithm and concepts of meaning in typed semantic
structures. The focus of [2] is on Type-Theory of Acyclic Algorithms (TTA
R) for computations that end up after a finite number of steps. The approa
ch\, in its varieties\, with full and acyclic recursion\, provides for new
developments of type theory of computation and new applications to comput
ational syntax-semantics interfaces in programming and natural languages.\
n\nIn this talk\, I present the formal language (LAR) of TTAR\, by extendi
ng it with a restrictor operator that sets conditions on denotations of te
rms. In addition\, the operator defines restricted memory and parameters.
TTAR provides two kinds of semantics of the formal language LAR\, denotati
onal and algorithmic. The reduction system of TTAR is essential for the no
tion of algorithm and syntax-semantics interfaces. I shall overview the re
duction calculus and some of the theoretical results of TTAR.\n\n[1] Yiann
is N Moschovakis. The formal language of recursion. Journal of Symbolic Lo
gic\, 54(04):1216–1252\, 1989.\n\n[2] Yiannis N. Moschovakis. A Logical
Calculus of Meaning and Synonymy. Linguistics and Philosophy\, 29(1):27–
89\, 2006.\n
LOCATION:https://stable.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:20260404T095425Z
UID:AlgAndLogic/34
DESCRIPTION:Title: Reduction Calculus of Type-Theory of Acyclic Algorithms\, II\nby Roussanka Loukanova (Institute of Mathematics and Informatics\, Bul
garian Academy of Sciences) as part of Algebra and Logic Seminar\n\n\nAbst
ract\nIn 1989\, Moschovakis [1] initiated a new theory of the mathematical
notion of algorithm\, within untyped\, full recursion. In 2006\, Moschova
kis [2] introduced the formal language of Type-Theory of Recursion (TTR)\,
which models the notion of algorithm and concepts of meaning in typed sem
antic structures. The focus of [2] is on Type-Theory of Acyclic Algorithms
(TTAR) for computations that end up after a finite number of steps. The a
pproach\, in its varieties\, with full and acyclic recursion\, provides fo
r new developments of type theory of computation and new applications to c
omputational syntax-semantics interfaces in programming and natural langua
ges.\n\nIn this talk\, I present the formal language (LAR) of TTAR\, by ex
tending it with a restrictor operator that sets conditions on denotations
of terms. In addition\, the operator defines restricted memory and paramet
ers. TTAR provides two kinds of semantics of the formal language LAR\, den
otational and algorithmic. The reduction system of TTAR is essential for t
he notion of algorithm and syntax-semantics interfaces. I shall overview t
he reduction calculus and some of the theoretical results of TTAR.\n\n[1]
Yiannis N Moschovakis. The formal language of recursion. Journal of Symbol
ic Logic\, 54(04):1216–1252\, 1989.\n\n[2] Yiannis N. Moschovakis. A Log
ical Calculus 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://stable.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:20260404T095425Z
UID:AlgAndLogic/35
DESCRIPTION:Title: On the Newton polytope of a Jacobian pair\nby Leonid Makar
-Limanov (Wayne State University\, Detroit\, USA and Weizmann Institute of
Science\, Rehovot\, Israel) as part of Algebra and Logic Seminar\n\n\nAbs
tract\nFirst\, I remind what is the Jacobian Conjecture and talk about som
e history related to it. Then I'll briefly explain what is the “shape”
of a minimal counterexample to the conjecture. After that the Newton poly
tope related to a “minimal” counterexample to the Jacobian conjecture
will be introduced and described. This description allows to obtain the be
st known estimate for the geometric degree of the polynomial mapping given
by a Jacobian pair.\n
LOCATION:https://stable.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:20260404T095425Z
UID:AlgAndLogic/36
DESCRIPTION:Title: Identities in Prime Rings\nby Jose Brox (Centre for Mathem
atics of the University of Coimbra\, Portugal) as part of Algebra and Logi
c Seminar\n\n\nAbstract\nGiven a ring\, a generalized polynomial identity
(GPI) is a polynomial identity in which the coefficients can be taken from
the ring. Prime rings are a class of rings very well suited to manage pro
blems related to identities\, as for example those coming from Herstein’
s theory\, which is the study of nonassociative objects and structures ari
sing from associative rings. After a motivating introduction to prime ring
s\, with some examples from Herstein’s theory\, I will show the usefulne
ss of Martindale’s lemma\, the key tool for solving GPIs in one variable
in prime rings\, and I will explain a new promising approach to solve the
m based on elementary algebraic geometry which avoids some shortcomings of
the lemma\, allowing to find the optimal solutions.\n
LOCATION:https://stable.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:20260404T095425Z
UID:AlgAndLogic/37
DESCRIPTION:Title: Enumeration Reducibility: 60 years of investigation\nby Hr
isto Ganchev (Faculty of Mathematics and Informatics\, Sofia University) a
s part of Algebra and Logic Seminar\n\n\nAbstract\nWe will make an overvie
w of the main results and problems in Еnumeration reducibility – one of
the two main reducibilities used to compare the complexity of the informa
tion content in sets of natural numbers.\n
LOCATION:https://stable.researchseminars.org/talk/AlgAndLogic/37/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dessislava Kochloukova (University of Campinas\, Brazil)
DTSTART:20210305T140000Z
DTEND:20210305T150000Z
DTSTAMP:20260404T095425Z
UID:AlgAndLogic/38
DESCRIPTION:Title: Finite presentability for metabelian groups\, Lie algebras and
restricted Lie algebras\nby Dessislava Kochloukova (University of Cam
pinas\, 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 fi
nite presentability (in terms of generators and relations) for metabelian
groups and metabelian Lie algebras. The case of groups was solved by Rober
t Bieri and Ralph Strebel in 1980s and that of Lie algebras was done by Ro
ger Bryant and John Groves in late 1990s. In the last part of the talk we
discuss new results about the classification of finitely presented metabel
ian restricted Lie algebras based on joint work with Adriana Leon\, J. Alg
ebra\, 560 (2020)\, 1107-1145.\n
LOCATION:https://stable.researchseminars.org/talk/AlgAndLogic/38/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ljudmila Kamenova (Stony Brook University\, USA)
DTSTART:20210312T143000Z
DTEND:20210312T160000Z
DTSTAMP:20260404T095425Z
UID:AlgAndLogic/39
DESCRIPTION:Title: Algebraic Non-hyperbolicity of Hyperkähler Manifolds\nby
Ljudmila Kamenova (Stony Brook University\, USA) as part of Algebra and Lo
gic Seminar\n\n\nAbstract\nA projective manifold is algebraically hyperbol
ic if the degree of any curve is bounded from above by its genus times a c
onstant\, which is independent from the curve. This is a property which fo
llows from Kobayashi hyperbolicity. We prove that hyperkahler manifolds ar
e not algebraically hyperbolic when the Picard rank is at least 3\, or if
the Picard rank is 2 and the SYZ conjecture on existence of Lagrangian fib
rations is true. We also prove that if the automorphism group of a hyperka
hler manifold is infinite\, then it is algebraically non-hyperbolic. These
results are joint with Misha Verbitsky.\n\nThese results are joint with M
isha Verbitsky.\n
LOCATION:https://stable.researchseminars.org/talk/AlgAndLogic/39/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andreas Weiermann (Ghent University\, Belgium)
DTSTART:20210319T140000Z
DTEND:20210319T153000Z
DTSTAMP:20260404T095425Z
UID:AlgAndLogic/40
DESCRIPTION:Title: Some applications of transfinite numbers to algebra and some a
pplications of number theory to transfinite numbers\nby Andreas Weierm
ann (Ghent University\, Belgium) as part of Algebra and Logic Seminar\n\n\
nAbstract\nIn the first part we will survey the role of transfinite number
s in the study of Hilbert's basis theorem and its extension by MacLagan. T
o this end we associate ordinals to some natural well partial orderings re
lated Cartesian products of the set of natural numbers and we apply this a
pparatus to monomial ideals in F[X_1\,...\,X_n] where F is a field.\n\nIn
the second part we use the machinery of Tauberian theorems to prove some s
tructural results about transfinite numbers regarding limit laws and phase
transitions.\n\nThe talk will be non technical and it is aimed at a gener
al mathematical audience.\n
LOCATION:https://stable.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:20260404T095425Z
UID:AlgAndLogic/41
DESCRIPTION:Title: Some axioms about rationality in infinite concurrent multiplay
er games with ordered objectives and temporary coalitions in QCTL*\nby
Dimitar Guelev (Institute of Mathematics and Informatics\, Bulgarian Acad
emy of Sciences) as part of Algebra and Logic Seminar\n\n\nAbstract\nTempo
ral winning conditions appear in both terminating and infinite games. Reac
hability (guarantee) winning conditions appear in terminating games. Safet
y conditions and conditions higher up in the (Manna & Pnueli\, 1989) hiera
rchy appear in non-terminating games. In a multiplayer game\, the latter c
lasses of winning conditions are natural to drive players into forming per
manent coalitions as the longevity of a coalition needs to match the durat
ion of its agenda\, which may take entire infinite plays to implement. How
ever\, a lifelong joint agenda is often inconsistent with the ability of p
layers to change alliances\, especially if there are multiple objectives w
ith preference. The dedicated constructs of established logical notations
for strategic behaviour such as Alternating-time Temporal Logic (ATL\, Alu
r Henzinger and Kupferman\, ICALP 1997\, J. of the ACM\, 2002) and Strateg
y Logic (SL\, Chatterjee\, Henzinger and Piterman\, I& C\, 2010\, Mogavero
\, Murano and Vardi\, FST TCS 2010)\, in their now many variants and exten
sions\, are off-the-shelf for permanent coalitions only. To the best of ou
r knowledge\, no dedicated constructs such as those of ATL and SL are avai
lable for temporary coalitioning.\n\nIn this talk we fall back onto Quanti
fied Computation Tree Logic\, QCTL*\, which admits embeddings of both ATL
and SL\, and is now an established intermediate notation for logics for st
rategic ability\, largely because of its decidability on the unwindings of
finite models (French\, Australian AI 2001\, Ph.D. Thesis 2006\, Laroussi
nie and Markey\, LMCS 2014). The embedding of ATL was introduced in (Da Co
sta Lopez 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 propose a vocabulary which extends this embedding to allow temporary
coalitions. We illustrate its use to formulate example sufficient conditio
ns for the rationality of shifting coalition structure and decisions in th
e extension of QCTL* by a temporal form of a binary preference operator af
ter (Von Wright\, 1963) which we introduced in (Guelev\, CoRR 2020). The c
onditions reflect naive game-theoretic reasoning and are considered to bec
ome part of analogons to backward induction to infinite concurrent games w
ith ordered objectives. We adopt ordered objectives from the thorough stud
y of pure Nash equilibria concurrent ω-regular games without coalitioning
in (Bouyer\, Brenguier and Markey and Ummels\, FoSSaCS 2012\, LMCS 2015).
