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CALSCALE:GREGORIAN
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BEGIN:VEVENT
SUMMARY:A. Ya. Kanel-Belov
DTSTART:20230715T140500Z
DTEND:20230715T153500Z
DTSTAMP:20260404T131156Z
UID:knotgraphgroup/1
DESCRIPTION:Title: Quantization\, polynomial automorphisms\, and the Jacobian p
roblem\nby A. Ya. Kanel-Belov as part of Knots\, graphs and groups\n\n
Abstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/knotgraphgroup/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:M. Chrisman
DTSTART:20230722T140500Z
DTEND:20230722T153500Z
DTSTAMP:20260404T131156Z
UID:knotgraphgroup/2
DESCRIPTION:Title: A sheaf-theoretic approach to classical and virtual knot the
ory\nby M. Chrisman as part of Knots\, graphs and groups\n\nAbstract:
TBA\n
LOCATION:https://stable.researchseminars.org/talk/knotgraphgroup/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vassily O. Manturov
DTSTART:20230729T140500Z
DTEND:20230729T153500Z
DTSTAMP:20260404T131156Z
UID:knotgraphgroup/3
DESCRIPTION:Title: Hexagonal rhombille tilings\, Groups G_{n}^{k}\, line confi
gurations\, and Desargues flips\nby Vassily O. Manturov as part of Kno
ts\, graphs and groups\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/knotgraphgroup/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hyungtae Baek (School of Mathematics\, Kyungpook National Universi
ty\, Republic of Korea)
DTSTART:20230805T140500Z
DTEND:20230805T153500Z
DTSTAMP:20260404T131156Z
UID:knotgraphgroup/4
DESCRIPTION:Title: $R[X]_A$ of zero-dimensional reduced rings\nby Hyungtae
Baek (School of Mathematics\, Kyungpook National University\, Republic of
Korea) as part of Knots\, graphs and groups\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/knotgraphgroup/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Scott Baldridge
DTSTART:20230812T140500Z
DTEND:20230812T153500Z
DTSTAMP:20260404T131156Z
UID:knotgraphgroup/5
DESCRIPTION:Title: A state sum for the total face color polynomial\nby Scot
t Baldridge as part of Knots\, graphs and groups\n\n\nAbstract\nThe total
face color polynomial is based upon the Poincaré polynomials of a family
of filtered n-color homologies. It is an abstract graph invariant when the
graph is trivalent and calculates the sum of n-face colorings of ribbon g
raphs of the graph for each positive integer n. As such\, it may be seen a
s a successor of the Penrose polynomial\, which at n = 3 counts 3-edge col
orings (and consequently 4-face colorings) of planar trivalent graphs. In
this talk we describe a simple-to-express state sum formula for calculatin
g the polynomial based upon earlier work of Lou Kauffman. This formula uni
tes two different perspectives about graph coloring: one based upon topolo
gical quantum field theory and the other on diagrammatic tensors.\n\nThis
is joint work with Lou Kauffman and Ben McCarty and is based upon the pape
r recently uploaded to the arXiv found here: https://arxiv.org/abs/2308.02
732\n
LOCATION:https://stable.researchseminars.org/talk/knotgraphgroup/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Wan Zheyan
DTSTART:20230819T140500Z
DTEND:20230819T153500Z
DTSTAMP:20260404T131156Z
UID:knotgraphgroup/6
DESCRIPTION:Title: Explicit cocycle formulas on finite abelian groups and Dijkg
raaf-Witten invariants of n-torus\nby Wan Zheyan as part of Knots\, gr
aphs and groups\n\n\nAbstract\nWe provide explicit and unified formulas fo
r the cocycles of all degrees on the normalized bar resolutions of finite
abelian groups. This is achieved by constructing a chain map from the norm
alized bar resolution to a Koszul-like resolution for any given finite abe
lian group. With the help of the obtained cocycle formulas\, we compute th
e Dijkgraaf-Witten invariants of the n-torus for all n. This talk is based
on https://arxiv.org/pdf/1703.03266.pdf\n
LOCATION:https://stable.researchseminars.org/talk/knotgraphgroup/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sergei Gukov
DTSTART:20230826T140500Z
DTEND:20230826T153500Z
DTSTAMP:20260404T131156Z
UID:knotgraphgroup/7
DESCRIPTION:Title: 3-manifolds and Vafa-Witten theory\nby Sergei Gukov as p
art of Knots\, graphs and groups\n\n\nAbstract\nWe initiate explicit compu
tations of Vafa-Witten invariants of 3-manifolds\, analogous to Floer grou
ps in the context of Donaldson theory. In particular\, we explicitly compu
te the Vafa-Witten invariants of 3-manifolds in a family of concrete examp
les relevant to various surgery operations (the Gluck twist\, knot surgeri
es\, log-transforms). We also describe the structural properties that are
expected to hold for general 3-manifolds\, including the modular group act
ion\, relation to Floer homology\, infinite-dimensionality for an arbitrar
y 3-manifold\, and the absence of instantons.\n
LOCATION:https://stable.researchseminars.org/talk/knotgraphgroup/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bao Vuong
DTSTART:20230902T140500Z
DTEND:20230902T153500Z
DTSTAMP:20260404T131156Z
UID:knotgraphgroup/8
DESCRIPTION:Title: Gram matrix of tetrahedron and volume\nby Bao Vuong as p
art of Knots\, graphs and groups\n\n\nAbstract\nWe review some properties
of Gram matrix for tetrahedra and give some integral formulas for the volu
me of hyperbolic and spherical tetrahedron.\n
LOCATION:https://stable.researchseminars.org/talk/knotgraphgroup/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Xujia Chen
DTSTART:20231007T140500Z
DTEND:20231007T153500Z
DTSTAMP:20260404T131156Z
UID:knotgraphgroup/9
DESCRIPTION:Title: Kontsevich’s invariants as topological invariants of confi
guration space bundles\nby Xujia Chen as part of Knots\, graphs and gr
oups\n\n\nAbstract\nKontsevich's invariants (also called “configuration
space integrals”) are invariants of certain framed smooth manifolds/fibe
r bundles. The result of Watanabe(’18) showed that Kontsevich’s invari
ants can distinguish smooth fiber bundles that are isomorphic as topologic
al fiber bundles. I will first give an introduction to Kontsevich's invari
ants\, and then state my work which provides a perspective on how to under
stand their ability of detecting exotic smooth structures: real blow up op
erations essentially depends on the smooth structure\, and thus given a sp
ace/bundle X\, the topological invariants of some spaces/bundles obtained
by doing some real blow-ups on X can be different for different smooth str
uctures on X.\n
LOCATION:https://stable.researchseminars.org/talk/knotgraphgroup/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vassily O. Manturov
DTSTART:20230909T140500Z
DTEND:20230909T153500Z
DTSTAMP:20260404T131156Z
UID:knotgraphgroup/10
DESCRIPTION:Title: Further directions in the photography method\nby Vassil
y O. Manturov as part of Knots\, graphs and groups\n\n\nAbstract\nI will d
iscuss the photography method according to the papers\n\nhttps://arxiv.org
/abs/2305.06316\n \nhttps://arxiv.org/pdf/2305.11945.pdf\n \nhttps://arxiv
.org/abs/2306.07079\n \nhttps://arxiv.org/abs/2307.03437\n \nhttps://arxiv
.org/abs/2309.01735\n \nand give a long list of unsolved problems covering
lots of topics in various fields of\nmathematics.\n
LOCATION:https://stable.researchseminars.org/talk/knotgraphgroup/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Seongjeong Kim (Jilin university)
DTSTART:20230916T140500Z
DTEND:20230916T153500Z
DTSTAMP:20260404T131156Z
UID:knotgraphgroup/11
DESCRIPTION:Title: Skein modules for $S^1 \\times S^2 \\ \\# \\ S^1 \\times S^
2$\nby Seongjeong Kim (Jilin university) as part of Knots\, graphs and
groups\n\n\nAbstract\nSkein modules were introduced by Józef H. Przytyck
i and by Vladimir Turaev independently. The Kauffman bracket skein module
(KBSM) is the most extensively studied one. However\, computing the KBSM o
f a 3-manifold is known to be notoriously hard\, especially over the ring
of Laurent polynomials. Marché conjectured that the KBSM of closed orient
ed $3$-manifolds splits into the direct sum of free and certain torsion mo
dules over the ring of Laurent polynomials. The counterexample to this con
jecture is given by the connected sum of two copies of the real projective
space. With the goal of finding a definite structure of the KBSM over thi
s ring\, we compute KBSM of $S^1 \\times S^2 \\ \\# \\ S^1 \\times S^2$. W
e show that it is isomorphic to KBSM of a genus two handlebody modulo some
specific handle sliding relations. Moreover\, these handle sliding relati
ons can be written in terms of Chebyshev polynomials. This is joint work
with Rhea Palak Bakshi and Xiao Wang\n
LOCATION:https://stable.researchseminars.org/talk/knotgraphgroup/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hyungtae Baek (School of Mathematics\, Kyungpook National Universi
ty\, Republic of Korea)
DTSTART:20230923T140500Z
DTEND:20230923T153500Z
DTSTAMP:20260404T131156Z
UID:knotgraphgroup/12
DESCRIPTION:Title: Generalization of prime ideals\nby Hyungtae Baek (Schoo
l of Mathematics\, Kyungpook National University\, Republic of Korea) as p
art of Knots\, graphs and groups\n\n\nAbstract\nIn 2011\, Anderson and Bad
awi generalized the concept of prime ideals and\nin 2020\, Hamed and Malek
generalized the concept of prime ideals using multiplicative sets.\n\nIn
this talk\,\nfor a commutative ring with identity $R$ and\na multiplicativ
e subset $S$ of $R$\,\nwe define an {\\it $S$-$n$-absorbing ideals} genera
lizing these and\nexamine following problems:\n\\begin{enumerate}\n\\item[
(1)]\nIf $I$ is an $S$-$n$-absorbing ideal of $R$\,\nthen is $IR_S$ an $n$
-absorbing ideal of $R_S$?\nWhat about the converse?\n\\item[(2)]\nWhen is
each ideal $I$ of $R$ disjoint from $S$ an $S$-$n_I$-absorbing ideal for
some $n_I \\in \\mathbb{N}$?\n\\item[(3)]\nWhen are $I \\bowtie^f J$\, $\\
overline{K}^f$ and $\\overline{I \\times K}^f$ $S^{\\bowtie^f}$-$n$-absorb
ing ideal of $A \\bowtie^f J$?\n\\item[(4)]\nConsider the ideal $H$ of $f(
A) + J$ such that $f(I)J \\subseteq H \\subseteq J$.\nWhen is $I \\bowtie^
f H$ an $S^{\\bowtie^f}$-$n$-absorbing ideal of $A \\bowtie^f J$?\n\\end{e
numerate}\n\n\\begin{thebibliography}{11}\n\\bibitem{Anderson}\nD. F. Ande
rson and A. Badawi\,\n{\\em On $n$-absorbing ideals of commutative rings}\
,\nComm. Alg. {\\bf 39(5)}\, 1646-1672 (2011).\n\n\\bibitem{Hamed}\nA. Ham
ed and A. Malek\,\n{\\it $S$-prime ideals of a commutative ring}\,\nBeitr
Algebra Geom {\\bf 61}\, 533-542 (2020).\n\\end{thebibliography}\n
LOCATION:https://stable.researchseminars.org/talk/knotgraphgroup/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Oleg Styrt
DTSTART:20230930T140500Z
DTEND:20230930T153500Z
DTSTAMP:20260404T131156Z
UID:knotgraphgroup/13
DESCRIPTION:Title: Matrix sets closed under conjugations and summing commuting
elements.\nby Oleg Styrt as part of Knots\, graphs and groups\n\n\nAb
stract\nThe talk is devoted to describing matrix sets closed under conjuga
tions and summing commuting elements. There are two well known important a
nd principally different sets satisfying these properties: the sets of all
semisimple and of all nilpotent matrices. It is also easy to see that the
general case is directly reduced to describing such sets lying in some of
these two special ones.\nThe talk is aimed to present the result obtained
for an algebraically closed field.\n
LOCATION:https://stable.researchseminars.org/talk/knotgraphgroup/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Zhuoke Yang
DTSTART:20231014T140500Z
DTEND:20231014T153500Z
DTSTAMP:20260404T131156Z
UID:knotgraphgroup/14
DESCRIPTION:Title: New approaches to Lie algebra weight systems\nby Zhuoke
Yang as part of Knots\, graphs and groups\n\n\nAbstract\nIn this talk we
introduce a universal weight system (a function on chord diagrams satisfyi
ng the 4-term relation) taking values in the ring of polynomials in infini
tely many variables\, whose particular specialisations are weight systems
associated with the Lie algebras gl(N) and Lie superalgebras gl(M|N). We e
xtend this weight system to permutations and provide an efficient recursio
n for its computation.\n
LOCATION:https://stable.researchseminars.org/talk/knotgraphgroup/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nikolay Abrosimov (Sobolev Institute of Mathematics\, Novosibirsk)
DTSTART:20231021T140500Z
DTEND:20231021T153500Z
DTSTAMP:20260404T131156Z
UID:knotgraphgroup/15
DESCRIPTION:Title: Euclidean volumes of cone manifolds are algebraic numbers\nby Nikolay Abrosimov (Sobolev Institute of Mathematics\, Novosibirsk)
as part of Knots\, graphs and groups\n\n\nAbstract\nThe hyperbolic structu
re on a 3-dimensional cone-manifold with a knot as singularity can often b
e deformed into a limiting Euclidean structure. In the present work [1] we
show that the respective normalised Euclidean volume is always an algebra
ic number which is reminiscent of Sabitov's theorem (the Bellows Conjectur
e). This fact also stands in contrast to hyperbolic volumes whose number-
theoretic nature is usually quite complicated. This is a joint work with A
lexander Kolpakov and Alexander Mednykh.\n\n[1] N. Abrosimov A. Kolpakov A
. Mednykh Euclidean volumes of hyperbolic knots // Proceedings of AMS 2023
(in press) DOI: 10.1090/proc/16353\n
LOCATION:https://stable.researchseminars.org/talk/knotgraphgroup/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Timur Nasybullov
DTSTART:20231028T140500Z
DTEND:20231028T153500Z
DTSTAMP:20260404T131156Z
UID:knotgraphgroup/16
DESCRIPTION:Title: Quandles with orbit series conditions\nby Timur Nasybul
lov as part of Knots\, graphs and groups\n\n\nAbstract\nThe notion of quan
dle was introduced independently by Joyce and Matveev as an invariant for
knots. This invariant is very strong\, however\, usually it is difficult t
o determine if two knot quandles are isomorphic. Various tricks are used t
o solve this problem for individual cases of quandles. For each quandle\,
one can construct its orbit series tree. If two quandles are isomorphic\,
then their orbit series trees are also isomorphic. During the talk we are
going to discuss relations between a quandle and its orbit series tree. In
particular\, we will discuss the question of when isomorphism of quandles
follows from isomorphism of orbit series trees of these quandles. In addi
tion\, we are going to discuss various results about quandles which are de
scribed in terms of its orbit series tree.\n
LOCATION:https://stable.researchseminars.org/talk/knotgraphgroup/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anna Taranenko
DTSTART:20231111T140500Z
DTEND:20231111T153500Z
DTSTAMP:20260404T131156Z
UID:knotgraphgroup/18
DESCRIPTION:Title: On transversals in iterated groups and quasigroups\nby
Anna Taranenko as part of Knots\, graphs and groups\n\n\nAbstract\nGiven a
binary quasigroup G of order n\, let the d-iterated quasigroup G[d] be th
e (d+1)-dimensional latin hypercube equal to the Cayley table of d times c
omposition of G with itself. A diagonal of a latin hypercube is said to be
a transversal if it contains all different symbols. We prove that for a g
iven binary quasigroup G the d-iterated quasigroup G[d] has a transversal
either only if d is even or for all large enough d. Moreover\, there is r
= r(G) such that if the number of transversals in G[d] is nonzero then\, i
t is equal to (1 + o(1)) n!^{d+1} / (r n^{n-1}) as d tends to infinity. If
G is a group\, then r is the order of its commutator subgroup.\n
LOCATION:https://stable.researchseminars.org/talk/knotgraphgroup/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vladimir A. Stukopin
DTSTART:20231118T140500Z
DTEND:20231118T153500Z
DTSTAMP:20260404T131156Z
UID:knotgraphgroup/19
DESCRIPTION:Title: Affine superYangian\nby Vladimir A. Stukopin as part of
Knots\, graphs and groups\n\n\nAbstract\nThe talk will discuss the Yangia
ns of Lie superalgebras\, an important example of quantum groups. Yangians
of simple Lie algebras\, as well as quantum groups\, were introduced by V
.G. Drinfeld in the eighties of the last century\, but began to be studied
somewhat earlier in the works of mathematical physicists\, within the fra
mework of the Bethe algebraic ansatz which is a method for studying quantu
m integrable models. Yangians are closely related to rational solutions of
the quantum Yang-Baxter equation and appear as deformations of the Lie bi
algebra of polynomial currents with values in the reductive Lie algebra. S
ince the mid-nineties of the last century\, Yangians of Lie superalgebras
(or superYangians) have also been studied. Currently\, numerous connection
s have been discovered between Yangians and many problems in representatio
n theory\, mathematical and theoretical physics\, including superstring th
eory\, and this is an intensively developing area of research. I will try
to talk about some\, including new results\, relating both to the Yangians
of basic Lie superalgebras and to the Yangians of affine Kac-Moody supera
lgebras (affine superYangians)\, which began to be studied quite recently.
\n
LOCATION:https://stable.researchseminars.org/talk/knotgraphgroup/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Oleg G. Styrt
DTSTART:20231125T140500Z
DTEND:20231125T153500Z
DTSTAMP:20260404T131156Z
UID:knotgraphgroup/20
DESCRIPTION:Title: Groups $\\Gamma_n^4$: algebraic properties\nby Oleg G.
