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BEGIN:VEVENT
SUMMARY:A. Ya. Kanel-Belov
DTSTART:20230715T140500Z
DTEND:20230715T153500Z
DTSTAMP:20260422T225701Z
UID:knotgraphgroup/1
DESCRIPTION:Title: Quantization\, polynomial automorphisms\, and the Jacobian problem<
/a>\nby A. Ya. Kanel-Belov as part of Knots\, graphs and groups\n\nAbstrac
t: TBA\n
LOCATION:https://researchseminars.org/talk/knotgraphgroup/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:M. Chrisman
DTSTART:20230722T140500Z
DTEND:20230722T153500Z
DTSTAMP:20260422T225701Z
UID:knotgraphgroup/2
DESCRIPTION:Title: A sheaf-theoretic approach to classical and virtual knot theory
\nby M. Chrisman as part of Knots\, graphs and groups\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/knotgraphgroup/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vassily O. Manturov
DTSTART:20230729T140500Z
DTEND:20230729T153500Z
DTSTAMP:20260422T225701Z
UID:knotgraphgroup/3
DESCRIPTION:Title: Hexagonal rhombille tilings\, Groups G_{n}^{k}\, line configuratio
ns\, and Desargues flips\nby Vassily O. Manturov as part of Knots\, gr
aphs and groups\n\nAbstract: TBA\n
LOCATION:https://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:20260422T225701Z
UID:knotgraphgroup/4
DESCRIPTION:Title: $R[X]_A$ of zero-dimensional reduced rings\nby Hyungtae Baek (S
chool of Mathematics\, Kyungpook National University\, Republic of Korea)
as part of Knots\, graphs and groups\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/knotgraphgroup/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Scott Baldridge
DTSTART:20230812T140500Z
DTEND:20230812T153500Z
DTSTAMP:20260422T225701Z
UID:knotgraphgroup/5
DESCRIPTION:Title: A state sum for the total face color polynomial\nby Scott Baldr
idge as part of Knots\, graphs and groups\n\n\nAbstract\nThe total face co
lor polynomial is based upon the Poincaré polynomials of a family of filt
ered n-color homologies. It is an abstract graph invariant when the graph
is trivalent and calculates the sum of n-face colorings of ribbon graphs o
f the graph for each positive integer n. As such\, it may be seen as a suc
cessor of the Penrose polynomial\, which at n = 3 counts 3-edge colorings
(and consequently 4-face colorings) of planar trivalent graphs. In this ta
lk we describe a simple-to-express state sum formula for calculating the p
olynomial based upon earlier work of Lou Kauffman. This formula unites two
different perspectives about graph coloring: one based upon topological q
uantum field theory and the other on diagrammatic tensors.\n\nThis is join
t work with Lou Kauffman and Ben McCarty and is based upon the paper recen
tly uploaded to the arXiv found here: https://arxiv.org/abs/2308.02732\n
LOCATION:https://researchseminars.org/talk/knotgraphgroup/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Wan Zheyan
DTSTART:20230819T140500Z
DTEND:20230819T153500Z
DTSTAMP:20260422T225701Z
UID:knotgraphgroup/6
DESCRIPTION:Title: Explicit cocycle formulas on finite abelian groups and Dijkgraaf-Wi
tten invariants of n-torus\nby Wan Zheyan as part of Knots\, graphs an
d groups\n\n\nAbstract\nWe provide explicit and unified formulas for the c
ocycles of all degrees on the normalized bar resolutions of finite abelian
groups. This is achieved by constructing a chain map from the normalized
bar resolution to a Koszul-like resolution for any given finite abelian gr
oup. With the help of the obtained cocycle formulas\, we compute the Dijkg
raaf-Witten invariants of the n-torus for all n. This talk is based on htt
ps://arxiv.org/pdf/1703.03266.pdf\n
LOCATION:https://researchseminars.org/talk/knotgraphgroup/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sergei Gukov
DTSTART:20230826T140500Z
DTEND:20230826T153500Z
DTSTAMP:20260422T225701Z
UID:knotgraphgroup/7
DESCRIPTION:Title: 3-manifolds and Vafa-Witten theory\nby Sergei Gukov as part of
Knots\, graphs and groups\n\n\nAbstract\nWe initiate explicit computations
of Vafa-Witten invariants of 3-manifolds\, analogous to Floer groups in t
he context of Donaldson theory. In particular\, we explicitly compute the
Vafa-Witten invariants of 3-manifolds in a family of concrete examples rel
evant to various surgery operations (the Gluck twist\, knot surgeries\, lo
g-transforms). We also describe the structural properties that are expecte
d to hold for general 3-manifolds\, including the modular group action\, r
elation to Floer homology\, infinite-dimensionality for an arbitrary 3-man
ifold\, and the absence of instantons.\n
LOCATION:https://researchseminars.org/talk/knotgraphgroup/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bao Vuong
DTSTART:20230902T140500Z
DTEND:20230902T153500Z
DTSTAMP:20260422T225701Z
UID:knotgraphgroup/8
DESCRIPTION:Title: Gram matrix of tetrahedron and volume\nby Bao Vuong as part of
Knots\, graphs and groups\n\n\nAbstract\nWe review some properties of Gram
matrix for tetrahedra and give some integral formulas for the volume of h
yperbolic and spherical tetrahedron.\n
LOCATION:https://researchseminars.org/talk/knotgraphgroup/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Xujia Chen
DTSTART:20231007T140500Z
DTEND:20231007T153500Z
DTSTAMP:20260422T225701Z
UID:knotgraphgroup/9
DESCRIPTION:Title: Kontsevich’s invariants as topological invariants of configuratio
n space bundles\nby Xujia Chen as part of Knots\, graphs and groups\n\
n\nAbstract\nKontsevich's invariants (also called “configuration space i
ntegrals”) are invariants of certain framed smooth manifolds/fiber bundl
es. The result of Watanabe(’18) showed that Kontsevich’s invariants ca
n distinguish smooth fiber bundles that are isomorphic as topological fibe
r bundles. I will first give an introduction to Kontsevich's invariants\,
and then state my work which provides a perspective on how to understand t
heir ability of detecting exotic smooth structures: real blow up operation
s essentially depends on the smooth structure\, and thus given a space/bun
dle X\, the topological invariants of some spaces/bundles obtained by doin
g some real blow-ups on X can be different for different smooth structures
on X.\n
LOCATION:https://researchseminars.org/talk/knotgraphgroup/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vassily O. Manturov
DTSTART:20230909T140500Z
DTEND:20230909T153500Z
DTSTAMP:20260422T225701Z
UID:knotgraphgroup/10
DESCRIPTION:Title: Further directions in the photography method\nby Vassily O. Ma
nturov as part of Knots\, graphs and groups\n\n\nAbstract\nI will discuss
the photography method according to the papers\n\nhttps://arxiv.org/abs/23
05.06316\n \nhttps://arxiv.org/pdf/2305.11945.pdf\n \nhttps://arxiv.org/ab
s/2306.07079\n \nhttps://arxiv.org/abs/2307.03437\n \nhttps://arxiv.org/ab
s/2309.01735\n \nand give a long list of unsolved problems covering lots o
f topics in various fields of\nmathematics.\n
LOCATION:https://researchseminars.org/talk/knotgraphgroup/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Seongjeong Kim (Jilin university)
DTSTART:20230916T140500Z
DTEND:20230916T153500Z
DTSTAMP:20260422T225701Z
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. Przytycki and b
y Vladimir Turaev independently. The Kauffman bracket skein module (KBSM)
is the most extensively studied one. However\, computing the KBSM of a 3-m
anifold is known to be notoriously hard\, especially over the ring of Laur
ent polynomials. Marché conjectured that the KBSM of closed oriented $3$-
manifolds splits into the direct sum of free and certain torsion modules o
ver the ring of Laurent polynomials. The counterexample to this conjecture
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 this ring\
, we compute KBSM of $S^1 \\times S^2 \\ \\# \\ S^1 \\times S^2$. We show
that it is isomorphic to KBSM of a genus two handlebody modulo some specif
ic handle sliding relations. Moreover\, these handle sliding relations can
be written in terms of Chebyshev polynomials. This is joint work with Rh
ea Palak Bakshi and Xiao Wang\n
LOCATION:https://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:20260422T225701Z
UID:knotgraphgroup/12
DESCRIPTION:Title: Generalization of prime ideals\nby Hyungtae Baek (School of Ma
thematics\, Kyungpook National University\, Republic of Korea) as part of
Knots\, graphs and groups\n\n\nAbstract\nIn 2011\, Anderson and Badawi gen
eralized the concept of prime ideals and\nin 2020\, Hamed and Malek genera
lized the concept of prime ideals using multiplicative sets.\n\nIn this ta
lk\,\nfor a commutative ring with identity $R$ and\na multiplicative subse
t $S$ of $R$\,\nwe define an {\\it $S$-$n$-absorbing ideals} generalizing
these and\nexamine following problems:\n\\begin{enumerate}\n\\item[(1)]\nI
f $I$ is an $S$-$n$-absorbing ideal of $R$\,\nthen is $IR_S$ an $n$-absorb
ing ideal of $R_S$?\nWhat about the converse?\n\\item[(2)]\nWhen is each i
deal $I$ of $R$ disjoint from $S$ an $S$-$n_I$-absorbing ideal for some $n
_I \\in \\mathbb{N}$?\n\\item[(3)]\nWhen are $I \\bowtie^f J$\, $\\overlin
e{K}^f$ and $\\overline{I \\times K}^f$ $S^{\\bowtie^f}$-$n$-absorbing ide
al 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{enumerat
e}\n\n\\begin{thebibliography}{11}\n\\bibitem{Anderson}\nD. F. Anderson an
d A. Badawi\,\n{\\em On $n$-absorbing ideals of commutative rings}\,\nComm
. Alg. {\\bf 39(5)}\, 1646-1672 (2011).\n\n\\bibitem{Hamed}\nA. Hamed 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://researchseminars.org/talk/knotgraphgroup/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Oleg Styrt
DTSTART:20230930T140500Z
DTEND:20230930T153500Z
DTSTAMP:20260422T225701Z
UID:knotgraphgroup/13
DESCRIPTION:Title: Matrix sets closed under conjugations and summing commuting elemen
ts.\nby Oleg Styrt as part of Knots\, graphs and groups\n\n\nAbstract\
nThe talk is devoted to describing matrix sets closed under conjugations a
nd summing commuting elements. There are two well known important and prin
cipally different sets satisfying these properties: the sets of all semisi
mple and of all nilpotent matrices. It is also easy to see that the genera
l 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://researchseminars.org/talk/knotgraphgroup/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Zhuoke Yang
DTSTART:20231014T140500Z
DTEND:20231014T153500Z
DTSTAMP:20260422T225701Z
UID:knotgraphgroup/14
DESCRIPTION:Title: New approaches to Lie algebra weight systems\nby Zhuoke Yang a
s part of Knots\, graphs and groups\n\n\nAbstract\nIn this talk we introdu
ce a universal weight system (a function on chord diagrams satisfying the
4-term relation) taking values in the ring of polynomials in infinitely ma
ny variables\, whose particular specialisations are weight systems associa
ted with the Lie algebras gl(N) and Lie superalgebras gl(M|N). We extend t
his weight system to permutations and provide an efficient recursion for i
ts computation.\n
LOCATION:https://researchseminars.org/talk/knotgraphgroup/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nikolay Abrosimov (Sobolev Institute of Mathematics\, Novosibirsk)
DTSTART:20231021T140500Z
DTEND:20231021T153500Z
DTSTAMP:20260422T225701Z
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 structure on a
3-dimensional cone-manifold with a knot as singularity can often be defor
med into a limiting Euclidean structure. In the present work [1] we show t
hat the respective normalised Euclidean volume is always an algebraic numb
er which is reminiscent of Sabitov's theorem (the Bellows Conjecture). Thi
s fact also stands in contrast to hyperbolic volumes whose number- theoret
ic nature is usually quite complicated. This is a joint work with Alexande
r Kolpakov and Alexander Mednykh.\n\n[1] N. Abrosimov A. Kolpakov A. Medny
kh Euclidean volumes of hyperbolic knots // Proceedings of AMS 2023 (in pr
ess) DOI: 10.1090/proc/16353\n
LOCATION:https://researchseminars.org/talk/knotgraphgroup/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Timur Nasybullov
DTSTART:20231028T140500Z
DTEND:20231028T153500Z
DTSTAMP:20260422T225701Z
UID:knotgraphgroup/16
DESCRIPTION:Title: Quandles with orbit series conditions\nby Timur Nasybullov as
part of Knots\, graphs and groups\n\n\nAbstract\nThe notion of quandle was
introduced independently by Joyce and Matveev as an invariant for knots.