\n\nKeywords: strategic ability\, temporary coalitions\, rational synthesi
s\, ordered objectives\, concurrent multiplayer games\n
LOCATION:https://stable.researchseminars.org/talk/AlgAndLogic/41/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ivan Penkov (Jacobs University Bremen\, Germany)
DTSTART:20210409T100000Z
DTEND:20210409T113000Z
DTSTAMP:20260404T095425Z
UID:AlgAndLogic/42
DESCRIPTION:Title: Universal tensor categories and “algebraic functional analys
is”\nby Ivan Penkov (Jacobs University Bremen\, Germany) as part of
Algebra and Logic Seminar\n\n\nAbstract\nIn this talk I will outline the c
onstruction of some tensor categories generated by two objects $X$\, $Y$ w
ith a pairing $X\\otimes Y$ → 1 to the monoidal unit 1. These categories
are categories of representations of certain infinite-dimensional Lie alg
ebras\, and they turn out to be universal in a sense which will be explain
ed in the talk. The interpretation of $Y$ as a dual space to $X$ allows an
analogy with functional analysis. Joint work with A. Chirvasitu\, based o
n earlier joint work with V. Serganova.\n
LOCATION:https://stable.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:20260404T095425Z
UID:AlgAndLogic/43
DESCRIPTION:Title: The Holographic Principle – Motivation and Applications\
nby Veselin Filev (Institute of Mathematics and Informatics\, Bulgarian Ac
ademy of Sciences) as part of Algebra and Logic Seminar\n\n\nAbstract\nI w
ill talk about the arguments that lead to the formulation of the holograph
ic principle and its realization in the framework of superstring theory vi
a the AdS/CFT correspondence. I will focus on the applications of the holo
graphic principle for the description of confinement\, chiral symmetry bre
aking and novel phases of strongly interacting matter.\n\nThis is the inau
gural lecture of Assoc. Prof. Veselin Filev.\n
LOCATION:https://stable.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:20260404T095425Z
UID:AlgAndLogic/44
DESCRIPTION:Title: On Krull dimension of Noetherian super-rings\nby Alexandr
Zubkov (United Arab Emirates University\, Al Ain\, UAE and Sobolev Institu
te of Mathematics (Omsk branch)\, Omsk\, Russia) as part of Algebra and Lo
gic Seminar\n\n\nAbstract\nThe notion of Krull dimension plays crucial rol
e in the algebraic geometry and in the theory of commutative rings. It see
ms quite natural to define such a notion for (supercommutative) super-ring
s in order to develop the algebraic supergeometry in more or less systemat
ic way\, similar to the classical case. This talk is partially based on th
e recent joint work with A. Masuoka (published in JPAA) and new results (y
et unpublished).\n
LOCATION:https://stable.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:20260404T095425Z
UID:AlgAndLogic/45
DESCRIPTION:Title: Commutative Group Rings and Abelian Groups\nby Peter Danch
ev (Institute of Mathematics and Informatics\, Bulgarian Academy of Scienc
es) as part of Algebra and Logic Seminar\n\n\nAbstract\nSome specific ques
tions from the theory of commutative group rings and Abelian groups are be
ing considered as complete solutions to some of them are given\, which def
initely generalize certain classical results in these directions.\n\nInaug
ural lecture of Assoc. Prof. Peter Danchev.\n
LOCATION:https://stable.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:20260404T095425Z
UID:AlgAndLogic/46
DESCRIPTION:Title: On the Degree of Dependence of Two Events\nby Valentin Ili
ev (Institute of Mathematics and Informatics\, Bulgarian Academy of Scienc
es) as part of Algebra and Logic Seminar\n\n\nAbstract\nWe define degree o
f dependence of two events A and B in a probability space by using Boltzma
nn-Shannon entropy function of an appropriate distribution produced by the
se events and depending on one parameter varying within a closed interval
I. The important particular case of discrete uniform probability space mot
ivates this definition in the following way. The entropy function has a gl
obal maximum exactly when the events A and B are independent. It has a min
imum at the left endpoint of I exactly when A is a subset of B^c or B^c is
a subset of A (maximal negative dependence). It has a minimum at the righ
t endpoint of I exactly when A is a subset of B or B is a subset of A (max
imal positive dependence).\n
LOCATION:https://stable.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:20260404T095425Z
UID:AlgAndLogic/47
DESCRIPTION:Title: Non-finitely based and limit varieties of algebraic systems\nby Vesselin Drensky (Institute of Mathematics and Informatics\, Bulgari
an Academy of Sciences) as part of Algebra and Logic Seminar\n\n\nAbstract
\nA variety of algebraic systems is non-finitely (or infinitely) based if
it does not have a finite basis of identities. It is just-non-finitely bas
ed (or limit) if it is non-finitely based but all its proper subvarieties
are finitely based. By the Zorn lemma every variety without a finite basis
of identities contains a just-non-finitely based subvariety.\n\nWe survey
results on non-finitely based varieties of groups\, semigroups and on ass
ociative\, Lie and nonassociative rings and algebras.\nWe also present exa
mples of just-non-finitely based varieties of nonassociative algebras and
varieties of pairs over fields of characteristic 0.\n
LOCATION:https://stable.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:20260404T095425Z
UID:AlgAndLogic/48
DESCRIPTION:Title: Group gradings on incidence algebras\nby Ednei Aparecido S
antulo Jr. (Universidade Estadual de Maringá\, Paraná\, Brazil) as part
of Algebra and Logic Seminar\n\n\nAbstract\nThis is a joint work with Feli
pe Y. Yasumura and Jonathan P. Souza.\n\nThe main goal of this talk is pre
senting the classification of group gradings on incidence algebras as obta
ined in [2]. To do so\, we start by defining incidence algebras and emphas
izing their resemblances and differences relative to the algebra of upper
triangular matrices. We recall the classification of group gradings on the
algebra of upper triangular matrices with entries in a field obtained by
Di Vincenzo\, Koshlukov and Valenti in [1] and generalized in [3] by Vale
nti and Zaicev. Then we present some examples to show that a similar resul
t cannot be true in the general context of incidence algebras. Since good
and elementary gradings play a major role in the classification of group g
radings in the case of upper triangular matrices\, we present the natural
generalization of those concepts in the context of incidence algebras (and
even in more general contexts than that of matrix algebras). Since it is
impossible\, due to time\, to present the proofs of the lemmas used to obt
ain the main result in a level of details necessary to understand them com
pletely\, we decided to describe how we were led to those lemmas\, believi
ng that\, with that approach\, the attendants can get more intuition about
the situation we dealt with and\, consequently\, they may be more interes
ted in studying incidence algebras (or group gradings on algebras)\, beyon
d the problem presented in our talk\, in the future.\n\n[1] O.M. Di Vincen
zo\, P. Koshlukov\, A. Valenti\, Gradings on the algebra of upper triangul
ar matrices and their graded identities\, J. Algebra 275(2) (2004) 550–5
66.\n\n[2] E.A. Santulo Jr.\, J.P. Souza\, F.Y. Yasumura\, Group gradings
on finite dimensional incidence algebras\, J. Algebra 544 (2) (2020) 302-3
28.\n\n[3] A. Valenti\, M.V. Zaicev\, Group gradings on upper triangular m
atrices\, Arch. Math. 89(1) (2007) 33–40.\n
LOCATION:https://stable.researchseminars.org/talk/AlgAndLogic/48/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ilinka Dimitrova (South-West University “Neofit Rilski”\, Blag
oevgrad)
DTSTART:20210528T100000Z
DTEND:20210528T113000Z
DTSTAMP:20260404T095425Z
UID:AlgAndLogic/49
DESCRIPTION:Title: Ranks of Monoids of Endomorphisms\, Partial Automorphisms and
Injective Partial Endomorphisms of a Finite Undirected Path\nby Ilinka
Dimitrova (South-West University “Neofit Rilski”\, Blagoevgrad) as pa
rt of Algebra and Logic Seminar\n\n\nAbstract\nIn the same way that automo
rphisms of graphs allow to establish natural connections between Graph The
ory 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 s
everal authors over the last decades. In fact\, from combinatorial propert
ies to more algebraic concepts have been extensively studied.\n\nLet $G=(V
\,E)$ be a simple graph (i.e. undirected graph without loops and without m
ultiple edges).\nLet $\\alpha$ be a partial transformation of $V$. Denote
by $\\mathop{\\mathrm{Dom}} \\alpha$ the domain of $\\alpha$ and by $\\mat
hop{\\mathrm{Im}} \\alpha$ the image of $\\alpha$.\nWe say that $\\alpha$
is:\n\n● a partial endomorphism of $G$ if $\\{u\,v\\}\\in E$ implies $\
\{u\\alpha\,v\\alpha\\}\\in E$\, 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 endomorph
ism 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 $\\{u\\al
pha\,v\\alpha\\}\\in E$\, for all $u\,v\\in V$\;\n\n● a partial automorp
hism of $G$ if $\\alpha$ is an injective mapping (i.e. a partial permutati
on) and $\\alpha$ and $\\alpha^{-1}$ are both partial endomorphisms\;\n\n
● if $\\alpha$ is a full mapping (i.e. $\\alpha\\in \\mathcal{T}(V)$) th
en to a partial endomorphism (respectively\, weak partial endomorphism and
partial automorphism) we just call endomorphism (respectively\, week endo
morphism 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 al
l weak endomorphisms of $G$\;\n\n● $\\mathrm{sEnd}(G)$ the set of all st
rong endomorphisms of $G$\;\n\n● $\\mathrm{swEnd}(G)$ the set of all str
ong weak endomorphisms of $G$\;\n\n● $\\mathrm{Aut}(G)$ the set of all a
utomorphisms of $G$.\n\n● $\\mathrm{wPEnd}(G)$ the set of all weak parti
al endomorphisms of $G$\;\n\n● $\\mathrm{PEnd}(G)$ the set of all partia
l endomorphisms of $G$\;\n\n● $\\mathrm{IEnd}(G)$ the set of all injecti
ve partial endomorphisms of $G$\;\n\n● $\\mathrm{PAut}(G)$ the set of al
l partial automorphisms of $G$\;\n\n\nClearly\, $\\mathrm{End}(G)$\, $\\ma
thrm{wEnd}(G)$\, $\\mathrm{sEnd}(G)$\, $\\mathrm{swEnd}(G)$\, $\\Aut(G)$\,
$\\mathrm{wPEnd}(G)$\, $\\mathrm{PEnd}(G)$\, $\\mathrm{IEnd}(G)$ and $\\m
athrm{PAut}(G)$ are monoids under composition of maps with the identity ma
pping $\\mathop{\\mathrm{id}}$ as the identity element. Moreover\, $\\math
rm{Aut}(G)$ is also a group and $\\mathrm{PAut}(G)$ is an inverse semigrou
p.\n\nThe 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
important notion of Semigroup Theory\, which has been\, in recent years\,
the subject of intensive research.\n\nWe study the widely considered endom
orphisms\, weak endomorphisms\, partial automorphisms and\, more generally
\, injective partial endomorphisms of a finite undirected path $P_n$ with
$n \\in \\mathbb{N}$ vertices from monoid generators perspective. Our main
objective 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 $\\mathrm{PAut}(P
_n)$. We also study Green's relations\, regularity\, and cardinality for s
ome of these monoids.\n
LOCATION:https://stable.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:20260404T095425Z
UID:AlgAndLogic/50
DESCRIPTION:Title: Schur’s exponent conjecture\nby Michael Vaughan-Lee (Oxf
ord University Mathematical Institute\, United Kingdom) as part of Algebra
and Logic 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. Schur that the exponent of $M(G)$ divides the exponent of $G$. It is e
asy 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
. However the truth or otherwise of this conjecture has remained open up t
ill now for groups of odd exponent.\n\nIn my talk I describe counterexampl
es to the conjecture of exponent 5 and exponent 9.\n
LOCATION:https://stable.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:20260404T095425Z
UID:AlgAndLogic/51
DESCRIPTION:Title: Distinctness of the “lifted” Kloosterman sums over the pri
me field F_p\nby Lyubomir Borissov (Institute of Mathematics and Infor
matics\, Bulgarian Academy of Sciences) as part of Algebra and Logic Semin
ar\n\n\nAbstract\nIn this talk I consider the Kloosterman sums over the fi
nite field $\\mathbb F_{q}$ of characteristic $p$\, defined by\n$$K_{q} (u
)= \\sum_{x \\in \\mathbb F^{*}_{q}} \\omega^{\\ Tr(x+ u x^{-1})}\,\n$$\nw
here $\\displaystyle\\omega=e^{\\frac{2 \\pi i}p}$ is a primitive $p-$th r
oot 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-cal
led "lifted" 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 finite field of order $q^{n}\, n > 1$.\n\nIt is well-known that the Kl
oosterman sums play an important role in algebraic coding theory and crypt
ography (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 presc
ribed trace and co-trace: \nhttps://arxiv.org/pdf/1711.08306.pdf\n\nThe is
sue of their distinctness is considered and partly solved for the first ti
me by Benjamin Fisher in 1992 [4]. In particular\, this author has proved
that fact for the simplest sums\, i.e.\, over the prime fields.\n\nRecentl
y\, in a personal communication with us\, Daqing Wan has announced that as
a co-product of his research [5] (based on deep algebraic number theory s
uch as Stickelberger's theorem) it follows the distinctness of \n"lifted"
Kloosterman sums over any prime field $\\mathbb F_p$ whenever the extensio
n degree is not a multiple of $p$. This statement generalizes our result f
or the fields whose extension degree is a power of $2$:\nhttps://link.spri
nger.com/article/10.1007/s12095-020-00443-1\n\nHere I am giving a proof fo
r the distinctness of the "lifted" Kloosterman sums over $\\mathbb F_3$ fo
r any degree of extension thus improving Wan's result in case $p = 3$. \n\
nI believe that (jointly with Y. Borissov)\, we have found a proof that al
l "lifted" Kloosterman sums over each prime field of characteristic $\\geq
3$ and any extension degree\, are distinct.\nIn the final slides I present
some arguments concerning this fact which is to be elaborated in a future
work. \n\nReferences\n\n[1] L. Carlitz\, "Kloosterman sums and finite fie
ld extensions"\, 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 class
ical Kloosterman sums"\, Cryptogr. and Commun.\, 11.3 (2019)\, pp. 461-496
.\n\n[4] \nB. Fischer\, "Distinctness of Kloosterman sums"\, Contemporary
Mathematics\, vol. 133 (1992)\, pp. 81-102.\n\n[5] \nD. Wan\, "Minimal pol
ynomials and distinctness of Kloosterman sums"\, Finite Fields Appl.\, 1 (
1995)\, pp. 189-203.\n
LOCATION:https://stable.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:20260404T095425Z
UID:AlgAndLogic/52
DESCRIPTION:Title: Primary decompositions of unital locally matrix algebras and S
teinitz numbers\nby Bogdana Oliynik (National University of Kyiv-Mohyl
a Academy\, Kyiv\, Ukraine) as part of Algebra and Logic Seminar\n\n\nAbst
ract\nLet $F$ be a ground field. An $F$-algebra $A$ with unit 1 is said to
be a locally matrix algebra if an arbitrary finite collection of elements
$a_1\, . . . \, a_s$ from $A$ lies in a subalgebra $B$ with 1 of the alge
bra $A$\, 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 alg
ebra A. In this talk\, we outline the construction of a unital locally mat
rix algebra of uncountable dimension that does not admit a primary de-comp
osition. It gives negative answers to the question posed in V. M. Kurochki
n\, 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 tha
t for an arbitrary infinite Steinitz number s there exists a unital locall
y matrix algebra A having the Steinitz number s and being not isomorphic t
o a tensor product of finite dimensional matrix algebras.\n\nThis talk is
based on the joint works with Oksana Bezushchak.\n
LOCATION:https://stable.researchseminars.org/talk/AlgAndLogic/52/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Arkadii Slinko (University of Auckland\, New Zealand)
DTSTART:20210625T080000Z
DTEND:20210625T093000Z
DTSTAMP:20260404T095425Z
UID:AlgAndLogic/53
DESCRIPTION:Title: Framing in secret sharing\nby Arkadii Slinko (University o
f Auckland\, New Zealand) as part of Algebra and Logic Seminar\n\n\nAbstra
ct\nSecret sharing\, a well-known cryptographic technique\, introduced 40
years ago as a private and reliable variant of classical storage\, has now
become a major cryptographic primitive with numerous real-world applicati
ons.\n\nIn this paper we consider the digital forensics aspects of secret
sharing. We investigate the problem of framing which occurs when a coaliti
on of participants is able to calculate the share of a participant who doe
s not belong to it. In the extreme case one authorized coalition can calcu
late shares of another authorized coalition\, obtain the secret and use it
in some way blaming another authorized coalition for their action. Our wo
rk shows that in an ideal secret sharing scheme an authorized coalition ca
nnot frame participants who are less senior than all members of the coalit
ion and is able to frame a participant who is more senior than at least on
e member of the coalition.\n\nThis is a joint paper with Yvo Desmedt and S
ongbao Mo. It has just been published in\n\nDesmedt\, Y.\, Mo\, S.\, & Sli
nko\, A. M. (2021). Framing in Secret Sharing. IEEE Transactions on Inform
ation Forensics and Security\, 16\, 2836-2842.\n
LOCATION:https://stable.researchseminars.org/talk/AlgAndLogic/53/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Natalia Iyudu (Lancaster University\, UK)
DTSTART:20210702T100000Z
DTEND:20210702T113000Z
DTSTAMP:20260404T095425Z
UID:AlgAndLogic/54
DESCRIPTION:Title: Noncommutative Poisson structures\, Hochschild type complexes
and Gröbner bases theory\nby Natalia Iyudu (Lancaster University\, UK
) as part of Algebra and Logic Seminar\n\n\nAbstract\nI will discuss Calab
i-Yau type conditions\, such as pre-Calabi-Yau and exact Calabi-Yau. We sh
ow that pre-Calabi-Yau structures give rise to double Poisson brackets of
Van den Bergh. The homological formulation of pre-Calabi-Yau structure can
be dealt 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 ex
act Calabi-Yau algebras as 3-Sklyanin. Here we are able\, for example\, to
improve the statement in Artin-Schelter classical paper\, based on argume
nts of topological nature\, that there is a finite group action on Sklyani
n algebras $S_{p\,q}$\, for which the orbits are exactly isomorphism class
es. We can say that this group is $SL_2(Z_3)$.\n