Styrt as part of Knots\, graphs and groups\n\n\nAbstract\nIn theory of kno
ts and braids\, there is a special type of groups closely connected with b
raid groups — namely\, groups $\\Gamma_n^4$. Each of them is given by in
volutive generators indexed by ordered $4$-tuples of pairwise distinct int
egers from $1$ to $n$ and some special relations between them.\nThe speake
r’s research is concentrated mainly on algebraic structure of groups $\\
Gamma_n^4$. His main result is that\, for any $n\\geqslant7$\, the groups
$\\Gamma_n^4$ and $\\Gamma_n^4/(\\Gamma_n^4)'$ are isomorphic to direct pr
oducts of finitely many copies of $\\mathbb{Z}_2$\, in part\, that $\\Gamm
a_n^4$ is a nilpotent finite $2$-group with $4$-torsion.\nIf time allows\,
all are the most of the proof will be presented.\n
LOCATION:https://stable.researchseminars.org/talk/knotgraphgroup/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Qingying Deng (Xiangtan University)
DTSTART:20231202T140500Z
DTEND:20231202T153500Z
DTSTAMP:20260404T131156Z
UID:knotgraphgroup/21
DESCRIPTION:Title: Twisted link and arrow polynomial\nby Qingying Deng (Xi
angtan University) as part of Knots\, graphs and groups\n\n\nAbstract\nIt
is well-known that a classical link diagram is checkerboard colorable. The
notion of a checkerboard coloring for a virtual link diagram was independ
ently introduced by V.O.Manturov (in 2000) and N. Kamada (in 2002) by us
ing atom and corresponding abstract link diagram\, respectively. M.O. Bour
goin introduced the twisted knot theory in 2008 and defined the notion of
a checkerboard coloring for a twisted link diagram.\nIn this talk\, we fir
st give two new criteria to detect the checkerboard colorability of virtua
l links by using odd writhe and arrow polynomial of virtual links\, respec
tively. Then by applying these criteria we determine the checkerboard colo
rability of virtual knots up to four crossings\, with only one exception.\
nSecond\, we reformulate the arrow polynomial of twisted links by using Ka
uffman’s formalism. In fact\, in 2012\, in case of using the pole diagra
m\, N. Kamada obtained the polynomial by generalizing a multivariable poly
nomial invariant of a virtual link to a twisted link. Moreover\, we figure
out three characteristics of the arrow polynomial of a checkerboard color
able twisted link\, which is a tool of detecting checkerboard colorability
of a twisted link. The latter two characteristics are the same as in the
case of checkerboard colorable virtual link diagram.\n
LOCATION:https://stable.researchseminars.org/talk/knotgraphgroup/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Aidan Mozayeni
DTSTART:20231216T140500Z
DTEND:20231216T153500Z
DTSTAMP:20260404T131156Z
UID:knotgraphgroup/22
DESCRIPTION:Title: Novel Applications of Theorem 2 (Sedrakyan-Mozayeni)\nb
y Aidan Mozayeni as part of Knots\, graphs and groups\n\n\nAbstract\nIn th
is presentation\, I will review progress in Dr. Sedrakyan’s and my work
to generalize the pentagon case of the photography principle. I will also
give a novel application\, go in depth on the derivation of Theorem 2 (Sed
rakyan-Mozayeni)\, and explain current issues with the pentagon case of th
e photography principle. Furthermore\, this presentation will explain anot
her application\, and close off by explaining a potential creation of a pe
ntagon theorem that could aid in generalizing the case.\n
LOCATION:https://stable.researchseminars.org/talk/knotgraphgroup/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Timorin Vladlen
DTSTART:20231209T140500Z
DTEND:20231209T153500Z
DTSTAMP:20260404T131156Z
UID:knotgraphgroup/23
DESCRIPTION:Title: Aperiodic points for outer billiards\nby Timorin Vladle
n as part of Knots\, graphs and groups\n\n\nAbstract\nThis is a joint proj
ect with A. Kanel-Belov\, Ph. Rukhovich\, and V. Zgurskii. A Euclidean out
er billiard on a convex figure in the plane is the map sending a point out
side the figure to the other endpoint of a segment touching the figure at
the middle. Iterating such a process was suggested by J. Moser as a crude
model of planetary motion. Polygonal outer billiards are arguably the prin
cipal examples of Euclidean piecewise rotations\, which serve as a natural
generalization of interval exchange maps. They also found applications in
electrical engineering. Previously known rigorous results on outer billia
rds on regular N-polygons are\, apart from “trivial” cases of N=3\,4\,
6\, based on dynamical self-similarities (this approach was originated by
S. Tabachnikov). Dynamical self-similarities have been found so far only f
or N=5\,7\,8\,9\,10\,12. In his ICM 2022 address\, R. Schwartz asked wheth
er “outer billiard on the regular N-gon has an aperiodic orbit if N is n
ot 3\, 4\, 6”. We answer this question in affirmative for N not divisibl
e by 4. Our methods are not based on self-similarity. Rather\, scissor con
gruence invariants (including that of Sah-Arnoux-Fathi) play a key role.\n
LOCATION:https://stable.researchseminars.org/talk/knotgraphgroup/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vadim Leshkov
DTSTART:20231223T140500Z
DTEND:20231223T153500Z
DTSTAMP:20260404T131156Z
UID:knotgraphgroup/24
DESCRIPTION:Title: A Functorial Generalization of Coxeter Groups\nby Vadim
Leshkov as part of Knots\, graphs and groups\n\n\nAbstract\nIn the work a
rXiv:2312.07939 we describe the category WC2 of weighted 2-complexes and i
ts subcategory WC1 of weighted graphs. Since a Coxeter group is defined by
its Coxeter graph\, the construction of Coxeter groups defines a functor
from WC1 to the category of groups. We generalize the notion of a Coxeter
group by extending the domain of the functor to the category WC2. It appea
rs that the resulting functor generalizes the construction of Coxeter grou
ps\, Gauss pure braid groups GVP_{n} (introduced by V. Bardakov\, P. Belli
ngeri\, and C. Damiani in 2015)\, k-free braid groups on n strands G_{n}^{
k} (introduced by V. Manturov in 2015)\, and other quotients of Coxeter gr
oups.\n
LOCATION:https://stable.researchseminars.org/talk/knotgraphgroup/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Euich Miztani
DTSTART:20231230T140500Z
DTEND:20231230T153500Z
DTSTAMP:20260404T131156Z
UID:knotgraphgroup/25
DESCRIPTION:Title: Transformation Groupoid Based on Quotient Vector Spaces —
A Mathematical Definition for Theory of Dimensionality\nby Euich Mizta
ni as part of Knots\, graphs and groups\n\n\nAbstract\nIn my last presenta
tion of this seminar on the 19th of December in 2023\, a new mapping (proj
ection) is given from any point in its original dimensional space to other
dimensional space. In the series of mappings\, any point has invariant or
symmetry. In other words\, the degree of freedom (the number of variables
) of any point is unchangeable in the series of mappings. In this time\, w
e explain mathematical definitions in terms of quotient vector space. The
first aim is to define our new notions in the last presentation more mathe
matically. The second aim is to introduce a more concrete mappings from a
higher dimensional space to a lower dimensional one.\n
LOCATION:https://stable.researchseminars.org/talk/knotgraphgroup/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hyungtae Baek
DTSTART:20240120T140500Z
DTEND:20240120T153500Z
DTSTAMP:20260404T131156Z
UID:knotgraphgroup/26
DESCRIPTION:Title: Star-operations on Anderson rings\nby Hyungtae Baek as
part of Knots\, graphs and groups\n\n\nAbstract\nLet $R$ be a commutative
ring with identity and\nlet $R[X]$ be the polynomial ring over $R$.\nConsi
der the following two subsets of $R[X]$:\n\\begin{center}\n$N := \\{f \\in
R[X] \\\,|\\\, c(f) = R\\}$ and\\\\\n$U := \\{f \\in R[X] \\\,|\\\, f {\\
rm \\ is \\ a \\ monic \\ polynomial} \\}$.\n\\end{center}\nThen $N$ and $
U$ are multiplicative subset of $R[X]$\,\nso we obtain the rings $R[X]_N$
and $R[X]_U$\,\nwhich are called the {\\it Nagata ring} of $R$ and {\\it S
erre's conjecture ring} of $R$ respectively.\nThe Nagata rings and the Ser
re's conjecture rings has been researched actively.\n\nIn this talk\, we i
nvestigate the Anderson ring which is a subring of the Nagata ring and the
Serre's conjecture ring\, and\nexamine star-operations on Anderson rings.
\nMore precisely\, we examine the following problems:\n\n\n(1)Can we chara
cterize the maximal spectrum of Anderson rings?\n\n(2)Can we characterize
the $w$-maximal spectrum of Anderson rings?\n\n\n\n\\begin{thebibliography
}{11}\n\n\\bibitem{anderson 1985} D. D. Anderson\, D. F. Anderson\, and R.
Markanda\,\n{\\it The rings $R(X)$ and $R \\left< X\\right>$}\,\nJ. Algeb
ra 95 (1985) 96-155.\n\n\\bibitem{kang 1989} B. G. Kang\,\n{\\em Pr\\"ufer
$v$-multiplication domains and the ring $R[X]_{N_v}$}\,\nJ. Algebra 123 (
1989) 151-170.\n\n\\bibitem{riche} L. R. Le Riche\,\n{\\it The ring $R\\le
ft< X \\right>$}\,\nJ. Algebra 67 (1980) 327-341.\n\\end{thebibliography}\
n
LOCATION:https://stable.researchseminars.org/talk/knotgraphgroup/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sergey Malev
DTSTART:20240127T140500Z
DTEND:20240127T153500Z
DTSTAMP:20260404T131156Z
UID:knotgraphgroup/27
DESCRIPTION:Title: Evaluations of multilinear polynomials on finite dimension
al algebras\nby Sergey Malev as part of Knots\, graphs and groups\n\n\
nAbstract\nLet p be a polynomial in several non-commuting variables with c
oefficients in an algebraically closed field K of arbitrary characteristic
. It has been conjectured that for any n\, for p multilinear\, the image o
f p evaluated on the set M_n(K) of n by n matrices is either zero\, or the
set of scalar matrices\, or the set sl_n(K) of matrices of trace 0\, or a
ll of M_n(K).\nIn this talk we will discuss the generalization of this res
ult for non-associative algebras such as Cayley-Dickson algebra (i.e. alge
bra of octonions)\, pure (scalar free) octonion Malcev algebra and basic l
ow rank Jordan algebras.\n
LOCATION:https://stable.researchseminars.org/talk/knotgraphgroup/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Han-Bom Moon (Department of Mathematics Fordham University)
DTSTART:20240309T140500Z
DTEND:20240309T153500Z
DTSTAMP:20260404T131156Z
UID:knotgraphgroup/28
DESCRIPTION:Title: Cluster algebras and generalized skein algebras\nby Han
-Bom Moon (Department of Mathematics Fordham University) as part of Knots\
, graphs and groups\n\n\nAbstract\nFor each punctured surface admitting a
triangulation\, we may associate two algebras. One is the cluster algebra
of surfaces\, and the other is the generalized skein algebra from quantum
topology. In this talk\, I will explain their compatibility and some conse
quences in the Teichmuller theory and the structure of cluster algebra.\n
LOCATION:https://stable.researchseminars.org/talk/knotgraphgroup/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vassily O. Manturov
DTSTART:20240203T140500Z
DTEND:20240203T153500Z
DTSTAMP:20260404T131156Z
UID:knotgraphgroup/29
DESCRIPTION:Title: Flat-virtual knots: A theory of knots in the full torus and
in the thickened Moebius band\nby Vassily O. Manturov as part of Knot
s\, graphs and groups\n\n\nAbstract\nIn 2022\, the author and I.M.Nikonov
have noticed that knots in the full cylinder\nS^{1}\\times D^{2} have some
"hidden" crossings. As a result\, this lead to the development\nof "flat-
virtual theory" and a map from knots/links in the thickened cylinder to kn
ots flat virtual knots/links.\n \nIn the present talk\, we discuss possibl
e ways of generalising this approach to the 3-dimensional\nthickening of t
he Moebius band and to the RP^{3} thought of as a 3-dimensional thickening
of RP^{3}.\n
LOCATION:https://stable.researchseminars.org/talk/knotgraphgroup/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jonathan Schneider
DTSTART:20240302T140500Z
DTEND:20240302T153500Z
DTSTAMP:20260404T131156Z
UID:knotgraphgroup/30
DESCRIPTION:Title: REALISTIC CROSSING DATA FOR CURVES IN THE PLANE\nby Jon
athan Schneider as part of Knots\, graphs and groups\n\n\nAbstract\nWhen d
oes a curve in R² with crossing data lift to a knot in R³\, or\, more ge
nerally\, to a fiberwise toral surface in R²×R²? I propose necessary an
d sufficient conditions. I consider three cases:\n1. Generic curves\, whic
h form the basis of familiar knot diagrams. No restrictions are necessary
on crossing data for the static curve\; however\, a homotopy of the curve
must carry the crossing data continuously and avoid "cyclic crossings".\n2
. Cellular curves\, where the curve is a finite cellular map. Here we add
itionally require that the static curve itself carries crossing data conti
nuously from point to point and avoids cyclic crossings.\n3. General curve
s. Here\, the "continuity" restriction of the first two cases is inadequat
e. A stronger pair of conditions\, which I call "monotonicity and stabilit
y"\, is necessary.\n
LOCATION:https://stable.researchseminars.org/talk/knotgraphgroup/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Дмитрий Александрович Шабанов
DTSTART:20240210T140500Z
DTEND:20240210T153500Z
DTSTAMP:20260404T131156Z
UID:knotgraphgroup/31
DESCRIPTION:Title: Дробные раскраски случайных гип
ерграфов\nby Дмитрий Александрович Шаб
анов as part of Knots\, graphs and groups\n\n\nAbstract\nПоиск т
очных пороговых вероятностей для различ
ных свойств является одним из центральн
ых направлений исследований в теории сл
учайных графов и гиперграфов. В докладе
пойдет речь об одной задаче подобного ро
да\, связанной с так называемыми дробным
и раскрасками. С помощью метода второго
момента и решения ряда экстремальных за
дач для стохастических матриц нам удало
сь получить очень точные оценки порогов
ой вероятности для свойства наличия дро
бной (4:2) раскраски в биномиальной модели
случайного гиперграфа. Полученные резу
льтаты также показывают\, что эта порого
вая вероятность строго превышает порого
вую вероятность для классического свойс
тва правильной 2-раскрашиваемости. Докла
д основан на совместной работе с П.А. Зах
аровым.\n
LOCATION:https://stable.researchseminars.org/talk/knotgraphgroup/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexey Sleptsov (Kurchaton institute (ITEP division)\, MIPT and II
TP)
DTSTART:20240224T140500Z
DTEND:20240224T153500Z
DTSTAMP:20260404T131156Z
UID:knotgraphgroup/32
DESCRIPTION:Title: Closed 4-braids and the Jones unknot problem\nby Alexey
Sleptsov (Kurchaton institute (ITEP division)\, MIPT and IITP) as part of
Knots\, graphs and groups\n\n\nAbstract\nJones polynomial is a famous kno
t invariant discovered by V.Jones in 1984. The Jones unknot problem is a q
uestion whether there is a non-trivial knot with the trivial Jones polynom
ial. The answer to this fundamental question is still unknown despite nume
rous attempts to solve it. In the talk I will give a brief review on diffe
rent approaches to this question. I will describe in more detail the const
ruction of Jones polynomials (and HOMFLY-\nPT) through the braid group and
its representations using quantum R-matrices. We will discuss in detail a
family of knots that are the closure of 4-braids. I will talk about what
options there are for solving the Jones problem in this case\, both positi
vely and negatively. The talk is based on a recent preprint arXiv:2402.025
53 (joint work of Dmitriy Korzun\, Elena\nLanina\, Alexey Sleptsov).\n
LOCATION:https://stable.researchseminars.org/talk/knotgraphgroup/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:V.O. Manturov
DTSTART:20240316T140500Z
DTEND:20240316T153500Z
DTSTAMP:20260404T131156Z
UID:knotgraphgroup/33
DESCRIPTION:Title: On the Chromatic Numbers of Integer and Rational Lattices\nby V.O. Manturov as part of Knots\, graphs and groups\n\n\nAbstract\nI
n this talk\, we give new upper bounds for the chromatic numbers for integ
er lattices and some rational spaces and other lattices. In particular\, w
e have proved that for any concrete integer number $d$\, the chromatic num
ber of $\\mathbb{Z}^{n}$ with critical distance $\\sqrt{2}d$ has a polynom
ial growth in $n$ with exponent less than or equal to $d$ (sometimes this
estimate is sharp). The same statement is true not only in the Euclidean n
orm\, but also in any $l_{p}$ norm. Moreover\, we have given concrete esti
mates for some small dimensions as well as upper bounds for the chromatic
number of $\\mathbb{Q}_{p}^{n}$ \, where by $\\mathbb{Q}_{p}$ we mean the
ring of all rational numbers having denominators not divisible by some pri
me numbers.\n
LOCATION:https://stable.researchseminars.org/talk/knotgraphgroup/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Roman Dribas
DTSTART:20240323T140500Z
DTEND:20240323T153500Z
DTSTAMP:20260404T131156Z
UID:knotgraphgroup/34
DESCRIPTION:Title: Ideal tetrahedra\, photography principle and invariants of
manifolds\nby Roman Dribas as part of Knots\, graphs and groups\n\n\nA
bstract\nWe apply the photography principle for hyperbolic 2-3 Pacner move
to construct invariants of 4-manifolds.\n
LOCATION:https://stable.researchseminars.org/talk/knotgraphgroup/34/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Soohyun Park
DTSTART:20240330T140500Z
DTEND:20240330T153500Z
DTSTAMP:20260404T131156Z
UID:knotgraphgroup/35
DESCRIPTION:Title: Hidden structures in (higher) Euler characteristic invarian
ts\nby Soohyun Park as part of Knots\, graphs and groups\n\n\nAbstract
\nWe will discuss the gamma vector\, which was originally considered in th
e context of the combinatorics of Eulerian polynomials and later resurface
d in a special case of the Hopf conjecture on Euler characteristics of (pi
ecewise Euclidean) nonpositively curved manifolds in work of Gal. Since th
en\, it has appeared in many different combinatorial applications. We find
explicit formulas which give a local-global interpretation and complement
/contrast lower bound properties stated earlier by Gal. In addition\, a fo
rmula involving Catalan numbers and binomial coefficients hints at connect
ions to noncrossing partitions and Coxeter groups in existing positivity e
xamples. Finally\, we note considering characteristic classes directly lea
d to log concavity and Schur positivity properties.\n
LOCATION:https://stable.researchseminars.org/talk/knotgraphgroup/35/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sachchidanand Prasad
DTSTART:20240406T140500Z
DTEND:20240406T153500Z
DTSTAMP:20260404T131156Z