This invariant is very strong\, however\, usually it is difficult to deter
mine if two knot quandles are isomorphic. Various tricks are used to solve
this problem for individual cases of quandles. For each quandle\, one can
construct its orbit series tree. If two quandles are isomorphic\, then th
eir orbit series trees are also isomorphic. During the talk we are going t
o discuss relations between a quandle and its orbit series tree. In partic
ular\, we will discuss the question of when isomorphism of quandles follow
s from isomorphism of orbit series trees of these quandles. In addition\,
we are going to discuss various results about quandles which are described
in terms of its orbit series tree.\n
LOCATION:https://researchseminars.org/talk/knotgraphgroup/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anna Taranenko
DTSTART:20231111T140500Z
DTEND:20231111T153500Z
DTSTAMP:20260422T225701Z
UID:knotgraphgroup/18
DESCRIPTION:Title: On transversals in iterated groups and quasigroups\nby Anna Ta
ranenko 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 the (d+1)
-dimensional latin hypercube equal to the Cayley table of d times composit
ion of G with itself. A diagonal of a latin hypercube is said to be a tran
sversal if it contains all different symbols. We prove that for a given bi
nary 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\, it is eq
ual 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://researchseminars.org/talk/knotgraphgroup/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vladimir A. Stukopin
DTSTART:20231118T140500Z
DTEND:20231118T153500Z
DTSTAMP:20260422T225701Z
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 Yangians of L
ie superalgebras\, an important example of quantum groups. Yangians of sim
ple Lie algebras\, as well as quantum groups\, were introduced by V.G. Dri
nfeld in the eighties of the last century\, but began to be studied somewh
at earlier in the works of mathematical physicists\, within the framework
of the Bethe algebraic ansatz which is a method for studying quantum integ
rable models. Yangians are closely related to rational solutions of the qu
antum Yang-Baxter equation and appear as deformations of the Lie bialgebra
of polynomial currents with values in the reductive Lie algebra. Since th
e mid-nineties of the last century\, Yangians of Lie superalgebras (or sup
erYangians) have also been studied. Currently\, numerous connections have
been discovered between Yangians and many problems in representation theor
y\, mathematical and theoretical physics\, including superstring theory\,
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 bas
ic Lie superalgebras and to the Yangians of affine Kac-Moody superalgebras
(affine superYangians)\, which began to be studied quite recently.\n
LOCATION:https://researchseminars.org/talk/knotgraphgroup/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Oleg G. Styrt
DTSTART:20231125T140500Z
DTEND:20231125T153500Z
DTSTAMP:20260422T225701Z
UID:knotgraphgroup/20
DESCRIPTION:Title: Groups $\\Gamma_n^4$: algebraic properties\nby Oleg G. Styrt a
s part of Knots\, graphs and groups\n\n\nAbstract\nIn theory of knots and
braids\, there is a special type of groups closely connected with braid gr
oups — namely\, groups $\\Gamma_n^4$. Each of them is given by involutiv
e generators indexed by ordered $4$-tuples of pairwise distinct integers f
rom $1$ to $n$ and some special relations between them.\nThe speaker’s r
esearch is concentrated mainly on algebraic structure of groups $\\Gamma_n
^4$. His main result is that\, for any $n\\geqslant7$\, the groups $\\Gamm
a_n^4$ and $\\Gamma_n^4/(\\Gamma_n^4)'$ are isomorphic to direct products
of finitely many copies of $\\mathbb{Z}_2$\, in part\, that $\\Gamma_n^4$
is a nilpotent finite $2$-group with $4$-torsion.\nIf time allows\, all ar
e the most of the proof will be presented.\n
LOCATION:https://researchseminars.org/talk/knotgraphgroup/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Qingying Deng (Xiangtan University)
DTSTART:20231202T140500Z
DTEND:20231202T153500Z
DTSTAMP:20260422T225701Z
UID:knotgraphgroup/21
DESCRIPTION:Title: Twisted link and arrow polynomial\nby Qingying Deng (Xiangtan
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 independently i
ntroduced by V.O.Manturov (in 2000) and N. Kamada (in 2002) by using ato
m and corresponding abstract link diagram\, respectively. M.O. Bourgoin in
troduced the twisted knot theory in 2008 and defined the notion of a check
erboard coloring for a twisted link diagram.\nIn this talk\, we first give
two new criteria to detect the checkerboard colorability of virtual links
by using odd writhe and arrow polynomial of virtual links\, respectively.
Then by applying these criteria we determine the checkerboard colorabilit
y of virtual knots up to four crossings\, with only one exception.\nSecond
\, we reformulate the arrow polynomial of twisted links by using Kauffman
’s formalism. In fact\, in 2012\, in case of using the pole diagram\, N.
Kamada obtained the polynomial by generalizing a multivariable polynomial
invariant of a virtual link to a twisted link. Moreover\, we figure out t
hree characteristics of the arrow polynomial of a checkerboard colorable t
wisted link\, which is a tool of detecting checkerboard colorability of a
twisted link. The latter two characteristics are the same as in the case o
f checkerboard colorable virtual link diagram.\n
LOCATION:https://researchseminars.org/talk/knotgraphgroup/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Aidan Mozayeni
DTSTART:20231216T140500Z
DTEND:20231216T153500Z
DTSTAMP:20260422T225701Z
UID:knotgraphgroup/22
DESCRIPTION:Title: Novel Applications of Theorem 2 (Sedrakyan-Mozayeni)\nby Aidan
Mozayeni as part of Knots\, graphs and groups\n\n\nAbstract\nIn this pres
entation\, I will review progress in Dr. Sedrakyan’s and my work to gene
ralize the pentagon case of the photography principle. I will also give a
novel application\, go in depth on the derivation of Theorem 2 (Sedrakyan-
Mozayeni)\, and explain current issues with the pentagon case of the photo
graphy principle. Furthermore\, this presentation will explain another app
lication\, and close off by explaining a potential creation of a pentagon
theorem that could aid in generalizing the case.\n
LOCATION:https://researchseminars.org/talk/knotgraphgroup/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Timorin Vladlen
DTSTART:20231209T140500Z
DTEND:20231209T153500Z
DTSTAMP:20260422T225701Z
UID:knotgraphgroup/23
DESCRIPTION:Title: Aperiodic points for outer billiards\nby Timorin Vladlen as pa
rt of Knots\, graphs and groups\n\n\nAbstract\nThis is a joint project wit
h A. Kanel-Belov\, Ph. Rukhovich\, and V. Zgurskii. A Euclidean outer bill
iard on a convex figure in the plane is the map sending a point outside th
e figure to the other endpoint of a segment touching the figure at the mid
dle. Iterating such a process was suggested by J. Moser as a crude model o
f planetary motion. Polygonal outer billiards are arguably the principal e
xamples of Euclidean piecewise rotations\, which serve as a natural genera
lization of interval exchange maps. They also found applications in electr
ical engineering. Previously known rigorous results on outer billiards on
regular N-polygons are\, apart from “trivial” cases of N=3\,4\,6\, bas
ed on dynamical self-similarities (this approach was originated by S. Taba
chnikov). Dynamical self-similarities have been found so far only for N=5\
,7\,8\,9\,10\,12. In his ICM 2022 address\, R. Schwartz asked whether “o
uter billiard on the regular N-gon has an aperiodic orbit if N is not 3\,
4\, 6”. We answer this question in affirmative for N not divisible by 4.
Our methods are not based on self-similarity. Rather\, scissor congruence
invariants (including that of Sah-Arnoux-Fathi) play a key role.\n
LOCATION:https://researchseminars.org/talk/knotgraphgroup/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vadim Leshkov
DTSTART:20231223T140500Z
DTEND:20231223T153500Z
DTSTAMP:20260422T225701Z
UID:knotgraphgroup/24
DESCRIPTION:Title: A Functorial Generalization of Coxeter Groups\nby Vadim Leshko
v as part of Knots\, graphs and groups\n\n\nAbstract\nIn the work arXiv:23
12.07939 we describe the category WC2 of weighted 2-complexes and its subc
ategory WC1 of weighted graphs. Since a Coxeter group is defined by its Co
xeter graph\, the construction of Coxeter groups defines a functor from WC
1 to the category of groups. We generalize the notion of a Coxeter group b
y extending the domain of the functor to the category WC2. It appears that
the resulting functor generalizes the construction of Coxeter groups\, Ga
uss pure braid groups GVP_{n} (introduced by V. Bardakov\, P. Bellingeri\,
and C. Damiani in 2015)\, k-free braid groups on n strands G_{n}^{k} (int
roduced by V. Manturov in 2015)\, and other quotients of Coxeter groups.\n
LOCATION:https://researchseminars.org/talk/knotgraphgroup/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Euich Miztani
DTSTART:20231230T140500Z
DTEND:20231230T153500Z
DTSTAMP:20260422T225701Z
UID:knotgraphgroup/25
DESCRIPTION:Title: Transformation Groupoid Based on Quotient Vector Spaces —A Mathe
matical Definition for Theory of Dimensionality\nby Euich Miztani as p
art of Knots\, graphs and groups\n\n\nAbstract\nIn my last presentation of
this seminar on the 19th of December in 2023\, a new mapping (projection)
is given from any point in its original dimensional space to other dimens
ional space. In the series of mappings\, any point has invariant or symmet
ry. In other words\, the degree of freedom (the number of variables) of an
y point is unchangeable in the series of mappings. In this time\, we expla
in mathematical definitions in terms of quotient vector space. The first a
im is to define our new notions in the last presentation more mathematical
ly. The second aim is to introduce a more concrete mappings from a higher
dimensional space to a lower dimensional one.\n
LOCATION:https://researchseminars.org/talk/knotgraphgroup/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hyungtae Baek
DTSTART:20240120T140500Z
DTEND:20240120T153500Z
DTSTAMP:20260422T225701Z
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 wi
th 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$U := \\{f \\in R[X] \\\,|\\\, f {\\rm \\ i
s \\ a \\ monic \\ polynomial} \\}$.\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 the Serre's co
njecture rings has been researched actively.\n\nIn this talk\, we investig
ate 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 characterize
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. Markan
da\,\n{\\it The rings $R(X)$ and $R \\left< X\\right>$}\,\nJ. Algebra 95 (
1985) 96-155.\n\n\\bibitem{kang 1989} B. G. Kang\,\n{\\em Pr\\"ufer $v$-mu
ltiplication domains and the ring $R[X]_{N_v}$}\,\nJ. Algebra 123 (1989) 1
51-170.\n\n\\bibitem{riche} L. R. Le Riche\,\n{\\it The ring $R\\left< X \
\right>$}\,\nJ. Algebra 67 (1980) 327-341.\n\\end{thebibliography}\n
LOCATION:https://researchseminars.org/talk/knotgraphgroup/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sergey Malev
DTSTART:20240127T140500Z
DTEND:20240127T153500Z
DTSTAMP:20260422T225701Z
UID:knotgraphgroup/27
DESCRIPTION:Title: Evaluations of multilinear polynomials on finite dimensional alge
bras\nby Sergey Malev as part of Knots\, graphs and groups\n\n\nAbstra
ct\nLet p be a polynomial in several non-commuting variables with coeffici
ents in an algebraically closed field K of arbitrary characteristic. It ha
s been conjectured that for any n\, for p multilinear\, the image of p eva
luated 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 all of M
_n(K).\nIn this talk we will discuss the generalization of this result for
non-associative algebras such as Cayley-Dickson algebra (i.e. algebra of
octonions)\, pure (scalar free) octonion Malcev algebra and basic low rank
Jordan algebras.\n
LOCATION:https://researchseminars.org/talk/knotgraphgroup/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Han-Bom Moon (Department of Mathematics Fordham University)
DTSTART:20240309T140500Z
DTEND:20240309T153500Z
DTSTAMP:20260422T225701Z
UID:knotgraphgroup/28
DESCRIPTION:Title: Cluster algebras and generalized skein algebras\nby Han-Bom Mo
on (Department of Mathematics Fordham University) as part of Knots\, graph
s and groups\n\n\nAbstract\nFor each punctured surface admitting a triangu
lation\, we may associate two algebras. One is the cluster algebra of surf
aces\, and the other is the generalized skein algebra from quantum topolog
y. In this talk\, I will explain their compatibility and some consequences
in the Teichmuller theory and the structure of cluster algebra.\n
LOCATION:https://researchseminars.org/talk/knotgraphgroup/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vassily O. Manturov
DTSTART:20240203T140500Z
DTEND:20240203T153500Z
DTSTAMP:20260422T225701Z
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 Knots\, gra
phs and groups\n\n\nAbstract\nIn 2022\, the author and I.M.Nikonov have no
ticed that knots in the full cylinder\nS^{1}\\times D^{2} have some "hidde
n" crossings. As a result\, this lead to the development\nof "flat-virtual
theory" and a map from knots/links in the thickened cylinder to knots fla
t virtual knots/links.\n \nIn the present talk\, we discuss possible ways
of generalising this approach to the 3-dimensional\nthickening of the Moeb
ius band and to the RP^{3} thought of as a 3-dimensional thickening of RP^
{3}.\n
LOCATION:https://researchseminars.org/talk/knotgraphgroup/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jonathan Schneider
DTSTART:20240302T140500Z
DTEND:20240302T153500Z
DTSTAMP:20260422T225701Z
UID:knotgraphgroup/30
DESCRIPTION:Title: REALISTIC CROSSING DATA FOR CURVES IN THE PLANE\nby Jonathan S
chneider as part of Knots\, graphs and groups\n\n\nAbstract\nWhen does a c
urve in R² with crossing data lift to a knot in R³\, or\, more generally
\, to a fiberwise toral surface in R²×R²? I propose necessary and suffi
cient conditions. I consider three cases:\n1. Generic curves\, which form
the basis of familiar knot diagrams. No restrictions are necessary on cros
sing data for the static curve\; however\, a homotopy of the curve must ca
rry the crossing data continuously and avoid "cyclic crossings".\n2. Cellu
lar curves\, where the curve is a finite cellular map. Here we additional
ly require that the static curve itself carries crossing data continuously
from point to point and avoids cyclic crossings.\n3. General curves. Here
\, the "continuity" restriction of the first two cases is inadequate. A st
ronger pair of conditions\, which I call "monotonicity and stability"\, is
necessary.\n
LOCATION:https://researchseminars.org/talk/knotgraphgroup/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Дмитрий Александрович Шабанов
DTSTART:20240210T140500Z
DTEND:20240210T153500Z
DTSTAMP:20260422T225701Z
UID:knotgraphgroup/31
DESCRIPTION:Title: Дробные раскраски случайных гиперг
рафов\nby Дмитрий Александрович Шабано
в as part of Knots\, graphs and groups\n\n\nAbstract\nПоиск точн
ых пороговых вероятностей для различных
свойств является одним из центральных н
аправлений исследований в теории случай
ных графов и гиперграфов. В докладе пойд
ет речь об одной задаче подобного рода\,
связанной с так называемыми дробными ра
скрасками. С помощью метода второго моме
нта и решения ряда экстремальных задач д
ля стохастических матриц нам удалось по
лучить очень точные оценки пороговой ве
роятности для свойства наличия дробной (
4:2) раскраски в биномиальной модели случ
айного гиперграфа. Полученные результат
ы также показывают\, что эта пороговая ве
роятность строго превышает пороговую ве
роятность для классического свойства пр
авильной 2-раскрашиваемости. Доклад осно
ван на совместной работе с П.А. Захаровым
.\n
LOCATION:https://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:20260422T225701Z
UID:knotgraphgroup/32
DESCRIPTION:Title: Closed 4-braids and the Jones unknot problem\nby Alexey Slepts
ov (Kurchaton institute (ITEP division)\, MIPT and IITP) as part of Knots\
, graphs and groups\n\n\nAbstract\nJones polynomial is a famous knot invar
iant discovered by V.Jones in 1984. The Jones unknot problem is a question
whether there is a non-trivial knot with the trivial Jones polynomial. Th
e answer to this fundamental question is still unknown despite numerous at
tempts to solve it. In the talk I will give a brief review on different ap
proaches to this question. I will describe in more detail the construction
of Jones polynomials (and HOMFLY-\nPT) through the braid group and its re
presentations 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 positively an
d negatively. The talk is based on a recent preprint arXiv:2402.02553 (joi
nt work of Dmitriy Korzun\, Elena\nLanina\, Alexey Sleptsov).\n
LOCATION:https://researchseminars.org/talk/knotgraphgroup/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:V.O. Manturov
DTSTART:20240316T140500Z
DTEND:20240316T153500Z
DTSTAMP:20260422T225701Z
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\nIn this
talk\, we give new upper bounds for the chromatic numbers for integer latt
ices and some rational spaces and other lattices. In particular\, we have
proved that for any concrete integer number $d$\, the chromatic number of
$\\mathbb{Z}^{n}$ with critical distance $\\sqrt{2}d$ has a polynomial gro
wth in $n$ with exponent less than or equal to $d$ (sometimes this estimat