LOCATION:https://stable.researchseminars.org/talk/AlgAndLogic/54/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Greta Panova (University of Southern California\, USA)
DTSTART:20210709T100000Z
DTEND:20210709T113000Z
DTSTAMP:20260404T095425Z
UID:AlgAndLogic/55
DESCRIPTION:Title: The mysterious Kronecker coefficients of the Symmetric group\nby Greta Panova (University of Southern California\, USA) as part of A
lgebra and Logic Seminar\n\n\nAbstract\nAlgebraic Combinatorics is a field
of mathematics which studies discrete objects often originating in Repres
entation Theory\, Algebra\, Algebraic Geometry\, Number Theory via combina
torial methods. One of its oldest problems concerns the Kronecker coeffici
ents of the Symmetric Group. They are originally defined by Murnaghan more
than 80 years ago as the multiplicities of the irreducible modules in the
factorization of the tensor product of two other irreducible modules. The
y actually generalize the Littlewood-Richardson coefficients in the analog
ous problem for the general linear group. Despite their algebraic nature a
s nonnegative integers\, no combinatorial formula or interpretation is kno
wn. Kronecker coefficients have recently played a role in Computational Co
mplexity Theory both as a problem and as a solution.\n\nIn this talk I wil
l give a brief overview of the developments over the past 10 years. I will
show how despite our very limited knowledge we can still use the Kronecke
r coefficients to solve other\, seemingly unrelated problems\, related to
enumeration of integer partitions (Sylvester’s unimodality theorem). I w
ill also discuss some of their computational complexity aspects.\n
LOCATION:https://stable.researchseminars.org/talk/AlgAndLogic/55/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Stefan Dantchev (Durham University\, United Kingdom)
DTSTART:20210716T100000Z
DTEND:20210716T113000Z
DTSTAMP:20260404T095425Z
UID:AlgAndLogic/56
DESCRIPTION:Title: Proof Complexity of Resolution over linear inequalities\nb
y Stefan Dantchev (Durham University\, United Kingdom) as part of Algebra
and Logic Seminar\n\n\nAbstract\nI will start by giving a brief and non-co
mprehensive introduction to the general research area\, Propositional Proo
f Complexity.\n\nI will then focus on a specific proof system that operate
s on linear inequalities with integral coefficients\, called Stabbing Plan
es (SP). Next\, a general method for proving depth lower bounds in SP will
be introduced\, which allows us to prove logarithmic depth lower bounds f
or several well-studied propositional contradictions\, such as the Pigeon-
Hole Principle and the Ordering Principle. Finally\, possible extensions a
nd generalisations of SP will be discussed\, plus some open questions.\n
LOCATION:https://stable.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:20260404T095425Z
UID:AlgAndLogic/57
DESCRIPTION:Title: Dessins d’enfants and moduli spaces of curves\nby George
Shabat (Russian State University for the Humanities and Independent Unive
rsity of Moscow\, Russia) as part of Algebra and Logic Seminar\n\n\nAbstra
ct\nDessins d'enfants theory\, initiated by Alexander Grothendieck in\n197
0's\, establishes an equivalence between the category of certain\ngraphs o
n topological surfaces and some arithmetic-geometric category\n(of $\\text
{\\it Belyi pairs}$\, 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
discuss two relations\nof this equivalence with the moduli spaces of curv
es.\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 decomposi
tion in which the cells are parametrized by certain\ndessins d'enfants. (I
n 1992 Kontsevich has applied this construction\nto the proof of the famou
s Witten conjecture). The relation of\nthis decomposition with the Grothen
dieck-Belyi construction will be\nexplained.\n\n\n(2) For any triple of na
tural numbers $(b\, d\, g)$ \nand for any algebraically closed ground fiel
d $\\mathbb K$ we consider the $\\text{\\it critical filtration}$ of the\n
moduli 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({\\mathbb 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 genus $g$ carrying rational functions of degree $d$\nwith no more than
$b$ critical values -- or\, alternatively\, admitting a\ndegree-$d$ coveri
ng of the projective line with no more than $b$ branch\npoints).\n\nAccord
ing to Grothendieck-Belyi\, the zero-dimensional stratum\n$\\text{\\tt Cr}
_{g\;d\,3}({\\mathbb C}) =\\text{\\tt Cr}_{g\;d\,3}(\\overline{{\\mathbb Q
}})$ corresponds to dessins d'enfants. \nThe combinatorial\, algebro-geome
trical and arithmetical problems\, related to the\nhigher-dimensional stra
ta of the critical filtration\, will be discussed.\n
LOCATION:https://stable.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:20260404T095425Z
UID:AlgAndLogic/58
DESCRIPTION:Title: On Some Special Decompositions of Matrices over Fields and Fin
ite Commutative Rings\nby Peter Danchev (Institute of Mathematics and
Informatics\, Bulgarian Academy of Sciences) as part of Algebra and Logic
Seminar\n\n\nAbstract\nIn order to find a suitable expression of an arbitr
ary square matrix over an arbitrary field\, we prove that every square mat
rix over an infinite field is always representable as a sum of a diagonali
zable matrix and a square-zero nilpotent matrix. In addition\, each 2 x 2
matrix over any field admits such a representation. We also show that\, fo
r all natural numbers n > 2\, every n x n matrix over a finite field havin
g no less than n + 1 elements also admits such a decomposition. As a conse
quence of these decompositions\, we show that every matrix over a finite f
ield can be expressed as the sum of a potent matrix and a square-zero nilp
otent matrix. Moreover\, we prove that every matrix over a finite commutat
ive ring is always representable as a sum of a potent matrix and a square-
zero nilpotent matrix\, provided the Jacobson radical of the former ring h
as 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 arti
cles:\n\n(1) P. Danchev\, E. Garcia\, M. G. Lozano\, Decompositions of mat
rices into diagonalizable and square-zero matrices\, Linear & Multilinear
Algebra (in press 2022)\, published online https://doi.org/10.1080/0308108
7.2020.1862742 .\n\n(2) P. Danchev\, E. Garcia\, M. G. Lozano\, Decomposit
ions of matrices into potent and square-zero matrices\, submitted to a sci
entific journal.\n\n(3) P. Danchev\, E. Garcia\, M. G. Lozano\, On some sp
ecial matrix decompositions over fields and finite commutative rings\, Pro
ceedings of the Fiftieth Spring Conference of the Union of Bulgarian Mathe
maticians\, 95-101\, 2021.\n
LOCATION:https://stable.researchseminars.org/talk/AlgAndLogic/58/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kalina Mincheva (Tulane University\, New Orleans\, USA)
DTSTART:20211029T140000Z
DTEND:20211029T153000Z
DTSTAMP:20260404T095425Z
UID:AlgAndLogic/59
DESCRIPTION:Title: Tropical Geometry and the Commutative Algebra of Semirings
\nby Kalina Mincheva (Tulane University\, New Orleans\, USA) as part of Al
gebra and Logic Seminar\n\n\nAbstract\nTropical geometry provides a new se
t of purely combinatorial tools\, which has been used to approach classica
l problems. In tropical geometry most algebraic computations are done on t
he classical side - using the algebra of the original variety. The theory
developed so far has explored the geometric aspect of tropical varieties a
s opposed to the underlying (semiring) algebra and there are still many co
mmutative algebra tools and notions without a tropical analogue. In the re
cent years\, there has been a lot of effort dedicated to developing the ne
cessary tools for commutative algebra using different frameworks\, among w
hich prime congruences\, tropical ideals\, tropical schemes. These approac
hes allows for the exploration of the properties of tropicalized spaces w
ithout tying them up to the original varieties and working with geometric
structures inherently defined in characteristic one (that is\, additively
idempotent) semifields. In this talk we explore the relationship between t
ropical ideals and congruences and what they remember about the geometry o
f a tropical variety.\n
LOCATION:https://stable.researchseminars.org/talk/AlgAndLogic/59/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Erkko Lehtonen (Universidade Nova de Lisboa\, Portugal)
DTSTART:20211105T110000Z
DTEND:20211105T123000Z
DTSTAMP:20260404T095425Z
UID:AlgAndLogic/60
DESCRIPTION:Title: Permutation groups and permutation patterns\nby Erkko Leht
onen (Universidade Nova de Lisboa\, Portugal) as part of Algebra and Logic
Seminar\n\n\nAbstract\nWe approach permutations from two different points
of view: the algebraic one of permutation groups and the combinatorial on
e of permutation patterns. While these two well-established notions do not
seem to have much in common\, there is a perhaps surprising connection th
at will be explained in this talk. Namely\, the class of permutations avoi
ding the complement of a permutation group is comprised of levels that are
permutation groups.\n\nWith the help of invariant relations\, we describe
the permutation groups that arise in this way from pattern avoidance. Fur
thermore\, we propose refinements to the work by Atkinson and Beals on per
mutation classes in which all levels are groups.\n\nThis talk is partly ba
sed on joint work with Reinhard Pöschel (Technische Universität Dresden)
.\n
LOCATION:https://stable.researchseminars.org/talk/AlgAndLogic/60/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexey V. Kislitsin (Altai State Pedagogical University\, Barnaul\
, Russia)
DTSTART:20211119T110000Z
DTEND:20211119T123000Z
DTSTAMP:20260404T095425Z
UID:AlgAndLogic/61
DESCRIPTION:Title: Identities of Vector Spaces and Nonassociative Linear Algebras
\nby Alexey V. Kislitsin (Altai State Pedagogical University\, Barnaul
\, Russia) as part of Algebra and Logic Seminar\n\n\nAbstract\nIn this tal
k\, we study the concept of the identity of the $L$-space as a weak identi
ty of the pair $(A\, E)$\, where $A$ is the associative $F$-algebra genera
ted 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 p
roved are also obtained for non-associative linear algebras satisfying the
identity $x(yz) = 0$.\n\nThis is a joint talk with Ismail M. Isaev (Altai
State Pedagogical University\, Barnaul\, Russia).\nThe talk will be deliv
ered in Russian\, the slides will be in English.\n
LOCATION:https://stable.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:20260404T095425Z
UID:AlgAndLogic/62
DESCRIPTION:Title: On a method of proving the non-existence of modal formulae sat
isfying certain syntactic properties and defining a given class of frames<
/a>\nby Petar Iliev (Institute of Philosophy and Sociology and Institute o
f Mathematics and Informatics\, Bulgarian Academy of Sciences) as part of
Algebra and Logic Seminar\n\n\nAbstract\nWe elaborate on semantically labe
led syntax trees\, which provide a method of proving the non-existence of
modal formulae satisfying certain syntactic properties and defining a give
n class of either models or frames\, and use them to show that there are c
lasses of Kripke frames that are definable by both non-Sahlqvist and Sahlq
vist formulae but the latter require more propositional variables.\n\nThe
talk is based on the following articles.\n\nP. Iliev. On a method of provi
ng the non-existence of modal formulae\nsatisfying certain syntactic prope
rties and defining a given class of frames (submitted).\n\nP. Balbiani\, D
. Fernandez-Duque\, A. Herzig\, and P. Iliev. Frame validity Games and Low
er Bounds on the Complexity of Modal Axioms. Logic Journal of the IGPL (20
20).\n
LOCATION:https://stable.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:20260404T095425Z
UID:AlgAndLogic/63
DESCRIPTION:Title: A Separation Theorem for Discrete Time Interval Temporal Logic
\nby Dimitar Guelev (Institute of Mathematics and Informatics\, Bulgar
ian Academy of Sciences) as part of Algebra and Logic Seminar\n\n\nAbstrac
t\nGabbay’s separation theorem about linear temporal logic with past is
admittedly one of the most useful theoretical results in temporal logic. I
n this talk\, we establish an analogous statement about Moszkowski’s dis
crete time propositional Interval Temporal Logic (ITL) with two sets of ex
panding modalities\, namely the unary neighbourhood modalities and the bin
ary weak inverses of ITL’s chop operator. (The two pairs of expanding mo
dalities are interexpressible.) We prove that separation holds for ITL bot
h with and without its loop construct chop-star. A considerable share of t
hese applications can be upgraded to the new case of ITL. We give brief pr
eliminaries on ITL and LTL\, and the relevance of separation to applicatio
ns as known about LTL first.\n\nThe talk is based on a joint work with Ben
Moszkowski.\n\nThe talk will be delivered in Bulgarian with presentation
in English.\n
LOCATION:https://stable.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:20260404T095425Z
UID:AlgAndLogic/64
DESCRIPTION:Title: Restricted Quantification in New Type-Theory of Algorithms
\nby Roussanka Loukanova (Institute of Mathematics and Informatics\, Bulga
rian Academy of Sciences) as part of Algebra and Logic Seminar\n\n\nAbstra
ct\nIn this talk\, I present an extended Type-Theory of Algorithms for res
tricted computations. The restrictor operator supports algorithmic rules o
f introduction and elimination\, for each of the existential and universal
quantifiers. I define and discuss new rules of existential quantification
.\n\nMy focus is on development of mathematics of Type Theory\, from the p
erspective of new\, advanced technological applications. I shall point to
one of its most important applications for representing semantic underspec
ification of quantifier scope.\n
LOCATION:https://stable.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:20260404T095425Z
UID:AlgAndLogic/65
DESCRIPTION:Title: A valuation theorem for Noetherian rings\nby Antoni Rangac
hev (Institute of Mathematics and Informatics\, Bulgarian Academy of Scien
ces) as part of Algebra and Logic Seminar\n\n\nAbstract\nA classical resul
t due to Krull says that a normal domain R is equal to the intersection of
the valuation rings in its field of fractions that contain R. If in addit
ion R is Noetherian\, then one can restrict the intersection to the discre
te valuation rings that contain R. Now consider the following relative set
ting. Let A and B be integral domains. Suppose A is Noetherian and B is a
finitely 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 fin
itely many unique discrete valuation rings. This result generalizes Rees
’ classical valuation theorem for ideals. If time permits I will obtain
a variant of Zariski’s main theorem.\n
LOCATION:https://stable.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:20260404T095425Z
UID:AlgAndLogic/66
DESCRIPTION:Title: Defeasible Preference Logic\nby Rosen Lutskanov (Institute
of Philosophy and Sociology\, Bulgarian Academy of Sciences) as part of A
lgebra and Logic Seminar\n\n\nAbstract\nThe talk explores a formal framewo
rk for reasoning about preferences that employs\ntwo types of preference:
defeasible and fixed. Preference learning is modeled as a process of\ngrad
ual substitution of defeasible preferences with fixed preferences. It is s
hown that\, under\nsome natural axiomatic conditions\, this logic admits a
semantics with partially ordered truth\nvalues. The partial order belongs
to the family of series-parallel semiorders whose properties\nare further
discussed.\n\nThe talk is part of a seminar dedicated to the Fourth World
Logic Day 2022\, January 14th.\n
LOCATION:https://stable.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:20260404T095425Z
UID:AlgAndLogic/67
DESCRIPTION:Title: Difference between material and behavioral implicatures\nb
y Elena Tsvetkova (Institute of Philosophy and Sociology\, Bulgarian Acade
my of Sciences) as part of Algebra and Logic Seminar\n\n\nAbstract\nIn Gri
ce’s theory of conversational implicatures a difference can be drawn bet
ween\nmaterial and behavioral implicatures. This distinction has been prop
osed by Mark Jary and\nsuggests that by material implicatures there is a l
ink between the explicit content of an\nutterance and the implicature that
is based on the conceptual content of the utterance\, while by behavioral
implicatures inference is drawn based on understanding the speaker’s be
havior and reasons for uttering a sentence. Considering this distinction\,
Grice’s definition of non-natural meaning is interpreted as a case of b
ehavioral implicature. In this talk I will consider a way of keeping the d
istinction between material and behavioral implicatures and at the same ti
me defend Grice’s notion of non-natural meaning.\n\nThe talk is part of
a seminar dedicated to the Fourth World Logic Day 2022\, January 14th.\n
LOCATION:https://stable.researchseminars.org/talk/AlgAndLogic/67/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lukasz T. Stepien (The Pedagogical University of Cracow)
DTSTART:20220114T093000Z
DTEND:20220114T101000Z
DTSTAMP:20260404T095425Z
UID:AlgAndLogic/68
DESCRIPTION:Title: On a proof of consistency of Arithmetic System\nby Lukasz
T. Stepien (The Pedagogical University of Cracow) as part of Algebra and L
ogic Seminar\n\n\nAbstract\nA sketch of a proof of consistency of Arithmet
ic System will be presented. This\nproof has been done within this Arithme
tic System.\n\nThe talk is part of a seminar dedicated to the Fourth World
Logic Day 2022\, January 14th.\n
LOCATION:https://stable.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:20260404T095425Z
UID:AlgAndLogic/69
DESCRIPTION:Title: On Space Bounds for Bimachine Constructions\nby Stoyan Mih
ov and Stefan Gerdzhikov (IICT-BAS and FMI-Sofia University) as part of Al
gebra and Logic Seminar\n\n\nAbstract\nBimachines are deterministic finite
-state devices which have the same expressive\npower as the class of regul
ar (rational) functions. The main practical advantage of the\nbimachines i
s the deterministic traversal\, which facilitates the computation of the i
mage of an\ninput string $S$ in time $O(|S|)$. Furthermore\, the class of
regular functions and hence the\nbimachines are closed under composition.