UID:knotgraphgroup/36
DESCRIPTION:Title: Cut Locus of Submanifolds: A Geometric Property of the Mani
fold\nby Sachchidanand Prasad as part of Knots\, graphs and groups\n\n
\nAbstract\nThe cut locus of a point in a Riemannian manifold is the colle
ction of all points beyond which a distance minimal geodesics fails to be
distance minimal. In this talk\, we will briefly discuss the cut locus of
a point and submanifolds. We will also review some recent results related
to this.\n
LOCATION:https://stable.researchseminars.org/talk/knotgraphgroup/36/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Illia Rogozhkin
DTSTART:20240413T140500Z
DTEND:20240413T153500Z
DTSTAMP:20260404T131156Z
UID:knotgraphgroup/37
DESCRIPTION:Title: Non-Reidemeister Knot Theory and pure braids invariants
\nby Illia Rogozhkin as part of Knots\, graphs and groups\n\n\nAbstract\nI
n this seminar I will talk about the non-Reidemeister knots theory suggest
ed by Manturov V.O. We will consider the invariant of pure braids $\\Gamma
_n^4$\, that is constructed by considering the braid as a dynamical system
and which gives representations for braids in the form of words and in th
e form of 2x2 matrices. Finally\, I will propose another pure braid invari
ant in matrices of (2n-4)x(2n-4) size\, which is naturally obtained from t
he Delaunay triangulation of a sphere.\n
LOCATION:https://stable.researchseminars.org/talk/knotgraphgroup/37/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Питаль Петя
DTSTART:20240420T140500Z
DTEND:20240420T153500Z
DTSTAMP:20260404T131156Z
UID:knotgraphgroup/38
DESCRIPTION:Title: Обобщенные факториалы и p-упоряд
очения\nby Питаль Петя as part of Knots\, graphs and g
roups\n\n\nAbstract\nВ докладе будет рассказано о
б интересном обобщении понятия факториа
ла\, предложенном М. Бхаргавой для дедек
индовых колец.\n
LOCATION:https://stable.researchseminars.org/talk/knotgraphgroup/38/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Канель-Белов Алексей Яковлевич
DTSTART:20240427T140500Z
DTEND:20240427T153500Z
DTSTAMP:20260404T131156Z
UID:knotgraphgroup/39
DESCRIPTION:Title: Проблема Шпехта\, гипотеза Гельф
анда и некоммутативная алгебраическая г
еометрия\nby Канель-Белов Алексей Яковл
евич as part of Knots\, graphs and groups\n\n\nAbstract\nТождес
твом алгебры $A$ называется многочлен\, то
ждественно обращающейся в ноль на ней. В
коммутативных алгебрах выполняется то
ждество $[x\,y]=xy-yx=0$\, в алгебре матриц втор
ого порядка - тождество $[[x\,y]^2\,z]=0$ и т.д. Т
ождество $g$ следует из набора $f_i$ если в
любой алгебре где выполняется система т
ождеств $f_i$ выполняется тождество $g$. Пр
облема Шпехта состоит в том\, что верно л
и\, что любая система тождеств в некоммут
ативном ассоциативном кольце следует из
конечной подсистемы? \nРешение этой про
блемы приводит к задачам комбинаторики
слов (в том числе элементарным)\, к новой
точки зрения на некоммутативную алгебра
ическую геометрию. Недавно А.Хорошкин\,
И.Воробьев и А.Я.Белов вывели из одного и
з версий доказательства гипотезу Гельф
анда о нетеровости действия полиномиал
ьных векторных полей без свободного чле
на на тензорных представлениях. \nКомбин
аторное идейное ядро заключается в след
ующей элементарной задаче. Рассмотрим к
ольцо многочленов от хватит двух переме
нных $x\,y$ . Рассмотрим подстановку $x\\to P(x)
\, y\\to P(y)$. Многочлен $P$ один и тот же. Тогд
а любое подпространство\, замкнутое отно
сительно такой подстановки выводится и
з конечной подсистемы (подстановками и
линейными действиями). Ей и будет уделен
о основное внимание.\n
LOCATION:https://stable.researchseminars.org/talk/knotgraphgroup/39/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Louis H Kauffman (UIC)
DTSTART:20240504T140500Z
DTEND:20240504T153500Z
DTSTAMP:20260404T131156Z
UID:knotgraphgroup/40
DESCRIPTION:Title: Multiple Virtual Knot Theory\nby Louis H Kauffman (UIC)
as part of Knots\, graphs and groups\n\n\nAbstract\nThis talk is an intro
duction to Multiple Virtual Knot Theory (MVKT) where one has classical cro
ssings\, flat crossings\, singular crossings and a multiplicity of virtual
crossings.\nAll virtual crossings can make detour moves over all the othe
r crossing types including the other virtuals. We will discuss a number of
different invariants in this theory and also its relationship with colori
ng problems and Penrose evaluations and Penrose perfect matching polynomia
ls (as related to joint work with Scott Baldrige and Ben McCarty). We will
discuss relationships of MVKT with virtual knot theories on surfaces of g
enus greater than zero\, with welded MVTK and braid groups for these theor
ies.\n
LOCATION:https://stable.researchseminars.org/talk/knotgraphgroup/40/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Maksim Zhukovskii
DTSTART:20240511T140500Z
DTEND:20240511T153500Z
DTSTAMP:20260404T131156Z
UID:knotgraphgroup/41
DESCRIPTION:Title: Stability of large cuts in random graphs\nby Maksim Zhu
kovskii as part of Knots\, graphs and groups\n\n\nAbstract\nWe prove that
the family of largest cuts in the binomial random graph exhibits the follo
wing stability property: with high probability\, there is a set of (1-o(1)
)n vertices that is partitioned in the same manner by all maximum cuts. We
also show some applications of this property - in particular\, to the val
idity of Simonovits's property in binomial random graphs.\nThe talk is bas
ed on joint work with Ilay Hoshen and Wojciech Samotij\n
LOCATION:https://stable.researchseminars.org/talk/knotgraphgroup/41/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hayk Sedrakyan
DTSTART:20240518T140500Z
DTEND:20240518T153500Z
DTSTAMP:20260404T131156Z
UID:knotgraphgroup/42
DESCRIPTION:Title: Novel Sedrakyan-Mozayeni theorem\, and its applications in
scientific research in topology and geometry\nby Hayk Sedrakyan as par
t of Knots\, graphs and groups\n\n\nAbstract\nIn this presentation\, we co
nsider several applications of the Sedrakyan-Mozayeni theorem. In particu
lar\, we investigate how it can be applied in novel mathematical scientif
ic research in topology and geometry to generalize the pentagon case of
the photography principle\, data transmission and invariants of manifolds
. We will also go in depth on the derivation of Sedrakyan-Mozayeni theorem
\, and explain current issues with the pentagon case of the photography p
rinciple. Besides having theoretical applications\, the formula can be us
ed in applied mathematics and lead to new real-world results. We will imp
lement the formula into a code and generate several computer simulations
applied in novel mathematical scientific research in topology and geometr
y.\n
LOCATION:https://stable.researchseminars.org/talk/knotgraphgroup/42/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Euich Miztani
DTSTART:20240525T140500Z
DTEND:20240525T153500Z
DTSTAMP:20260404T131156Z
UID:knotgraphgroup/43
DESCRIPTION:Title: How Should We Interpret Space Dimenion?\nby Euich Mizta
ni as part of Knots\, graphs and groups\n\n\nAbstract\nIn modern physics w
e could say that space dimension is derived from some physical conditions
. Kaluza-Klein theory and D-brane are typical examples. However\, not onl
y by such conditions\, we should also think about space dimension with in
sights from known facts possibly without physical conditions. In this tal
k we rethink space dimensionality from scratch.\n
LOCATION:https://stable.researchseminars.org/talk/knotgraphgroup/43/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Seongjeong Kim
DTSTART:20240601T140500Z
DTEND:20240601T153500Z
DTSTAMP:20260404T131156Z
UID:knotgraphgroup/44
DESCRIPTION:Title: The groups $G_{n}^{3}$ and rhombi tilings of 2n-gons\nb
y Seongjeong Kim as part of Knots\, graphs and groups\n\n\nAbstract\nIn th
is talk we will consider a map from the set of rhombi tilings of 2n-gon to
the group $G_{n}^{3}$ and will discuss our further researches.\n
LOCATION:https://stable.researchseminars.org/talk/knotgraphgroup/44/
END:VEVENT
BEGIN:VEVENT
SUMMARY:O.G. Styrt
DTSTART:20240608T130500Z
DTEND:20240608T143500Z
DTSTAMP:20260404T131156Z
UID:knotgraphgroup/45
DESCRIPTION:Title: Compact linear groups with quotient space homeomorphic to a
cell.\nby O.G. Styrt as part of Knots\, graphs and groups\n\n\nAbstra
ct\nThe main part of my research is devoted to the following question: whe
n the quotient space of a linear representation of a compact Lie group is
homeomorphic to a vector space.\nThe first result for finite linear groups
was obtained in 1984 by M.A. Michailova: it should be generated by pseudo
reflections.\nI have investigated the cases of groups with commutative con
nected components and of irreducible simple groups of classical types. I a
m going to speak in detail on the first of these cases. The condition is h
ardly formulated in terms of the weight system of the torus and requires a
special procedure of reducing a general case to that with indecomposable
and «$2$-stable» weight system\; further\, the criterion for namely this
particular case is obtained (but still hard even to formulate). This redu
cing procedure uses a construction provided by one key example of a repres
entation when the quotient is a vector space. For more understanding\, I p
lan to describe this key representation whose weights have exactly one (up
to constants) nontrivial linear relation without zero coefficients and to
construct explicitly a factorization mapping onto a space.\n
LOCATION:https://stable.researchseminars.org/talk/knotgraphgroup/45/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sergei Gukov
DTSTART:20240622T130500Z
DTEND:20240622T143500Z
DTSTAMP:20260404T131156Z
UID:knotgraphgroup/46
DESCRIPTION:Title: New quantum invariants from braiding Verma modules\nby
Sergei Gukov as part of Knots\, graphs and groups\n\n\nAbstract\nIn this t
alk\, I will describe recent construction of new link and 3-manifold invar
iants associated with Verma modules of $U_q (sl_N)$ at generic $q$. The re
sulting invariants can be combined into a Spin$^c$-decorated TQFT and have
a nice property that\, for links in general 3-manifolds\, they have integ
er coefficients. In particular\, they are expected to admit a categorifica
tion and\, if time permits\, I will outline various ingredients that may g
o into a construction of 3-manifold homology categorifying these $U_q (sl_
N)$ invariants at generic $q$.\n
LOCATION:https://stable.researchseminars.org/talk/knotgraphgroup/46/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jian Liu
DTSTART:20240615T130500Z
DTEND:20240615T143500Z
DTSTAMP:20260404T131156Z
UID:knotgraphgroup/47
DESCRIPTION:Title: Interaction homotopy and interaction homology\nby Jian
Liu as part of Knots\, graphs and groups\n\n\nAbstract\nInteractions in co
mplex systems are widely observed across various fields\, drawing increase
d attention from researchers. In mathematics\, efforts are made to develop
various theories and methods for studying the interactions between spaces
. In this talk\, we present an algebraic topology framework to explore int
eractions between spaces. We introduce the concept of interaction spaces a
nd investigate their homotopy\, singular homology\, and simplicial homolog
y. Furthermore\, we demonstrate that interaction singular homology serves
as an invariant under interaction homotopy. We believe that the proposed f
ramework holds potential for practical applications.\n
LOCATION:https://stable.researchseminars.org/talk/knotgraphgroup/47/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Elena Lanina
DTSTART:20240629T130500Z
DTEND:20240629T143500Z
DTSTAMP:20260404T131156Z
UID:knotgraphgroup/48
DESCRIPTION:Title: Tug-the-hook symmetry for quantum 6j-symbols\nby Elena
Lanina as part of Knots\, graphs and groups\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/knotgraphgroup/48/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alina Pital
DTSTART:20240706T130500Z
DTEND:20240706T143500Z
DTSTAMP:20260404T131156Z
UID:knotgraphgroup/49
DESCRIPTION:Title: Non-bipartite knots\nby Alina Pital as part of Knots\,
graphs and groups\n\n\nAbstract\nThe existence of non-bipartite knot was c
onjectured in 1987 by J. Przytycki and proven by S.V. Duzhin\nin 2011. We
will disprove the conjecture that bipartite knots should have trivial seco
nd Alexander ideal. We will\nconstruct a family inside the class of bipart
ite knots that contains all rational knots and has trivial second\nAlexand
er ideal. We will present a matched diagram of the knot 818. Also we will
demonstrate a combinatorial\ntechniques that could be useful for further r
esearch on bipartite knots.\n
LOCATION:https://stable.researchseminars.org/talk/knotgraphgroup/49/
END:VEVENT
BEGIN:VEVENT
SUMMARY:O.G. Styrt
DTSTART:20240713T100500Z
DTEND:20240713T113500Z
DTSTAMP:20260404T131156Z
UID:knotgraphgroup/50
DESCRIPTION:Title: Compact linear groups with quotient space homeomorphic to a
cell\nby O.G. Styrt as part of Knots\, graphs and groups\n\n\nAbstrac
t\nThe main part of my research is devoted to the following question: when
the quotient space of a linear representation of a compact Lie group is h
omeomorphic to a vector space.\nThe first result for finite linear groups
was obtained in 1984 by M.A. Michailova: it should be generated by pseudor
eflections.\nI have investigated the cases of groups with commutative conn
ected components and of irreducible simple groups of classical types. I am
going to speak in detail on the first of these cases. The condition is ha
rdly formulated in terms of the weight system of the torus and requires a
special procedure of reducing a general case to that with indecomposable a
nd «$2$-stable» weight system\; further\, the criterion for namely this
particular case is obtained (but still hard even to formulate). This reduc
ing procedure uses a construction provided by one key example of a represe
ntation when the quotient is a vector space. For more understanding\, I pl
an to describe this key representation whose weights have exactly one (up
to constants) nontrivial linear relation without zero coefficients and to
construct explicitly a factorization mapping onto a space.\n
LOCATION:https://stable.researchseminars.org/talk/knotgraphgroup/50/
END:VEVENT
BEGIN:VEVENT
SUMMARY:V.O. Manturov
DTSTART:20240720T100500Z
DTEND:20240720T113500Z
DTSTAMP:20260404T131156Z
UID:knotgraphgroup/51
DESCRIPTION:Title: The photography method. The state of the art. Review and un
solved problem\nby V.O. Manturov as part of Knots\, graphs and groups\
n\n\nAbstract\nIn 2023\, the author formulated the photography method whic
h allows one to \nto solve various equations and calculate invariants of
various objects.\n \nOne starts with some object (say\, pentagon) with a s
tate (say\, triangulation) and\ndata (say\, edge lengths) a data transform
ation rule (say\, a flip of a triangulation).\nThen by using some geometri
cal considerations\, one can prove "for free" that\nsuch data transformati
on rules give rise to solutions to some equation\n[say\, Ptolemy transform
ation satisfies the Pentagon equation] and\nconstruct invariants of many o
bjects [say\, braids].\n \nThe formula can be taken from any geometrical c
onsiderations (say\, formulas\nin the hyperbolic space)\; having such a fo
rmula "for free" one can prove it\nalgebraically and pass to the more abst
ract objects (say\, formal variables instead of\nlengths).\n \n \nThis me
thod is very broad. Here we mention just some directions of (further resea
rch):\ninvariants of knots\, braids\, manifolds\, solutions to the pentago
n\, hexagon\, YBE equations\nand formulate relations to cluster algebras\,
tropical geometry\, and many other areas of\nmathematics.\n
LOCATION:https://stable.researchseminars.org/talk/knotgraphgroup/51/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexei Vernitski
DTSTART:20240817T100500Z
DTEND:20240817T113500Z
DTSTAMP:20260404T131156Z
UID:knotgraphgroup/52
DESCRIPTION:Title: Approaches to realisability of Gauss diagrams\nby Alexe
i Vernitski as part of Knots\, graphs and groups\n\n\nAbstract\nThe shape
of a closed curve can be summarised by a chord diagram called the Gauss di
agram of the curve. Not every chord diagram is the Gauss diagram of a curv
e\; if it is\, it is called realisable. I will present a number of elegant
constructions which were introduced in the context of describing realisab
le Gauss diagrams. These constructions include graphs summarising Gauss di
agrams and moves transforming Gauss diagrams. I will discuss some open pro
blems. The talk is partially based on paper https://www.worldscientific.c
om/doi/10.1142/S0218216523500591 and preprint https://arxiv.org/pdf/2407
.09144\n
LOCATION:https://stable.researchseminars.org/talk/knotgraphgroup/52/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Seongjeong Kim
DTSTART:20240727T100500Z
DTEND:20240727T113500Z
DTSTAMP:20260404T131156Z
UID:knotgraphgroup/53
DESCRIPTION:Title: Knot in $S_{g}\\times S^{1}$ of degree one and long knot in
variants\nby Seongjeong Kim as part of Knots\, graphs and groups\n\n\n
Abstract\nIn this talk we construct invariants for knots in $S_{g}\\times
S^{1}$ of degree one by using long knot invariants.\n
LOCATION:https://stable.researchseminars.org/talk/knotgraphgroup/53/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alina Pital
DTSTART:20240803T100500Z
DTEND:20240803T113500Z
DTSTAMP:20260404T131156Z
UID:knotgraphgroup/54
DESCRIPTION:Title: Phenomena of emptiness in different theories\nby Alina
Pital as part of Knots\, graphs and groups\n\n\nAbstract\nI would like to
touch some notions in knot and set theory and talk about relationships be
tween emptiness in knot theory (aka phenomena of empty knot in terms of f
ib-ration) and famous empty set.\n
LOCATION:https://stable.researchseminars.org/talk/knotgraphgroup/54/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Алена Жукова
DTSTART:20240810T100500Z
DTEND:20240810T113500Z
DTSTAMP:20260404T131156Z
UID:knotgraphgroup/55
DESCRIPTION:by Алена Жукова as part of Knots\, graphs and group
s\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/knotgraphgroup/55/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Louis H Kauffman
DTSTART:20240824T130500Z
DTEND:20240824T143500Z
DTSTAMP:20260404T131156Z
UID:knotgraphgroup/57
DESCRIPTION:Title: Empty Knots and Negative Dimensions in Combinatorics and To