e is sharp). The same statement is true not only in the Euclidean norm\, b
ut also in any $l_{p}$ norm. Moreover\, we have given concrete estimates f
or 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 prime numb
ers.\n
LOCATION:https://researchseminars.org/talk/knotgraphgroup/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Roman Dribas
DTSTART:20240323T140500Z
DTEND:20240323T153500Z
DTSTAMP:20260422T225701Z
UID:knotgraphgroup/34
DESCRIPTION:Title: Ideal tetrahedra\, photography principle and invariants of manifol
ds\nby Roman Dribas as part of Knots\, graphs and groups\n\n\nAbstract
\nWe apply the photography principle for hyperbolic 2-3 Pacner move to con
struct invariants of 4-manifolds.\n
LOCATION:https://researchseminars.org/talk/knotgraphgroup/34/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Soohyun Park
DTSTART:20240330T140500Z
DTEND:20240330T153500Z
DTSTAMP:20260422T225701Z
UID:knotgraphgroup/35
DESCRIPTION:Title: Hidden structures in (higher) Euler characteristic invariants\
nby Soohyun Park as part of Knots\, graphs and groups\n\n\nAbstract\nWe wi
ll discuss the gamma vector\, which was originally considered in the conte
xt of the combinatorics of Eulerian polynomials and later resurfaced in a
special case of the Hopf conjecture on Euler characteristics of (piecewise
Euclidean) nonpositively curved manifolds in work of Gal. Since then\, it
has appeared in many different combinatorial applications. We find explic
it formulas which give a local-global interpretation and complement/contra
st lower bound properties stated earlier by Gal. In addition\, a formula i
nvolving Catalan numbers and binomial coefficients hints at connections to
noncrossing partitions and Coxeter groups in existing positivity examples
. Finally\, we note considering characteristic classes directly lead to lo
g concavity and Schur positivity properties.\n
LOCATION:https://researchseminars.org/talk/knotgraphgroup/35/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sachchidanand Prasad
DTSTART:20240406T140500Z
DTEND:20240406T153500Z
DTSTAMP:20260422T225701Z
UID:knotgraphgroup/36
DESCRIPTION:Title: Cut Locus of Submanifolds: A Geometric Property of the Manifold\nby Sachchidanand Prasad as part of Knots\, graphs and groups\n\n\nAbstr
act\nThe cut locus of a point in a Riemannian manifold is the collection o
f all points beyond which a distance minimal geodesics fails to be distanc
e 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://researchseminars.org/talk/knotgraphgroup/36/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Illia Rogozhkin
DTSTART:20240413T140500Z
DTEND:20240413T153500Z
DTSTAMP:20260422T225701Z
UID:knotgraphgroup/37
DESCRIPTION:Title: Non-Reidemeister Knot Theory and pure braids invariants\nby Il
lia Rogozhkin as part of Knots\, graphs and groups\n\n\nAbstract\nIn this
seminar I will talk about the non-Reidemeister knots theory suggested by M
anturov 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 wh
ich gives representations for braids in the form of words and in the form
of 2x2 matrices. Finally\, I will propose another pure braid invariant in
matrices of (2n-4)x(2n-4) size\, which is naturally obtained from the Dela
unay triangulation of a sphere.\n
LOCATION:https://researchseminars.org/talk/knotgraphgroup/37/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Питаль Петя
DTSTART:20240420T140500Z
DTEND:20240420T153500Z
DTSTAMP:20260422T225701Z
UID:knotgraphgroup/38
DESCRIPTION:Title: Обобщенные факториалы и p-упорядоче
ния\nby Питаль Петя as part of Knots\, graphs and groups\
n\n\nAbstract\nВ докладе будет рассказано об ин
тересном обобщении понятия факториала\,
предложенном М. Бхаргавой для дедекиндо
вых колец.\n
LOCATION:https://researchseminars.org/talk/knotgraphgroup/38/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Канель-Белов Алексей Яковлевич
DTSTART:20240427T140500Z
DTEND:20240427T153500Z
DTSTAMP:20260422T225701Z
UID:knotgraphgroup/39
DESCRIPTION:Title: Проблема Шпехта\, гипотеза Гельфанд
а и некоммутативная алгебраическая геом
етрия\nby Канель-Белов Алексей Яковлеви
ч as part of Knots\, graphs and groups\n\n\nAbstract\nТождество
м алгебры $A$ называется многочлен\, тожде
ственно обращающейся в ноль на ней. В ко
ммутативных алгебрах выполняется тожде
ство $[x\,y]=xy-yx=0$\, в алгебре матриц второго
порядка - тождество $[[x\,y]^2\,z]=0$ и т.д. Тожд
ество $g$ следует из набора $f_i$ если в люб
ой алгебре где выполняется система тожд
еств $f_i$ выполняется тождество $g$. Пробл
ема Шпехта состоит в том\, что верно ли\, ч
то любая система тождеств в некоммутати
вном ассоциативном кольце следует из ко
нечной подсистемы? \nРешение этой пробле
мы приводит к задачам комбинаторики сло
в (в том числе элементарным)\, к новой точ
ки зрения на некоммутативную алгебраиче
скую геометрию. Недавно А.Хорошкин\, И.Во
робьев и А.Я.Белов вывели из одного из ве
рсий доказательства гипотезу Гельфанда
о нетеровости действия полиномиальных
векторных полей без свободного члена на
тензорных представлениях. \nКомбинаторн
ое идейное ядро заключается в следующей
элементарной задаче. Рассмотрим кольцо
многочленов от хватит двух переменных $x\
,y$ . Рассмотрим подстановку $x\\to P(x)\, y\\to P(y
)$. Многочлен $P$ один и тот же. Тогда любое
подпространство\, замкнутое относитель
но такой подстановки выводится из коне
чной подсистемы (подстановками и линейн
ыми действиями). Ей и будет уделено основ
ное внимание.\n
LOCATION:https://researchseminars.org/talk/knotgraphgroup/39/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Louis H Kauffman (UIC)
DTSTART:20240504T140500Z
DTEND:20240504T153500Z
DTSTAMP:20260422T225701Z
UID:knotgraphgroup/40
DESCRIPTION:Title: Multiple Virtual Knot Theory\nby Louis H Kauffman (UIC) as par
t of Knots\, graphs and groups\n\n\nAbstract\nThis talk is an introduction
to Multiple Virtual Knot Theory (MVKT) where one has classical crossings\
, flat crossings\, singular crossings and a multiplicity of virtual crossi
ngs.\nAll virtual crossings can make detour moves over all the other cross
ing types including the other virtuals. We will discuss a number of differ
ent invariants in this theory and also its relationship with coloring prob
lems and Penrose evaluations and Penrose perfect matching polynomials (as
related to joint work with Scott Baldrige and Ben McCarty). We will discus
s relationships of MVKT with virtual knot theories on surfaces of genus gr
eater than zero\, with welded MVTK and braid groups for these theories.\n
LOCATION:https://researchseminars.org/talk/knotgraphgroup/40/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Maksim Zhukovskii
DTSTART:20240511T140500Z
DTEND:20240511T153500Z
DTSTAMP:20260422T225701Z
UID:knotgraphgroup/41
DESCRIPTION:Title: Stability of large cuts in random graphs\nby Maksim Zhukovskii
as part of Knots\, graphs and groups\n\n\nAbstract\nWe prove that the fam
ily of largest cuts in the binomial random graph exhibits the following st
ability property: with high probability\, there is a set of (1-o(1))n vert
ices that is partitioned in the same manner by all maximum cuts. We also s
how some applications of this property - in particular\, to the validity o
f Simonovits's property in binomial random graphs.\nThe talk is based on j
oint work with Ilay Hoshen and Wojciech Samotij\n
LOCATION:https://researchseminars.org/talk/knotgraphgroup/41/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hayk Sedrakyan
DTSTART:20240518T140500Z
DTEND:20240518T153500Z
DTSTAMP:20260422T225701Z
UID:knotgraphgroup/42
DESCRIPTION:Title: Novel Sedrakyan-Mozayeni theorem\, and its applications in scienti
fic research in topology and geometry\nby Hayk Sedrakyan as part of Kn
ots\, graphs and groups\n\n\nAbstract\nIn this presentation\, we consider
several applications of the Sedrakyan-Mozayeni theorem. In particular\, w
e investigate how it can be applied in novel mathematical scientific rese
arch in topology and geometry to generalize the pentagon case of the pho
tography principle\, data transmission and invariants of manifolds. We wi
ll also go in depth on the derivation of Sedrakyan-Mozayeni theorem\, and
explain current issues with the pentagon case of the photography principl
e. Besides having theoretical applications\, the formula can be used in a
pplied mathematics and lead to new real-world results. We will implement
the formula into a code and generate several computer simulations applied
in novel mathematical scientific research in topology and geometry.\n
LOCATION:https://researchseminars.org/talk/knotgraphgroup/42/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Euich Miztani
DTSTART:20240525T140500Z
DTEND:20240525T153500Z
DTSTAMP:20260422T225701Z
UID:knotgraphgroup/43
DESCRIPTION:Title: How Should We Interpret Space Dimenion?\nby Euich Miztani as p
art of Knots\, graphs and groups\n\n\nAbstract\nIn modern physics we could
say that space dimension is derived from some physical conditions. Kaluz
a-Klein theory and D-brane are typical examples. However\, not only by su
ch conditions\, we should also think about space dimension with insights
from known facts possibly without physical conditions. In this talk we re
think space dimensionality from scratch.\n
LOCATION:https://researchseminars.org/talk/knotgraphgroup/43/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Seongjeong Kim
DTSTART:20240601T140500Z
DTEND:20240601T153500Z
DTSTAMP:20260422T225701Z
UID:knotgraphgroup/44
DESCRIPTION:Title: The groups $G_{n}^{3}$ and rhombi tilings of 2n-gons\nby Seong
jeong Kim as part of Knots\, graphs and groups\n\n\nAbstract\nIn this talk
we will consider a map from the set of rhombi tilings of 2n-gon to the gr
oup $G_{n}^{3}$ and will discuss our further researches.\n
LOCATION:https://researchseminars.org/talk/knotgraphgroup/44/
END:VEVENT
BEGIN:VEVENT
SUMMARY:O.G. Styrt
DTSTART:20240608T130500Z
DTEND:20240608T143500Z
DTSTAMP:20260422T225701Z
UID:knotgraphgroup/45
DESCRIPTION:Title: Compact linear groups with quotient space homeomorphic to a cell.<
/a>\nby O.G. Styrt as part of Knots\, graphs and groups\n\n\nAbstract\nThe
main part of my research is devoted to the following question: when the q
uotient space of a linear representation of a compact Lie group is homeomo
rphic to a vector space.\nThe first result for finite linear groups was ob
tained in 1984 by M.A. Michailova: it should be generated by pseudoreflect
ions.\nI have investigated the cases of groups with commutative connected
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 hardly f
ormulated in terms of the weight system of the torus and requires a specia
l procedure of reducing a general case to that with indecomposable and «$
2$-stable» weight system\; further\, the criterion for namely this partic
ular case is obtained (but still hard even to formulate). This reducing pr
ocedure uses a construction provided by one key example of a representatio
n when the quotient is a vector space. For more understanding\, I plan to
describe this key representation whose weights have exactly one (up to con
stants) nontrivial linear relation without zero coefficients and to constr
uct explicitly a factorization mapping onto a space.\n
LOCATION:https://researchseminars.org/talk/knotgraphgroup/45/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sergei Gukov
DTSTART:20240622T130500Z
DTEND:20240622T143500Z
DTSTAMP:20260422T225701Z
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 talk\, I
will describe recent construction of new link and 3-manifold invariants a
ssociated with Verma modules of $U_q (sl_N)$ at generic $q$. The resulting
invariants can be combined into a Spin$^c$-decorated TQFT and have a nice
property that\, for links in general 3-manifolds\, they have integer coef
ficients. In particular\, they are expected to admit a categorification an
d\, if time permits\, I will outline various ingredients that may go into
a construction of 3-manifold homology categorifying these $U_q (sl_N)$ inv
ariants at generic $q$.\n
LOCATION:https://researchseminars.org/talk/knotgraphgroup/46/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jian Liu
DTSTART:20240615T130500Z
DTEND:20240615T143500Z
DTSTAMP:20260422T225701Z
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 complex s
ystems are widely observed across various fields\, drawing increased atten
tion from researchers. In mathematics\, efforts are made to develop variou
s theories and methods for studying the interactions between spaces. In th
is talk\, we present an algebraic topology framework to explore interactio
ns between spaces. We introduce the concept of interaction spaces and inve
stigate their homotopy\, singular homology\, and simplicial homology. Furt
hermore\, we demonstrate that interaction singular homology serves as an i
nvariant under interaction homotopy. We believe that the proposed framewor
k holds potential for practical applications.\n
LOCATION:https://researchseminars.org/talk/knotgraphgroup/47/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Elena Lanina
DTSTART:20240629T130500Z
DTEND:20240629T143500Z
DTSTAMP:20260422T225701Z
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://researchseminars.org/talk/knotgraphgroup/48/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alina Pital
DTSTART:20240706T130500Z
DTEND:20240706T143500Z
DTSTAMP:20260422T225701Z
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 conjectu
red in 1987 by J. Przytycki and proven by S.V. Duzhin\nin 2011. We will di
sprove the conjecture that bipartite knots should have trivial second Alex
ander ideal. We will\nconstruct a family inside the class of bipartite kno
ts that contains all rational knots and has trivial second\nAlexander idea
l. We will present a matched diagram of the knot 818. Also we will demonst
rate a combinatorial\ntechniques that could be useful for further research
on bipartite knots.\n
LOCATION:https://researchseminars.org/talk/knotgraphgroup/49/
END:VEVENT
BEGIN:VEVENT
SUMMARY:O.G. Styrt
DTSTART:20240713T100500Z
DTEND:20240713T113500Z
DTSTAMP:20260422T225701Z
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\nAbstract\nThe
main part of my research is devoted to the following question: when the qu
otient space of a linear representation of a compact Lie group is homeomor
phic to a vector space.\nThe first result for finite linear groups was obt
ained in 1984 by M.A. Michailova: it should be generated by pseudoreflecti
ons.\nI have investigated the cases of groups with commutative connected c
omponents and of irreducible simple groups of classical types. I am going
to speak in detail on the first of these cases. The condition is hardly fo
rmulated 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 particu
lar case is obtained (but still hard even to formulate). This reducing pro
cedure uses a construction provided by one key example of a representation
when the quotient is a vector space. For more understanding\, I plan to d
escribe this key representation whose weights have exactly one (up to cons
tants) nontrivial linear relation without zero coefficients and to constru
ct explicitly a factorization mapping onto a space.\n
LOCATION:https://researchseminars.org/talk/knotgraphgroup/50/
END:VEVENT
BEGIN:VEVENT
SUMMARY:V.O. Manturov
DTSTART:20240720T100500Z
DTEND:20240720T113500Z
DTSTAMP:20260422T225701Z
UID:knotgraphgroup/51
DESCRIPTION:Title: The photography method. The state of the art. Review and unsolved
problem\nby V.O. Manturov as part of Knots\, graphs and groups\n\n\nAb
stract\nIn 2023\, the author formulated the photography method which allow
s one to \nto solve various equations and calculate invariants of various
objects.\n \nOne starts with some object (say\, pentagon) with a state (s
ay\, triangulation) and\ndata (say\, edge lengths) a data transformation r
ule (say\, a flip of a triangulation).\nThen by using some geometrical con
siderations\, one can prove "for free" that\nsuch data transformation rule
s give rise to solutions to some equation\n[say\, Ptolemy transformation s
atisfies the Pentagon equation] and\nconstruct invariants of many objects
[say\, braids].\n \nThe formula can be taken from any geometrical consider
ations (say\, formulas\nin the hyperbolic space)\; having such a formula "
for free" one can prove it\nalgebraically and pass to the more abstract ob
jects (say\, formal variables instead of\nlengths).\n \n \nThis method is
very broad. Here we mention just some directions of (further research):\n
invariants of knots\, braids\, manifolds\, solutions to the pentagon\, hex
agon\, YBE equations\nand formulate relations to cluster algebras\, tropic
al geometry\, and many other areas of\nmathematics.\n
LOCATION:https://researchseminars.org/talk/knotgraphgroup/51/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexei Vernitski
DTSTART:20240817T100500Z
DTEND:20240817T113500Z
DTSTAMP:20260422T225701Z
UID:knotgraphgroup/52
DESCRIPTION:Title: Approaches to realisability of Gauss diagrams\nby Alexei Verni
tski as part of Knots\, graphs and groups\n\n\nAbstract\nThe shape of a cl
osed curve can be summarised by a chord diagram called the Gauss diagram o
f the curve. Not every chord diagram is the Gauss diagram of a curve\; if
it is\, it is called realisable. I will present a number of elegant constr
uctions which were introduced in the context of describing realisable Gaus
s diagrams. These constructions include graphs summarising Gauss diagrams
and moves transforming Gauss diagrams. I will discuss some open problems.