We first show a direct algorithm for constructing a\nbimachine from a tran
sducer representing a regular function. Following this construction\nevery
successful run of the bimachine corresponds to a successful path in the o
riginal\ntransducer and the outputs of the bimachine correspond to the out
puts of the transducer\ntransitions on the given path. Afterwards\, we pre
sent an optimized algorithm which constructs\na bimachine with $O(2^N)$ st
ates\, where $N$ is the number of states in the original transducer. In\nt
his construction the runs of the bimachine do not correspond to the output
s of the transducer\ntransitions. Finally\, we show an asymptotical lower
bound of $O(2^{N/2})$ for any construction that\nproduces a bimachine equi
valent to a given functional transducer with N states.\n\nThe talk is part
of a seminar dedicated to the Fourth World Logic Day 2022\, January 14th.
\n
LOCATION:https://stable.researchseminars.org/talk/AlgAndLogic/69/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yana Rumenova and Tinko Tinchev (FMI-Sofia University)
DTSTART:20220114T123000Z
DTEND:20220114T130000Z
DTSTAMP:20260404T095425Z
UID:AlgAndLogic/70
DESCRIPTION:Title: Modal definability of some classes of modal products\nby Y
ana Rumenova and Tinko Tinchev (FMI-Sofia University) as part of Algebra a
nd Logic Seminar\n\n\nAbstract\nhttps://math.bas.bg/wp-content/uploads/202
2/01/RumenovaTinchev.pdf\n\nThe talk is part of a seminar dedicated to the
Fourth World Logic Day 2022\, January 14th.\n
LOCATION:https://stable.researchseminars.org/talk/AlgAndLogic/70/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Petar Iliev (IPS-BAS and IMI-BAS)
DTSTART:20220114T114000Z
DTEND:20220114T121000Z
DTSTAMP:20260404T095425Z
UID:AlgAndLogic/71
DESCRIPTION:Title: On the formula-size of the parity function\nby Petar Iliev
(IPS-BAS and IMI-BAS) as part of Algebra and Logic Seminar\n\n\nAbstract\
nOn the formula-size of the parity function. Subbotovskaya'\;s and Khra
pchenko'\;s\ntheorems\, both providing lower bounds on the formula-size
of the parity function\, are\ncornerstones of Boolean function complexity
. We are going to give a slow-paced introduction\nto these results and som
e related open problems.\n\nThe talk is part of a seminar dedicated to the
Fourth World Logic Day 2022\, January 14th.\n
LOCATION:https://stable.researchseminars.org/talk/AlgAndLogic/71/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ivan Georgiev (FMI-Sofia University)
DTSTART:20220114T130000Z
DTEND:20220114T133000Z
DTSTAMP:20260404T095425Z
UID:AlgAndLogic/72
DESCRIPTION:Title: On the computational complexity of some representations of irr
ational numbers\nby Ivan Georgiev (FMI-Sofia University) as part of Al
gebra and Logic Seminar\n\n\nAbstract\nIn this talk we consider different
representations of irrational numbers: Cauchy\nsequences\, Dedekind cuts\,
continued fractions and Hurwitz characteristics. All of them are\ncomputa
tionally equivalent when using full Turing computability. However\, this i
s not the\ncase for restricted notions of computability. We make a survey
of some known results\,\nleading to an open problem on graphs of continued
fractions. In the end of the talk\, we take a\nglimpse of an unexplored d
irection concerning the small Grzegorczyk classes.\n\nThe talk is part of
a seminar dedicated to the Fourth World Logic Day 2022\, January 14th.\n
LOCATION:https://stable.researchseminars.org/talk/AlgAndLogic/72/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tatyana Todorova (FMI\, Sofia University\, Bulgaria)
DTSTART:20220121T110000Z
DTEND:20220121T123000Z
DTSTAMP:20260404T095425Z
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 p
art of Algebra and Logic Seminar\n\n\nAbstract\nIt is a long-standing conj
ecture that there are infinitely many primes of the form $n^2+1$. Several
approximations 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 $p = aq^2 + 1$\, wher
e $a ≤ p^{1/2+ε}$ and $q$ is a prime.\n\nWe prove that there are infini
tely 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://stable.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:20260404T095425Z
UID:AlgAndLogic/74
DESCRIPTION:Title: Bicommutative algebras from commutative point of view\nby
Vesselin Drensky (Institute of Mathematics and Informatics\, Bulgarian Aca
demy of Sciences) as part of Algebra and Logic Seminar\n\n\nAbstract\nThe
nonassociative algebra R is right-commutative if\n\n$(ab)c = (ac)b$ for al
l $a\, b\, c$ in $R$\,\n\n$R$ is left-commutative if\n\n$a(bc) = b(ac)$ fo
r all $a\, b\, c$ in $R$.\n\nBicommutative algebras are algebras which are
both left- and right-commutative. One-sided commutative algebras appeared
for the first time in a paper by Cayley in 1857. Their important subclass
of Gelfand-Dorfman-Novikov algebras were studied by Gelfand and Dorfman f
or the needs of the Hamiltonian operator in finite-dimensional mechanics a
nd by Balinskii and Novikov in relation with the equations of hydrodynamic
s.\n\nDzhumadil’daev\, Ismailov and Tulenbaev described the free bicommu
tative algebra and in the case of characteristic 0 determined the main par
ameters needed in the study of varieties of bicommutative algebras. They p
roved that the square $F^2$ of the free bicommutative algebra $F$ is a com
mutative associative algebra. This idea was further explored by the speake
r and Zhakhayev who applied classical methods of commutative algebra in th
e study of bicommutative algebras.\n\nRecently Yuxiu Bai\, Yuqun Chen and
Zerui Zhang have established that the ideals of finitely generated free bi
commutative algebras have finite Gröbner-Shirshov bases. In this way they
have demonstrated the power of the methods of Shirshov for the study of i
deals of nonassociative algebras. Bai\, Chen and Zhang also have shown the
integrality of the Gelfand-Kirillov dimension of finitely generated bicom
mutative algebras.\n\nOnce results are established it is natural to search
for new proofs and further generalizations. The idea of the talk is to sh
ow that many results for bicommutative algebras can be obtained with well
known results in commutative algebra. Additionally this approach allows th
e usage of popular computer packages for calculations with bicommutative a
lgebras.\n
LOCATION:https://stable.researchseminars.org/talk/AlgAndLogic/74/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yana Rumenova (FMI\, Sofia University\, Bulgaria)
DTSTART:20220211T110000Z
DTEND:20220211T123000Z
DTSTAMP:20260404T095425Z
UID:AlgAndLogic/75
DESCRIPTION:Title: Modal definability of some classes of modal products\nby Y
ana Rumenova (FMI\, Sofia University\, Bulgaria) as part of Algebra and Lo
gic Seminar\n\n\nAbstract\nAbstract\n\nThis is a
joint work with Tinko Tinchev (Sofia University).\n
LOCATION:https://stable.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:20260404T095425Z
UID:AlgAndLogic/76
DESCRIPTION:Title: The Bulgarian Solitaire and Other Games on Partitions\nby
Vesselin Drensky (Institute of Mathematics and Informatics\, Bulgarian Aca
demy of Sciences) as part of Algebra and Logic Seminar\n\n\nAbstract\nIn 2
020 the L.N. Gumilyov Eurasian National University (Nur-Sultan\, Kazakhsta
n) decided to organize International Scientific Conference "Algebra and Lo
gic" dedicated to the 60th anniversary of Professor Ualbai Umirbaev and th
e 75th anniversary of Professor Leonid Makar-Limanov. The meeting was canc
elled because of the Covid-19 pandemic. The present talk is based on the t
alk I planned to give in Nur-Sultan.\n\nThe (quite amusing) story presente
d in the talk is an example of how an elementary mathematical game can ins
pirit serious mathematical investigations in Combinatorics\, Graph theory\
, Discrete dynamical systems\, Cellular automata\, Linear algebra\, Statis
tics\, Economical models. The topic has the advantage that most of the pro
blems can be stated in a form which attracts young people to mathematical
research.\n\nThe Bulgarian solitaire is a mathematical card game played by
one person. 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 colle
cting the removed cards to form a new deck. The game ends when the same po
sition occurs twice. It has turned out that when $n = k(k + 1)/2$ is a tri
angular number\, the game reaches the same stable configuration with size
of the piles $1\, 2\, ...\, k$. In the talk we discuss mathematical proble
ms related with the Bulgarian solitaire. The talk is based on the paper (w
ith additional information collected after its publishing):\n\nV. Drensky\
, The Bulgarian solitaire and the mathematics around it\, Math. and Educat
ion in Math.\, Proc. of the 44-th Spring Conf. of the Union of Bulgar. Mat
hematicians\, SOK-Kamchia\, April 2-6\, 2015\, 79-91\; arXiv:1503.00885v1
[math.CO].\nhttp://www.math.bas.bg/smb/2015_PK/tom_2015/pdf/079-091.pdf\n
LOCATION:https://stable.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:20260404T095425Z
UID:AlgAndLogic/77
DESCRIPTION:Title: On the Degree of Dependence of Two Events as a Relative Invari
ant of the Dihedral Group of Order 8\nby Valentin Iliev (Institute of
Mathematics and Informatics\, Bulgarian Academy of Sciences) as part of Al
gebra and 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 probabili
ty space can be produced not only by the ordered pair $(A\,B)$ but by a se
t consisting\, in general\, of 24 ordered pairs of events (named Yule's pa
irs). The probabilities $ξ_1$\, $ξ_2$\, $ξ_3$\, $ξ_4$ of the four resu
lts 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 c
onstitute a probability distribution. The symmetric group $S_4$ of degree
four has 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 24 Yule's pairs. The corresponding action of $S_4$ permutes the comp
onents of the probability distribution $(ξ_1\, ξ_2\, ξ_3\, ξ_4)$\, and
\, in particular\, its entropy function is $S_4$-invariant. The function o
f degree of dependence of two events\, defined via modifying the entropy f
unction\, turns out to be a relative invariant of the dihedral group of or
der 8.\n
LOCATION:https://stable.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:20260404T095425Z
UID:AlgAndLogic/78
DESCRIPTION:Title: Multi-summation in difference rings and applications\nby C
arsten Schneider (Research Institute for Symbolic Computation\, Johannes K
epler University\, Linz\, Austria) as part of Algebra and Logic Seminar\n\
n\nAbstract\nSymbolic summation in difference fields started with Karr's s
ummation algorithm (1981) which can be considered as the discrete version
of Risch's indefinite integration algorithm in differential fields. In the
last 20 years this approach has been generalized and enhanced to a constr
uctive summation theory of difference rings.\n\nIn general\, one can repre
sent algorithmically any expression in terms of indefinite nested sums def
ined over hypergeometric products in such rings. As a crucial by-product o
ne obtains optimal representations where the arising sums and products are
algebraically independent among each other. In particular\, difference ri
ng algorithms have been developed that enable one to simplify certain clas
ses of definite multi-sums to expressions in terms of indefinite nested su
ms defined over hypergeometric products.\n\nWithin this machinery one can
apply Zeilberger's creative telescoping paradigm in order to compute linea
r recurrences for definite multi-sums and one can find all solutions of li
near recurrences that can be expressed in terms of indefinite nested sums
and products. In this talk we will present this algorithmic difference rin
g theory for symbolic summation implemented in the summation package Sigma
and will illustrate its potential by non-trivial applications coming\, e.