pology\nby Louis H Kauffman as part of Knots\, graphs and groups\n\n\n
Abstract\nNotions of topological structures remain significant as we appro
ach zero dimensions or even go below them.\nWe are all familiar with the s
ignificance of the empty set for mathematics as a whole - since the empty
set { } is the beginning of set construction and indeed stands for the con
cept of a set as a container. Similarly there are empty knots in the circl
e S^{1}.\nNote that we may\, by analogy\, take an empty knot in S^{1} as h
aving dimension -1 since it should be two dimensions down from the dimensi
on of its containing sphere. And the empty knots in S^{1} have Milnor fibe
rings psi_{a} : S^{1} —> S^{1} defined by\npsi_{a}(z) = z^{a} where z =
exp(I Theta) is an S^{1} parameter. We shall explain and show how the Kauf
fman-Neumann notion of Knot Products (circa 1978) produces first\, torus k
nots from products of empty knots\, and then all Brieskorn varieties as pr
oducts of empty knots\, hence exotic spheres and much more\, including rec
ent work of Kauffman and Ogasa. That is part one of this talk. Part two co
nsiders how the “negative dimensional tensors” of Roger Penrose are re
lated to the Kauffman bracket polynomial and the Jones polynomial and how
negative dimensions become generalized to arbitrary parameters in the subj
ect of quantum link invariants. Is there a relationship between the negati
ve dimensions of empty knots and quantum invariants of knots? This can be
a topic for discussion after the talk.\n
LOCATION:https://stable.researchseminars.org/talk/knotgraphgroup/57/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bernhard Keller (Universite Paris Cite)
DTSTART:20240907T140500Z
DTEND:20240907T153500Z
DTSTAMP:20260404T131156Z
UID:knotgraphgroup/58
DESCRIPTION:Title: From quiver representations to cluster variables\nby Be
rnhard Keller (Universite Paris Cite) as part of Knots\, graphs and groups
\n\n\nAbstract\nIn this expository talk\, we will recall Gabriel's theorem
on quiver representations and Fomin-Zelevinsky's theorem on cluster-finit
e cluster algebras. Then we will link the two theorems using Caldero-Chapo
ton's formula\, which assigns a Laurent polynomial to a quiver representat
ion using the Euler characteristics of its varieties of subrepresentations
(quiver Grassmannians). This link is the beginning of the theory of "addi
tive categorification" of cluster algebras.\n
LOCATION:https://stable.researchseminars.org/talk/knotgraphgroup/58/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Louis kauffman
DTSTART:20240914T140500Z
DTEND:20240914T153500Z
DTSTAMP:20260404T131156Z
UID:knotgraphgroup/59
DESCRIPTION:by Louis kauffman as part of Knots\, graphs and groups\n\nAbst
ract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/knotgraphgroup/59/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nilangshu Bhattacharyya
DTSTART:20240921T140500Z
DTEND:20240921T153500Z
DTSTAMP:20260404T131156Z
UID:knotgraphgroup/60
DESCRIPTION:Title: Lipschitz-Sarkar Stable Homotopy Type for Planar Trivalent
Graph with Perfect Matchings\nby Nilangshu Bhattacharyya as part of Kn
ots\, graphs and groups\n\n\nAbstract\nLipschitz-Sarkar constructed Stable
Homotopy Types for the Khovanov Homology of links in $S^3$. Following tha
t\, Kauffman-Nikonov-Ogasa found a family of Stable Homotopy types for the
Homotopical Khovanov homology for links in thickened surfaces. Baldridge
gave a cohomology theory which categorifies 2-factor polynomial of planar
trivalent graphs with perfect matchings. In this talk\, I will present on
the construction of the Khovanov-Lipschitz-Sarkar stable Homotopy type for
the Baldridge cohomology theory.\n
LOCATION:https://stable.researchseminars.org/talk/knotgraphgroup/60/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dmitry N. Hudoteplov
DTSTART:20240928T140500Z
DTEND:20240928T153500Z
DTSTAMP:20260404T131156Z
UID:knotgraphgroup/61
DESCRIPTION:Title: Kernel of $sl(N)$ weight systems\nby Dmitry N. Hudotepl
ov as part of Knots\, graphs and groups\n\n\nAbstract\nIn theory of Vassil
iev invariants\, each knot is mapped to a series of trivalent graphs (Jaco
bi diagrams) by the Kontsevich integral. Kontsevich intagral contains all
the Vassiliev knot invariants and quantum knot polynomials (HOMFLY\, Kauff
man etc.) can be extracted from the Kontsevich integral by applying a corr
esponding Lie algebra weight system.\n\nIn this talk\, the case of $sl(N)$
weight systems will be discussed. $sl(N)$ weight systems correspond to th
e colored HOMFLY polynomial. Jacobi diagrams in the kernel of $sl(N)$ weig
ht systems can be associated with Vassiliev invariants missing from the HO
MFLY polynomial. This kernel can be constructed explicitly using the findi
ngs of Pierre Vogel\, who developed a framework to operate with Jacobi dia
grams and Lie algebra weight systems.\n
LOCATION:https://stable.researchseminars.org/talk/knotgraphgroup/61/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mika Nelimov
DTSTART:20241005T140500Z
DTEND:20241005T153500Z
DTSTAMP:20260404T131156Z
UID:knotgraphgroup/62
DESCRIPTION:Title: Functions of Hyperbolicity of groups\nby Mika Nelimov a
s part of Knots\, graphs and groups\n\n\nAbstract\nThe article introduces
the concept of the δ-function of space. It measures the growth of the opt
imal hyperbolicity constant of a ball of radius R. The function is bounded
equivalent to the hyperbolicity of the group. The asymptotics of this fun
ction for various non-hyperbolic spaces and groups are studied. Examples o
f metric spaces for which it grows in a given manner are constructed. Its
linearity is proved for the Baumslag-Solitar group $BS(1\,2)$\, as well as
for the Lampochnik group.\n
LOCATION:https://stable.researchseminars.org/talk/knotgraphgroup/62/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Seongjeong Kim
DTSTART:20241012T140500Z
DTEND:20241012T153500Z
DTSTAMP:20260404T131156Z
UID:knotgraphgroup/63
DESCRIPTION:Title: Classification of knots in $S_{g} \\times S^{1}$ with small
number of crossings\nby Seongjeong Kim as part of Knots\, graphs and
groups\n\n\nAbstract\nIn knot theory not only classical knots\, which are
embedded circles in S^{3} up to isotopy\, but also knots in other 3-mani
folds are interesting for mathematicians. In particular\, virtual knots\,
which are knots in thickened surface $S_{g} \\times [0\,1]$ with an orie
ntable surface $S_{g}$ of genus $g$\, are studied and they provide intere
sting properties.\nIn this talk\, we will talk about knots in $S_{g} \\t
imes S^{1}$ where $S_{g}$ is an oriented surface of genus $g$. We introdu
ce basic notions and properties for them. In particular\, for knots in $S
_{g} \\times S^{1}$ one of important information is “how many times a h
alf ot a crossing turns around $S^{1}$”\, and we call it winding parity
of a crossing. We extend this notion more generally and introduce a top
ological model. In the end we apply it to classify knots in $S_{g}\\times
S^{1}$ with small number of crossings.\n
LOCATION:https://stable.researchseminars.org/talk/knotgraphgroup/63/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexei Y. Kanel-Belov
DTSTART:20241019T140500Z
DTEND:20241019T153500Z
DTSTAMP:20260404T131156Z
UID:knotgraphgroup/64
DESCRIPTION:Title: Алгоритмическая неразрешимость
проблемы вложения\nby Alexei Y. Kanel-Belov as part o
f Knots\, graphs and groups\n\n\nAbstract\nЧрезвычайно инте
ресной и фундаментальной является задач
а об алгоритмической разрешимости прове
рки наличия изоморфизма между двумя алг
ебраическими многообразиями. Родственн
ой и более простой задачей является зада
ча о вложимости. В общем виде она формули
руется так: пусть A и B – два алгебраическ
их многообразия\; определить\, существуе
т ли вложение A в B\, найти алгоритм или до
казать его отсутствие. Доклад посвящен о
трицательному решению данного вопроса д
ля аффинных многообразий над произвольн
ом полем характеристики нуль\, чьи коорд
инатные кольца заданы образующими и опр
еделяющими соотношениями.\n
LOCATION:https://stable.researchseminars.org/talk/knotgraphgroup/64/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hayk Sedrakyan
DTSTART:20241026T140500Z
DTEND:20241026T153500Z
DTSTAMP:20260404T131156Z
UID:knotgraphgroup/65
DESCRIPTION:Title: The general case (any pentagon). Photography principle\, da
ta transmission\, and invariants of manifolds\nby Hayk Sedrakyan as pa
rt of Knots\, graphs and groups\n\n\nAbstract\nThis work builds on the wor
k previously done by Professors L.Kauffman\, V.O.Manturov\, I.M.Nikonov\,
and S.Kim in their paper at Photography principle\, data transmission\, an
d invariants of manifolds. Please read the beginning of this paper to unde
rstand what we are trying to do here. On page 6 of their paper\, they use
Ptolemy’s theorem to establish a lemma and proceed from there. We will b
e covering the case where the pentagon in question is not cyclic\, and thu
s Ptolemy’s Theorem is not usable.\n
LOCATION:https://stable.researchseminars.org/talk/knotgraphgroup/65/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anna Taranenko
DTSTART:20241102T140500Z
DTEND:20241102T153500Z
DTSTAMP:20260404T131156Z
UID:knotgraphgroup/66
DESCRIPTION:Title: On vertices of the polytope of polystochastic matrices\
nby Anna Taranenko as part of Knots\, graphs and groups\n\n\nAbstract\nA m
ultidimensional matrix is polystochastic if it has nonnegative entries and
the sum of entries in each line is equal to 1. A set of d-dimensional pol
ystochastic matrices of order n is the Birkhoff polytope.\n The well-known
Birkhoff theorem states that all vertices of the polytope of 2-dimensiona
l polystochastic matrices are permutation matrices. For greater dimensions
the Birkhoff polytope has vertices different from multidimensional permut
ations.\n In this talk\, we review bounds on the numbers of vertices of th
e Birkhoff polytope and propose several iterative constructions of vertice
s. We pay special attention to the polytope of polystochastic matrices of
order 3. In particular\, we show that this polytope has many vertices diff
erent from multidimensional permutations and find all vertices of the poly
tope of 4-dimensional polystochastic matrices of order 3.\n
LOCATION:https://stable.researchseminars.org/talk/knotgraphgroup/66/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Seongjeong Kim
DTSTART:20241109T140500Z
DTEND:20241109T153500Z
DTSTAMP:20260404T131156Z
UID:knotgraphgroup/67
DESCRIPTION:Title: The groups $G_{n}^{k}$\, $2n$-gon tilings\, and stacking of
cubes\nby Seongjeong Kim as part of Knots\, graphs and groups\n\n\nAb
stract\nIn the present talk we discuss three ways of looking at rhombile t
ilings: stacking 3-dimensional cubes\, elements of groups\, and configurat
ions of lines and points.\n
LOCATION:https://stable.researchseminars.org/talk/knotgraphgroup/67/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Louis H Kauffman
DTSTART:20241123T140500Z
DTEND:20241123T153500Z
DTSTAMP:20260404T131156Z
UID:knotgraphgroup/68
DESCRIPTION:Title: Physics\, Braiding and the Dirac equation\nby Louis H K
auffman as part of Knots\, graphs and groups\n\n\nAbstract\nMathematically
\, electrons (Fermions) are seen to correspond to operators F and F* (the
anti-particle) such that\nF^2 = F*^2 = 0 (Pauli Exclusion Principle) and F
F* + F*F = 1 (a basic quantum relation). And mathematically you can achiev
e these algebraic relations from Clifford algebra by taking\nGenerators a
and b so that s^2=b^2 = 1 and ab = -ba. Let F = (a+ ib)/2 and F* = (a -ib)
/2. The 4F^2 = a^2 -b^2 + i ( ab + ba) = 0 and similarly F*^2 = 0. But the
n 1 = a^2 = (F + F*)^2 = FF* + F* F.\nSo a mathematical electron F can be
created from two “Majorana Fermions” (a and b). Is there a physical re
ality behind this decomposition? Experiments over the last twenty years su
ggest that it is so and that there is a possibility to use topological pro
perties (braiding and braid group representations) of the Majorana Fermion
s to accomplish topological quantum computing. In this talk we will discus
s those braid group representations and we will discuss how Majorana Fermi
ons (and Fermions) are related to solutions to the Dirac equation.\n
LOCATION:https://stable.researchseminars.org/talk/knotgraphgroup/68/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Антон Белецкий
DTSTART:20241116T140500Z
DTEND:20241116T153500Z
DTSTAMP:20260404T131156Z
UID:knotgraphgroup/69
DESCRIPTION:Title: Теория малых сокращений и ее при
менение к проблеме Бернсайда в подходе И
. Рипса\nby Антон Белецкий as part of Knots\, graphs
and groups\n\n\nAbstract\nПроблема Бернсайда широк
о известна как один из важнейших вопросо
в теории групп. Ключевой областью\, позво
лившей достичь успехов в ее решении\, ста
ла так называемая теория малых сокращен
ий\, изучающая группы\, образующие соотно
шения в которых слабо пересекаются друг
с другом (обобщения этой теории использу
ются в классической работе С. И. Адяна и П
. С. Новикова\, а также в работах А. Ю. Ольш
анского).\nМы начнем с того что дадим крат
кое напоминание основных идей этой теор
ии. После этого мы попробуем построить о
бобщение этой теории (разработанное И. Р
ипсом)\, позволяющее применить ее для ана
лиза групп Бернсайда и анализа диаграмм
Ван-Кампена\, в которых соотношения *схо
жих размеров* слабо зацепляются друг за
друга. Мы постараемся давать все необход
имые определения по ходу доклада (хотя б
ы неформально)\, однако для более глубоко
го понимания темы может быть полезным пр
едварительное знакомство с основами тео
рией малых сокращений.\n
LOCATION:https://stable.researchseminars.org/talk/knotgraphgroup/69/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Aritra Bhowmick
DTSTART:20241130T140500Z
DTEND:20241130T153500Z
DTSTAMP:20260404T131156Z
UID:knotgraphgroup/70
DESCRIPTION:Title: h-Principle for Maps Transverse to Bracket-Generating Distr
ibutions\nby Aritra Bhowmick as part of Knots\, graphs and groups\n\n\
nAbstract\nThe goal of an h-principle is to transform a "hard" problem in
geometry\, which involves solving a partial differential equation\, into a
"soft" problem in algebraic topology. In his monograph Partial Differenti
al Relations (1986)\, Mikhael Gromov asked the reader to prove the h-princ
iple for maps transverse to a bracket-generating distribution. Recall that
a distribution on a manifold is said to be bracket-generating if it Lie-b
racket generates the tangent space in a finite number of steps at each poi
nt. In 2020\, this problem was solved by Álvaro del Pino and Tobias Shin
for real-analytic distributions using tools from algebraic geometry.\n\nIn
the first part of this talk\, we shall introduce what an h-principle is a
nd present several examples of h-principles. Then\, we shall briefly outli
ne a general strategy to prove an h-principle statement\, following the an
alytic and sheaf-theoretic techniques of Gromov. We shall see how this str
ategy applies to proving h-principles for immersions that are horizontal t
o a given distribution. Finally\, we shall present an outline of a proof f
or the question posed by Gromov in the smooth case using mostly elementary
techniques.\n
LOCATION:https://stable.researchseminars.org/talk/knotgraphgroup/70/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Scott Baldridge
DTSTART:20241207T140500Z
DTEND:20241207T153500Z
DTSTAMP:20260404T131156Z
UID:knotgraphgroup/71
DESCRIPTION:Title: Four face colorings of a planar graph correspond to three f
ace colorings on a special collection of surfaces\nby Scott Baldridge
as part of Knots\, graphs and groups\n\n\nAbstract\nThe four color problem
states that every plane graph without a bridge has a 4-face coloring\, i.
e.\, there exists a coloring of the faces of the graph with four colors su
ch that no two adjacent faces along an edge share the same color. In this
talk we prove that every 4-face coloring of a plane graph corresponds in a
4-to-1 way to a 3-face coloring on some possibly higher genus\, possibly
non-orientable surface. Thus\, the four color problem is really about stud
ying 3-face colorings on non-planar surfaces! These ideas come from unders
tanding our filtered 3-color homology of graphs\, which will be described
as part of the talk.\n
LOCATION:https://stable.researchseminars.org/talk/knotgraphgroup/71/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Amit Kumar
DTSTART:20241214T140500Z
DTEND:20241214T153500Z
DTSTAMP:20260404T131156Z
UID:knotgraphgroup/72
DESCRIPTION:Title: Coloring Trivalent Graphs: A Defect TFT Approach\nby Am
it Kumar as part of Knots\, graphs and groups\n\n\nAbstract\nWe show that
the combinatorial matter of graph coloring is\, in fact\, quantum in the s
ense of satisfying the sum over all the possible intermediate state proper
ties of a path integral. In our case\, the topological field theory (TFT)
with defects gives meaning to it. This TFT has the property that when eval
uated on a planar trivalent graph\, it provides the number of Tait-Colorin
g of it. Defects can be considered as a generalization of groups. With the
Klein-four group as a 1-defect condition\, we reinterpret graph coloring
as sections of a certain bundle\, distinguishing a coloring (global-sectio
ns) from a coloring process (local-sections.) These constructions also lea
d to an interpretation of the word problem\, for a finitely presented grou
p\, as a cobordism problem and a generalization of (trivial) bundles at th
e level of higher categories.\n
LOCATION:https://stable.researchseminars.org/talk/knotgraphgroup/72/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Галина Константиновна Соколова
DTSTART:20241221T140500Z
DTEND:20241221T153500Z
DTSTAMP:20260404T131156Z
UID:knotgraphgroup/73
DESCRIPTION:Title: Сопровождающая матрица суперпо
зиции полиномов и ее применение к теории
узлов\nby Галина Константиновна Соколо
ва as part of Knots\, graphs and groups\n\n\nAbstract\nВ докладе
приводится новая форма для сопровождаю
щей матрицы суперпозиции двух полиномов
над коммутативным кольцом. Полученные р
езультаты используются для проведения к
онструктивного доказательства теоремы
Планса для двумостовых узлов\, которая у
тверждает\, что первая группа гомологий
нечетно-листного и группа гомологий чет
но-листного накрытия сферы над узлом\, пр
офакторизованная по гомологии двулистн
ого накрытия\, распадаются в прямую сумм
у двух копий некоторой абелевой группы.