The talk is partially based on paper https://www.worldscientific.com/doi/
10.1142/S0218216523500591 and preprint https://arxiv.org/pdf/2407.09144\
n
LOCATION:https://researchseminars.org/talk/knotgraphgroup/52/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Seongjeong Kim
DTSTART:20240727T100500Z
DTEND:20240727T113500Z
DTSTAMP:20260422T225701Z
UID:knotgraphgroup/53
DESCRIPTION:Title: Knot in $S_{g}\\times S^{1}$ of degree one and long knot invariant
s\nby Seongjeong Kim as part of Knots\, graphs and groups\n\n\nAbstrac
t\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://researchseminars.org/talk/knotgraphgroup/53/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alina Pital
DTSTART:20240803T100500Z
DTEND:20240803T113500Z
DTSTAMP:20260422T225701Z
UID:knotgraphgroup/54
DESCRIPTION:Title: Phenomena of emptiness in different theories\nby Alina Pital a
s part of Knots\, graphs and groups\n\n\nAbstract\nI would like to touch s
ome notions in knot and set theory and talk about relationships between e
mptiness in knot theory (aka phenomena of empty knot in terms of fib-rati
on) and famous empty set.\n
LOCATION:https://researchseminars.org/talk/knotgraphgroup/54/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Алена Жукова
DTSTART:20240810T100500Z
DTEND:20240810T113500Z
DTSTAMP:20260422T225701Z
UID:knotgraphgroup/55
DESCRIPTION:by Алена Жукова as part of Knots\, graphs and group
s\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/knotgraphgroup/55/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Louis H Kauffman
DTSTART:20240824T130500Z
DTEND:20240824T143500Z
DTSTAMP:20260422T225701Z
UID:knotgraphgroup/57
DESCRIPTION:Title: Empty Knots and Negative Dimensions in Combinatorics and Topology<
/a>\nby Louis H Kauffman as part of Knots\, graphs and groups\n\n\nAbstrac
t\nNotions of topological structures remain significant as we approach zer
o dimensions or even go below them.\nWe are all familiar with the signific
ance of the empty set for mathematics as a whole - since the empty set { }
is the beginning of set construction and indeed stands for the concept of
a set as a container. Similarly there are empty knots in the circle S^{1}
.\nNote that we may\, by analogy\, take an empty knot in S^{1} as having d
imension -1 since it should be two dimensions down from the dimension of i
ts containing sphere. And the empty knots in S^{1} have Milnor fiberings p
si_{a} : S^{1} —> S^{1} defined by\npsi_{a}(z) = z^{a} where z = exp(I T
heta) is an S^{1} parameter. We shall explain and show how the Kauffman-Ne
umann notion of Knot Products (circa 1978) produces first\, torus knots fr
om products of empty knots\, and then all Brieskorn varieties as products
of empty knots\, hence exotic spheres and much more\, including recent wor
k of Kauffman and Ogasa. That is part one of this talk. Part two considers
how the “negative dimensional tensors” of Roger Penrose are related t
o the Kauffman bracket polynomial and the Jones polynomial and how negativ
e dimensions become generalized to arbitrary parameters in the subject of
quantum link invariants. Is there a relationship between the negative dime
nsions of empty knots and quantum invariants of knots? This can be a topic
for discussion after the talk.\n
LOCATION:https://researchseminars.org/talk/knotgraphgroup/57/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bernhard Keller (Universite Paris Cite)
DTSTART:20240907T140500Z
DTEND:20240907T153500Z
DTSTAMP:20260422T225701Z
UID:knotgraphgroup/58
DESCRIPTION:Title: From quiver representations to cluster variables\nby Bernhard
Keller (Universite Paris Cite) as part of Knots\, graphs and groups\n\n\nA
bstract\nIn this expository talk\, we will recall Gabriel's theorem on qui
ver representations and Fomin-Zelevinsky's theorem on cluster-finite clust
er algebras. Then we will link the two theorems using Caldero-Chapoton's f
ormula\, which assigns a Laurent polynomial to a quiver representation usi
ng the Euler characteristics of its varieties of subrepresentations (quive
r Grassmannians). This link is the beginning of the theory of "additive ca
tegorification" of cluster algebras.\n
LOCATION:https://researchseminars.org/talk/knotgraphgroup/58/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Louis kauffman
DTSTART:20240914T140500Z
DTEND:20240914T153500Z
DTSTAMP:20260422T225701Z
UID:knotgraphgroup/59
DESCRIPTION:by Louis kauffman as part of Knots\, graphs and groups\n\nAbst
ract: TBA\n
LOCATION:https://researchseminars.org/talk/knotgraphgroup/59/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nilangshu Bhattacharyya
DTSTART:20240921T140500Z
DTEND:20240921T153500Z
DTSTAMP:20260422T225701Z
UID:knotgraphgroup/60
DESCRIPTION:Title: Lipschitz-Sarkar Stable Homotopy Type for Planar Trivalent Graph w
ith Perfect Matchings\nby Nilangshu Bhattacharyya as part of Knots\, g
raphs and groups\n\n\nAbstract\nLipschitz-Sarkar constructed Stable Homoto
py Types for the Khovanov Homology of links in $S^3$. Following that\, Kau
ffman-Nikonov-Ogasa found a family of Stable Homotopy types for the Homoto
pical Khovanov homology for links in thickened surfaces. Baldridge gave a
cohomology theory which categorifies 2-factor polynomial of planar trivale
nt graphs with perfect matchings. In this talk\, I will present on the con
struction of the Khovanov-Lipschitz-Sarkar stable Homotopy type for the Ba
ldridge cohomology theory.\n
LOCATION:https://researchseminars.org/talk/knotgraphgroup/60/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dmitry N. Hudoteplov
DTSTART:20240928T140500Z
DTEND:20240928T153500Z
DTSTAMP:20260422T225701Z
UID:knotgraphgroup/61
DESCRIPTION:Title: Kernel of $sl(N)$ weight systems\nby Dmitry N. Hudoteplov as p
art of Knots\, graphs and groups\n\n\nAbstract\nIn theory of Vassiliev inv
ariants\, each knot is mapped to a series of trivalent graphs (Jacobi diag
rams) by the Kontsevich integral. Kontsevich intagral contains all the Vas
siliev knot invariants and quantum knot polynomials (HOMFLY\, Kauffman etc
.) can be extracted from the Kontsevich integral by applying a correspondi
ng Lie algebra weight system.\n\nIn this talk\, the case of $sl(N)$ weight
systems will be discussed. $sl(N)$ weight systems correspond to the color
ed HOMFLY polynomial. Jacobi diagrams in the kernel of $sl(N)$ weight syst
ems can be associated with Vassiliev invariants missing from the HOMFLY po
lynomial. This kernel can be constructed explicitly using the findings of
Pierre Vogel\, who developed a framework to operate with Jacobi diagrams a
nd Lie algebra weight systems.\n
LOCATION:https://researchseminars.org/talk/knotgraphgroup/61/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mika Nelimov
DTSTART:20241005T140500Z
DTEND:20241005T153500Z
DTSTAMP:20260422T225701Z
UID:knotgraphgroup/62
DESCRIPTION:Title: Functions of Hyperbolicity of groups\nby Mika Nelimov as part
of Knots\, graphs and groups\n\n\nAbstract\nThe article introduces the con
cept of the δ-function of space. It measures the growth of the optimal hy
perbolicity constant of a ball of radius R. The function is bounded equiva
lent to the hyperbolicity of the group. The asymptotics of this function f
or various non-hyperbolic spaces and groups are studied. Examples of metri
c spaces for which it grows in a given manner are constructed. Its lineari
ty is proved for the Baumslag-Solitar group $BS(1\,2)$\, as well as for th
e Lampochnik group.\n
LOCATION:https://researchseminars.org/talk/knotgraphgroup/62/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Seongjeong Kim
DTSTART:20241012T140500Z
DTEND:20241012T153500Z
DTSTAMP:20260422T225701Z
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 embedd
ed circles in S^{3} up to isotopy\, but also knots in other 3-manifolds a
re interesting for mathematicians. In particular\, virtual knots\, which
are knots in thickened surface $S_{g} \\times [0\,1]$ with an orientable
surface $S_{g}$ of genus $g$\, are studied and they provide interesting
properties.\nIn this talk\, we will talk about knots in $S_{g} \\times S^
{1}$ where $S_{g}$ is an oriented surface of genus $g$. We introduce basi
c notions and properties for them. In particular\, for knots in $S_{g} \\
times S^{1}$ one of important information is “how many times a half 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 topologica
l model. In the end we apply it to classify knots in $S_{g}\\times S^{1}$
with small number of crossings.\n
LOCATION:https://researchseminars.org/talk/knotgraphgroup/63/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexei Y. Kanel-Belov
DTSTART:20241019T140500Z
DTEND:20241019T153500Z
DTSTAMP:20260422T225701Z
UID:knotgraphgroup/64
DESCRIPTION:Title: Алгоритмическая неразрешимость про
блемы вложения\nby Alexei Y. Kanel-Belov as part of Knots
\, graphs and groups\n\n\nAbstract\nЧрезвычайно интерес
ной и фундаментальной является задача о
б алгоритмической разрешимости проверк
и наличия изоморфизма между двумя алгеб
раическими многообразиями. Родственной
и более простой задачей является задача
о вложимости. В общем виде она формулиру
ется так: пусть A и B – два алгебраических
многообразия\; определить\, существует л
и вложение A в B\, найти алгоритм или доказ
ать его отсутствие. Доклад посвящен отри
цательному решению данного вопроса для
аффинных многообразий над произвольном
полем характеристики нуль\, чьи координа
тные кольца заданы образующими и опреде
ляющими соотношениями.\n
LOCATION:https://researchseminars.org/talk/knotgraphgroup/64/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hayk Sedrakyan
DTSTART:20241026T140500Z
DTEND:20241026T153500Z
DTSTAMP:20260422T225701Z
UID:knotgraphgroup/65
DESCRIPTION:Title: The general case (any pentagon). Photography principle\, data tran
smission\, and invariants of manifolds\nby Hayk Sedrakyan as part of K
nots\, graphs and groups\n\n\nAbstract\nThis work builds on the work previ
ously done by Professors L.Kauffman\, V.O.Manturov\, I.M.Nikonov\, and S.K
im in their paper at Photography principle\, data transmission\, and invar
iants of manifolds. Please read the beginning of this paper to understand
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 be cover
ing the case where the pentagon in question is not cyclic\, and thus Ptole
my’s Theorem is not usable.\n
LOCATION:https://researchseminars.org/talk/knotgraphgroup/65/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anna Taranenko
DTSTART:20241102T140500Z
DTEND:20241102T153500Z
DTSTAMP:20260422T225701Z
UID:knotgraphgroup/66
DESCRIPTION:Title: On vertices of the polytope of polystochastic matrices\nby Ann
a Taranenko as part of Knots\, graphs and groups\n\n\nAbstract\nA multidim
ensional matrix is polystochastic if it has nonnegative entries and the su
m of entries in each line is equal to 1. A set of d-dimensional polystocha
stic matrices of order n is the Birkhoff polytope.\n The well-known Birkho
ff theorem states that all vertices of the polytope of 2-dimensional polys
tochastic matrices are permutation matrices. For greater dimensions the Bi
rkhoff polytope has vertices different from multidimensional permutations.