g.\, from combinatorics and elementary particle physics.\n
LOCATION:https://stable.researchseminars.org/talk/AlgAndLogic/78/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ece Yetkin Celikel (Hasan Kalyoncu University\, Turkey)
DTSTART:20220318T140000Z
DTEND:20220318T153000Z
DTSTAMP:20260404T095425Z
UID:AlgAndLogic/79
DESCRIPTION:Title: Absorbing ideal structures of commutative rings\nby Ece Ye
tkin Celikel (Hasan Kalyoncu University\, Turkey) as part of Algebra and L
ogic Seminar\n\n\nAbstract\nLet R be a commutative ring with nonzero ident
ity. As generalizations\nof prime ideals\, the absorbing ideals were first
defined 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
researches have been done to introduce\nvarious extensions of this concep
t.\nIn this talk\, we present some absorbing ideals of this class of ideal
s in\ngeneral aspect with a number of examples\, and also we give many\nch
aracterizations for some particular rings such as quasi-local rings\,\nDed
ekind domains\, fields in terms of absorbing ideals.\n
LOCATION:https://stable.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:20260404T095425Z
UID:AlgAndLogic/80
DESCRIPTION:Title: An Application of Separation in Discrete Time Interval Tempora
l Logic to Branching Time\nby Dimitar Guelev (Institute of Mathematics
and Informatics\, Bulgarian Academy of Sciences) as part of Algebra and L
ogic Seminar\n\n\nAbstract\nIn this talk we make an application of our sep
aration theorem for discrete time Interval Temporal Logic (ITL) to the stu
dy of Interval-based Computation Tree Logic (ICTL*). We prove that the exp
ressibility of the expanding modalities and\, most importantly\, propositi
onal quantification\, carry over from linear time ITL to the branching tim
e system of ICTL*. The relevance of this follows from the fact that point-
based propositionally quantified CTL* (QCTL*) is the established intermedi
ate language for temporal logics of agency as propositional quantification
enables expressing the existence of strategies with given temporal proper
ties. By moving to ITL we move a step further\, using the expressibility o
f propositional quantification in the logic\, which is markedly more expre
ssive than point-based CTL* and facilitates the compositionality of specif
ications.\n
LOCATION:https://stable.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:20260404T095425Z
UID:AlgAndLogic/81
DESCRIPTION:Title: Automorphisms of simple quotients of the Poisson and universal
enveloping algebras of $\\text{sl}_2$\nby Altyngul Naurazbekova (L. N
. Gumilyov Eurasian National University\, Nur-Sultan\, Kazakhstan) as part
of Algebra and Logic Seminar\n\n\nAbstract\nLet $P(\\text{sl}_2(K))$ be t
he Poisson enveloping algebra of the Lie algebra $\\text{sl}_2(K)$ over an
algebraically closed field $K$ of characteristic zero. U. Umirbaev\, V. Z
helyabin proved that the quotient algebras $P(\\text{sl}_2(K))/(C_P – λ
)$\, where $C_P$ is the standard Casimir element of $\\text{sl}_2(K)$ in $
P(\\text{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 desc
ribe generators of the automorphism group of $P(\\text{sl}_2(K))/(C_P –
λ)$ and represent this group as an amalgamated product of its subgroups.
Moreover\, using similar results by J. Dixmier and O. Fleury for the quoti
ent algebras $U(\\text{sl}_2(K))/(C_U – λ)$\, where $C_U$ is the standa
rd Casimir element of $\\text{sl}_2(K)$ in the universal enveloping algebr
a $U(\\text{sl}_2(K))$\, we prove that the automorphism groups of $P(\\tex
t{sl}_2(K))/(C_P – λ)$ and $U(\\text{sl}_2(K))/(C_U – λ)$ are isomor
phic.\n\nThis is a joint work with professor U. Umirbaev.\n
LOCATION:https://stable.researchseminars.org/talk/AlgAndLogic/81/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexander V. Mikhailov (University of Leeds\, UK)
DTSTART:20220415T100000Z
DTEND:20220415T113000Z
DTSTAMP:20260404T095425Z
UID:AlgAndLogic/82
DESCRIPTION:Title: Quantisation of free associative dynamical systems. Bi-quantum
structure of the stationary KdV hierarchy. Non-deformation quantisation o
f the Volterra hierarchy\nby Alexander V. Mikhailov (University of Lee
ds\, UK) as part of Algebra and Logic Seminar\n\n\nAbstract\nTraditional q
uantisation theories start with classical Hamiltonian systems with variabl
es taking values in commutative algebras and then study their non-commutat
ive deformations\, such that the commutators of observables tend to the co
rresponding Poisson brackets as the (Planck) constant of deformation goes
to zero. I am proposing to depart from dynamical systems defined on a free
associative algebra A. In this approach the quantisation problem is reduc
ed to the problem of finding of a two-sided ideal J ⸦ A satisfying two c
onditions: the ideal J has to be invariant with respect to the dynamics of
the system and to define a complete set of commutation relations in the q
uotient algebras A_J = A / J.\n\nTo illustrate this approach I’ll consid
er the quantisation problem for N-th Novikov equations and the correspondi
ng finite KdV hierarchy. I will show that stationary KdV equations and Nov
ikov’s equations admit two compatible quantisations\, i.e. two distinct
commutation relations between the variables\, such that a linear combinati
on of the corresponding commutators is also a valid quantisation rule lead
ing to the Heisenberg form of quantum equations. The picture is very simil
ar to the bi-Hamiltonian structure in the case of classical integrable equ
ations.\n\nAlso\, I am going to discuss quantisation of the Bogoyavlensky
family of integrable systems. In particular\, I will show that odd degree
symmetries of the Volterra chain admit two quantisations\, one of them is
a well-known quantisation of the Volterra chain\, and another one is new a
nd not a deformation quantisation.\n\nThe talk is partially based on:\n\nA
VM\, Quantisation ideals of nonabelian integrable systems\, arXiv:2009.018
38\, 2020 (Published in Russ. Math. Surv. v.75:5\, pp 199-200\, 2020)\n\nV
. M. Buchstaber and AVM\, KdV hierarchies and quantum Novikov’s equation
s\, arXiv:2109.06357v2\, 2021.\n
LOCATION:https://stable.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:20260404T095425Z
UID:AlgAndLogic/83
DESCRIPTION:Title: Images of multilinear polynomials on upper triangular matrices
\nby Thiago Castilho de Mello (Universidade Federal de São Paulo\, Br
azil) as 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 the polynomial $f$ is multilinear\, the famous Lvov-Kaplansky conjec
ture asks whether the image of a multilinear polynomial on a matrix algebr
a 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 t
he associative and nonassociative settings. \n\nIn particular\, we discus
s a joint work with I. Gargate about images of multilinear polynomials on
upper triangular matrices.\n
LOCATION:https://stable.researchseminars.org/talk/AlgAndLogic/83/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Diego García-Lucas (Universidad de Murcia\, Spain)
DTSTART:20220513T100000Z
DTEND:20220513T113000Z
DTSTAMP:20260404T095425Z
UID:AlgAndLogic/84
DESCRIPTION:Title: A counterexample to the modular isomorphism problem\nby Di
ego García-Lucas (Universidad de Murcia\, Spain) as part of Algebra and L
ogic Seminar\n\n\nAbstract\nThe modular isomorphism problem asks whether t
he isomorphism type of the modular group algebra of a $p$-group $G$ over a
field of characteristic $p$ determines the isomorphism type of $G$. It wa
s explicitly mentioned in a survey by Richard Brauer in 1963\, and was the
only classical version of the isomorphism problem for group rings which h
ad resisted a solution\, though it received considerable attention. Severa
l partial positive solutions were obtained imposing very strong conditions
on the group $G$\, for instance the one of being metacyclic.\n\nIn a join
t work with Leo Margolis and Ángel del Río\, we solve the modular isomor
phism problem in the negative by exhibiting a series of pairs of non-isomo
rphic 2-groups with isomorphic modular group algebras over every field of
characteristic 2. These groups are two-generated with cyclic derived subgr
oup. We will also discuss the (lack of) possibility of obtaining\, in a na
ive way\, analogues to the counterexamples for $p > 2$ verifying this cond
ition.\n
LOCATION:https://stable.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:20260404T095425Z
UID:AlgAndLogic/85
DESCRIPTION:Title: Bootstrap percolation: merging operations for polytopes\nb
y Ivailo Hartarsky (Université Paris-Dauhpine\, PSL\, France\, visiting s
cholar at Instituto de Matemática Pura e Aplicada\, Rio de Janeiro\, Braz
il) as part of Algebra and Logic Seminar\n\n\nAbstract\nBootstrap percolat
ion is a group of statistical physics models intensively studied since the
1970s in mathematics\, physics\, computer science\, as well as social sci
ences. They are cellular automata generalising the following paradigmatic
example. Arbitrarily declare some sites of $Z^2$ initially infected. Itera
tively\, at each discrete-time round\, additionally infect each site with
at least 2 infected neighbours.\n\nThe last decade has seen the accomplish
ment of a full classification of all such models into `universality classe
s’\, depending on their behavior when few sites are initially infected.
In this talk\, we will overview universality results\, mostly in two dimen
sions. We will focus particularly on a key aspect of the proof of the lowe
r bounds for the `critical’ class. Thаt is a natural polygon merging pr
ocedure to be discussed in detail.\n\nNo prerequisites (particularly in pr
obability) are required\, as we will exclusively focus on the combinatoria
l side of the subject\, which is completely elementary.\n
LOCATION:https://stable.researchseminars.org/talk/AlgAndLogic/85/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Plamen Koev (San José State University\, USA)
DTSTART:20220610T130000Z
DTEND:20220610T143000Z
DTSTAMP:20260404T095425Z
UID:AlgAndLogic/86
DESCRIPTION:Title: Computing Eigenvectors of Symmetric Tridiagonals with the Corr
ect Number of Sign Changes\nby Plamen Koev (San José State University
\, USA) as part of Algebra and Logic Seminar\n\n\nAbstract\nThe symmetric
tridiagonal eigenvector problem has been a central research topic in numer
ical linear algebra since its inception. Of the myriad of algorithms today
\, none is provably optimal and accurate at the same time. “Optimal” m
eans\, a subset of $k$ eigenvectors is computed in O($kn$) time. “Accura
te” means that the computes eigenvectors are orthogonal and satisfy the
typical relative gap error bound.\n\nIn this talk\, we focus our attention
on a neglected oscillating property of the eigenvectors: the $i$-th eigen
vector has exactly $i-1$ changes of sign in its entries. Long considered i
rrelevant\, because the tiny entries of the eigenvectors don't seem to be
of any practical importance\, this property may hold the key to accurate e
igenvectors computed in optimal time!\n\nSuch an approach is not without p
recedent: the preservation of the mathematical properties of the computed
objects has lead to major progress in various computations.\n\nWe present
a new algorithm that computes individual eigenvectors in optimal\, O($n$)
time\, each guaranteed to have the correct number of sign changes\, and sa
tisfying the conventional relative gap error bound. The numerical experime
nts in this work in progress look promising in that the computed eigenvect
ors seem to also be orthogonal.\n
LOCATION:https://stable.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:20260404T095425Z
UID:AlgAndLogic/87
DESCRIPTION:Title: Dependent-Type Theory of Situated Information with Context Ass
essments\nby Roussanka Loukanova (Institute of Mathematics and Informa
tics\, Bulgarian Academy of Sciences) as part of Algebra and Logic Seminar
\n\n\nAbstract\nI shall introduce an enriched formal language of informati
on that establishes propositions dependent on situations and types. The ty
pes can be basic or complex. Complex propositional types are defined recur
sively. The language supports structured data of situated information\, wh
ich can be partial\, parametric\, and underspecified. Information can be a
ssociated with quantitative evaluations depending on situations. The forma
l terms can integrate propositional types of situated information with sta
tistical and other quantitative evaluations. Structured content integrated
with quantitative data facilitates development of new techniques for amal
gamating logic representation of situated\, propositional content with num
erical data. Numerical data can be provided by techniques from mathematica
l statistics and probability. Furthermore\, information can be dynamically
updated by integration with techniques of machine learning.\n
LOCATION:https://stable.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:20260404T095425Z
UID:AlgAndLogic/88
DESCRIPTION:Title: On the parity of the coefficients of minimal polynomial of Klo
osterman sums over F_p\nby Lyubomir Borisov (Institute of Mathematics
and Informatics\, Bulgarian Academy of Sciences) as part of Algebra and Lo
gic Seminar\n\n\nAbstract\nKloosterman sums over finite fields play an imp
ortant role in “Algebraic Coding Theory” and “Cryptography”. E.g.\
, they are related to some families of algebraic codes (Melas\, Kloosterma
n) and (hyper-)bent functions. Particularly\, the divisibility properties
of some quantities connected with the Kloosterman sums\, e.g.\, of minimal
polynomial coefficients and power moments\, were also investigated (see\,
e.g.\, [1]\; [2]).\nIn this talk I shall present some results about the d
ivisibility by 2 of the coefficients of minimal polynomials of the Klooste
rman sums.\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\,
“Congruences for Sums of Powers of Kloosterman Sums”\, International J
ournal of Number Theory\, vol. 3(1): 105-117\, 2007.\n
LOCATION:https://stable.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:20260404T095425Z
UID:AlgAndLogic/89
DESCRIPTION:Title: Modal Descriptive Complexity\nby Petar Iliev (Institute of
Philosophy and Sociology and Institute of Mathematics and Informatics\, B
ulgarian Academy of Sciences) as part of Algebra and Logic Seminar\n\n\nAb
stract\nThe study of the descriptive complexity of a class of structures $
S$ relative to a class of formulae $F$ from a logic $L$ revolves around th
e question: what can we say about the definability of $S$ with formulae fr
om $F$? For example\, we might want to know whether there is a formula fro
m $F$ defining $S$ or\, if not\, whether there is a countably infinite seq
uence of F-formulae such that each formula from the sequence defines a sub
set of $S$ and the union of all these subsets is the whole $S$. If we have
the former situation\, it is natural to ask about the minimal number of v
ariables in any $F$-formula defining $S$\, or its minimal length\, or the
minimal number of operators like quantifiers\, disjunctions and conjunctio
ns\, and the minimal depth of their nesting. In the latter situation\, we