Структура абелевых групп описываются че
рез полиномы Чебышева четвертого и втор
ого рода.\n
LOCATION:https://stable.researchseminars.org/talk/knotgraphgroup/73/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Seongjeong Kim
DTSTART:20241228T140500Z
DTEND:20241228T153500Z
DTSTAMP:20260404T131156Z
UID:knotgraphgroup/74
DESCRIPTION:Title: On invariants for surface-links valued in entropic magmas\nby Seongjeong Kim as part of Knots\, graphs and groups\n\n\nAbstract\n
M. Niebrzydowski and J. H. Przytycki defined a Kauffman bracket magma and
constructed the invariant P of framed links in 3-space. The invariant is c
losely related to the Kauffman bracket polynomial. The normalized bracket
polynomial is obtained from the Kauffman bracket polynomial by the multipl
ication of indeterminate and it is an ambient isotopy invariant for links.
In this talk\, we reformulate the multiplication by using a map from the
set of framed links to a Kauffman bracket magma in order that P is invaria
nt for links in 3-space. We define a generalization of a Kauffman bracket
magma\, which is called a marked Kauffman bracket magma. We find the condi
tions to be invariant under Yoshikawa moves except the first one and use a
map from the set of admissible marked graph diagrams to a marked Kauffman
bracket magma to obtain the invariant for surface-links in 4-space.\n
LOCATION:https://stable.researchseminars.org/talk/knotgraphgroup/74/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ф.В.Петров
DTSTART:20250104T140500Z
DTEND:20250104T153500Z
DTSTAMP:20260404T131156Z
UID:knotgraphgroup/75
DESCRIPTION:Title: Ветвление в плоской задаче Джил
берта - Штейнера имеет степень не выше 3\nby Ф.В.Петров as part of Knots\, graphs and groups\n\n\nAbstrac
t\nПусть на плоскости дано два конечных н
абора материальных точек равной суммарн
ой массы. Перевести $t$ килограмм на расст
ояние $d$ стоит $d t^p$ рублей\, где $0< p <1$ . Мин
имальная стоимость плана перевозки масс
ы из первого набора во второй реализуетс
я некоторым деревом. Мы доказываем\, что
степени его вершин не превосходят 3. Дока
зательство основано на теории Бохнера и
Шёнберга вполне положительных функций.
По совместной работе с Д. Черкашиным.\n
LOCATION:https://stable.researchseminars.org/talk/knotgraphgroup/75/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vassily O. Manturov
DTSTART:20250111T140500Z
DTEND:20250111T153500Z
DTSTAMP:20260404T131156Z
UID:knotgraphgroup/76
DESCRIPTION:Title: Towards invariants of knots and links via $G_{n}^{k}$\n
by Vassily O. Manturov as part of Knots\, graphs and groups\n\n\nAbstract\
nIt has been 10 years since the author introduced groups G_{n}^{k} dependi
ng on two natural numbers n>k and constructed invariants of many configura
tion spaces valued in such groups. https://www.arxiv.org/abs/1501.05208 Th
e first two natural invariants dealt with braids on n strands\, n>3\, valu
ed in G_{n}^{3} and G_{n}^{4}.\nWe shall discuss how to construct similar
invariants for n-component\nlinks and describe various possible ways what
to do with knots (single component). The approach uses closed braids and M
arkov moves.\nMany unsolved problems will be formulated.\n
LOCATION:https://stable.researchseminars.org/talk/knotgraphgroup/76/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vassily O. Manturov
DTSTART:20250118T140500Z
DTEND:20250118T153500Z
DTSTAMP:20260404T131156Z
UID:knotgraphgroup/77
DESCRIPTION:Title: Уравнение пятиугольника и инвар
ианты кос: преобразование Птолемея\, тро
пическая геометрия\, shear-координаты\nby V
assily O. Manturov as part of Knots\, graphs and groups\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/knotgraphgroup/77/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mehdi Golafshan
DTSTART:20250125T140500Z
DTEND:20250125T153500Z
DTSTAMP:20260404T131156Z
UID:knotgraphgroup/78
DESCRIPTION:Title: Thue-Morse Words: From Complexity Measures to Real-World Ap
plications\nby Mehdi Golafshan as part of Knots\, graphs and groups\n\
n\nAbstract\nThe Thue-Morse word stands as one of the most celebrated infi
nite sequences in combinatorics on words\, noted for its self-similar cons
truction and fractal-like characteristics. This talk delves into the diver
se complexity measures of the Thue-Morse word—ranging from factor comple
xity and abelian complexity to binomial complexity—and explores how thes
e measures capture the rich combinatorial and dynamical behavior of the se
quence. We will also highlight the surprising breadth of applications\, fr
om coding theory and automata to number theory and physics\, where the uni
que properties of the Thue-Morse word offer insight into phenomena such as
diffraction patterns in quasicrystals. Attendees will gain an integrated
view of both the theoretical underpinnings and the practical impact of thi
s fascinating object.\n
LOCATION:https://stable.researchseminars.org/talk/knotgraphgroup/78/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nikolay Moshchevitin
DTSTART:20250208T140500Z
DTEND:20250208T153500Z
DTSTAMP:20260404T131156Z
UID:knotgraphgroup/79
DESCRIPTION:Title: Approximations of real numbers in various norms.\nby Ni
kolay Moshchevitin as part of Knots\, graphs and groups\n\n\nAbstract\nUsu
ally\, when we are looking for approximations of the irrational \\alpha by
rational fractions p/q\, we want to solve the system of inequalities\n|\\
alpha q - p|< \\varepsilon\, 1\\le q \\le Q\nin integers p\,q.\nThis formu
lation of the problem (corresponding to the L_\\infty-norm) leads to ordin
ary continued fractions.\nSimilar formulations corresponding to the L_2 an
d L_1-norms go back to Hermite and Minkowski. They are related to other (i
rregular) continued fraction expansion algorithms. We will discuss these a
lgorithms and explain how these constructions are related to the relativ
ely new concept of Dirichlet improvability.\n
LOCATION:https://stable.researchseminars.org/talk/knotgraphgroup/79/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vuong Bao
DTSTART:20250215T140500Z
DTEND:20250215T153500Z
DTSTAMP:20260404T131156Z
UID:knotgraphgroup/80
DESCRIPTION:Title: Fox-Milnor condition for concordant knots in homology 3-sph
eres\nby Vuong Bao as part of Knots\, graphs and groups\n\n\nAbstract\
nI will show that the Alexander polynomial of a knot\, which is of slice t
ype in an oriented homology 3-sphere\, obeys the Fox-Milnor poly- nomial c
ondition. A relation between Alexander polynomial of concordant knots in a
n oriented homology 3-sphere is established.\n
LOCATION:https://stable.researchseminars.org/talk/knotgraphgroup/80/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Medhi Golfshan
DTSTART:20250222T140500Z
DTEND:20250222T153500Z
DTSTAMP:20260404T131156Z
UID:knotgraphgroup/81
DESCRIPTION:Title: Geometry\, Factor Dynamics\, Unipotent Flows on Tori\, and
Leading Digits\nby Medhi Golfshan as part of Knots\, graphs and groups
\n\n\nAbstract\nIn this talk\, we provide a geometric perspective on symbo
lic and factor dynamics\, illustrating how these ideas illuminate unipoten
t flows on tori. We then discuss the connection of unipotent flows to the
uniform distribution of digits and examine how this framework informs our
understanding of leading digits and their complexity. Along the way\, we r
eview key classical results\, including Weyl's criterion\, Kronecker's the
orem\, and Ratner's theorem\, to show how they connect to questions of dig
it distribution. Finally\, we investigate the factor complexity of the lea
ding digits in sequences of the form $a^{n^d}$\, highlighting both the the
oretical insights and potential avenues for further exploration.\n
LOCATION:https://stable.researchseminars.org/talk/knotgraphgroup/81/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hyungtae Baek
DTSTART:20250301T140500Z
DTEND:20250301T153500Z
DTSTAMP:20260404T131156Z
UID:knotgraphgroup/82
DESCRIPTION:Title: $w$-maximal specturm of Anderson rings\nby Hyungtae Bae
k as part of Knots\, graphs and groups\n\n\nAbstract\nLet $R$ be a commuta
tive ring with identity and\nlet $R[X]$ be the polynomial ring over $R$.\n
Consider the following two subsets of $R[X]$:\n\\begin{center}\n$N := \\{f
\\in R[X] \\\,|\\\, c(f) = R\\}$ and\\\\\n$U := \\{f \\in R[X] \\\,|\\\,
f {\\rm \\ is \\ a \\ monic \\ polynomial} \\}$.\n\\end{center}\nThen $N$
and $U$ are multiplicative subset of $R[X]$\,\nso we obtain the rings $R[X
]_N$ and $R[X]_U$\,\nwhich are called the {\\it Nagata ring} of $R$ and {\
\it Serre's conjecture ring} of $R$ respectively.\nThe Nagata rings and th
e Serre's conjecture rings has been researched actively.\n\nIn this talk\,
we investigate the Anderson ring which is a subring of the Nagata ring an
d the Serre's conjecture ring\, and\nexamine star-operations on Anderson r
ings.\nMore precisely\, we investigate $w$-operation on the Anderson ring.
\n
LOCATION:https://stable.researchseminars.org/talk/knotgraphgroup/82/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hyungtae Baek
DTSTART:20250308T140500Z
DTEND:20250308T153500Z
DTSTAMP:20260404T131156Z
UID:knotgraphgroup/83
DESCRIPTION:Title: Krull-like domain arising from Anderson rings\nby Hyung
tae Baek as part of Knots\, graphs and groups\n\n\nAbstract\nLet $R$ be a
commutative ring with identity and\nlet $R[X]$ be the polynomial ring over
$R$.\nConsider the following two subsets of $R[X]$:\n\\begin{center}\n$N
:= \\{f \\in R[X] \\\,|\\\, c(f) = R\\}$ and\\\\\n$U := \\{f \\in R[X] \\\
,|\\\, f {\\rm \\ is \\ a \\ monic \\ polynomial} \\}$.\n\\end{center}\nTh
en $N$ and $U$ are multiplicative subset of $R[X]$\,\nso we obtain the rin
gs $R[X]_N$ and $R[X]_U$\,\nwhich are called the {\\it Nagata ring} of $R$
and {\\it Serre's conjecture ring} of $R$ respectively.\nThe Nagata rings
and the Serre's conjecture rings has been researched actively.\n\nIn this
talk\, we investigate the Anderson ring which is a subring of the Nagata
ring and the Serre's conjecture ring\, and\nexamine star-operations on And
erson rings.\nMore precisely\, we examine some conditions of $R$ under whi
ch the Anderson ring becomes Krull-like domain.\n
LOCATION:https://stable.researchseminars.org/talk/knotgraphgroup/83/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sachchidanand Prasad
DTSTART:20250322T140500Z
DTEND:20250322T153500Z
DTSTAMP:20260404T131156Z
UID:knotgraphgroup/85
DESCRIPTION:Title: Cut and focal locus of a Finsler submanifold\nby Sachch
idanand Prasad as part of Knots\, graphs and groups\n\n\nAbstract\nIn this
talk\, we explore key aspects of Finsler geometry with a focus on the str
ucture of the cut and focal loci. We begin by revisiting fundamental conce
pts in Finsler geometry before defining the cut locus and illustrating exa
mples in Riemannian manifolds. The discussion culminates with a proof of a
special case of the generalized Klingenberg lemma for Finsler manifolds\,
specifically for N-geodesic loops\, where $N$ is a closed submanifold of
a Finsler manifold $M$. This is a joint work with Aritra Bhowmick.\n
LOCATION:https://stable.researchseminars.org/talk/knotgraphgroup/85/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Louis Kauffman
DTSTART:20250315T140500Z
DTEND:20250315T153500Z
DTSTAMP:20260404T131156Z
UID:knotgraphgroup/86
DESCRIPTION:Title: Three Talks about Knots and Functional Integrals 1\nby
Louis Kauffman as part of Knots\, graphs and groups\n\n\nAbstract\nThis ta
lk will discuss physical background: Electromagnetism via differential for
ms\, and how this led Hermann Weyl to suggest a unification of Electromagn
etism and General Relativity. How the Weyl Theory became reformulated as g
auge theory. Background on quantum mechanics and path integrals of Feynman
. Beginning of measuring knots via holonomy in a gauge field.\n
LOCATION:https://stable.researchseminars.org/talk/knotgraphgroup/86/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Louis Kauffman
DTSTART:20250329T140500Z
DTEND:20250329T153500Z
DTSTAMP:20260404T131156Z
UID:knotgraphgroup/87
DESCRIPTION:Title: Three Talks about Knots and Functional Integrals 2\nby
Louis Kauffman as part of Knots\, graphs and groups\n\n\nAbstract\nWitten
Chern-Simons functional integral\, Wilson loops\, three manifold invariant
s and knot and link invariants.\n
LOCATION:https://stable.researchseminars.org/talk/knotgraphgroup/87/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Louis Kauffman
DTSTART:20250405T140500Z
DTEND:20250405T153500Z
DTSTAMP:20260404T131156Z
UID:knotgraphgroup/88
DESCRIPTION:Title: Three Talks about Knots and Functional Integrals 3\nby
Louis Kauffman as part of Knots\, graphs and groups\n\n\nAbstract\nHow the
Kontsevich Integral for Vasiliev invariants is related to the perturbativ
e expansion of the Witten Chern-Simons integral.\n
LOCATION:https://stable.researchseminars.org/talk/knotgraphgroup/88/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Louis Kauffman
DTSTART:20250412T140500Z
DTEND:20250412T153500Z
DTSTAMP:20260404T131156Z
UID:knotgraphgroup/89
DESCRIPTION:by Louis Kauffman as part of Knots\, graphs and groups\n\nAbst
ract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/knotgraphgroup/89/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Louis Kauffman
DTSTART:20250419T140500Z
DTEND:20250419T153500Z
DTSTAMP:20260404T131156Z
UID:knotgraphgroup/90
DESCRIPTION:by Louis Kauffman as part of Knots\, graphs and groups\n\nAbst
ract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/knotgraphgroup/90/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Igor Nikonov
DTSTART:20250426T140500Z
DTEND:20250426T153500Z
DTSTAMP:20260404T131156Z
UID:knotgraphgroup/91
DESCRIPTION:Title: The crossing and the arc from the topological viewpoint
\nby Igor Nikonov as part of Knots\, graphs and groups\n\n\nAbstract\nComb
inatorial approach to knot theory treats knots as diagrams modulo Reidemei
ster moves. Many constructions of knot invariants (e.g.\, index polynomial
s\, quandle colorings etc.) use elements of diagrams such as arcs and cros
sings by assigning invariant labels to them. The universal invariant label
s\, which carry the most information\, can be thought of as equivalence cl
asses of arcs and crossings modulo the relation\, which identifies corresp
onding elements of diagrams connected by a Reidemeister move. One can call
these equivalence classes the arcs and crossings of the knot. In the talk
we give a topological description of sets of these classes.\n
LOCATION:https://stable.researchseminars.org/talk/knotgraphgroup/91/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yury Belousov
DTSTART:20250503T140500Z
DTEND:20250503T153500Z
DTSTAMP:20260404T131156Z
UID:knotgraphgroup/92
DESCRIPTION:Title: Meander diagrams of classical and virtual knots\nby Yur
y Belousov as part of Knots\, graphs and groups\n\n\nAbstract\nIn this tal
k\, we survey the theory of meander and semimeander diagrams of knots\, co
vering both the classical setting and its recent extensions to virtual kno
ts. We begin with classical results: every knot admits semimeander and mea
nder diagrams. A diagram is called semimeander if it decomposes into two s
mooth\, simple arcs\; if\, additionally\, the endpoints of these arcs lie
on the boundary of the convex hull of the diagram\, it is called meander.