\n In this talk\, we review bounds on the numbers of vertices of the Birkh
off polytope and propose several iterative constructions of vertices. We p
ay special attention to the polytope of polystochastic matrices of order 3
. In particular\, we show that this polytope has many vertices different f
rom multidimensional permutations and find all vertices of the polytope of
4-dimensional polystochastic matrices of order 3.\n
LOCATION:https://researchseminars.org/talk/knotgraphgroup/66/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Seongjeong Kim
DTSTART:20241109T140500Z
DTEND:20241109T153500Z
DTSTAMP:20260422T225701Z
UID:knotgraphgroup/67
DESCRIPTION:Title: The groups $G_{n}^{k}$\, $2n$-gon tilings\, and stacking of cubes<
/a>\nby Seongjeong Kim as part of Knots\, graphs and groups\n\n\nAbstract\
nIn the present talk we discuss three ways of looking at rhombile tilings:
stacking 3-dimensional cubes\, elements of groups\, and configurations of
lines and points.\n
LOCATION:https://researchseminars.org/talk/knotgraphgroup/67/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Louis H Kauffman
DTSTART:20241123T140500Z
DTEND:20241123T153500Z
DTSTAMP:20260422T225701Z
UID:knotgraphgroup/68
DESCRIPTION:Title: Physics\, Braiding and the Dirac equation\nby Louis H Kauffman
as part of Knots\, graphs and groups\n\n\nAbstract\nMathematically\, elec
trons (Fermions) are seen to correspond to operators F and F* (the anti-pa
rticle) such that\nF^2 = F*^2 = 0 (Pauli Exclusion Principle) and FF* + F*
F = 1 (a basic quantum relation). And mathematically you can achieve these
algebraic relations from Clifford algebra by taking\nGenerators a and b s
o 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 then 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 reality b
ehind this decomposition? Experiments over the last twenty years suggest t
hat it is so and that there is a possibility to use topological properties
(braiding and braid group representations) of the Majorana Fermions to ac
complish topological quantum computing. In this talk we will discuss those
braid group representations and we will discuss how Majorana Fermions (an
d Fermions) are related to solutions to the Dirac equation.\n
LOCATION:https://researchseminars.org/talk/knotgraphgroup/68/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Антон Белецкий
DTSTART:20241116T140500Z
DTEND:20241116T153500Z
DTSTAMP:20260422T225701Z
UID:knotgraphgroup/69
DESCRIPTION:Title: Теория малых сокращений и ее примен
ение к проблеме Бернсайда в подходе И. Ри
пса\nby Антон Белецкий as part of Knots\, graphs and g
roups\n\n\nAbstract\nПроблема Бернсайда широко из
вестна как один из важнейших вопросов те
ории групп. Ключевой областью\, позволив
шей достичь успехов в ее решении\, стала
так называемая теория малых сокращений\,
изучающая группы\, образующие соотношен
ия в которых слабо пересекаются друг с д
ругом (обобщения этой теории используют
ся в классической работе С. И. Адяна и П. С
. Новикова\, а также в работах А. Ю. Ольшан
ского).\nМы начнем с того что дадим кратко
е напоминание основных идей этой теории.
После этого мы попробуем построить обоб
щение этой теории (разработанное И. Рипс
ом)\, позволяющее применить ее для анализ
а групп Бернсайда и анализа диаграмм Ва
н-Кампена\, в которых соотношения *схожих
размеров* слабо зацепляются друг за дру
га. Мы постараемся давать все необходимы
е определения по ходу доклада (хотя бы не
формально)\, однако для более глубокого п
онимания темы может быть полезным предв
арительное знакомство с основами теорие
й малых сокращений.\n
LOCATION:https://researchseminars.org/talk/knotgraphgroup/69/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Aritra Bhowmick
DTSTART:20241130T140500Z
DTEND:20241130T153500Z
DTSTAMP:20260422T225701Z
UID:knotgraphgroup/70
DESCRIPTION:Title: h-Principle for Maps Transverse to Bracket-Generating Distribution
s\nby Aritra Bhowmick as part of Knots\, graphs and groups\n\n\nAbstra
ct\nThe goal of an h-principle is to transform a "hard" problem in geometr
y\, which involves solving a partial differential equation\, into a "soft"
problem in algebraic topology. In his monograph Partial Differential Rela
tions (1986)\, Mikhael Gromov asked the reader to prove the h-principle fo
r maps transverse to a bracket-generating distribution. Recall that a dist
ribution on a manifold is said to be bracket-generating if it Lie-bracket
generates the tangent space in a finite number of steps at each point. In
2020\, this problem was solved by Álvaro del Pino and Tobias Shin for rea
l-analytic distributions using tools from algebraic geometry.\n\nIn the fi
rst part of this talk\, we shall introduce what an h-principle is and pres
ent several examples of h-principles. Then\, we shall briefly outline a ge
neral strategy to prove an h-principle statement\, following the analytic
and sheaf-theoretic techniques of Gromov. We shall see how this strategy a
pplies to proving h-principles for immersions that are horizontal to a giv
en distribution. Finally\, we shall present an outline of a proof for the
question posed by Gromov in the smooth case using mostly elementary techni
ques.\n
LOCATION:https://researchseminars.org/talk/knotgraphgroup/70/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Scott Baldridge
DTSTART:20241207T140500Z
DTEND:20241207T153500Z
DTSTAMP:20260422T225701Z
UID:knotgraphgroup/71
DESCRIPTION:Title: Four face colorings of a planar graph correspond to three face col
orings 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.\, th
ere exists a coloring of the faces of the graph with four colors such 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-ori
entable surface. Thus\, the four color problem is really about studying 3-
face colorings on non-planar surfaces! These ideas come from understanding
our filtered 3-color homology of graphs\, which will be described as part
of the talk.\n
LOCATION:https://researchseminars.org/talk/knotgraphgroup/71/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Amit Kumar
DTSTART:20241214T140500Z
DTEND:20241214T153500Z
DTSTAMP:20260422T225701Z
UID:knotgraphgroup/72
DESCRIPTION:Title: Coloring Trivalent Graphs: A Defect TFT Approach\nby Amit Kuma
r as part of Knots\, graphs and groups\n\n\nAbstract\nWe show that the com
binatorial matter of graph coloring is\, in fact\, quantum in the sense of
satisfying the sum over all the possible intermediate state properties of
a path integral. In our case\, the topological field theory (TFT) with de
fects gives meaning to it. This TFT has the property that when evaluated o
n a planar trivalent graph\, it provides the number of Tait-Coloring 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 sect
ions of a certain bundle\, distinguishing a coloring (global-sections) fro
m a coloring process (local-sections.) These constructions also lead to an
interpretation of the word problem\, for a finitely presented group\, as
a cobordism problem and a generalization of (trivial) bundles at the level
of higher categories.\n
LOCATION:https://researchseminars.org/talk/knotgraphgroup/72/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Галина Константиновна Соколова
DTSTART:20241221T140500Z
DTEND:20241221T153500Z
DTSTAMP:20260422T225701Z
UID:knotgraphgroup/73
DESCRIPTION:Title: Сопровождающая матрица суперпозици
и полиномов и ее применение к теории узл
ов\nby Галина Константиновна Соколова as
part of Knots\, graphs and groups\n\n\nAbstract\nВ докладе при
водится новая форма для сопровождающей
матрицы суперпозиции двух полиномов над
коммутативным кольцом. Полученные резу
льтаты используются для проведения конс
труктивного доказательства теоремы Пла
нса для двумостовых узлов\, которая утве
рждает\, что первая группа гомологий неч
етно-листного и группа гомологий четно-л
истного накрытия сферы над узлом\, профа
кторизованная по гомологии двулистного
накрытия\, распадаются в прямую сумму дв
ух копий некоторой абелевой группы. Стру
ктура абелевых групп описываются через
полиномы Чебышева четвертого и второго
рода.\n
LOCATION:https://researchseminars.org/talk/knotgraphgroup/73/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Seongjeong Kim
DTSTART:20241228T140500Z
DTEND:20241228T153500Z
DTSTAMP:20260422T225701Z
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\nM. Nieb
rzydowski and J. H. Przytycki defined a Kauffman bracket magma and constru
cted the invariant P of framed links in 3-space. The invariant is closely
related to the Kauffman bracket polynomial. The normalized bracket polynom
ial is obtained from the Kauffman bracket polynomial by the multiplication
of indeterminate and it is an ambient isotopy invariant for links. In thi
s 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 invariant 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 conditions t
o be invariant under Yoshikawa moves except the first one and use a map fr
om the set of admissible marked graph diagrams to a marked Kauffman bracke
t magma to obtain the invariant for surface-links in 4-space.\n
LOCATION:https://researchseminars.org/talk/knotgraphgroup/74/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ф.В.Петров
DTSTART:20250104T140500Z
DTEND:20250104T153500Z
DTSTAMP:20260422T225701Z
UID:knotgraphgroup/75
DESCRIPTION:Title: Ветвление в плоской задаче Джилберт
а - Штейнера имеет степень не выше 3\nby Ф
.В.Петров as part of Knots\, graphs and groups\n\n\nAbstract\nПу
сть на плоскости дано два конечных набор
а материальных точек равной суммарной м
ассы. Перевести $t$ килограмм на расстоян
ие $d$ стоит $d t^p$ рублей\, где $0< p <1$ . Минима
льная стоимость плана перевозки массы и
з первого набора во второй реализуется н
екоторым деревом. Мы доказываем\, что сте
пени его вершин не превосходят 3. Доказат
ельство основано на теории Бохнера и Шён
берга вполне положительных функций. По с
овместной работе с Д. Черкашиным.\n
LOCATION:https://researchseminars.org/talk/knotgraphgroup/75/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vassily O. Manturov
DTSTART:20250111T140500Z
DTEND:20250111T153500Z
DTSTAMP:20260422T225701Z
UID:knotgraphgroup/76
DESCRIPTION:Title: Towards invariants of knots and links via $G_{n}^{k}$\nby Vass
ily 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} depending on t
wo natural numbers n>k and constructed invariants of many configuration sp
aces valued in such groups. https://www.arxiv.org/abs/1501.05208 The first
two natural invariants dealt with braids on n strands\, n>3\, valued in G
_{n}^{3} and G_{n}^{4}.\nWe shall discuss how to construct similar invaria
nts for n-component\nlinks and describe various possible ways what to do w
ith knots (single component). The approach uses closed braids and Markov m
oves.\nMany unsolved problems will be formulated.\n
LOCATION:https://researchseminars.org/talk/knotgraphgroup/76/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vassily O. Manturov
DTSTART:20250118T140500Z
DTEND:20250118T153500Z
DTSTAMP:20260422T225701Z
UID:knotgraphgroup/77
DESCRIPTION:Title: Уравнение пятиугольника и инвариан
ты кос: преобразование Птолемея\, тропич
еская геометрия\, shear-координаты\nby Vassily
O. Manturov as part of Knots\, graphs and groups\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/knotgraphgroup/77/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mehdi Golafshan
DTSTART:20250125T140500Z
DTEND:20250125T153500Z
DTSTAMP:20260422T225701Z
UID:knotgraphgroup/78
DESCRIPTION:Title: Thue-Morse Words: From Complexity Measures to Real-World Applicati
ons\nby Mehdi Golafshan as part of Knots\, graphs and groups\n\n\nAbst
ract\nThe Thue-Morse word stands as one of the most celebrated infinite se
quences in combinatorics on words\, noted for its self-similar constructio
n and fractal-like characteristics. This talk delves into the diverse comp
lexity measures of the Thue-Morse word—ranging from factor complexity an
d abelian complexity to binomial complexity—and explores how these measu
res capture the rich combinatorial and dynamical behavior of the sequence.