might want to know how (some of) these measures scale with the index of in
dividual formulae.\n\nIn my talk\, I am going to survey several recent res
ults\, in some of which I have been involved\, coming from the area of the
descriptive complexity of classes of Kripke frames (directed graphs) and
classes of Kripke models (edge-and vertex-coloured directed graphs) relati
ve to some well-known modal logics.\n
LOCATION:https://stable.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:20260404T095425Z
UID:AlgAndLogic/90
DESCRIPTION:Title: Examples of non-reduced components of the Hilbert Scheme of sm
ooth projective curves using ruled surfaces\nby Hristo Iliev (American
University in Bulgaria and Institute of Mathematics and Informatics\, Bul
garian Academy of Sciences) as part of Algebra and Logic Seminar\n\nLectur
e held in Room 578 of IMI - BAS.\n\nAbstract\nLet $I_{d\, g\, r}$ be the u
nion of irreducible components of the Hilbert scheme whose general points
represent smooth irreducible non-degenerate curves of degree $d$ and genus
$g$ in $P^r$. Using a family of curves found on ruled surfaces over smoot
h curves 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 $D
′$ such that $\\text{dim } T[X′]D′ = \\text{dim }D′ + 1$ for a gen
eral point $[X′] ∈ D′$.\n
LOCATION:https://stable.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:20260404T095425Z
UID:AlgAndLogic/91
DESCRIPTION:Title: Timing delays in cyber-physical systems\nby Naijun Zhan (I
nstitute of Software\, Chinese Academy of Sciences ISCAS\, China) as part
of Algebra and Logic Seminar\n\n\nAbstract\nWith the rapid development of
feedback control\, sensor techniques and computer control\, time delay has
become an essential feature of cyber-physical systems (CPSs)\, underlying
both the continuous evolution of physical plants and the discrete transit
ion of computer programs\, which may well annihilate the stability/safety
certificate and control performance of CPSs. In the safety-critical contex
t\, automatic verification and synthesis methods addressing time-delay in
CPSs should therefore abound. However\, surprisingly\, they do not\, altho
ugh time-delay has been extensively studied in the literature of mathemati
cs and control theory from a qualitative perspective. In this talk\, we wi
ll report our recent efforts to tackle these issues\, including bounded an
d unbounded verification of delay differential equations and controller sy
nthesis for time-delayed systems\, and discuss remaining challenges and fu
ture trends.\n
LOCATION:https://stable.researchseminars.org/talk/AlgAndLogic/91/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alaa Abouhalaka (Çukurova University\, Adana\, Turkey)
DTSTART:20220916T110000Z
DTEND:20220916T123000Z
DTSTAMP:20260404T095425Z
UID:AlgAndLogic/92
DESCRIPTION:Title: Almost Prime Ideal and Almost Prime Radical\nby Alaa Abouh
alaka (Çukurova University\, Adana\, Turkey) as part of Algebra and Logic
Seminar\n\n\nAbstract\nIn this talk\, we introduce the concept of almost
prime (right) ideals in noncommutative rings and provide some equivalent d
efinitions 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
\, Unique factorization and birth of almost primes\, Comm. Algebra\, 33(1)
\, 43-49\, (2005).\n\n[2] W.D. Blair\, H. Tsutsui\, Fully prime rings\, Co
mm. Algebra\, 22(13)\, 5389-5400\, (1994).\n
LOCATION:https://stable.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:20260404T095425Z
UID:AlgAndLogic/93
DESCRIPTION:Title: Families of triple coverings of algebraic curves\nby Hrist
o Iliev (American University in Bulgaria and Institute of Mathematics and
Informatics of BAS) as part of Algebra and Logic Seminar\n\n\nAbstract\nTh
e talk is a continuation of my previous talk "Examples of non-reduced comp
onents of the Hilbert scheme of smooth projective curves using ruled surfa
ces" that I gave on August 19\, 2022. In the present talk we consider curv
es that are triple covers of smooth projective curves of genus γ ≥ 0. W
e obtain families of curves on smooth surface scrolls which\, under suitab
le numerical assumptions\, yield components of the Hilbert scheme of curve
s.\n
LOCATION:https://stable.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:20260404T095425Z
UID:AlgAndLogic/94
DESCRIPTION:Title: Ranks and Presentations for Order-Preserving Transformations w
ith One Fixed Point\nby Jörg Koppitz (Institute of Mathematics and In
formatics\, Bulgarian Academy of Sciences) as part of Algebra and Logic Se
minar\n\n\nAbstract\nWe consider the semigroup (no monoid) of all order-pr
eserving 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 particu
lar\, the semigroup $O_{n\,1}$ (i.e. $p = 1$) is already well studied\, si
nce it is the maximal nilpotent subsemigroup of the Catalan monoid. But th
e semigroup $O_{n\,p}$ is still not well studied for $p > 1$ except of $p
= n$ since $O_{n\,n}$ is isomorphic to $O_{n\,1}$. We determine the rank o
f $O_{n\,p}$ (it is $C_{p-1}C_{n-p} – C_{p-2}C_{n-p-1}$) and give a pres
entation 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 f
or $n = 4$.\n\nThis is a joint work with S. Worawiset.\n
LOCATION:https://stable.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:20260404T095425Z
UID:AlgAndLogic/95
DESCRIPTION:Title: Gabbay Separation for the Duration Calculus\nby Dimitar Gu
elev (Institute of Mathematics and Informatics\, Bulgarian Academy of Scie
nces) as part of Algebra and Logic Seminar\n\n\nAbstract\nGabbay's separat
ion theorem about linear temporal logic (LTL) with past has proved to be o
ne of the most useful theoretical results in temporal logic. Is expressive
power ultimately affected\, if past constructs are not allowed in the sco
pe of future ones\, or vice versa? Separation implies that it does not\, a
nd also provides a technically convenient normal form for temporal conditi
ons.\n\nInterval Temporal Logic (ITL) and the Duration Calculus (DC) are i
nterval-based logics. Unlike LTL\, they are based on modalities which allo
w reference to subintervals of the reference intervals only. Adding the ne
ighbourhood modalities\, which are written $\\lt A\\gt$ and $\\lt A-1\\gt$
in the notation stemming from Allen's system of interval relations\, enab
les reference outside the reference interval and this way makes temporal s
eparation relevant. In this talk I propose a DC analogue of a separation t
heorem for discrete time ITL which I established in a joint work with Ben
Moszkowski.\n\nBoth theorems are analogous to Gabbay's pioneering result a
nd can be spelled out in similar terms\, but the technical differences are
significant. I take the opportunity to not repeat my previous talk on sep
aration for ITL and instead discuss some aspects of the proofs for both th
e ITL and the DC theorems. Interestingly\, these theorems admit proofs tha
t are based on syntactical transformations of the formulas in the respecti
ve logics\, and are therefore compositional and very intuitive. I will foc
us on the common and the distinct features of the proofs\, and on some sid
e corollaries.\n
LOCATION:https://stable.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:20260404T095425Z
UID:AlgAndLogic/96
DESCRIPTION:Title: Logic Operators and Quantifiers in Type-Theory of Algorithms\nby Roussanka Loukanova (Institute of Mathematics and Informatics\, Bul
garian Academy of Sciences) as part of Algebra and Logic Seminar\n\n\nAbst
ract\nI shall introduce an extension of Moschovakis Type-Theory of Algorit
hms (LR) and its reduction calculus\, by adding logic operators and quanti
fiers. The LR has two kinds of terms of formulae\, for designating state-i
ndependent and state-dependent propositions and predications. The logic op
erators include conjunction\, disjunction\, implication\, and negation. I
extend the formal language of LR by state-dependent quantifiers\, for enha
ncing the standard quantifiers of predicate logic. I provide an extended r
eduction calculus of the Type-Theory of Acyclic Algorithms\, for reduction
s of LR terms to their canonical forms.\n
LOCATION:https://stable.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:20260404T095425Z
UID:AlgAndLogic/97
DESCRIPTION:Title: Derivations of upper triangular matrix rings vs Derivations of
upper triangular matrix semirings\nby Dimitrinka Vladeva (Institute o
f Mathematics and Informatics\, Bulgarian Academy of Sciences) as part of
Algebra and Logic Seminar\n\n\nAbstract\nThe motivation for this talk is t
he problem how to represent a derivation of a matrix ring and of an additi
vely idempotent matrix semiring as a sum of well-known derivations.\n\nThe
results of two of my articles\, published in 2022\, will be compared and
we will draw conclusions about the advantages and disadvantages of these r
esults.\n\nWe begin by considering the nature of derivations of triangular
matrices over an additively idempotent semiring $R$ generated by left and
right semicentral idempotents. Then we construct a semiring $D$ of these
derivations and find a basis of $D$\, considered as an $R$-semimodule. The
main result of the first article states that an arbitrary derivation of $
\\text{UTM}_n(R)$ (the semiring of upper triangular matrices over an addit
ively idempotent semiring $R$) is a linear combination of a derivations fr
om the basis of $R$-semimodule $D$. When $R$ is an associative ring with i
dentity and $\\text{UTM}_n(R)$ is the ring of upper triangular $n \\times
n$ matrices over $R$\, we propose a basis of an additive group $D$ of deri
vations 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 di
agonal 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 ma
trix $A$.\n
LOCATION:https://stable.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:20260404T095425Z
UID:AlgAndLogic/98
DESCRIPTION:Title: AdS/CFT Correspondence\, Metropolis-Hastings algorithm and Gen
erative Adversarial Networks\nby Veselin Filev (Institute of Mathemati
cs 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
construction of a backreacted D0/D4 background. I will discuss the releva
nce 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 revi
ew the Metropolis-Hastings algorithm and report on possible applications o
f the Generative Adversarial Networks (GANs) in the simulation of computat
ionally expensive matrix models.\n
LOCATION:https://stable.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:20260404T095425Z
UID:AlgAndLogic/99
DESCRIPTION:Title: Hitchin base: Seiberg-Witten differentials and their derivativ
es\nby Peter Dalakov (American University in Bulgaria and Institute of
Mathematics and Informatics\, Bul. Acad. Sci.) as part of Algebra and Log
ic Seminar\n\n\nAbstract\nWe consider a variation of Hodge structures of w
eight 1 and a Seiberg-Witten differential on the Hitchin base and discuss
an explicit formula its Gauss-Manin derivative.\n
LOCATION:https://stable.researchseminars.org/talk/AlgAndLogic/99/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yacine Barhoumi-Andréani (Ruhr-Universität Bochum\, Germany)
DTSTART:20230210T110000Z
DTEND:20230210T123000Z
DTSTAMP:20260404T095425Z
UID:AlgAndLogic/100
DESCRIPTION:Title: A New Approach to the Characteristic Polynomial of a Random U
nitary Matrix\nby Yacine Barhoumi-Andréani (Ruhr-Universität Bochum\
, Germany) as part of Algebra and Logic Seminar\n\n\nAbstract\nThe charact
eristic polynomial of a random (Haar-distributed) unitary matrix is consid
ered as an interesting toy model for the probabilistic study of the Rieman
n Zeta function. We will recall the history of the topic starting with the
Montgommery-Dyson correspondance\, the Keating-Snaith moments conjecture
and some recent developments on other functionals. We will then give a con
ceptual comparison of some of the techniques used in the field and a zoo o
f results one can achieve\, with a particular focus on a recent technique
that allows to rederive all the results in a unified way using symmetric f
unction theory and local Central Limit Theorems.\n
LOCATION:https://stable.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:20260404T095425Z
UID:AlgAndLogic/101
DESCRIPTION:Title: Invariant theory for reductive subgroups of reductive groups<
/a>\nby Valdemar Tsanov (Institute of Mathematics and Informatics\, Bulgar
ian Academy of Sciences) as part of Algebra and Logic Seminar\n\n\nAbstrac
t\nLet $H \\subset G$ be an embedding of connected complex reductive linea
r algebraic groups. A classical question with several important interpreta
tions is: which irreducible $G$-modules contain nonzero $H$-invariant vect
ors? An approach based on the Geometric Invariant Theory of Hilbert-Mumfor
d was developed in works of Heckman\, Berenstein-Sjamaar\, Belkale-Kumar a
nd Ressayre\, culminating in a description of the generalized Littlewood-R
ichadson cone - the convex hull of set of the highest weights of the $G$-m
odules containing $H$-invariants. The discrepancy between the convex hull
and the actual set of weights presents the so-called saturation problem\,
famously solved by Knutson and Tao for diagonal embeddings of $GL_n$\, and
widely open in general. Ressayre's description of the cone demands extens
ive calculations even in relatively tame cases\, which makes applications
difficult. Further development of the structure theory seems desirable.\n\
nIn this talk\, based on joint works with Seppänen and Staneva\, I will p
resent some structural properties of generalized Littlewood-Richardson con
es\, allowing to partition the subgroups of a given $G$ into types accordi
ng to the properties of the cones. We derive a new numerical invariant of
reductive groups\, and use it to show that for “generic” subgroups the
cone fills the entire Weyl chamber of $G$. This greatly reduces the diffi
culty of the saturation problem and allows it to be solved for some new ca
ses\, e.g. $SL_2$-subgroups of classical groups.\n
LOCATION:https://stable.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:20260404T095425Z
UID:AlgAndLogic/102
DESCRIPTION:Title: Real Hamiltonian forms of affine Toda field theories: spectra
l aspects\nby Vladimir Gerdjikov (Institute of Mathematics and Informa
tics\, Bulgarian Academy of Sciences) as part of Algebra and Logic Seminar
\n\n\nAbstract\n(Joint work with G. G. Grahovski and A. A. Stefanov)\n\nTh
e talk is devoted to real Hamiltonian forms of 2-dimensional Toda field th
eories related to exceptional simple Lie algebras\, and to the spectral th
eory of the associated Lax operators. Real Hamiltonian forms are a special
type of reductions of Hamiltonian systems\, similar to real forms of semi
simple Lie algebras. The real Hamiltonian forms of affine Toda field theor
ies related to exceptional complex untwisted affine Kac - Moody algebras a
re studied. Along with the associated Lax representations\, we also formul
ate the relevant Riemann - Hilbert problems and derive the minimal sets of
scattering data that uniquely determine the scattering matrices and the p
otentials of the Lax operators.\n\nReferences \n\n[1] V. S. Gerdjikov\, G.