We then consider virtual knots\, introducing two possible generalizations
of semimeander and meander diagrams\, and proving the universality of thes
e diagram classes (that is\, each virtual knot has a diagram within these
classes). Motivated by these constructions\, we define a new class of knot
invariants -- the (virtual) k-arc crossing numbers -- and discuss their r
elationship with the classical crossing number. The talk is based on joint
works with V. Chernov\, A. Malyutin\, and R. Sadykov.\n
LOCATION:https://stable.researchseminars.org/talk/knotgraphgroup/92/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Louis Kauffman (UIC)
DTSTART:20250524T140500Z
DTEND:20250524T153500Z
DTSTAMP:20260404T131156Z
UID:knotgraphgroup/93
DESCRIPTION:Title: Multiple Virtual Knot Theory\nby Louis Kauffman (UIC) a
s part of Knots\, graphs and groups\n\n\nAbstract\nThis talk will discuss
a generalization of virtual knot theory where there are any number of virt
ual crossings such that each virtual crossing type can perform detour move
s over any of the others. The roots of this generalization are in our work
on Penrose polynomials for graphs with perfect matchings. These graph pol
ynomials motivate a number of constructions in knot theory\, as we shall e
xplain.\n
LOCATION:https://stable.researchseminars.org/talk/knotgraphgroup/93/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marco Castelli
DTSTART:20250517T140500Z
DTEND:20250517T153500Z
DTSTAMP:20260404T131156Z
UID:knotgraphgroup/94
DESCRIPTION:Title: Involutive (and indecomposable) set-theoretic solutions of
the Yang-Baxter equation\nby Marco Castelli as part of Knots\, graphs
and groups\n\n\nAbstract\nThe Yang-Baxter equation is one of the central e
quations in mathematical physics\, first\nintroduced in the works of Yang
(1967) and Baxter (1972). In 1992\, Drinfeld proposed the\nclassification
of its so-called set-theoretic solutions. The seminal papers of Gateva-Iva
nova and Van den Bergh (1998)\, and of Etingof\, Schedler\, and Soloviev (
1999)\, led many mathematicians to the study of involutive non-degenerate
set-theoretic solutions. In the first part of this talk\, we will provide
an introduction to the Yang-Baxter equation\, with a particular focus on i
nvolutive set-theoretic solutions\, and we will show how indecomposable so
lutions are\, in a sense\, the fundamental building blocks. In the second
part\, which will be the core of the talk\, we will focus on indecomposabl
e involutive solutions\, offering an overview of the theoretical tools and
the main results developed for their investigation and classification.\n
LOCATION:https://stable.researchseminars.org/talk/knotgraphgroup/94/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sergei Gukov
DTSTART:20250510T140500Z
DTEND:20250510T153500Z
DTSTAMP:20260404T131156Z
UID:knotgraphgroup/95
DESCRIPTION:Title: First examples of categorification of $U_{q} (sl_{2})$ inva
riants of 3-manifolds\nby Sergei Gukov as part of Knots\, graphs and g
roups\n\n\nAbstract\nBraiding of Verma modules for the quantum group $U_{q
} (sl_{2})$ leads to a TQFT that associates q-series invariants to 3-manif
olds equipped with Spin-C structures. One of the main interests in these i
nvariants is that they are expected to admit categorification\, thus provi
ding new insights into the mysterious world of smooth 4-maniolds. Building
on recent works with M.Jagadale and P.Putrov\, we describe what this homo
logical lift looks like with mod 2 coefficients. We prove that the propose
d categorification is invariant under Kirby moves for all weakly negative
definite plumbed manifolds.\n
LOCATION:https://stable.researchseminars.org/talk/knotgraphgroup/95/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Younghan Yoon
DTSTART:20250531T140500Z
DTEND:20250531T153500Z
DTSTAMP:20260404T131156Z
UID:knotgraphgroup/96
DESCRIPTION:Title: Weyl Groups and Real Toric Varieties\nby Younghan Yoon
as part of Knots\, graphs and groups\n\n\nAbstract\nWeyl groups can be und
erstood by studying the real toric varieties associated with them.\nIn thi
s talk\, we discuss the rational cohomology of these varieties.\nWe presen
t complete computations of their Betti numbers for all types of Weyl group
s.\nFurthermore\, for types A and B\, we introduce explicit descriptions o
f the multiplicative structures of the cohomology rings in terms of altern
ating permutations and B-snakes\, respectively.\n
LOCATION:https://stable.researchseminars.org/talk/knotgraphgroup/96/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Louis kauffman
DTSTART:20250607T140500Z
DTEND:20250607T153500Z
DTSTAMP:20260404T131156Z
UID:knotgraphgroup/97
DESCRIPTION:by Louis kauffman as part of Knots\, graphs and groups\n\n\nAb
stract\nWe introduce a new algebra\, the crossing algebra\, that is applie
d to count the number of components for arborescent knots\, links\, tangle
s or states (of a state polynomial expansion such as the Kauffman bracket)
. This algebra is elementary and foundational\, and it is related to gener
alisations of boolean logic and to aspects of foundations based in diagram
s and distinctions. Applications are given to logic circuits\, rational kn
ots\, links and tangles and to the structure of the bracket polynomial and
the beginnings of Khovanov homology.\n
LOCATION:https://stable.researchseminars.org/talk/knotgraphgroup/97/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sergei Lando
DTSTART:20250614T140500Z
DTEND:20250614T153500Z
DTSTAMP:20260404T131156Z
UID:knotgraphgroup/98
DESCRIPTION:Title: An algebro-geometric proof of Witten's conjecture\nby S
ergei Lando as part of Knots\, graphs and groups\n\n\nAbstract\nWe present
a new proof of Witten's conjecture. The proof is based on the analysis of
the relationship between intersection indices on moduli spaces of complex
curves and Hurwitz numbers enumerating ramified coverings of the 2-sphere
.\n
LOCATION:https://stable.researchseminars.org/talk/knotgraphgroup/98/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Seongjeong Kim
DTSTART:20250621T140500Z
DTEND:20250621T153500Z
DTSTAMP:20260404T131156Z
UID:knotgraphgroup/99
DESCRIPTION:Title: Winding parity projection and embedding of virtual knots\nby Seongjeong Kim as part of Knots\, graphs and groups\n\n\nAbstract\nI
t is known that knots in the product space of an oriented surface $S_{g}$
and the circle $S^{1}$ can be presented by virtual diagrams with decoratio
ns up to local moves. By using the first homology of $S^{1}$ one can defin
e a parity-like invariant for knots in $S_{g} \\times S^{1}$\, which is ca
lled a winding parity. In this talk\, we define a projection of knots in $
S_{g}\\times S^{1}$ with degree $0$ onto a knots with zero winding parity
for all crossings. By using the projection\, we prove that virtual knots a
re “almost” embedded into knots in $S_{g} \\times S^{1}$.\n
LOCATION:https://stable.researchseminars.org/talk/knotgraphgroup/99/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Platon Marulev
DTSTART:20250628T140500Z
DTEND:20250628T153500Z
DTSTAMP:20260404T131156Z
UID:knotgraphgroup/100
DESCRIPTION:Title: CLASSIFICATION OF NODAL CURVES ON SURFACES AND BRAID INVAR
IANTS\nby Platon Marulev as part of Knots\, graphs and groups\n\n\nAbs
tract\nThis work is divided into two parts.\nThe first part is devoted to
the classification of nodal curves on closed surfaces under modified three
Reidemeester moves obtained in the article "INCIDENCES AND TILING" by Ser
gey Fomin and Pavlo Pylyavsky\, and finding the minimal element of these e
quivalence classes.\n\nIn the second part\, several different braid invari
ants considered in the articles "Braids act on configurations of lines" an
d "Shear coordinates and braid invariants" by V.O. Manturov are calculated
.\n
LOCATION:https://stable.researchseminars.org/talk/knotgraphgroup/100/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Thomas Fiedler
DTSTART:20250705T140500Z
DTEND:20250705T153500Z
DTSTAMP:20260404T131156Z
UID:knotgraphgroup/101
DESCRIPTION:Title: The tangle-valued 1-cocycle for knots\nby Thomas Fiedl
er as part of Knots\, graphs and groups\n\n\nAbstract\nWe replace the Yang
-Baxter equation by the tetrahedron equation and use it to construct an in
finit ordered set of Alexander (or Conway) polynomials\, called the Alexan
der tree\, as a knot invariant. As an application we prove that the knot 8
_17 is not invertible by using just the first coefficients of some of the
Conway polynomials in the invariant. This makes the Alexander tree a serio
us candidate for a complete and calculable invariant for classical knots.\
n
LOCATION:https://stable.researchseminars.org/talk/knotgraphgroup/101/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gurnoor Singh
DTSTART:20250712T140500Z
DTEND:20250712T153500Z
DTSTAMP:20260404T131156Z
UID:knotgraphgroup/102
DESCRIPTION:Title: Tropical Ptolemy Transformations and Invariants of Braids<
/a>\nby Gurnoor Singh as part of Knots\, graphs and groups\n\n\nAbstract\n
We present a new construction of invariants for spherical braids using tro
pical geometry. Given a braid on \\( n \\geq 5 \\) strands on the 2-sphere
\, we associate to it a sequence of Delaunay triangulations connected by e
dge flips. Each triangulation carries edge labels valued in a tropical sem
ifield\, and each flip updates the labels via the tropical Ptolemy relatio
n:\n\\[\nx \\oplus y = (a \\oplus c) \\otimes (b \\oplus d)\, \\quad \\tex
t{where } \\oplus = \\max\, \\ \\otimes = +.\n\\]\nThis process respects f
lip identities such as involution\, far-commutativity\, and the pentagon r
elation. We show that the resulting label at the end of the sequence defin
es an invariant of the braid up to isotopy. This construction offers a com
binatorial framework for studying braid groups through tropical methods an
d enriches the connection between low-dimensional topology and tropical ge
ometry.\n
LOCATION:https://stable.researchseminars.org/talk/knotgraphgroup/102/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bao Vuong
DTSTART:20250719T140500Z
DTEND:20250719T153500Z
DTSTAMP:20260404T131156Z
UID:knotgraphgroup/103
DESCRIPTION:Title: Fox-Milnor condition for concordant knots in homology 3-s
pheres\nby Bao Vuong as part of Knots\, graphs and groups\n\n\nAbstrac
t\nI will talk about the proof of the following Theorems\n\n{\\bf Theorem
A}. Let $k_0\, k_1$ be concordant knots in an oriented homology 3-sphere $
M$. Then the Alexander polynomials of the knots are related by the followi
ng equation\n\\[\\Delta_{k_0}(t) ~\\dot{=} ~p(t)p(1/t) \\Delta_{k_1}(t)\\]
\n\nwhere $\\Delta_{k_0}(t)\, \\Delta_{k_1}(t)$ are the Alexander polynomi
als in $t$ of the knots $k_0\,k_1$ respectively and $p(t)$ is a polynomial
with integer coefficients.\n\n{\\bf Theorem B}. Let $M\, M'$ be homologic
al spheres. Let $\\mathcal{W}$ be a cobordism between $M$ and $M'$\, and t
he boundary of $\\mathcal{W}$ is disjoint union $\\partial \\mathcal{W} =
M \\cup M'$. More over the inclusions $M \\hookrightarrow \\mathcal{W}$ an
d $M' \\hookrightarrow \\mathcal{W}$ induce isomorphisms on homology. Let
$k$ and $k'$ be knots in $M$ and $M'$ correspondingly. If there exist a co
ncordance $g: S^1 \\times I \\rightarrow \\mathcal{W}$ between $k$ and $k'
$. Then the Alexander polynomials of the knots $k$ and $k'$ are related by
the following equation\n\n\\[\\Delta_{k}(t) ~\\dot{=} ~p(t)p(1/t) \\Delta
_{k'}(t)\\]\n\nwhere $\\Delta_{k}(t)\, \\Delta_{k'}(t)$ are the Alexander
polynomials in $t$ of the knots $k\,k'$ respectively and $p(t)$ is a polyn
omial with integer coefficients.\n
LOCATION:https://stable.researchseminars.org/talk/knotgraphgroup/103/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Louis Kauffman
DTSTART:20250823T140500Z
DTEND:20250823T153500Z
DTSTAMP:20260404T131156Z
UID:knotgraphgroup/104
DESCRIPTION:Title: Non-Commutative Worlds\nby Louis Kauffman as part of K
nots\, graphs and groups\n\n\nAbstract\nAspects of gauge theory\, Hamilton
ian mechanics and quantum mechanics arise naturally in the mathematics of
a non-commutative framework for calculus and differential geometry. This t
alk consists in a number of sections including the introduction. The intro
duction sketches our general results in this domain. The second section gi
ves a derivation of a generalization of the Feynman-Dyson derivation of el
ectromagnetism using our non-commutative context and using diagrammatic te
chniques. The third section discusses\, in more depth\, relationships with
gauge theory and differential geometry. The last section discusses the st
ructure of curvature\, Bianchi identity and general relativity.\nWe begin
the talk by showing how constructing sqrt[-1] naturally leads to Clifford
Algebras and the seeds of this non-commutative context.\n
LOCATION:https://stable.researchseminars.org/talk/knotgraphgroup/104/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Аллеманд Аллан Олегович
DTSTART:20250726T140500Z
DTEND:20250726T153500Z
DTSTAMP:20260404T131156Z
UID:knotgraphgroup/105
DESCRIPTION:Title: Применение метода Арнольда для
доказательства топологической неразреш
имости некоторых уравнений в элементарн
ых функциях\nby Аллеманд Аллан Олегович
as part of Knots\, graphs and groups\n\n\nAbstract\nВ докладе б
удет дан общий обзор на применение метод
а Арнольда\, доказана неразрешимость ура
внений sin(z) − z = a и cos(z) − z = a в элементарн
ых функциях\, а также рассмотрены другие
случае и примеры\n
LOCATION:https://stable.researchseminars.org/talk/knotgraphgroup/105/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexander Zavesov
DTSTART:20250802T140500Z
DTEND:20250802T153500Z
DTSTAMP:20260404T131156Z
UID:knotgraphgroup/106
DESCRIPTION:Title: Quantum Probabilistic Interpretation and Quaternion Matric
es\nby Alexander Zavesov as part of Knots\, graphs and groups\n\n\nAbs
tract\nWe describe the theory\, which shapes a probabilistic (statistical)
\ninterpretation of quantum mechanics in terms of quaternion matrices. Upo
n introducing the\nnotion of a quaternionic density matrix\, we define the
expressions for calculating the observed\nmeans and entropy of a quantum
system.\nThe difference between quaternion and complex matrices is that th
e former are not linear\noperators. This fact forces us to rebuild the the
ory of quaternionic matrix operators and to show\nthat all the basic theor
ems related to complex matrices are held\, with some reservations. The\nco
nstructed theory of quaternionic matrix operators also presents interest f
rom a purely\nmathematical point of view\, regardless of its application i
n quantum mechanics.\n\nReferences: https://www.researchgate.net/publicati
on/349303667_Quantum_Probabilistic_Interpretation_and_Quaternion_Matrices_
Eng\n
LOCATION:https://stable.researchseminars.org/talk/knotgraphgroup/106/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Seongjeong Kim
DTSTART:20250809T140500Z
DTEND:20250809T153500Z
DTSTAMP:20260404T131156Z
UID:knotgraphgroup/107
DESCRIPTION:Title: A characterization of virtual knots as knots in $S_{g} \\t
imes S^{1}$\nby Seongjeong Kim as part of Knots\, graphs and groups\n\
n\nAbstract\nIn this talk we will show that virtual knots are embedded in
the set of knots in $S_{g} \\times S^{1}$. We will also provide a sufficie
nt condition for knots in $S_{g} \\times S^{1}$ to have virtual knot diagr
ams. Based on this\, we derive a sufficient condition for 2-component clas
sical links to be separable.\n
LOCATION:https://stable.researchseminars.org/talk/knotgraphgroup/107/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bernhard Keller (Université Paris Cité)
DTSTART:20250816T140500Z
DTEND:20250816T153500Z
DTSTAMP:20260404T131156Z
UID:knotgraphgroup/108
DESCRIPTION:Title: Grassmannian braiding categorified\nby Bernhard Keller
(Université Paris Cité) as part of Knots\, graphs and groups\n\n\nAbstr
act\nIn 2017\, Chris Fraser discovered an action of the extended affine br
aid group on d strands on the Grassmannian of k-subspaces in n-space\, end
owed with its cluster structure due to Scott (2006). Here\, the integer d
stands for the greatest common divisor of k and n. In joint work with Fras
er and Haoyu Wang\, we construct a categorical lift of this action using J
ensen-King-Su's (additive) categorification of the Grassmannian via Cohen-
Macaulay modules over a singular quotient of the preprojective algebra P o
f extended type A_{n-1}. A key ingredient is\nSeidel-Thomas' braid group a
ction (2000) on the derived category of P.\n
LOCATION:https://stable.researchseminars.org/talk/knotgraphgroup/108/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Евгений Коган
DTSTART:20250830T140500Z
DTEND:20250830T153500Z
DTSTAMP:20260404T131156Z
UID:knotgraphgroup/109
DESCRIPTION:Title: Когомологии Нийенхейса\nby Евг
ений Коган as part of Knots\, graphs and groups\n\n\nAbstract\nП
о операторному полю на многообразии (т.е.
тензору с одним верхним и одним нижним и
ндексом) можно построить однородное ото
бражение степени 1\, действующее на диффе
ренциальных формах. Операторное поле на
зывается оператором Нийенхейса\, если эт
о отображение является дифференциалом.
Сразу возникает вопрос: а каковы когомол
огии получившегося комплекса? Эти когом
ологии называются малыми когомологиями
Нийенхейса. В случае\, когда оператор в к
аждой точке тождественный\, рассматрива
емый дифференциал совпадает с внешним д
ифференциалом\, комплекс совпадает с ком
плексом де Рама\, и малые когомологии Ний
енхейса совпадают с когомологиями де Ра
ма. Оказывается\, что если оператор Нийен
хейса невырожден в каждой точке многооб
разия\, то малые когомологии все еще изом
орфны когомологиям де Рама — но в общем
случае это не так.\n\nВ докладе будет расс
казано про несколько результатов\, касаю
щихся свойств малых когомологий Нийенхе
йса\, а также (при наличии времени) про ещ
е пару вопросов\, связанных с так называе
мыми большими когомологиями Нийенхейса
и возможности построения дифференциала
для любого операторного поля постоянног
о ранга\, поточечные образы которого обр
азуют интегрируемое распределение.\n
LOCATION:https://stable.researchseminars.org/talk/knotgraphgroup/109/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Алексей Суворов
DTSTART:20250913T140500Z
DTEND:20250913T153500Z
DTSTAMP:20260404T131156Z
UID:knotgraphgroup/110
DESCRIPTION:Title: Обобщение Теоремы Кези и геомет
рия окружностей\nby Алексей Суворов as par
t of Knots\, graphs and groups\n\n\nAbstract\nЕсть формула дл
ины вектора с координатами $x\, y$:$\\sqrt{x^2 + y^
2}.$\n\nНо что будет\, если поменять плюс на
минус? Тогда получится альтернативная г
еометрия\, в которой вместо окружности б
удет гипербола. Большинство теорем\, вер
ных в евклидовой геометрии\, здесь тоже в
ерны.\n\nНеожиданно\, это геометрия доволь
но сильно связана с окружностями на плос
кости.\n\nС помощью понимания этой связи м
ы обобщим теорему Кези на произвольное ч
исло окружностей.\n\n\\section*{Теорема Кези}\n\
nЕсли четыре окружности касаются данной\
, то верно следующее равенство:\n$L_{1324} = L_{1
234} + L_{2314}\,$\nгде $L_{ij}$ — длина общей внешне
й касательной к соответствующим окружно
стям\, пронумерованным в порядке обхода
точек касания.\n\nТакже\, если останется в
ремя\, поговорим о геометрии окружностей
поподробнее.\n
LOCATION:https://stable.researchseminars.org/talk/knotgraphgroup/110/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Елена Николаевна Ланина
DTSTART:20250927T140500Z
DTEND:20250927T153500Z
DTSTAMP:20260404T131156Z
UID:knotgraphgroup/111
DESCRIPTION:Title: Differential operators approach to Khovanov–Rozansky cal
culus\nby Елена Николаевна Ланина as part of Knot
s\, graphs and groups\n\n\nAbstract\nFor Khovanov–Rozansky cohomologies\
, we develop a construction of differential operators in odd variables\, a
ssociated with all link diagrams\, including tangles with open ends. These
operators become nilpotent only for diagram with no external legs\, but e
ven for open tangles one can develop a factorization formalism\, which pre
serve Reidemeister/topological invariance -- the symmetry of the problem.