We will also highlight the surprising breadth of applications\, from codi
ng theory and automata to number theory and physics\, where the unique pro
perties of the Thue-Morse word offer insight into phenomena such as diffra
ction patterns in quasicrystals. Attendees will gain an integrated view of
both the theoretical underpinnings and the practical impact of this fasci
nating object.\n
LOCATION:https://researchseminars.org/talk/knotgraphgroup/78/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nikolay Moshchevitin
DTSTART:20250208T140500Z
DTEND:20250208T153500Z
DTSTAMP:20260422T225701Z
UID:knotgraphgroup/79
DESCRIPTION:Title: Approximations of real numbers in various norms.\nby Nikolay M
oshchevitin as part of Knots\, graphs and groups\n\n\nAbstract\nUsually\,
when we are looking for approximations of the irrational \\alpha by ration
al 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 formulation
of the problem (corresponding to the L_\\infty-norm) leads to ordinary con
tinued fractions.\nSimilar formulations corresponding to the L_2 and L_1-n
orms go back to Hermite and Minkowski. They are related to other (irregula
r) continued fraction expansion algorithms. We will discuss these algorith
ms and explain how these constructions are related to the relatively new
concept of Dirichlet improvability.\n
LOCATION:https://researchseminars.org/talk/knotgraphgroup/79/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vuong Bao
DTSTART:20250215T140500Z
DTEND:20250215T153500Z
DTSTAMP:20260422T225701Z
UID:knotgraphgroup/80
DESCRIPTION:Title: Fox-Milnor condition for concordant knots in homology 3-spheres\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 type in
an oriented homology 3-sphere\, obeys the Fox-Milnor poly- nomial conditio
n. A relation between Alexander polynomial of concordant knots in an orien
ted homology 3-sphere is established.\n
LOCATION:https://researchseminars.org/talk/knotgraphgroup/80/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Medhi Golfshan
DTSTART:20250222T140500Z
DTEND:20250222T153500Z
DTSTAMP:20260422T225701Z
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\nA
bstract\nIn this talk\, we provide a geometric perspective on symbolic and
factor dynamics\, illustrating how these ideas illuminate unipotent flows
on tori. We then discuss the connection of unipotent flows to the uniform
distribution of digits and examine how this framework informs our underst
anding of leading digits and their complexity. Along the way\, we review k
ey classical results\, including Weyl's criterion\, Kronecker's theorem\,
and Ratner's theorem\, to show how they connect to questions of digit dist
ribution. Finally\, we investigate the factor complexity of the leading di
gits in sequences of the form $a^{n^d}$\, highlighting both the theoretica
l insights and potential avenues for further exploration.\n
LOCATION:https://researchseminars.org/talk/knotgraphgroup/81/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hyungtae Baek
DTSTART:20250301T140500Z
DTEND:20250301T153500Z
DTSTAMP:20260422T225701Z
UID:knotgraphgroup/82
DESCRIPTION:Title: $w$-maximal specturm of Anderson rings\nby Hyungtae Baek as pa
rt of Knots\, graphs and groups\n\n\nAbstract\nLet $R$ be a commutative ri
ng with identity and\nlet $R[X]$ be the polynomial ring over $R$.\nConside
r 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 $R[X]_N$ an
d $R[X]_U$\,\nwhich are called the {\\it Nagata ring} of $R$ and {\\it Ser
re's conjecture ring} of $R$ respectively.\nThe Nagata rings and the Serre
's conjecture rings has been researched actively.\n\nIn this talk\, we inv
estigate the Anderson ring which is a subring of the Nagata ring and the S
erre's conjecture ring\, and\nexamine star-operations on Anderson rings.\n
More precisely\, we investigate $w$-operation on the Anderson ring.\n
LOCATION:https://researchseminars.org/talk/knotgraphgroup/82/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hyungtae Baek
DTSTART:20250308T140500Z
DTEND:20250308T153500Z
DTSTAMP:20260422T225701Z
UID:knotgraphgroup/83
DESCRIPTION:Title: Krull-like domain arising from 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 examine some conditions of $R$ under which the
Anderson ring becomes Krull-like domain.\n
LOCATION:https://researchseminars.org/talk/knotgraphgroup/83/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sachchidanand Prasad
DTSTART:20250322T140500Z
DTEND:20250322T153500Z
DTSTAMP:20260422T225701Z
UID:knotgraphgroup/85
DESCRIPTION:Title: Cut and focal locus of a Finsler submanifold\nby Sachchidanand
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 structure
of the cut and focal loci. We begin by revisiting fundamental concepts in
Finsler geometry before defining the cut locus and illustrating examples i
n Riemannian manifolds. The discussion culminates with a proof of a specia
l case of the generalized Klingenberg lemma for Finsler manifolds\, specif
ically for N-geodesic loops\, where $N$ is a closed submanifold of a Finsl
er manifold $M$. This is a joint work with Aritra Bhowmick.\n
LOCATION:https://researchseminars.org/talk/knotgraphgroup/85/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Louis Kauffman
DTSTART:20250315T140500Z
DTEND:20250315T153500Z
DTSTAMP:20260422T225701Z
UID:knotgraphgroup/86
DESCRIPTION:Title: Three Talks about Knots and Functional Integrals 1\nby Louis K
auffman as part of Knots\, graphs and groups\n\n\nAbstract\nThis talk will
discuss physical background: Electromagnetism via differential forms\, an
d how this led Hermann Weyl to suggest a unification of Electromagnetism a
nd General Relativity. How the Weyl Theory became reformulated as gauge th
eory. Background on quantum mechanics and path integrals of Feynman. Begin
ning of measuring knots via holonomy in a gauge field.\n
LOCATION:https://researchseminars.org/talk/knotgraphgroup/86/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Louis Kauffman
DTSTART:20250329T140500Z
DTEND:20250329T153500Z
DTSTAMP:20260422T225701Z
UID:knotgraphgroup/87
DESCRIPTION:Title: Three Talks about Knots and Functional Integrals 2\nby Louis K
auffman as part of Knots\, graphs and groups\n\n\nAbstract\nWitten Chern-S
imons functional integral\, Wilson loops\, three manifold invariants and k
not and link invariants.\n
LOCATION:https://researchseminars.org/talk/knotgraphgroup/87/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Louis Kauffman
DTSTART:20250405T140500Z
DTEND:20250405T153500Z
DTSTAMP:20260422T225701Z
UID:knotgraphgroup/88
DESCRIPTION:Title: Three Talks about Knots and Functional Integrals 3\nby Louis K
auffman as part of Knots\, graphs and groups\n\n\nAbstract\nHow the Kontse
vich Integral for Vasiliev invariants is related to the perturbative expan
sion of the Witten Chern-Simons integral.\n
LOCATION:https://researchseminars.org/talk/knotgraphgroup/88/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Louis Kauffman
DTSTART:20250412T140500Z
DTEND:20250412T153500Z
DTSTAMP:20260422T225701Z
UID:knotgraphgroup/89
DESCRIPTION:by Louis Kauffman as part of Knots\, graphs and groups\n\nAbst
ract: TBA\n
LOCATION:https://researchseminars.org/talk/knotgraphgroup/89/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Louis Kauffman
DTSTART:20250419T140500Z
DTEND:20250419T153500Z
DTSTAMP:20260422T225701Z
UID:knotgraphgroup/90
DESCRIPTION:by Louis Kauffman as part of Knots\, graphs and groups\n\nAbst
ract: TBA\n
LOCATION:https://researchseminars.org/talk/knotgraphgroup/90/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Igor Nikonov
DTSTART:20250426T140500Z
DTEND:20250426T153500Z
DTSTAMP:20260422T225701Z
UID:knotgraphgroup/91
DESCRIPTION:Title: The crossing and the arc from the topological viewpoint\nby Ig
or Nikonov as part of Knots\, graphs and groups\n\n\nAbstract\nCombinatori
al approach to knot theory treats knots as diagrams modulo Reidemeister mo
ves. Many constructions of knot invariants (e.g.\, index polynomials\, qua
ndle colorings etc.) use elements of diagrams such as arcs and crossings b
y assigning invariant labels to them. The universal invariant labels\, whi
ch carry the most information\, can be thought of as equivalence classes o
f arcs and crossings modulo the relation\, which identifies corresponding
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 giv
e a topological description of sets of these classes.\n
LOCATION:https://researchseminars.org/talk/knotgraphgroup/91/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yury Belousov
DTSTART:20250503T140500Z
DTEND:20250503T153500Z
DTSTAMP:20260422T225701Z
UID:knotgraphgroup/92
DESCRIPTION:Title: Meander diagrams of classical and virtual knots\nby Yury Belou
sov as part of Knots\, graphs and groups\n\n\nAbstract\nIn this talk\, we
survey the theory of meander and semimeander diagrams of knots\, covering
both the classical setting and its recent extensions to virtual knots. We
begin with classical results: every knot admits semimeander and meander di
agrams. A diagram is called semimeander if it decomposes into two smooth\,
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 semi
meander and meander diagrams\, and proving the universality of these diagr
am classes (that is\, each virtual knot has a diagram within these classes
). Motivated by these constructions\, we define a new class of knot invari
ants -- the (virtual) k-arc crossing numbers -- and discuss their relation
ship with the classical crossing number. The talk is based on joint works
with V. Chernov\, A. Malyutin\, and R. Sadykov.\n
LOCATION:https://researchseminars.org/talk/knotgraphgroup/92/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Louis Kauffman (UIC)
DTSTART:20250524T140500Z
DTEND:20250524T153500Z
DTSTAMP:20260422T225701Z
UID:knotgraphgroup/93
DESCRIPTION:Title: Multiple Virtual Knot Theory\nby Louis Kauffman (UIC) as part
of Knots\, graphs and groups\n\n\nAbstract\nThis talk will discuss a gener
alization of virtual knot theory where there are any number of virtual cro
ssings such that each virtual crossing type can perform detour moves over
any of the others. The roots of this generalization are in our work on Pen
rose polynomials for graphs with perfect matchings. These graph polynomial
s motivate a number of constructions in knot theory\, as we shall explain.
\n
LOCATION:https://researchseminars.org/talk/knotgraphgroup/93/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marco Castelli
DTSTART:20250517T140500Z
DTEND:20250517T153500Z
DTSTAMP:20260422T225701Z
UID:knotgraphgroup/94
DESCRIPTION:Title: Involutive (and indecomposable) set-theoretic solutions of the Yan
g-Baxter equation\nby Marco Castelli as part of Knots\, graphs and gro
ups\n\n\nAbstract\nThe Yang-Baxter equation is one of the central equation
s 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-Ivanova an
d Van den Bergh (1998)\, and of Etingof\, Schedler\, and Soloviev (1999)\,
led many mathematicians to the study of involutive non-degenerate set-the
oretic solutions. In the first part of this talk\, we will provide an intr
oduction to the Yang-Baxter equation\, with a particular focus on involuti
ve set-theoretic solutions\, and we will show how indecomposable solutions
are\, in a sense\, the fundamental building blocks. In the second part\,
which will be the core of the talk\, we will focus on indecomposable invol
utive solutions\, offering an overview of the theoretical tools and the ma
in results developed for their investigation and classification.\n
LOCATION:https://researchseminars.org/talk/knotgraphgroup/94/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sergei Gukov
DTSTART:20250510T140500Z
DTEND:20250510T153500Z
DTSTAMP:20260422T225701Z
UID:knotgraphgroup/95
DESCRIPTION:Title: First examples of categorification of $U_{q} (sl_{2})$ invariants
of 3-manifolds\nby Sergei Gukov as part of Knots\, graphs and groups\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-manifolds eq
uipped with Spin-C structures. One of the main interests in these invarian
ts is that they are expected to admit categorification\, thus providing ne
w insights into the mysterious world of smooth 4-maniolds. Building on rec
ent works with M.Jagadale and P.Putrov\, we describe what this homological
lift looks like with mod 2 coefficients. We prove that the proposed categ
orification is invariant under Kirby moves for all weakly negative definit
e plumbed manifolds.\n
LOCATION:https://researchseminars.org/talk/knotgraphgroup/95/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Younghan Yoon
DTSTART:20250531T140500Z
DTEND:20250531T153500Z
DTSTAMP:20260422T225701Z
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 understood
by studying the real toric varieties associated with them.\nIn this talk\
, we discuss the rational cohomology of these varieties.\nWe present compl
ete computations of their Betti numbers for all types of Weyl groups.\nFur
thermore\, for types A and B\, we introduce explicit descriptions of the m
ultiplicative structures of the cohomology rings in terms of alternating p
ermutations and B-snakes\, respectively.\n
LOCATION:https://researchseminars.org/talk/knotgraphgroup/96/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Louis kauffman
DTSTART:20250607T140500Z
DTEND:20250607T153500Z
DTSTAMP:20260422T225701Z
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://researchseminars.org/talk/knotgraphgroup/97/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sergei Lando
DTSTART:20250614T140500Z
DTEND:20250614T153500Z
DTSTAMP:20260422T225701Z
UID:knotgraphgroup/98
DESCRIPTION:Title: An algebro-geometric proof of Witten's conjecture\nby Sergei L
ando 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 re
lationship between intersection indices on moduli spaces of complex curves
and Hurwitz numbers enumerating ramified coverings of the 2-sphere.\n
LOCATION:https://researchseminars.org/talk/knotgraphgroup/98/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Seongjeong Kim
DTSTART:20250621T140500Z
DTEND:20250621T153500Z
DTSTAMP:20260422T225701Z
UID:knotgraphgroup/99
DESCRIPTION:Title: Winding parity projection and embedding of virtual knots\nby S
eongjeong Kim as part of Knots\, graphs and groups\n\n\nAbstract\nIt is kn
own that knots in the product space of an oriented surface $S_{g}$ and the
circle $S^{1}$ can be presented by virtual diagrams with decorations up t
o local moves. By using the first homology of $S^{1}$ one can define a par
ity-like invariant for knots in $S_{g} \\times S^{1}$\, which is called 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 are “a
lmost” embedded into knots in $S_{g} \\times S^{1}$.\n
LOCATION:https://researchseminars.org/talk/knotgraphgroup/99/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Platon Marulev
DTSTART:20250628T140500Z
DTEND:20250628T153500Z
DTSTAMP:20260422T225701Z
UID:knotgraphgroup/100
DESCRIPTION:Title: CLASSIFICATION OF NODAL CURVES ON SURFACES AND BRAID INVARIANTS\nby Platon Marulev as part of Knots\, graphs and groups\n\n\nAbstract\n
This work is divided into two parts.\nThe first part is devoted to the cla
ssification of nodal curves on closed surfaces under modified three Reidem
eester moves obtained in the article "INCIDENCES AND TILING" by Sergey Fom
in and Pavlo Pylyavsky\, and finding the minimal element of these equivale
nce classes.\n\nIn the second part\, several different braid invariants co
nsidered in the articles "Braids act on configurations of lines" and "Shea
r coordinates and braid invariants" by V.O. Manturov are calculated.\n
LOCATION:https://researchseminars.org/talk/knotgraphgroup/100/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Thomas Fiedler
DTSTART:20250705T140500Z
DTEND:20250705T153500Z
DTSTAMP:20260422T225701Z
UID:knotgraphgroup/101
DESCRIPTION:Title: The tangle-valued 1-cocycle for knots\nby Thomas Fiedler as p
art of Knots\, graphs and groups\n\n\nAbstract\nWe replace the Yang-Baxter
equation by the tetrahedron equation and use it to construct an infinit o
rdered set of Alexander (or Conway) polynomials\, called the Alexander tre
e\, 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 serious cand
idate for a complete and calculable invariant for classical knots.\n
LOCATION:https://researchseminars.org/talk/knotgraphgroup/101/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gurnoor Singh
DTSTART:20250712T140500Z
DTEND:20250712T153500Z
DTSTAMP:20260422T225701Z
UID:knotgraphgroup/102
DESCRIPTION:Title: Tropical Ptolemy Transformations and Invariants of Braids\nby
Gurnoor Singh as part of Knots\, graphs and groups\n\n\nAbstract\nWe pres
ent a new construction of invariants for spherical braids using tropical g
eometry. Given a braid on \\( n \\geq 5 \\) strands on the 2-sphere\, we a
ssociate to it a sequence of Delaunay triangulations connected by edge fli
ps. Each triangulation carries edge labels valued in a tropical semifield\
, and each flip updates the labels via the tropical Ptolemy relation:\n\\[
\nx \\oplus y = (a \\oplus c) \\otimes (b \\oplus d)\, \\quad \\text{where
} \\oplus = \\max\, \\ \\otimes = +.\n\\]\nThis process respects flip ide
ntities such as involution\, far-commutativity\, and the pentagon relation
. We show that the resulting label at the end of the sequence defines an i
nvariant of the braid up to isotopy. This construction offers a combinator
ial framework for studying braid groups through tropical methods and enric
hes the connection between low-dimensional topology and tropical geometry.