G. Grahovski\, A. A. Stefanov. Real Hamiltonian forms of affine Toda fiel
d theories: spectral aspects. Theoretical and Mathematical Physics\, 212(2
): 1053-1072 (2022)\; arXiv:2205.03844v1 [nlin.SI]\n
LOCATION:https://stable.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:20260404T095425Z
UID:AlgAndLogic/103
DESCRIPTION:Title: Exact values of exponential Følner functions and the Coulhon
and Saloff-Coste inequality\nby Bogdan Stankov (Institut Camille Jord
an\, Université Claude Bernard Lyon 1\, France) as part of Algebra and Lo
gic Seminar\n\n\nAbstract\nFor infinite groups\, the Følner criterion sta
tes that a group is amenable if and only if the isoperimetric constant of
its Cayley graph is 0. In that case\, a more precise description of its is
operimetric profile is given by the Følner function. It depends on the ch
oice of generating set\, but different functions on the same group are asy
mptotically equivalent. Multiple results have been obtained on Følner fun
ctions\, but only up to asymptotic equivalence class. In this talk\, we wi
ll consider fixed generating sets and obtain (to our knowledge) the first
results (outside of virtually nilpotent groups) on the exact values of Fø
lner functions – on wreath products ℤ ≀ D for a finite group D. We w
ill consider possible applications. In particular\, we’re interested in
the connections with the Coulhon and Saloff-Coste inequality. That inequal
ity gives a lower bound on the Følner function. In joint work with Christ
ophe Pittet\, for groups of exponential growth we obtain a description of
the optimal multiplicative constant in the Coulhon and Saloff-Coste inequa
lity. We show that the optimal value over all groups of this constant is b
etween 1 and 2.\n
LOCATION:https://stable.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:20260404T095425Z
UID:AlgAndLogic/104
DESCRIPTION:Title: Algebraic Properties of Transformation Semigroups\nby Jö
rg Koppitz (Institute of Mathematics and Informatics\, Bulgarian Academy o
f Sciences) as part of Algebra and Logic Seminar\n\n\nAbstract\nEach semig
roup is isomorphic to a semigroup of transformations on a suitable set (Ca
yley Theorem for semigroups). If we know generating sets of minimal size (
rank) of a finitely generating semigroup then we have important informatio
n about the algebraic structure of the semigroup itself. For not finitely
generated semigroups\, we consider relative generating sets of minimal siz
e modulo a given subset of the semigroup (relative rank). We determine the
(relative) rank of several semigroups of transformations. These semigroup
s were already considered by other authors.\n\nBy the study of congruences
on a semigroup\, we obtain further important information about the struct
ure of a given semigroup\, which are related to its ideals. We discuss the
congruence lattice of an infinite transformation semigroup as well of the
maximal nilpotent subsemigroups of the Catalan Monoid.\n
LOCATION:https://stable.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:20260404T095425Z
UID:AlgAndLogic/105
DESCRIPTION:Title: Old and new aspects of the Poincaré-Birkhoff-Witt theorem\nby Vladimir Dotsenko (Institute for Advanced Mathematical Research (IRM
A)\, University of Strasbourg and CNRS\, France) as part of Algebra and Lo
gic Seminar\n\n\nAbstract\nThe Poincaré-Birkhoff-Witt theorem on universa
l enveloping algebras of Lie algebras is a fundamental result in many area
s of mathematics: from differential geometry and representation theory to
homological algebra and deformation quantization. I shall give a short ove
rview of that result and some of its proofs that emerged in about 120 year
s since Poincaré published a paper about it\, and outline a new proof whi
ch perhaps captures its category-theoretic essence in the best way possibl
e. The talk is based on a joint work with Pedro Tamaroff.\n
LOCATION:https://stable.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:20260404T095425Z
UID:AlgAndLogic/106
DESCRIPTION:Title: Polynomial identities in Novikov algebras\nby Nurlan Isma
ilov (Astana IT University and Suleyman Demirel University\, Kaskelen\, Ka
zakhstan) as part of Algebra and Logic Seminar\n\n\nAbstract\nThe talk is
devoted to Novikov algebras satisfying nontrivial identities. We show that
a Novikov algebra over a field of zero characteristic that satisfies a no
ntrivial identity satisfies some unexpected “universal” identities\, i
n particular\, right associator nilpotence\, and right nilpotence of the c
ommutator ideal. This\, in particular\, implies that a Novikov algebra ove
r a field of zero characteristic satisfies a nontrivial identity if and on
ly if it is Lie-solvable. We also establish that any system of identities
of Novikov algebras over a field of zero characteristic follows from finit
ely many of them\, and that the same holds over any field for multilinear
Novikov identities. Some analogous simpler statements are also proved for
commutative differential algebras.\n\nJoint work with V. Dotsenko and U. U
mirbaev\n
LOCATION:https://stable.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:20260404T095425Z
UID:AlgAndLogic/107
DESCRIPTION:Title: Reset Controller Synthesis\nby Naijun Zhan (Institute of
Software Chinese Academy of Sciences (ISCAS)) as part of Algebra and Logic
Seminar\n\n\nAbstract\nController synthesis provides a Correct-by-constru
ction mechanism to guarantee the correctness and reliability of hybrid sys
tems (HS) by design. Depending on the types of controls\, controllers can
be classified into reset controllers\, feedback controllers\, and switchin
g logic controllers. Reset controllers steer the behaviour of a HS to atta
in system objective through restricting its initial set and redefining the
reset map associated with discrete jumps\, which is less explored in the
literature\, although it is of theoretical and practical significance. In
this talk\, I will summarize our recent work on the reset controller synth
esis for HS. The basic idea is to reduce the problem of guaranteeing safet
y and liveness properties to differential invariant generation and general
ized reach-avoid problems. For polynomial hybrid systems\, those problems
can be solved by further reduced to convex optimizations.\n\nMoreover\, fo
r reality\, we discuss this issue in the context of time-delay\, as time d
elay is inevitable in practice. So\, we investigate the reset controller s
ynthesis problem for delay hybrid systems (dHS).\n
LOCATION:https://stable.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:20260404T095425Z
UID:AlgAndLogic/108
DESCRIPTION:Title: Emmy Noether’s Theorem on the Finite Generation of the Alge
bra of Invariants\nby Marin Genov (Institute of Mathematics and Inform
atics\, Bulgarian Academy of Sciences) as part of Algebra and Logic Semina
r\n\n\nAbstract\nI will introduce Emmy Noether’s theorem on the finite g
eneration of invariants and give two proofs of it. As an example\, I will
also calculate the algebra of invariants of the dihedral group of order $2
n$ acting on $C[x\,y]$.\n
LOCATION:https://stable.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:20260404T095425Z
UID:AlgAndLogic/109
DESCRIPTION:Title: Prime numbers and random walks in a square grid\nby Alber
to Fraile (Czech Technical University in Prague\, Czech Republic) as part
of Algebra and Logic Seminar\n\nLecture held in Room 578 of IMI - BAS\, So
fia\, Bulgaria.\n\nAbstract\nOne can argue that prime numbers present perp
lexing features\, in a hybrid of local unpredictability and global regular
behavior. It is this interplay between randomness and regularity that mot
ivated searches for both local and global patterns that could potentially
become signatures for certain underlying fundamental mathematical properti
es.In recent years\, computer simulations are playing a fundamental role i
n unveiling some of the most intriguing features of prime numbers. In this
work\, we define an algorithm for a deterministic walk through a two-dime
nsional 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
sequence\, the resulting structure – both in 2d and 3d – created by th
e algorithm presents remarkable properties and regularities in its pattern
that we proceed to analyze in detail [1].\n\n[1] A. Fraile\, O. Kinouchi\
, P. Dwivedi\, R. Martínez\, T. E. Raptis\, D. Fernández\, Prime numbers
and random walks in a square grid\, Phys. Rev. E 104 (5)\, 054114-054120
(2021).\n\nJoint work with Osame Kinouchi\, Prashant Dwivedi\, Roberto Mar
tínez\, Theophanes E. Raptis\, and Daniel Fernández.\n
LOCATION:https://stable.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:20260404T095425Z
UID:AlgAndLogic/110
DESCRIPTION:Title: A Reduction of Temporary Coalitions in Infinite Multiplayer G
ames\nby Dimitar Guelev (Institute of Mathematics and Informatics\, Bu
lgarian Academy of Sciences) as part of Algebra and Logic Seminar\n\n\nAbs
tract\nWe propose a transformation of Concurrent Game Models which enables
the reduction of infinite multiplayer games where players can form tempor
ary coalitions to games with no coalitions by extending moves to include t
he negotiation steps that lead to the formation of coalitions. We adopt co
nditional promises as the building blocks of negotiation. Temporary coalit
ions and their agendas arise as the logical consequences of mutual promise
s. The transformation enables the use of established solution concepts abo
ut games with no coalitions for the analysis of games with temporary coali
tions.\n
LOCATION:https://stable.researchseminars.org/talk/AlgAndLogic/110/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mishel Carelli (Technion – Israel Institute of Technology\, Isra
el)
DTSTART:20231110T110000Z
DTEND:20231110T123000Z
DTSTAMP:20260404T095425Z
UID:AlgAndLogic/111
DESCRIPTION:Title: Transfinite version of the Mittag-Leffler condition for the v
anishing of the derived limit\nby Mishel Carelli (Technion – Israel
Institute of Technology\, Israel) as part of Algebra and Logic Seminar\n\n
\nAbstract\nWe give a necessary and sufficient condition for an inverse se
quence $S_0 ← S_1 ← \\dots$ indexed by natural numbers to have $\\li
m^1 S = 0$. This condition can be treated as a transfinite version of the
Mittag-Leffler condition. We consider inverse sequences in the category of
abelian groups. We also show that the class of inverse sequences S such t
hat $\\lim S = \\lim^1S = 0$ is the least class of inverse sequences cont
aining the trivial inverse sequence and closed with respect to small limit
s and a certain type of extensions.\n
LOCATION:https://stable.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:20260404T095425Z
UID:AlgAndLogic/112
DESCRIPTION:Title: Noncommutative invariants of dihedral groups\nby Boyan Ko
stadinov (Institute of Mathematics and Informatics\, Bulgarian Academy of
Sciences) as part of Algebra and Logic Seminar\n\n\nAbstract\nWe consider
the 2-generated free metabelian associative and Lie algebras over the comp
lex field and the invariants of the dihedral groups of finite order acting
on these algebras. In the associative case we find a finite set of genera
tors of the algebra of invariants. In the Lie case\, when the algebra of i
nvariants is not finitely generated\, we give a minimal system of generato
rs of the invariants in the commutator ideal as a module of the algebra of
the invariants in the polynomial algebra in two variables. In both associ
ative and Lie cases we compute the Hilbert series of the algebras of invar
iants.\n\nThe results are obtained jointly with Vesselin Drensky.\n
LOCATION:https://stable.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:20260404T095425Z
UID:AlgAndLogic/113
DESCRIPTION:Title: Catalan numbers and additively idempotent semirings\nby D
imitrinka Vladeva (Institute of Mathematics and Informatics\, Bulgarian Ac
ademy of Sciences) as part of Algebra and Logic Seminar\n\n\nAbstract\nThe
purpose of the present talk is to provide new applications of remarkable
Catalan numbers. In Richard Stanley’s book Enumerative Combinatorics\, V
olume II (Cambridge University Press) there are many combinatorial objects
that are counted by the Catalan numbers as well as applications in graph
theory\, Young diagrams\, lattice theory\, real matrices\, real polynomial
s and so on. We show applications of Catalan numbers in some additively id
empotent semirings which appeared in my results in 5 papers published betw
een 2011 and 2023.\nThe set of nilpotent endomorphisms in the endomorphism
semiring of a finite chain is a semiring of order $(n - 1)$-th Catalan nu
mber and is an ideal in another semiring of order $n$-th Catalan number. T
he semiring 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 C
atalan numbers we describe the roots of arbitrary idempotent of the endomo
rphism semiring of a finite chain.\nIn an additively idempotent semiring w
hich is a generalization of the endomorphism semiring of a finite chain co
nsidered as a simplex we prove that the subsimplex of nilpotent elements i
s of order $(n - 1)$-th Catalan number and it is closed under derivations
which are projections of the simplex to some simplices.\nIn the last paper
\, 2023\, we prove that an additively idempotent semiring which is an $S0$
-semialgebra\, where $S0$ is a commutative additively idempotent semiring\
, and with a finite basis of a special type is isomorphic to a matrix semi
ring. As a consequence we obtain two different semirings of upper triangul
ar matrices over the Boolean semiring\, which are of order $(n + 1)$-th Ca
talan number.\n
LOCATION:https://stable.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:20260404T095425Z
UID:AlgAndLogic/114
DESCRIPTION:Title: Semantics of Propositional Attitudes in Type-Theory of Algori
thms\nby Roussanka Loukanova (Institute of Mathematics and Informatics
\, Bulgarian Academy of Sciences) as part of Algebra and Logic Seminar\n\n
\nAbstract\nNatural language (NL) is notorious for various kinds of ambigu
ities. Among the most difficult ones\, for computational handling of NL\
, are expressions with multiple occurrences of quantifiers\, which contrib
ute to quantifier scope ambiguities. Far more difficult for computational
linguistics are NL expressions having occurrences of so-called attitude co
mponents designating knowledge\, believes\, statements\, and similar seman
tic information.\n\nOften\, the syntactic complement of an attitude lexeme
is a sentential expression. The sentential complement may have subexpress
ions that designate semantic information belonging to varying scopes. De
pending on context\, some components can be semantic parts of the attitudi
nal information\, which is in the scope of the propositional attitude\, or
external to it.\n\nThe first formal representation of NL attitudes was by
Montague\, 1973\, along with the quantifier scope ambiguities\, by the no
tions of extension and intension\, and using extra-syntactic disambiguatio
n of NL expressions. That approach\, while unsatisfactory in important asp
ects\, was adopted and adapted by some variants of Montague grammars\, for
specific purposes. The problem has been largely open\, due to its purely
semantic nature and computational difficulties\, without direct syntactic
appearance.\n\nThe semantic phenomena of attitudes include statements in n
atural language\, including in the domains of mathematical texts and proof
s.\n\nIn this presentation of a recent paper\, I extend the type-theory of
algorithms\, to cover algorithmic semantics of some of the major attitude
expressions and their semantic underspecification. I provide reduction ca
lculus for deriving semantic specifications in contexts.\n
LOCATION:https://stable.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:20260404T095425Z
UID:AlgAndLogic/115
DESCRIPTION:Title: Characterization of Ideals of Q-algebras Related to its G-par
t\nby Jörg Koppitz (Institute of Mathematics and Informatics\, Bulgar
ian Academy of Sciences) as part of Algebra and Logic Seminar\n\n\nAbstrac
t\nIn this presentation\, we study the $G$-part of $Q$-algebras $X$\, i.e.