During this talk\, I am going to introduce our approach\, consider relatio
ns which allows one to simplify calculations of the Khovanov–Rozansky po
lynomials and provide examples.\n
LOCATION:https://stable.researchseminars.org/talk/knotgraphgroup/111/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Egor Morozov
DTSTART:20250906T140500Z
DTEND:20250906T153500Z
DTSTAMP:20260404T131156Z
UID:knotgraphgroup/112
DESCRIPTION:Title: Generalized problem of Apollonius\nby Egor Morozov as
part of Knots\, graphs and groups\n\n\nAbstract\nThe problem of Apollonius
(3d century BC) is to construct a circle tangent to the three given circl
es in the plane. Counting the number of solutions is often considered as o
ne of the first questions of enumerative geometry. It turns out that in ge
neral position the problem has 8 solutions and\, if not all the given circ
les are tangent at the same point\, then this number is maximal possible.
This fact has a plenty of proofs using a wide range of methods\, from elem
entary ones to such as Lie sphere geometry and intersection theory.\n\nBut
what happens if one increases the number of given circles? Clearly\, coun
ting the number of solutions in general position is not interesting in thi
s case since this number is always zero. However\, the question about the
maximal possible number of solution still makes sense. It turns out that i
f not all the given circles are tangent at the same point\, then the probl
em has at most 6 solutions. The proof of this fact leads to beautiful conf
igurations of tangent circles. In the talk I will describe these construct
ion\, give precise statements and proofs\, and (if time permits) mention o
ther interesting generalizations of the Apollonius' problem.\n
LOCATION:https://stable.researchseminars.org/talk/knotgraphgroup/112/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Илья Иванов-Погодаев
DTSTART:20250920T140500Z
DTEND:20250920T153500Z
DTSTAMP:20260404T131156Z
UID:knotgraphgroup/113
DESCRIPTION:Title: Пути на графе как элементы полу
группы\nby Илья Иванов-Погодаев as part of Kno
ts\, graphs and groups\n\n\nAbstract\nБудем рассматриват
ь слова в конечном алфавите. Допустим\, к
онечное множество слов. объявлены запре
щенными\, то есть приравнены к нулю. Тогд
а и все слова\, содержащие запрещенные то
же равны нулю. Множество ненулевых слов
при этом может оказаться конечным или бе
сконечным. Не очень сложная олимпиадная
задача: Если множество ненулевых слов б
есконечно\, то существует и бесконечное
периодическое слово\, не содержащее запр
ещенных подслов.\n \nМножество слов относ
ительно операции приписывания одного сл
ова к другому является полугруппой.\nНа я
зыке полугрупп утверждение задачи выше
означает\, что в конечно порожденной (кон
ечный алфавит) конечно представленной (к
онечное число запрещенных слов) мономиа
льной (каждое определяющее соотношение
вида W=0)\, бесконечной (множество ненулев
ых слов бесконечно) полугруппе существу
ет элемент\, являющийся ненулевым в любо
й степени.\nПользуясь определением ниль-
элемента\, то есть слова\, некоторая степ
ень которого равна нулю\, можно дать экви
валентное определение. Полугруппа назыв
ается нильполугруппой\, если каждый элем
ент в некоторой степени равен нулю.\nТогд
а эквивалентная формулировка: любая кон
ечнопорожденная конечно представленная
мономиальная нильполугруппа является к
онечной.\n \nЧто же будет\, если делать не т
олько запрещенные слова\, но и приравнив
ать некоторые слова друг к другу? Тогда с
итуация заметно усложняется\, и этот воп
рос был поставлен в Свердловской тетрад
и Л.Н.Шевриным и М.В.Сапиром. Оказывается\
, что в этом случае бесконечную конечно п
редставленную нильполугруппу построить
можно. Но для этого пришлось применить д
ополнительные идеи. \n \nСлова полугруппы
интерпретируются как кодировки путей на
специально построенном графе. Эквивале
нтность слов\nозначает эквивалентность
путей на графе\, то есть возможность пере
вести один путь в другой локальными заме
нами.\nЗапрещающие соотношения соответс
твуют невозможным кодировкам.\n \nВсе это
приводит к новому подходу к построению а
лгебраических объектов\, который и будем
обсуждать в докладе.\n
LOCATION:https://stable.researchseminars.org/talk/knotgraphgroup/113/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Oleg Styrt
DTSTART:20251018T140500Z
DTEND:20251018T153500Z
DTSTAMP:20260404T131156Z
UID:knotgraphgroup/114
DESCRIPTION:by Oleg Styrt as part of Knots\, graphs and groups\n\nAbstract
: TBA\n
LOCATION:https://stable.researchseminars.org/talk/knotgraphgroup/114/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vladlen Timorin
DTSTART:20251004T140500Z
DTEND:20251004T153500Z
DTSTAMP:20260404T131156Z
UID:knotgraphgroup/115
DESCRIPTION:Title: Renormalization\, equipotential annuli\, and the Hausdorff
measure\nby Vladlen Timorin as part of Knots\, graphs and groups\n\n\
nAbstract\n(based on a joint work with A. Blokh\, G. Levin\, and L. Overst
eegen)\n \nFor a complex single variable polynomial f of degree d\, let K(
f) be its filled Julia set\, i.e.\, the union of all bounded orbits. Assum
e that K(f) has an invariant component K* on which f acts as a degree d* <
d map. This is a simplest instance of holomorphic polynomial-like renorma
lization (Douady-Hubbard): the dynamics of a higher degree (degree d) poly
nomial f near K* can be understood in terms of a suitable lower degree (de
gree d*) polynomial to which the restriction of f to K* is semiconjugate.
One can associate a certain Cantor-like subset G’ of the circle with K*\
; the latter is defined in a combinatorial way. We will describe a role th
e Hausdorff dimension of G’ and the respective Hausdorff measure play in
geometry of K*.\n
LOCATION:https://stable.researchseminars.org/talk/knotgraphgroup/115/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Петр Ким
DTSTART:20251025T140500Z
DTEND:20251025T153500Z
DTSTAMP:20260404T131156Z
UID:knotgraphgroup/116
DESCRIPTION:Title: Об обобщённых треугольниках\n
by Петр Ким as part of Knots\, graphs and groups\n\n\nAbstract\nТ
ри стороны треугольника можно восприним
ать как очень вырожденную плоскую кубич
ескую кривую. Но есть ли какие-нибудь ана
логи теорем из привычной геометрии треу
гольника для произвольной кубической кр
ивой? \nВыясняется\, что да\, есть! \nНа докл
аде будет рассказано о получающихся на э
том пути обобщениях теоремы Фейербаха (о
касании вписанной окружности и окружно
сти 9 точек) и теоремы Емельяновых\, а так
же их связи с поризмом Понселе и изополя
рным преобразованием Суворова.\n
LOCATION:https://stable.researchseminars.org/talk/knotgraphgroup/116/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Louis H Kauffman
DTSTART:20251011T140500Z
DTEND:20251011T153500Z
DTSTAMP:20260404T131156Z
UID:knotgraphgroup/117
DESCRIPTION:Title: Knot Logic and Majorana Fermions\nby Louis H Kauffman
as part of Knots\, graphs and groups\n\n\nAbstract\nWe discuss topological
quantum computing from the point of view of knot theory and we discuss kn
ot theory from the point of view of form and knot logic. This means that w
e do not begin with three dimensional space and subspace placement as the
source of the knot theory. Rather we begin with the notion of distinction
and how that notion gives rise to concepts of logic\, of boundaries\, of v
ery elementary algebras\, self-referential structures and the beginnings o
f both topology and geometry. Starting the discussion of foundations from
such a place means that there are many pathways outward from very simple s
tructures\, and we can only sketch some of them. Nevertheless\, we will di
scuss the belt trick\, non-locality\, Majorana fermions and the Fibonacci
model for topological quantum computing that is related to the quantum Hal
l effect.\n
LOCATION:https://stable.researchseminars.org/talk/knotgraphgroup/117/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Louis Kauffman
DTSTART:20251101T140500Z
DTEND:20251101T153500Z
DTSTAMP:20260404T131156Z
UID:knotgraphgroup/118
DESCRIPTION:Title: Topological Computing and Majorana Fermions\nby Louis
Kauffman as part of Knots\, graphs and groups\n\n\nAbstract\nWe will discu
ss how to use Temperley Lieb Recoupling Theory to produce unitary transfor
mations for quantum computing and we will discuss how to use Clifford alge
bra to give unitary representations related to Majorana Fermions. In the c
ourse of this we shall discuss relationships of diagrammatics\, topology a
nd physics.\n
LOCATION:https://stable.researchseminars.org/talk/knotgraphgroup/118/
END:VEVENT
BEGIN:VEVENT
SUMMARY:B. Sobirov
DTSTART:20251108T140500Z
DTEND:20251108T153500Z
DTSTAMP:20260404T131156Z
UID:knotgraphgroup/119
DESCRIPTION:Title: Множество значений конечной ме
ры\nby B. Sobirov as part of Knots\, graphs and groups\n\n\nAbstract
\nВ работе элементарными методами доказы
вается факт о том\, что множество значени
й произвольной конечной меры является к
омпактом. В отличие от подхода Пола Халм
оша\, доказательство обходится без привл
ечения теории ординалов и опирается лиш
ь на счётные конструкции. Сначала теорем
а устанавливается для борелевских мер н
а прямой. Затем общий случай сводится к э
тому частному с помощью хитрой измеримо
й функции. В качестве следствия показыва
ется\, что для безатомной меры множество
её значений является отрезоком.\n
LOCATION:https://stable.researchseminars.org/talk/knotgraphgroup/119/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mariia Rubanenko
DTSTART:20251115T140500Z
DTEND:20251115T153500Z
DTSTAMP:20260404T131156Z
UID:knotgraphgroup/120
DESCRIPTION:Title: Succinct data structures for strings\nby Mariia Rubane
nko as part of Knots\, graphs and groups\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/knotgraphgroup/120/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Louis Kauffman
DTSTART:20251122T140500Z
DTEND:20251122T153500Z
DTSTAMP:20260404T131156Z
UID:knotgraphgroup/121
DESCRIPTION:Title: Recoupling Theory\, Majorana Fermions and the Dirac equati
on\nby Louis Kauffman as part of Knots\, graphs and groups\n\n\nAbstra
ct\nThis talk will continue previous talks about topological quantum compu
ting based on\n1. solutions to the Yang-Baxter Equation\n2. Temperley-Lieb
Recoupling theory.\n3. Braid group representations related to Clifford al
gebras.\nWe will describe how the Clifford algebra approach is related to
the Majorana version of the Dirac equation.\n
LOCATION:https://stable.researchseminars.org/talk/knotgraphgroup/121/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Xu Xu
DTSTART:20251206T140500Z
DTEND:20251206T153500Z
DTSTAMP:20260404T131156Z
UID:knotgraphgroup/122
DESCRIPTION:Title: Combinatorial curvature flows on surfaces and 3-dimensiona
l manifolds\nby Xu Xu as part of Knots\, graphs and groups\n\n\nAbstra
ct\nCombinatorial Ricci flow was first introduced by Chow and Luo for Thur
ston’s circle packings on surfaces. It provides effective algorithms for
finding polyhedral metrics on surfaces with prescribed singularities. Aft
er Chow and Luo’s work\, combinatorial curvature flows have been extensi
vely studied for different types of discrete conformal structures on surfa
ces and 3-dimensional manifolds. In this talk\, I will give an introductio
n of these combinatorial curvature flows\, and present some recent progres
ses on the study of combinatorial curvature flows on surfaces and 3-dimens
ional manifolds.\n
LOCATION:https://stable.researchseminars.org/talk/knotgraphgroup/122/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yangzhou Liu
DTSTART:20251129T140500Z
DTEND:20251129T153500Z
DTSTAMP:20260404T131156Z
UID:knotgraphgroup/123
DESCRIPTION:Title: The Unfaithfulness of the Manturov-Nikonov Map for k > 5\nby Yangzhou Liu as part of Knots\, graphs and groups\n\n\nAbstract\nTh
e representation theory of classical braids is well-established\, with key
examples including the Burau representation (unfaithful for n≥5)\, the
Temperley–Lieb representation\, and the faithful Lawrence–Krammer–Bi
gelow representation. In contrast\, virtual knots exhibit distinct propert
ies such as parity. The Manturov-Nikonov (M-N) map bridges these domains b
y embedding classical braids into virtual braids. In this talk\, we prove
that the M-N map is unfaithful for k>5. By analyzing the kernel of the Bur
au representation\, we explicitly construct elements in the kernel of the
M-N map\, revealing new obstructions to faithfulness in virtual braid repr
esentations.\n
LOCATION:https://stable.researchseminars.org/talk/knotgraphgroup/123/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Seongjeong Kim
DTSTART:20251213T140500Z
DTEND:20251213T153500Z
DTSTAMP:20260404T131156Z
UID:knotgraphgroup/124
DESCRIPTION:Title: Braids for Knots in $S_{g} \\times S^{1}$ and Iwahori-Heck
e algebra\nby Seongjeong Kim as part of Knots\, graphs and groups\n\n\
nAbstract\nIn \\cite{Kim} for an oriented surface $S_{g}$ of genus $g$ it
is shown that links in $S_{g} \\times S^{1}$ can be presented by virtual d
iagrams with a decoration\, so called\, {\\em double lines}. In this paper
\, first we define braids with double lines for links in $S_{g}\\times S^{
1}$. We denote the group of braids with double lines by $VB_{n}^{dl}$. Ale
xander and Markov theorem for links in $S_{g}\\times S^{1}$ can be proved
analogously to the work in \\cite{NegiPrabhakarKamada}. We show that\, if
we restrict our interest to the group $B_{n}^{dl}$ generated by braids wit
h double lines\, but without virtual crossings\, then the Hecke algebra of
$B_{n}^{dl}$ is isomorphic to Iwahori-Hecke algebra.\n\n\\bibitem{Kim}\nS
. Kim\, {\\it The Groups $G_{n}^{k}$ with additional structures\,} Matemat
icheskie Zametki\, Vol. 103\, No. 4 (2018)\, pp. 549 -- 567.\n\n\\bibitem{
NegiPrabhakarKamada}\nK. Negi\, M. Prabhakar\, S. Kamada\, {\\it Twisted v
irtual braids and twisted links\,} Osaka J. Math. 61(4): 569-590 (October
2024).\n
LOCATION:https://stable.researchseminars.org/talk/knotgraphgroup/124/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Louis Kauffman (UIC\, SCKM^2)
DTSTART:20251220T140500Z
DTEND:20251220T153500Z
DTSTAMP:20260404T131156Z
UID:knotgraphgroup/125
DESCRIPTION:Title: Topological Quantum Computing - Fibonacci Model and Majora
na Fermions\nby Louis Kauffman (UIC\, SCKM^2) as part of Knots\, graph
s and groups\n\n\nAbstract\nWe will discuss topological quantum computing
from the point of view of the Fibonacci model (via Temperley-Lieb recoupli
ng theory based on Kauffman bracket polynomial) and also in terms of braid
group representations associated with Majorana Fermions. The talk will be
self-contained and we will quickly review what we discussed in the previo
us talks in this series.\n
LOCATION:https://stable.researchseminars.org/talk/knotgraphgroup/125/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Maria Rubanenko
DTSTART:20251227T140500Z
DTEND:20251227T153500Z
DTSTAMP:20260404T131156Z
UID:knotgraphgroup/126
DESCRIPTION:Title: Distance multiplication algorithms for Monge\, unit-Monge
matrices\nby Maria Rubanenko as part of Knots\, graphs and groups\n\n\
nAbstract\nDistance (tropical) matrix multiplication is a fundamental tool
for designing algorithms operating on distances in graphs and different p
roblems solvable by dynamic programming. In applications such as longest c
ommon subsequence\, edit distance\, and longest increasing subsequence\, t
he matrices are even more structured: they are like Monge matrices. We dis
cuss SMAWK\, MMT(Multiple Maxima Trees) algorithms for the tropical produc
t of Monge and unit-Monge matrices\, core-sparse Monge matrix multiplicati
on and Tiskin's algorithm for simple unit-Monge matrices.\n
LOCATION:https://stable.researchseminars.org/talk/knotgraphgroup/126/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Natalia V. Maslova
DTSTART:20260314T140500Z
DTEND:20260314T153500Z
DTSTAMP:20260404T131156Z
UID:knotgraphgroup/127
DESCRIPTION:Title: On Gruenberg-Kegel graphs and beyond\nby Natalia V. Ma
slova as part of Knots\, graphs and groups\n\n\nAbstract\nThe Gruenberg--K
egel graph (or the prime graph) of a finite group $G$ is a simple graph wh
ose vertices are the prime divisors of $|G|$\, with primes $p$ and $q$ adj
acent in this graph if and only if $pq$ is an element order of $G$. The co
ncept of Gruenberg--Kegel graph proved to be very useful in finite group t
heory and in algebraic combinatorics as well as with connection to researc
h of some cohomological questions in integral group rings. In this talk\,
we discuss recent results on characterization of finite groups by Gruenber
g-Kegel graph and by isomorphism type of Gruenberg-Kegel graph as well as
combinatorial properties of Gruenberg--Kegel graphs.\n
LOCATION:https://stable.researchseminars.org/talk/knotgraphgroup/127/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marianna Zinovieva
DTSTART:20260321T140500Z
DTEND:20260321T153500Z
DTSTAMP:20260404T131156Z
UID:knotgraphgroup/129
DESCRIPTION:Title: Finite groups with the given condition on the prime graph<
/a>\nby Marianna Zinovieva as part of Knots\, graphs and groups\n\n\nAbstr
act\nThe prime graph (or the Gruenberg–Kegel graph) of a finite group G
is a simple graph GK(G) whose vertices are the prime divisors of the order
of G\, and two distinct vertices p and q are adjacent in GK(G) if and onl
y if G contains an element of order pq.\n\nThe concept of Gruenberg–Kege
l graph is very useful in finite group theory and in algebraic combinatori
cs.\n\nIn this talk\, we discuss results on finite groups with the given c
ondition on the prime graph (the Gruenberg-Kegel graph). In the “Kourovk
a Notebook”\, A.V. Vasiliev posed question 16.26: Does there exist a nat
ural number k such that no k pairwise nonisomorphic finite nonabelian simp
le groups can have the same prime graph? Conjecture: k = 5.\n\nWe discuss
author’s results obtained on A.V. Vasiliev’s Conjecture. We also consi
der other results about the prime graph (the Gruenberg-Kegel graph).\n
LOCATION:https://stable.researchseminars.org/talk/knotgraphgroup/129/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yangzhou Liu
DTSTART:20260103T140500Z
DTEND:20260103T153500Z
DTSTAMP:20260404T131156Z
UID:knotgraphgroup/131
DESCRIPTION:Title: Braids presentation and secant-quandle invariant of knots<