\n
LOCATION:https://researchseminars.org/talk/knotgraphgroup/102/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bao Vuong
DTSTART:20250719T140500Z
DTEND:20250719T153500Z
DTSTAMP:20260422T225701Z
UID:knotgraphgroup/103
DESCRIPTION:Title: Fox-Milnor condition for concordant knots in homology 3-spheres<
/a>\nby Bao Vuong as part of Knots\, graphs and groups\n\n\nAbstract\nI wi
ll 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 $M$. The
n the Alexander polynomials of the knots are related by the following equa
tion\n\\[\\Delta_{k_0}(t) ~\\dot{=} ~p(t)p(1/t) \\Delta_{k_1}(t)\\]\n\nwhe
re $\\Delta_{k_0}(t)\, \\Delta_{k_1}(t)$ are the Alexander polynomials in
$t$ of the knots $k_0\,k_1$ respectively and $p(t)$ is a polynomial with i
nteger coefficients.\n\n{\\bf Theorem B}. Let $M\, M'$ be homological sphe
res. Let $\\mathcal{W}$ be a cobordism between $M$ and $M'$\, and the boun
dary of $\\mathcal{W}$ is disjoint union $\\partial \\mathcal{W} = M \\cup
M'$. More over the inclusions $M \\hookrightarrow \\mathcal{W}$ and $M' \
\hookrightarrow \\mathcal{W}$ induce isomorphisms on homology. Let $k$ and
$k'$ be knots in $M$ and $M'$ correspondingly. If there exist a concordan
ce $g: S^1 \\times I \\rightarrow \\mathcal{W}$ between $k$ and $k'$. Then
the Alexander polynomials of the knots $k$ and $k'$ are related by the fo
llowing 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 polynom
ials in $t$ of the knots $k\,k'$ respectively and $p(t)$ is a polynomial w
ith integer coefficients.\n
LOCATION:https://researchseminars.org/talk/knotgraphgroup/103/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Louis Kauffman
DTSTART:20250823T140500Z
DTEND:20250823T153500Z
DTSTAMP:20260422T225701Z
UID:knotgraphgroup/104
DESCRIPTION:Title: Non-Commutative Worlds\nby Louis Kauffman as part of Knots\,
graphs and groups\n\n\nAbstract\nAspects of gauge theory\, Hamiltonian mec
hanics and quantum mechanics arise naturally in the mathematics of a non-c
ommutative framework for calculus and differential geometry. This talk con
sists in a number of sections including the introduction. The introduction
sketches our general results in this domain. The second section gives a d
erivation of a generalization of the Feynman-Dyson derivation of electroma
gnetism using our non-commutative context and using diagrammatic technique
s. The third section discusses\, in more depth\, relationships with gauge
theory and differential geometry. The last section discusses the structure
of curvature\, Bianchi identity and general relativity.\nWe begin the tal
k by showing how constructing sqrt[-1] naturally leads to Clifford Algebra
s and the seeds of this non-commutative context.\n
LOCATION:https://researchseminars.org/talk/knotgraphgroup/104/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Аллеманд Аллан Олегович
DTSTART:20250726T140500Z
DTEND:20250726T153500Z
DTSTAMP:20260422T225701Z
UID:knotgraphgroup/105
DESCRIPTION:Title: Применение метода Арнольда для док
азательства топологической неразрешимо
сти некоторых уравнений в элементарных
функциях\nby Аллеманд Аллан Олегович as p
art of Knots\, graphs and groups\n\n\nAbstract\nВ докладе буде
т дан общий обзор на применение метода А
рнольда\, доказана неразрешимость уравн
ений sin(z) − z = a и cos(z) − z = a в элементарных
функциях\, а также рассмотрены другие сл
учае и примеры\n
LOCATION:https://researchseminars.org/talk/knotgraphgroup/105/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexander Zavesov
DTSTART:20250802T140500Z
DTEND:20250802T153500Z
DTSTAMP:20260422T225701Z
UID:knotgraphgroup/106
DESCRIPTION:Title: Quantum Probabilistic Interpretation and Quaternion Matrices\
nby Alexander Zavesov as part of Knots\, graphs and groups\n\n\nAbstract\n
We describe the theory\, which shapes a probabilistic (statistical)\ninter
pretation of quantum mechanics in terms of quaternion matrices. Upon intro
ducing the\nnotion of a quaternionic density matrix\, we define the expres
sions for calculating the observed\nmeans and entropy of a quantum system.
\nThe difference between quaternion and complex matrices is that the forme
r are not linear\noperators. This fact forces us to rebuild the theory of
quaternionic matrix operators and to show\nthat all the basic theorems rel
ated to complex matrices are held\, with some reservations. The\nconstruct
ed theory of quaternionic matrix operators also presents interest from a p
urely\nmathematical point of view\, regardless of its application in quant
um mechanics.\n\nReferences: https://www.researchgate.net/publication/3493
03667_Quantum_Probabilistic_Interpretation_and_Quaternion_Matrices_Eng\n
LOCATION:https://researchseminars.org/talk/knotgraphgroup/106/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Seongjeong Kim
DTSTART:20250809T140500Z
DTEND:20250809T153500Z
DTSTAMP:20260422T225701Z
UID:knotgraphgroup/107
DESCRIPTION:Title: A characterization of virtual knots as knots in $S_{g} \\times S^
{1}$\nby Seongjeong Kim as part of Knots\, graphs and groups\n\n\nAbst
ract\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 sufficient cond
ition for knots in $S_{g} \\times S^{1}$ to have virtual knot diagrams. Ba
sed on this\, we derive a sufficient condition for 2-component classical l
inks to be separable.\n
LOCATION:https://researchseminars.org/talk/knotgraphgroup/107/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bernhard Keller (Université Paris Cité)
DTSTART:20250816T140500Z
DTEND:20250816T153500Z
DTSTAMP:20260422T225701Z
UID:knotgraphgroup/108
DESCRIPTION:Title: Grassmannian braiding categorified\nby Bernhard Keller (Unive
rsité Paris Cité) as part of Knots\, graphs and groups\n\n\nAbstract\nIn
2017\, Chris Fraser discovered an action of the extended affine braid gro
up on d strands on the Grassmannian of k-subspaces in n-space\, endowed wi
th 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 Fraser and
Haoyu Wang\, we construct a categorical lift of this action using Jensen-K
ing-Su's (additive) categorification of the Grassmannian via Cohen-Macaula
y modules over a singular quotient of the preprojective algebra P of exten
ded type A_{n-1}. A key ingredient is\nSeidel-Thomas' braid group action (
2000) on the derived category of P.\n
LOCATION:https://researchseminars.org/talk/knotgraphgroup/108/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Евгений Коган
DTSTART:20250830T140500Z
DTEND:20250830T153500Z
DTSTAMP:20260422T225701Z
UID:knotgraphgroup/109
DESCRIPTION:Title: Когомологии Нийенхейса\nby Евгени
й Коган as part of Knots\, graphs and groups\n\n\nAbstract\nПо о
ператорному полю на многообразии (т.е. те
нзору с одним верхним и одним нижним инд
ексом) можно построить однородное отобр
ажение степени 1\, действующее на диффере
нциальных формах. Операторное поле назы
вается оператором Нийенхейса\, если это
отображение является дифференциалом. Ср
азу возникает вопрос: а каковы когомолог
ии получившегося комплекса? Эти когомол
огии называются малыми когомологиями Ни
йенхейса. В случае\, когда оператор в каж
дой точке тождественный\, рассматриваем
ый дифференциал совпадает с внешним диф
ференциалом\, комплекс совпадает с компл
ексом де Рама\, и малые когомологии Нийен
хейса совпадают с когомологиями де Рама.
Оказывается\, что если оператор Нийенхе
йса невырожден в каждой точке многообра
зия\, то малые когомологии все еще изомор
фны когомологиям де Рама — но в общем сл
учае это не так.\n\nВ докладе будет расска
зано про несколько результатов\, касающи
хся свойств малых когомологий Нийенхейс
а\, а также (при наличии времени) про еще п
ару вопросов\, связанных с так называемы
ми большими когомологиями Нийенхейса и
возможности построения дифференциала д
ля любого операторного поля постоянного
ранга\, поточечные образы которого обра
зуют интегрируемое распределение.\n
LOCATION:https://researchseminars.org/talk/knotgraphgroup/109/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Алексей Суворов
DTSTART:20250913T140500Z
DTEND:20250913T153500Z
DTSTAMP:20260422T225701Z
UID:knotgraphgroup/110
DESCRIPTION:Title: Обобщение Теоремы Кези и геометрия
окружностей\nby Алексей Суворов as part of Kn
ots\, graphs and groups\n\n\nAbstract\nЕсть формула длины
вектора с координатами $x\, y$:$\\sqrt{x^2 + y^2}.$\n\
nНо что будет\, если поменять плюс на мину
с? Тогда получится альтернативная геоме
трия\, в которой вместо окружности будет
гипербола. Большинство теорем\, верных в
евклидовой геометрии\, здесь тоже верны.\
n\nНеожиданно\, это геометрия довольно си
льно связана с окружностями на плоскост
и.\n\nС помощью понимания этой связи мы об
общим теорему Кези на произвольное числ
о окружностей.\n\n\\section*{Теорема Кези}\n\nЕс
ли четыре окружности касаются данной\, т
о верно следующее равенство:\n$L_{1324} = L_{1234}
+ L_{2314}\,$\nгде $L_{ij}$ — длина общей внешней
касательной к соответствующим окружнос
тям\, пронумерованным в порядке обхода т
очек касания.\n\nТакже\, если останется вр
емя\, поговорим о геометрии окружностей
поподробнее.\n
LOCATION:https://researchseminars.org/talk/knotgraphgroup/110/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Елена Николаевна Ланина
DTSTART:20250927T140500Z
DTEND:20250927T153500Z
DTSTAMP:20260422T225701Z
UID:knotgraphgroup/111
DESCRIPTION:Title: Differential operators approach to Khovanov–Rozansky calculus\nby Елена Николаевна Ланина as part of Knots\, gra
phs and groups\n\n\nAbstract\nFor Khovanov–Rozansky cohomologies\, we de
velop a construction of differential operators in odd variables\, associat
ed with all link diagrams\, including tangles with open ends. These operat
ors become nilpotent only for diagram with no external legs\, but even for
open tangles one can develop a factorization formalism\, which preserve R
eidemeister/topological invariance -- the symmetry of the problem. During
this talk\, I am going to introduce our approach\, consider relations whic
h allows one to simplify calculations of the Khovanov–Rozansky polynomia
ls and provide examples.\n
LOCATION:https://researchseminars.org/talk/knotgraphgroup/111/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Egor Morozov
DTSTART:20250906T140500Z
DTEND:20250906T153500Z
DTSTAMP:20260422T225701Z
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 ce
ntury BC) is to construct a circle tangent to the three given circles in t
he plane. Counting the number of solutions is often considered as one of t
he first questions of enumerative geometry. It turns out that in general p
osition the problem has 8 solutions and\, if not all the given circles are
tangent at the same point\, then this number is maximal possible. This fa
ct has a plenty of proofs using a wide range of methods\, from elementary
ones to such as Lie sphere geometry and intersection theory.\n\nBut what h
appens if one increases the number of given circles? Clearly\, counting th
e number of solutions in general position is not interesting in this case
since this number is always zero. However\, the question about the maximal
possible number of solution still makes sense. It turns out that if not a
ll the given circles are tangent at the same point\, then the problem has
at most 6 solutions. The proof of this fact leads to beautiful configurati
ons of tangent circles. In the talk I will describe these construction\, g
ive precise statements and proofs\, and (if time permits) mention other in
teresting generalizations of the Apollonius' problem.\n
LOCATION:https://researchseminars.org/talk/knotgraphgroup/112/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Илья Иванов-Погодаев
DTSTART:20250920T140500Z
DTEND:20250920T153500Z
DTSTAMP:20260422T225701Z
UID:knotgraphgroup/113
DESCRIPTION:Title: Пути на графе как элементы полугруп
пы\nby Илья Иванов-Погодаев as part of Knots\, gra
phs and groups\n\n\nAbstract\nБудем рассматривать сло
ва в конечном алфавите. Допустим\, конечн
ое множество слов. объявлены запрещенны
ми\, то есть приравнены к нулю. Тогда и вс
е слова\, содержащие запрещенные тоже ра
вны нулю. Множество ненулевых слов при э
том может оказаться конечным или бескон
ечным. Не очень сложная олимпиадная зада
ча: Если множество ненулевых слов беско
нечно\, то существует и бесконечное пери
одическое слово\, не содержащее запрещен
ных подслов.\n \nМножество слов относител
ьно операции приписывания одного слова
к другому является полугруппой.\nНа язык
е полугрупп утверждение задачи выше озн
ачает\, что в конечно порожденной (конечн
ый алфавит) конечно представленной (коне
чное число запрещенных слов) мономиальн
ой (каждое определяющее соотношение вид
а W=0)\, бесконечной (множество ненулевых
слов бесконечно) полугруппе существует
элемент\, являющийся ненулевым в любой с
тепени.\nПользуясь определением ниль-эле
мента\, то есть слова\, некоторая степень
которого равна нулю\, можно дать эквивал
ентное определение. Полугруппа называет
ся нильполугруппой\, если каждый элемент
в некоторой степени равен нулю.\nТогда э
квивалентная формулировка: любая конечн
опорожденная конечно представленная мо
номиальная нильполугруппа является кон
ечной.\n \nЧто же будет\, если делать не тол
ько запрещенные слова\, но и приравниват
ь некоторые слова друг к другу? Тогда сит
уация заметно усложняется\, и этот вопро
с был поставлен в Свердловской тетради Л
.Н.Шевриным и М.В.Сапиром. Оказывается\, ч
то в этом случае бесконечную конечно пре
дставленную нильполугруппу построить м
ожно. Но для этого пришлось применить до
полнительные идеи. \n \nСлова полугруппы и
нтерпретируются как кодировки путей на
специально построенном графе. Эквивален
тность слов\nозначает эквивалентность п
утей на графе\, то есть возможность перев
ести один путь в другой локальными замен
ами.\nЗапрещающие соотношения соответст
вуют невозможным кодировкам.\n \nВсе это п
риводит к новому подходу к построению ал
гебраических объектов\, который и будем
обсуждать в докладе.\n
LOCATION:https://researchseminars.org/talk/knotgraphgroup/113/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Oleg Styrt
DTSTART:20251018T140500Z
DTEND:20251018T153500Z
DTSTAMP:20260422T225701Z
UID:knotgraphgroup/114
DESCRIPTION:by Oleg Styrt as part of Knots\, graphs and groups\n\nAbstract
: TBA\n
LOCATION:https://researchseminars.org/talk/knotgraphgroup/114/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vladlen Timorin
DTSTART:20251004T140500Z
DTEND:20251004T153500Z
DTSTAMP:20260422T225701Z
UID:knotgraphgroup/115
DESCRIPTION:Title: Renormalization\, equipotential annuli\, and the Hausdorff measur
e\nby Vladlen Timorin as part of Knots\, graphs and groups\n\n\nAbstra
ct\n(based on a joint work with A. Blokh\, G. Levin\, and L. Oversteegen)\
n \nFor a complex single variable polynomial f of degree d\, let K(f) be i
ts filled Julia set\, i.e.\, the union of all bounded orbits. Assume 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 renormalizatio
n (Douady-Hubbard): the dynamics of a higher degree (degree d) polynomial
f near K* can be understood in terms of a suitable lower degree (degree 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 l
atter is defined in a combinatorial way. We will describe a role the Hausd
orff dimension of G’ and the respective Hausdorff measure play in geomet
ry of K*.\n
LOCATION:https://researchseminars.org/talk/knotgraphgroup/115/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Петр Ким
DTSTART:20251025T140500Z
DTEND:20251025T153500Z
DTSTAMP:20260422T225701Z
UID:knotgraphgroup/116
DESCRIPTION:Title: Об обобщённых треугольниках\nby Пе
тр Ким as part of Knots\, graphs and groups\n\n\nAbstract\nТри с
тороны треугольника можно воспринимать
как очень вырожденную плоскую кубическу
ю кривую. Но есть ли какие-нибудь аналоги
теорем из привычной геометрии треуголь
ника для произвольной кубической кривой
? \nВыясняется\, что да\, есть! \nНа докладе
будет рассказано о получающихся на этом
пути обобщениях теоремы Фейербаха (о кас
ании вписанной окружности и окружности 9
точек) и теоремы Емельяновых\, а также их
связи с поризмом Понселе и изополярным
преобразованием Суворова.\n
LOCATION:https://researchseminars.org/talk/knotgraphgroup/116/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Louis H Kauffman
DTSTART:20251011T140500Z
DTEND:20251011T153500Z
DTSTAMP:20260422T225701Z
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 quantu
m computing from the point of view of knot theory and we discuss knot theo
ry from the point of view of form and knot logic. This means that we do no
t 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 very ele
mentary algebras\, self-referential structures and the beginnings of both
topology and geometry. Starting the discussion of foundations from such a
place means that there are many pathways outward from very simple structur
es\, and we can only sketch some of them. Nevertheless\, we will discuss t
he belt trick\, non-locality\, Majorana fermions and the Fibonacci model f
or topological quantum computing that is related to the quantum Hall effec
t.\n
LOCATION:https://researchseminars.org/talk/knotgraphgroup/117/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Louis Kauffman
DTSTART:20251101T140500Z
DTEND:20251101T153500Z
DTSTAMP:20260422T225701Z
UID:knotgraphgroup/118
DESCRIPTION:Title: Topological Computing and Majorana Fermions\nby Louis Kauffma
n as part of Knots\, graphs and groups\n\n\nAbstract\nWe will discuss how
to use Temperley Lieb Recoupling Theory to produce unitary transformations
for quantum computing and we will discuss how to use Clifford algebra to
give unitary representations related to Majorana Fermions. In the course o
f this we shall discuss relationships of diagrammatics\, topology and phys
ics.\n
LOCATION:https://researchseminars.org/talk/knotgraphgroup/118/
END:VEVENT
BEGIN:VEVENT
SUMMARY:B. Sobirov
DTSTART:20251108T140500Z
DTEND:20251108T153500Z
DTSTAMP:20260422T225701Z
UID:knotgraphgroup/119
DESCRIPTION:Title: Множество значений конечной меры
\nby B. Sobirov as part of Knots\, graphs and groups\n\n\nAbstract\nВ р
аботе элементарными методами доказывае
тся факт о том\, что множество значений п
роизвольной конечной меры является комп
актом. В отличие от подхода Пола Халмоша\
, доказательство обходится без привлече
ния теории ординалов и опирается лишь на
счётные конструкции. Сначала теорема ус
танавливается для борелевских мер на пр
ямой. Затем общий случай сводится к этом
у частному с помощью хитрой измеримой фу
нкции. В качестве следствия показываетс
я\, что для безатомной меры множество её
значений является отрезоком.\n
LOCATION:https://researchseminars.org/talk/knotgraphgroup/119/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mariia Rubanenko
DTSTART:20251115T140500Z
DTEND:20251115T153500Z
DTSTAMP:20260422T225701Z
UID:knotgraphgroup/120
DESCRIPTION:Title: Succinct data structures for strings\nby Mariia Rubanenko as
part of Knots\, graphs and groups\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/knotgraphgroup/120/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Louis Kauffman
DTSTART:20251122T140500Z
DTEND:20251122T153500Z
DTSTAMP:20260422T225701Z
UID:knotgraphgroup/121
DESCRIPTION:Title: Recoupling Theory\, Majorana Fermions and the Dirac equation\
nby Louis Kauffman as part of Knots\, graphs and groups\n\n\nAbstract\nThi
s talk will continue previous talks about topological quantum computing ba
sed on\n1. solutions to the Yang-Baxter Equation\n2. Temperley-Lieb Recoup
ling theory.\n3. Braid group representations related to Clifford algebras.