the set $G(X)=\\{x\\in X:0x=x\\}$. We show that $G(X)$ is an abelian grou
p\, whenever $G(X)$ is an ideal and characterize all $Q$-algebras $X$ such
that $G(X)$ is an ideal of $X$. Moreover\, we show that\, up to isomorphi
sm\, there is only one $Q$-algebra $X$ with $G(X)=X$\, which is only possi
ble if $|X|=2^{k}$ ($k\\in \\mathbb{N}$).\n
LOCATION:https://stable.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:20260404T095425Z
UID:AlgAndLogic/116
DESCRIPTION:Title: Annual Scientific Session of the Algebra and Logic Department
\nby Annual Scientific Session (Institute of Mathematics and Informati
cs\, Bulgarian Academy of Sciences) as part of Algebra and Logic Seminar\n
\nLecture held in Room 578 of IMI - BAS\, Sofia\, Bulgaria.\n\nAbstract\nP
ROGRAMME\n\n9:55 – 10:00 Opening\n\n10:00 – 10:30 Ivan Chipchakov: Dio
phantine and cohomological dimensions of fields\n\n10:30 – 10:50 Elitza
Hristova: Some new results on the GL(n)-module structure of relatively fr
ee algebras and applications to noncommutative invariant theory\n\n10:50
– 11:00 Break\n\n11:00 – 11:30 Hristo Iliev: On the Tschirnhausen modu
le of multiple coverings and some applications\n\n11:30 – 11:50 Veselin
Filev: A Sampling Approach for Tackling Large-Scale Linear Optimization P
roblems\n\n11:50 – 11:55 Break\n\n11:55 – 12:15 Marin Genov: Some Aspe
cts of Holomorphy 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 Iliev: There are no Sahlqvist formulae containing at most a logarit
hmic number of variables that define the n-density or the n-width of Kripk
e frames\n\n13:50 – 14:10 Tatyana Ivanova: The fragment of elementary pl
ane Euclidean geometry based on perpendicularity alone - a complete axioma
tization\n\n14:10 – 14:25 Vilislav Boutchaktchiev: Methods for estimatio
n of the Inferred Loss Given Default of credit portfolios\n
LOCATION:https://stable.researchseminars.org/talk/AlgAndLogic/116/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bruce Westbury (retired from University of Warwick\, UK)
DTSTART:20240108T110000Z
DTEND:20240108T123000Z
DTSTAMP:20260404T095425Z
UID:AlgAndLogic/117
DESCRIPTION:Title: On the exceptional series and its siblings\nby Bruce West
bury (retired from University of Warwick\, UK) as part of Algebra and Logi
c Seminar\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 in
troduce a parameter so that the exceptional series is a set of eight point
s on a line. Then the values of the quadratic Casimir are linear functions
of this parameter and the dimensions are rational functions of this param
eter. \n\nThe exceptional series is one row in the Freudenthal magic squar
e and all the preferred representations for each row also have analogous c
ommon structure. These series are lines. I will give a broad context for t
his common structure. \n\nThere is a plane which contains the first and fo
urth rows of the magic square and a three-dimensional space which contains
the Vogel plane.\n
LOCATION:https://stable.researchseminars.org/talk/AlgAndLogic/117/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yuri Bahturin (Memorial University of Newfoundland\, Canada)
DTSTART:20240118T110000Z
DTEND:20240118T123000Z
DTSTAMP:20260404T095425Z
UID:AlgAndLogic/118
DESCRIPTION:Title: Nilpotent algebras\, groups and beyond\nby Yuri Bahturin
(Memorial University of Newfoundland\, Canada) as part of Algebra and Logi
c Seminar\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
associative algebras or by the Baker-Campbell-Hausdorff formulas in the th
e case of Lie algebras or their generalizations. In the particular case of
Malcev's correspondence\, we obtain some new results about groups using L
ie algebras and vice versa.\n\nJoint work with Alexander Olshanskii.\n
LOCATION:https://stable.researchseminars.org/talk/AlgAndLogic/118/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Niall Hir (University of Glasgow\, UK)
DTSTART:20240223T110000Z
DTEND:20240223T123000Z
DTSTAMP:20260404T095425Z
UID:AlgAndLogic/119
DESCRIPTION:Title: Invariant subalgebras of the rational Cherednik algebra\n
by Niall Hir (University of Glasgow\, UK) as part of Algebra and Logic Sem
inar\n\n\nAbstract\nThe rational Cherednik algebra is a degeneration of th
e double affine Hecke algebra and an object of interest to many representa
tion theorists\, it also has strong connections to integrable systems. In
my talk I will discuss two subalgebras that arise from considering the inv
ariants of the action of reductive subgroups of the special linear group.
In particular we will examine the centres of these invariant subalgebras a
nd compare with the algebra of invariants of the centre of the entire rati
onal Cherednik algebra under the same groups. These subalgebras arise natu
rally in the study of rational Cherednik algebras\, one of which is the Du
nkl angular momentum algebra and the other is generated by all degree zero
elements.\n
LOCATION:https://stable.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:20260404T095425Z
UID:AlgAndLogic/120
DESCRIPTION:Title: On the uniqueness of maximal solvable extensions of nilpotent
Lie algebras\nby Bakhrom A. Omirov (Harbin Institute of Technologies\
, Harbin\, China and Romanovskiy Institute of Mathematics\, Uzbekistan Aca
demy of Sciences\, Uzbekistan) as part of Algebra and Logic Seminar\n\n\nA
bstract\nDuring the talk it will be shown that under certain condition an
arbitrary complex finite-dimensional maximal extension of a nilpotent Lie
algebra N is isomorphic to the semidirect sum of N and its maximal torus.
A criterion of the completeness for a finite-dimensional solvable Lie alge
bra is established. Comparisons with some existing results will also be di
scussed.\n
LOCATION:https://stable.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:20260404T095425Z
UID:AlgAndLogic/121
DESCRIPTION:Title: Generalized Definability of Discrete Time Interval-based Temp
oral Connectives\nby Dimitar Guelev (Institute of Mathematics and Info
rmatics\, Bulgarian Academy of Sciences) as part of Algebra and Logic Semi
nar\n\n\nAbstract\nIn Linear Temporal Logic with past (PLTL)\, expressive
completeness implies that any first-order definable connective is also def
inable in the temporal language based on the Since and Until temporal oper
ators. This is not the case about discrete time interval-based temporal lo
gics with state-based semantics for the propositional variables. In this t
alk I prove the next best thing about the extension ITLNL of Moszkowski's
discrete time propositional Interval Temporal Logic (ITL) by the neighbour
hood modalities: given an interval-based connective # which admits a first
-order definition\, a star-free ITLNL defining formula for $\\#(A_1\,...\,
A_m)$ can be produced that is built from the past\, future and introspecti
ve formulas appearing in some separated equivalents of the operands $A_1\,
...\,A_m$. The proof is based in an interval-based analogue of Gabbay's se
paration theorem about PLTL that was previously established about ITLNL by
the neighbourhood modalities by me and Moszkowski and have now used to pr
ove the expressive completeness of ITLNL. As a side result I have come upo
n new proofs of expressive completeness and temporal separation for ITLNL'
s star-free subset that I will briefly discuss too.\n
LOCATION:https://stable.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:20260404T095425Z
UID:AlgAndLogic/122
DESCRIPTION:Title: On an Aspect of Second Quantum Revolution\nby Valentin Il
ieav (Institute of Mathematics and Informatics\, Bulgarian Academy of Scie
nces) as part of Algebra and Logic Seminar\n\n\nAbstract\nThe 2022 Nobel P
rize in Physics has been awarded to Alain Aspect\, John Clauser\, and Anto
n Zeilinger for their work in Quantum Theory. Mass media called this event
part of second quantum revolution which includes mainly quantum computing
and other super-technologies. Here we discuss Alain Aspect's version of E
instein-Podolsky-Rosen thought experiment and show that there exists an in
ternal dependence of the simultaneous measurements made by the two pairs o
f linear polarizers operated in each leg of the apparatus during this expe
riment. The corresponding Shannon-Kolmogorov information flow (or\, noise?
) linking a polarizer from one leg to a polarizer from the other leg is pr
oportional to the absolute value of this function of dependence. It turns
out that 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://stable.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:20260404T095425Z
UID:AlgAndLogic/123
DESCRIPTION:Title: Protection Against Noise for a Type of Quantum Computation\nby Valentin Iliev (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.\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/AlgAndLogic/123/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Plamen Koshlukov (State University of Campinas\, Brazil)
DTSTART:20250328T110000Z
DTEND:20250328T123000Z
DTSTAMP:20260404T095425Z
UID:AlgAndLogic/124
DESCRIPTION:Title: Graded algebras that are the sum of two homogeneous subalgebr
as\nby Plamen Koshlukov (State University of Campinas\, Brazil) as par
t of Algebra 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 homogeneou
s subalgebras of $A$ such that $A=B+C$. We study the following problem: If
$B$ and $C$ 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 $A$
satisfies specific graded semi-identities. In this case\, if $C$ satisfies
some graded identity in neutral variables\, we show that $A$ satisfies gr
aded identities. We also find upper bounds for the degrees of such identit
ies. Here we use methods that go back to the classical Regev theorem on th
e growth of the codimensions of an associative algebra.\n\nFinally we exhi
bit an example that shows that the graded version of the Kępczyk theorem
is no longer valid.\n\nThis is a joint work with P. S. Fagundes.\n
LOCATION:https://stable.researchseminars.org/talk/AlgAndLogic/124/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Soowhan Yoon (American University in Bulgaria)
DTSTART:20250516T100000Z
DTEND:20250516T113000Z
DTSTAMP:20260404T095425Z
UID:AlgAndLogic/126
DESCRIPTION:Title: Grätzer-Schmidt Theorem in arithmetical transfinite recursio
n\nby Soowhan Yoon (American University in Bulgaria) as part of Algebr
a and Logic Seminar\n\n\nAbstract\nWe assess the reverse mathematical stre
ngth of the Grätzer-Schmidt theorem (GS) as a principle in second order a
rithmetic. The theorem GS was studied in an article by Katie Brodhead\, Mu
shfeq Khan\, Bjørn Kjos-Hanssen\, William A. Lampe\, Paul Kim Long V. Ngu
yen\, and 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 arithmetical comprehension (ACA$_0$). It will be shown that the arithme
tical transfinite recursion (ATR$_0$) is sufficient to prove GS. Additiona
lly\, other variants of GS will be explored as well. Some will be proved i
n 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 Hyperarithmetic Analysis” (ATHA) by Shore in 2023.\n
LOCATION:https://stable.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:20260404T095425Z
UID:AlgAndLogic/127
DESCRIPTION:Title: Holographic probe branes and artificial neural networks\n
by Veselin Filev (Institute of Mathematics and Informatics\, Bulgarian Aca
demy of Sciences) as part of Algebra and Logic Seminar\n\n\nAbstract\nIn h
olography\, flavour probe branes are used to introduce fundamental matter
to the AdS/CFT correspondence. At a technical level\, the probes are descr
ibed by extremizing the DBI action and solving the Lagrange–Euler equati
ons of motion. I will report on applications of artificial neural networks
that allow direct minimization of the regularized DBI action (interpreted
as a free energy) without the need to derive and solve the equations of m
otion. I will consider\, as examples\, magnetic catalysis of chiral symmet
ry breaking and the meson melting phase transition in the D3/D7 holographi
c set-up.\n
LOCATION:https://stable.researchseminars.org/talk/AlgAndLogic/127/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hristo Iliev (American University in Bulgaria and IMI-BAS)
DTSTART:20251003T100000Z
DTEND:20251003T113000Z
DTSTAMP:20260404T095425Z
UID:AlgAndLogic/128
DESCRIPTION:Title: Decomposition of Tschirnhausen Modules for Coverings on Decom
posable P^1-Bundles\nby Hristo Iliev (American University in Bulgaria
and IMI-BAS) as part of Algebra and Logic Seminar\n\n\nAbstract\nLet $\\va
rphi : X → Y$ 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$$0 → \\mathcal{
O}_Y \\stackrel{\\varphi^\\sharp}{\\to}\\varphi∗\\mathcal{O}X → \\math
cal{E}^∨ → 0\,$$\nwhere $\\mathcal{E}^∨$ is known as the Tschirnhaus
en module the covering $\\varphi$.\n\nIn the talk\, we focus on the case w
here $Y$ is smooth and $X$ is a smooth $m$-multisection of the $\\mathbb{P
}^1$-bundle\n$$f : \\mathbb{P}(\\mathcal{O}_Y ⊕ \\mathcal O_Y (E)) \\lon
grightarrow Y\,$$\nwith $E$ an effective divisor on $Y$ such that $H^1(Y\,
\\mathcal O_Y (kE)) = 0$ for all $k = 1\, . . . \, m − 1$. We show that
the Tschirnhausen module of the induced covering $f|_X : X \\longrightarr
ow Y$ is completely decomposable\, after which we discuss applications of
this result.\n
LOCATION:https://stable.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:20260404T095425Z
UID:AlgAndLogic/129
DESCRIPTION:Title: On Z_5 reduction of soliton equations related to sl(5) algeb
ra\nby Vladimir Gerdjikov (Institute of Mathematics and Informatics\,
Bulgarian Academy of Sciences) as part of Algebra and Logic Seminar\n\n\nA
bstract\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 o
n an effective parametrization of the Riemann-Hilbert problem\, which allo
ws one to extend the class of Lax pairs and effectively derive only the co
rresponding NLEE as compatibility condition of two linear problems. This m
ethod is based on the possibility to treat the solution of the RHP as a fu
ndamental analytic solution of the Lax pair\, and then to apply the dressi
ng Zakharov-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 parametrization of the Z5 RHP. The NLEE that we obtained are dispersi
onless.\n\nPublished in Journal of Physics: Conference Series\, Vol. 3002:
(1)\, id. 012014\, 14 pp.\n\nJoint meeting of the the Algebra and Logic Se
minar and the Seminar of the Department of Differential Equations and Math
ematical Physics at the Institute of Mathematics and Informatics\, Bulgari
an Academy of Sciences.\n
LOCATION:https://stable.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:20260404T095425Z
UID:AlgAndLogic/130
DESCRIPTION:Title: Classical Results in ITL with the Neighbourhood Modalities a
nd Their Short Proofs Using Separation\nby Dimitar Guelev (Institute o
f Mathematics and Informatics\, Bulgarian Academy of Sciences) as part of
Algebra and Logic Seminar\n\nAbstract: TBA\n
LOCATION:https://stable.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:20260404T095425Z
UID:AlgAndLogic/131
DESCRIPTION:Title: On Pairs of Non-commuting Hermitian Operators on the Unitary
Plane which are Permutable Measurements\nby Valentin Iliev (Institute
of Mathematics and Informatics\, Bulgarian Academy of Sciences) as part of
Algebra and Logic Seminar\n\n\nAbstract\nIn this presentation we study ob
servables with spectre {-1\,1} on quantum systems with the unitary plane a
s a space of states. Examples of such quantum systems are spin-1/2 particl
es. We find necessary and sufficient conditions for two non-commuting obse
rvables to be permutable measurements\, that is\, the probability of obtai
ning a particular pair of results does not depend on the order of taking t
hese measurements. Several examples are presented.\n
LOCATION:https://stable.researchseminars.org/talk/AlgAndLogic/131/
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