/a>\nby Yangzhou Liu as part of Knots\, graphs and groups\n\n\nAbstract\nI
n this talk we construct an invariant of braids based on horizontal trisec
ants and their equivalent classes\, called the secant-quandle. Based on th
is\, we further construct braid invariants such as the linear secant-quand
le\, which may provide a representation of ′G3n and pure braid group. Th
en\, we generalize secant-quandle to knots.\n
LOCATION:https://stable.researchseminars.org/talk/knotgraphgroup/131/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Oleg German
DTSTART:20260124T140500Z
DTEND:20260124T153500Z
DTSTAMP:20260404T131156Z
UID:knotgraphgroup/132
DESCRIPTION:Title: On irrationality measure and geometric aspects of Diophant
ine approximation\nby Oleg German as part of Knots\, graphs and groups
\n\n\nAbstract\nIn 1842\, Dirichlet published his famous theorem which bec
ame the foundation of Diophantine approximation. The phenomenon he found i
nspired Liouville to study how well algebraic numbers can be approximated
by rationals\, and thus\, to come up with a method of constructing transce
ndental numbers explicitly. The development of these ideas led to the conc
epts of irrationality measure and transcendence measure. Thanks to Minkows
ki\, it became clear that many problems arising in the theory of Diophanti
ne approximation could be addressed quite effectively using the tools of g
eometry of numbers. In particular\, the geometric approach naturally offer
s a wide variety of multidimensional analogues of the concept of irrationa
lity measure — so called Diophantine exponents. In the talk\, we will di
scuss various Diophantine exponents and the geometry that arises when stud
ying them.\n
LOCATION:https://stable.researchseminars.org/talk/knotgraphgroup/132/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yangzhou Liu
DTSTART:20260110T140500Z
DTEND:20260110T153500Z
DTSTAMP:20260404T131156Z
UID:knotgraphgroup/133
DESCRIPTION:Title: Braids presentation and secant-quandle invariant of knots
II\nby Yangzhou Liu as part of Knots\, graphs and groups\n\n\nAbstract
\nIn the last speech\, we introduced basic definitions and theorems of sec
ant-quandle as invariant of braids even knots. In this speech\, we discuss
more detail\, according a specific example. Further more\, we plan to gen
eralize this invariant to secant-biquandle and virtual secant-quandle.\n
LOCATION:https://stable.researchseminars.org/talk/knotgraphgroup/133/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yangzhou Liu
DTSTART:20260131T140500Z
DTEND:20260131T153500Z
DTSTAMP:20260404T131156Z
UID:knotgraphgroup/134
DESCRIPTION:Title: Secant-Quandle and Its Generalization: Loop-Quandle as an
Invariant of Knots\nby Yangzhou Liu as part of Knots\, graphs and grou
ps\n\n\nAbstract\nWe construct an interesting invariant for braids\, the s
ecant-quandle (SQ)\, derived from homotopy classes of generic secants and
generic trisecants. We provide an algebraic-topological interpretation of
this invariant by showing that each generator in SQ corresponds to a speci
al element of the fundamental group of the braid complement\, specifically
\, a meridian encircling exactly two braid strands. This interpretation en
ables a natural generalization of the secant-quandle to an invariant of kn
ots and links\, the loop-quandle (LQ). Furthermore\, we extend the constru
ction to the virtual braids. As an application\, we compute the SQ and LQ
for the Hopf link.\n
LOCATION:https://stable.researchseminars.org/talk/knotgraphgroup/134/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Semih Özlem
DTSTART:20260207T140500Z
DTEND:20260207T153500Z
DTSTAMP:20260404T131156Z
UID:knotgraphgroup/135
DESCRIPTION:Title: Weakened axioms\, idempotent splittings\, and the structur
e of learning: From algebra to AI\nby Semih Özlem as part of Knots\,
graphs and groups\n\n\nAbstract\nWe often think of mathematics as a tower
of abstractions\, but it begins with something deeply human: the act of te
lling things apart. In this talk\, I'll explore how this simple idea—spl
itting and focusing—manifests across different fields\, from linear alge
bra to motives to machine learning. We'll start with a basic observation:
if we relax the unit axiom in a vector space\, the scalar multiplication b
y 1 becomes an idempotent\, splitting the space into what is preserved and
what is annihilated. This splitting phenomenon appears in surprising plac
es: in the theory of motives\, where projectors decompose varieties\; in k
not theory\, where Jones–Wenzl projectors filter diagram algebras\; and
in deep learning\, where attention mechanisms focus on relevant features.
I'll introduce the topos-theoretic model of neural networks (Belfiore–Be
nnequin) and suggest that learning difficulties like catastrophic forgetti
ng and generalization gaps can be viewed as homotopical obstructions to ac
hieving "nice" (fibrant) network states. Architectural tools like residual
connections and attention can then be seen as learned\, conditional idemp
otents—adaptable splitters that help networks organize information. This
talk is an invitation to think structurally across disciplines. I won't p
resent finished theorems\, but a framework of connections that links motiv
ic philosophy\, categorical algebra\, and the practice of machine learning
. The goal is to start a conversation: can tools from pure mathematics—o
bstruction theory\, homotopy colimits\, derivators—help us design more r
obust\, interpretable\, and composable learning systems? No expertise in m
otives\, knots\, or AI is required—only curiosity about how ideas weave
together.\n
LOCATION:https://stable.researchseminars.org/talk/knotgraphgroup/135/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Радомир Степанов
DTSTART:20260404T140500Z
DTEND:20260404T153500Z
DTSTAMP:20260404T131156Z
UID:knotgraphgroup/136
DESCRIPTION:Title: Редукция гомологий Хованова-Ро
жанского для бипартитных узлов\nby Радо
мир Степанов as part of Knots\, graphs and groups\n\n\nAbstract
\nВ работах по гомологиям Хованова–Роза
нского вычисление инвариантов для узлов
и зацеплений с помощью матричных фактор
изаций было громоздким даже для простых
диаграмм\, но для бипартитных узлов вычи
сления существенно упрощаются. В этом сл
учае бикомплекс Хованова-Рожанского сво
дится к обычному монокомплексу на векто
рных пространствах и мы покажем\, как най
ти операторы действующие в новом компле
ксе.\n
LOCATION:https://stable.researchseminars.org/talk/knotgraphgroup/136/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Louis Kauffman
DTSTART:20260228T140500Z
DTEND:20260228T153500Z
DTSTAMP:20260404T131156Z
UID:knotgraphgroup/137
DESCRIPTION:Title: Temperley-Lieb Algebra - Visualizing Meanders and Idempote
nts\nby Louis Kauffman as part of Knots\, graphs and groups\n\n\nAbstr
act\nThe Temperley–Lieb algebra first arose as a matrix algebra describi
ng transfer functions in statistical mechanics models such as the Potts an
d Ising models. The algebra acquired a formal definition in terms of gener
ators and relations that allowed its representations to be identified in m
ultiple contexts.\n\nIn the early 1980's Vaughan Jones found the algebra o
nce again in a context between mathematics and physics as an algebra of pr
ojectors that arose in a tower construction of von Neumann algebras. For t
his context\, Jones investigated the formally defined algebra and its matr
ix representations\, and he constructed a trace function on the Temperley
–Lieb (TL) algebra (a function tr to a commutative ring such that tr(ab)
= tr(ba) for ab a product in the (non-commutative) Temperley–Lieb algeb
ra). He also discovered a representation of the Artin braid group to the T
L algebra. By composing this representation with the trace tr\, Jones defi
ned an invariant of braids that could be modified via the Markov Theorem f
or braids\, knots\, and links to produce a polynomial invariant of knots t
hat is now known as the Jones polynomial.\n\nThe speaker discovered knot d
iagrammatic and combinatorial interpretations of the Jones polynomial and
the Temperley–Lieb algebra that allow the polynomial to be seen as part
of a generalized Potts model partition function defined on planar link dia
grams and planar graphs. The combinatorial interpretation of the Temperley
–Lieb algebra allows the Jones trace to be interpreted as a loop count f
or closures of Connection Monoid representations of the Temperley–Lieb a
lgebra. The multiplicative structure of the Temperley–Lieb algebra is re
presented in the speaker's work by a Connection Monoid and Connection Cate
gory whose elements are families of planar connections between two rows of
points where the connections can go from row to row or from one row to th
e other.\n\nThe talk will begin with the formal definition of the TL monoi
d and will show how it is modeled by the Connection Monoid and similarly w
ith the TL Category and a Connection Category. This interpretation allows
us to see answers to algebra questions about the Temperley–Lieb Monoid t
hat would be invisible without the combinatorial interpretation. In partic
ular we will show how the structure of repeated powers of elements in TL a
ppears and how idempotents correspond to generalized meanders. A meander i
s a Jordan curve in the plane cut through transversely by a straight line.
The fascinating and highly visual combinatorics of the meanders informs t
he structure of the TL algebra via the way meanders correspond to factoriz
ations of the identity in the Temperley–Lieb Category.\n\nWe continue th
e discussion to include generalized meanders in relation to idempotents in
the Brauer Monoid and in Tangle Categories and other Monoidal Categories.
\n
LOCATION:https://stable.researchseminars.org/talk/knotgraphgroup/137/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sviatoslav Dzhenzher
DTSTART:20260307T140500Z
DTEND:20260307T153500Z
DTSTAMP:20260404T131156Z
UID:knotgraphgroup/138
DESCRIPTION:Title: Kolmogorov--Arnold Stability\nby Sviatoslav Dzhenzher
as part of Knots\, graphs and groups\n\n\nAbstract\nRegarding the represen
tation theorem of Kolmogorov and Arnold (KA) as an algorithm for represent
ing or <> functions\, we test its robustness by analyzing its
stability to withstand re-parameterizations of the hidden space.\nOne may
think of such re-parameterizations as the work of an adversary attempting
to foil the construction of the KA outer function.\nWe find KA to be stabl
e under countable collections of continuous re-parameterizations\, but une
arth a question about the equi-continuity of the outer functions that\, so
far\, obstructs taking limits and defeating continuous groups of re-param
eterizations.\nThis question on the regularity of the outer functions is r
elevant to the debate over the applicability of KA to the general theory o
f NNs.\n
LOCATION:https://stable.researchseminars.org/talk/knotgraphgroup/138/
END:VEVENT
BEGIN:VEVENT
SUMMARY:A. Allemand
DTSTART:20260214T140500Z
DTEND:20260214T153500Z
DTSTAMP:20260404T131156Z
UID:knotgraphgroup/139
DESCRIPTION:Title: Topological Galois Theory\nby A. Allemand as part of K
nots\, graphs and groups\n\n\nAbstract\nWe will discuss Vladimir Arnold's
elegant method for proving the unsolvability of many equations in elementa
ry functions.\n
LOCATION:https://stable.researchseminars.org/talk/knotgraphgroup/139/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hayk Sedrakyan
DTSTART:20260221T140500Z
DTEND:20260221T153500Z
DTSTAMP:20260404T131156Z
UID:knotgraphgroup/140
DESCRIPTION:Title: Novel Generalizations of Sedrakyan's inequality and equali
ty conditions\nby Hayk Sedrakyan as part of Knots\, graphs and groups\
n\n\nAbstract\nNovel Generalizations of Sedrakyan's inequality are foundat
ional comparison principles that establish sharp lower bounds for structur
ed sums. Beyond its classical role in algebraic inequality theory\, they s
erve as a methodological tool for estimating quantities that arise in dive
rse mathematical sciences. In topology and knot theory\, it can support bo
unding arguments for invariants and energy-type functionals. In group theo
ry\, analogous inequality structures appear in estimates involving weights
\, measures\, and representation norms. In discrete geometry\, it assists
in optimizing configurations and proving extremal properties of finite poi
nt sets and graphs. More broadly\, its conceptual framework—transforming
complex weighted relationships into simpler global bounds—makes it valu
able in theoretical physics\, optimization\, and information science\, whe
re controlling aggregate behavior from local data is essential.\n
LOCATION:https://stable.researchseminars.org/talk/knotgraphgroup/140/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tumpa Mahato
DTSTART:20260328T140500Z
DTEND:20260328T153500Z
DTSTAMP:20260404T131156Z
UID:knotgraphgroup/141
DESCRIPTION:Title: Arc shift move and region arc shift move for twisted knots
\nby Tumpa Mahato as part of Knots\, graphs and groups\n\n\nAbstract\n
In this paper\, we study the unknotting operation for twisted knots\, call
ed arc shift move. First\, we find a family of twisted knots with arc shif
t number n for any given $n \\in \\mathbb{N}$. Then we define a new unk
notting operation\, called the region arc shift move for twisted knots and
find family of twisted knots whose region arc shift number is less than o
r equal to n for any given $n \\in \\mathbb{N}$. Later\, we explore bou
nds for region arc shift number and forbidden number.\n
LOCATION:https://stable.researchseminars.org/talk/knotgraphgroup/141/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ivan Remizov
DTSTART:20260321T123000Z
DTEND:20260321T140000Z
DTSTAMP:20260404T131156Z
UID:knotgraphgroup/142
DESCRIPTION:Title: The Rate of Convergence of Chernoff Approximations to Oper
ator Semigroups and Approximate Solution of Differential Equations\nby
Ivan Remizov as part of Knots\, graphs and groups\n\n\nAbstract\nWe will
discuss a (surprisingly simple) proof of a theorem on the rate of converge
nce of Chernoff approximations to a strongly continuous operator semigroup
exp(tL) parameterized by a non-negative real number t. A theorem similar
to this has been sought for over 50 years\, since the publication of Chern
off's theorem in 1968. Colleagues from all over the world used a wide rang
e of tools of functional analysis to find it\, but a result was only recen
tly obtained\, and with very simple techniques.\n \nThe one-dimensional an
alogue of Chernoff's theorem states the following: if S is a real-valued f
unction of a real variable\, S(0) = 1\, S'(0) = L\, then for every real nu
mber t\, the numbers (S(t/n))^n tend to exp(tL) as n tends to infinity. Th
is simple fact is easily proven using the "second remarkable limit theorem
" from a course in mathematical analysis. The infinite-dimensional version
of this statement is called Chernoff's theorem. In it\, L is a closed\, d
ensely defined linear operator on a Banach space\, exp(tL) is a C0-semigro
up of operators with generator L\, and S is called the Chernoff function f
or L. Thus\, to approximately find a semigroup\, it suffices to find at le
ast one Chernoff function for the semigroup's generator. This simplifies t
he problem\, as it is much easier to find a Chernoff function than\, for e
xample\, the generator's resolvent. This is because if an operator is the
generator of a semigroup\, then this semigroup is unique\, and this operat
or's resolvent is also uniwue. However\, there are always many Chernoff fu
nctions for the generator\, so finding one of the Chernoff functions is ea
sier than finding a unique semigroup or a unique resolvent. Given this Che
rnoff function\, we can use Chernoff's theorem to first obtain a semigroup
and then a resolvent — since the resolvent is obtained from the semigro
up using the Laplace transform.\n \nChernoff's original theorem doesn't sp
ecify any properties of the Chernoff function that influence the rate of c
onvergence of Chernoff approximations as n tends to infinity\, and even in
the one-dimensional case\, this is a nontrivial problem. The general solu
tion to this problem will be discussed in the talk.\n \nWe will also discu
ss how to use Chernoff approximations to find the resolvent of a semigroup
generator\, and how to use it to find solutions to differential equations
with variable coefficients — ordinary and elliptic partial differential
equations.\n \nNote that the theory of operator semigroups initially aros
e from the need to express solutions to linear evolution partial different
ial equations (parabolic and Schrödinger) in the language of operator the
ory. Chernoff's theorem allows\, in many cases\, to express arbitrarily ac
curate approximations to the solution of the Cauchy problem in terms of th
e coefficients of these equations and the initial condition\, as well as t
o mathematically justify the correctness of representing the solution as a
Feynman integral. Many works and results in this area are attributed to t
he distinguished professor of Moscow State University Oleg Georgievich Smo
lyanov\, the teacher of the report's co-authors\, who introduced them to t
his topic.\n
LOCATION:https://stable.researchseminars.org/talk/knotgraphgroup/142/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ivan Remizov
DTSTART:20260411T123000Z
DTEND:20260411T140000Z
DTSTAMP:20260404T131156Z
UID:knotgraphgroup/143
DESCRIPTION:by Ivan Remizov as part of Knots\, graphs and groups\n\nAbstra
ct: TBA\n
LOCATION:https://stable.researchseminars.org/talk/knotgraphgroup/143/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Raphael Pinarbasi
DTSTART:20260502T140500Z
DTEND:20260502T153500Z
DTSTAMP:20260404T131156Z
UID:knotgraphgroup/144
DESCRIPTION:by Raphael Pinarbasi as part of Knots\, graphs and groups\n\nA
bstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/knotgraphgroup/144/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Arno Mikaelyan
DTSTART:20260509T140500Z
DTEND:20260509T153500Z
DTSTAMP:20260404T131156Z
UID:knotgraphgroup/145
DESCRIPTION:by Arno Mikaelyan as part of Knots\, graphs and groups\n\nAbst
ract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/knotgraphgroup/145/
END:VEVENT
END:VCALENDAR