\nWe will describe how the Clifford algebra approach is related to the Maj
orana version of the Dirac equation.\n
LOCATION:https://researchseminars.org/talk/knotgraphgroup/121/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Xu Xu
DTSTART:20251206T140500Z
DTEND:20251206T153500Z
DTSTAMP:20260422T225701Z
UID:knotgraphgroup/122
DESCRIPTION:Title: Combinatorial curvature flows on surfaces and 3-dimensional manif
olds\nby Xu Xu as part of Knots\, graphs and groups\n\n\nAbstract\nCom
binatorial Ricci flow was first introduced by Chow and Luo for Thurston’
s circle packings on surfaces. It provides effective algorithms for findin
g polyhedral metrics on surfaces with prescribed singularities. After Chow
and Luo’s work\, combinatorial curvature flows have been extensively st
udied for different types of discrete conformal structures on surfaces and
3-dimensional manifolds. In this talk\, I will give an introduction of th
ese combinatorial curvature flows\, and present some recent progresses on
the study of combinatorial curvature flows on surfaces and 3-dimensional m
anifolds.\n
LOCATION:https://researchseminars.org/talk/knotgraphgroup/122/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yangzhou Liu
DTSTART:20251129T140500Z
DTEND:20251129T153500Z
DTSTAMP:20260422T225701Z
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\nThe repre
sentation theory of classical braids is well-established\, with key exampl
es including the Burau representation (unfaithful for n≥5)\, the Temperl
ey–Lieb representation\, and the faithful Lawrence–Krammer–Bigelow r
epresentation. In contrast\, virtual knots exhibit distinct properties suc
h as parity. The Manturov-Nikonov (M-N) map bridges these domains by embed
ding classical braids into virtual braids. In this talk\, we prove that th
e M-N map is unfaithful for k>5. By analyzing the kernel of the Burau repr
esentation\, we explicitly construct elements in the kernel of the M-N map
\, revealing new obstructions to faithfulness in virtual braid representat
ions.\n
LOCATION:https://researchseminars.org/talk/knotgraphgroup/123/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Seongjeong Kim
DTSTART:20251213T140500Z
DTEND:20251213T153500Z
DTSTAMP:20260422T225701Z
UID:knotgraphgroup/124
DESCRIPTION:Title: Braids for Knots in $S_{g} \\times S^{1}$ and Iwahori-Hecke algeb
ra\nby Seongjeong Kim as part of Knots\, graphs and groups\n\n\nAbstra
ct\nIn \\cite{Kim} for an oriented surface $S_{g}$ of genus $g$ it is show
n that links in $S_{g} \\times S^{1}$ can be presented by virtual diagrams
with a decoration\, so called\, {\\em double lines}. In this paper\, firs
t we define braids with double lines for links in $S_{g}\\times S^{1}$. We
denote the group of braids with double lines by $VB_{n}^{dl}$. Alexander
and Markov theorem for links in $S_{g}\\times S^{1}$ can be proved analogo
usly to the work in \\cite{NegiPrabhakarKamada}. We show that\, if we rest
rict our interest to the group $B_{n}^{dl}$ generated by braids with doubl
e 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\,} Matematicheski
e Zametki\, Vol. 103\, No. 4 (2018)\, pp. 549 -- 567.\n\n\\bibitem{NegiPra
bhakarKamada}\nK. Negi\, M. Prabhakar\, S. Kamada\, {\\it Twisted virtual
braids and twisted links\,} Osaka J. Math. 61(4): 569-590 (October 2024).\
n
LOCATION:https://researchseminars.org/talk/knotgraphgroup/124/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Louis Kauffman (UIC\, SCKM^2)
DTSTART:20251220T140500Z
DTEND:20251220T153500Z
DTSTAMP:20260422T225701Z
UID:knotgraphgroup/125
DESCRIPTION:Title: Topological Quantum Computing - Fibonacci Model and Majorana Ferm
ions\nby Louis Kauffman (UIC\, SCKM^2) as part of Knots\, graphs and g
roups\n\n\nAbstract\nWe will discuss topological quantum computing from th
e point of view of the Fibonacci model (via Temperley-Lieb recoupling theo
ry based on Kauffman bracket polynomial) and also in terms of braid group
representations associated with Majorana Fermions. The talk will be self-c
ontained and we will quickly review what we discussed in the previous talk
s in this series.\n
LOCATION:https://researchseminars.org/talk/knotgraphgroup/125/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Maria Rubanenko
DTSTART:20251227T140500Z
DTEND:20251227T153500Z
DTSTAMP:20260422T225701Z
UID:knotgraphgroup/126
DESCRIPTION:Title: Distance multiplication algorithms for Monge\, unit-Monge matrice
s\nby Maria Rubanenko as part of Knots\, graphs and groups\n\n\nAbstra
ct\nDistance (tropical) matrix multiplication is a fundamental tool for de
signing algorithms operating on distances in graphs and different problems
solvable by dynamic programming. In applications such as longest common s
ubsequence\, edit distance\, and longest increasing subsequence\, the matr
ices are even more structured: they are like Monge matrices. We discuss SM
AWK\, MMT(Multiple Maxima Trees) algorithms for the tropical product of Mo
nge and unit-Monge matrices\, core-sparse Monge matrix multiplication and
Tiskin's algorithm for simple unit-Monge matrices.\n
LOCATION:https://researchseminars.org/talk/knotgraphgroup/126/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Natalia V. Maslova
DTSTART:20260314T140500Z
DTEND:20260314T153500Z
DTSTAMP:20260422T225701Z
UID:knotgraphgroup/127
DESCRIPTION:Title: On Gruenberg-Kegel graphs and beyond\nby Natalia V. Maslova a
s part of Knots\, graphs and groups\n\n\nAbstract\nThe Gruenberg--Kegel gr
aph (or the prime graph) of a finite group $G$ is a simple graph whose ver
tices are the prime divisors of $|G|$\, with primes $p$ and $q$ adjacent i
n this graph if and only if $pq$ is an element order of $G$. The concept o
f Gruenberg--Kegel graph proved to be very useful in finite group theory a
nd in algebraic combinatorics as well as with connection to research of so
me cohomological questions in integral group rings. In this talk\, we disc
uss recent results on characterization of finite groups by Gruenberg-Kegel
graph and by isomorphism type of Gruenberg-Kegel graph as well as combina
torial properties of Gruenberg--Kegel graphs.\n
LOCATION:https://researchseminars.org/talk/knotgraphgroup/127/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marianna Zinovieva
DTSTART:20260321T140500Z
DTEND:20260321T153500Z
DTSTAMP:20260422T225701Z
UID:knotgraphgroup/129
DESCRIPTION:Title: Finite groups with the given condition on the prime graph\nby
Marianna Zinovieva as part of Knots\, graphs and groups\n\n\nAbstract\nTh
e prime graph (or the Gruenberg–Kegel graph) of a finite group G is a si
mple 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 only if G
contains an element of order pq.\n\nThe concept of Gruenberg–Kegel graph
is very useful in finite group theory and in algebraic combinatorics.\n\n
In this talk\, we discuss results on finite groups with the given conditio
n on the prime graph (the Gruenberg-Kegel graph). In the “Kourovka Noteb
ook”\, A.V. Vasiliev posed question 16.26: Does there exist a natural nu
mber k such that no k pairwise nonisomorphic finite nonabelian simple grou
ps can have the same prime graph? Conjecture: k = 5.\n\nWe discuss author
’s results obtained on A.V. Vasiliev’s Conjecture. We also consider ot
her results about the prime graph (the Gruenberg-Kegel graph).\n
LOCATION:https://researchseminars.org/talk/knotgraphgroup/129/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yangzhou Liu
DTSTART:20260103T140500Z
DTEND:20260103T153500Z
DTSTAMP:20260422T225701Z
UID:knotgraphgroup/131
DESCRIPTION:Title: Braids presentation and secant-quandle invariant of knots\nby
Yangzhou Liu as part of Knots\, graphs and groups\n\n\nAbstract\nIn this
talk we construct an invariant of braids based on horizontal trisecants an
d their equivalent classes\, called the secant-quandle. Based on this\, we
further construct braid invariants such as the linear secant-quandle\, wh
ich may provide a representation of ′G3n and pure braid group. Then\, we
generalize secant-quandle to knots.\n
LOCATION:https://researchseminars.org/talk/knotgraphgroup/131/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Oleg German
DTSTART:20260124T140500Z
DTEND:20260124T153500Z
DTSTAMP:20260422T225701Z
UID:knotgraphgroup/132
DESCRIPTION:Title: On irrationality measure and geometric aspects of Diophantine app
roximation\nby Oleg German as part of Knots\, graphs and groups\n\n\nA
bstract\nIn 1842\, Dirichlet published his famous theorem which became the
foundation of Diophantine approximation. The phenomenon he found inspired
Liouville to study how well algebraic numbers can be approximated by rati
onals\, and thus\, to come up with a method of constructing transcendental
numbers explicitly. The development of these ideas led to the concepts of
irrationality measure and transcendence measure. Thanks to Minkowski\, it
became clear that many problems arising in the theory of Diophantine appr
oximation could be addressed quite effectively using the tools of geometry
of numbers. In particular\, the geometric approach naturally offers a wid
e variety of multidimensional analogues of the concept of irrationality me
asure — so called Diophantine exponents. In the talk\, we will discuss v
arious Diophantine exponents and the geometry that arises when studying th
em.\n
LOCATION:https://researchseminars.org/talk/knotgraphgroup/132/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yangzhou Liu
DTSTART:20260110T140500Z
DTEND:20260110T153500Z
DTSTAMP:20260422T225701Z
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 th
e last speech\, we introduced basic definitions and theorems of secant-qua
ndle as invariant of braids even knots. In this speech\, we discuss more d
etail\, according a specific example. Further more\, we plan to generalize
this invariant to secant-biquandle and virtual secant-quandle.\n
LOCATION:https://researchseminars.org/talk/knotgraphgroup/133/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yangzhou Liu
DTSTART:20260131T140500Z
DTEND:20260131T153500Z
DTSTAMP:20260422T225701Z
UID:knotgraphgroup/134
DESCRIPTION:Title: Secant-Quandle and Its Generalization: Loop-Quandle as an Invaria
nt of Knots\nby Yangzhou Liu as part of Knots\, graphs and groups\n\n\
nAbstract\nWe construct an interesting invariant for braids\, the secant-q
uandle (SQ)\, derived from homotopy classes of generic secants and generic
trisecants. We provide an algebraic-topological interpretation of this in
variant by showing that each generator in SQ corresponds to a special elem
ent of the fundamental group of the braid complement\, specifically\, a me
ridian encircling exactly two braid strands. This interpretation enables a
natural generalization of the secant-quandle to an invariant of knots and
links\, the loop-quandle (LQ). Furthermore\, we extend the construction t
o the virtual braids. As an application\, we compute the SQ and LQ for the
Hopf link.\n
LOCATION:https://researchseminars.org/talk/knotgraphgroup/134/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Semih Özlem
DTSTART:20260207T140500Z
DTEND:20260207T153500Z
DTSTAMP:20260422T225701Z
UID:knotgraphgroup/135
DESCRIPTION:Title: Weakened axioms\, idempotent splittings\, and the structure of le
arning: 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 abst
ractions\, but it begins with something deeply human: the act of telling t
hings apart. In this talk\, I'll explore how this simple idea—splitting
and focusing—manifests across different fields\, from linear algebra to
motives to machine learning. We'll start with a basic observation: if we r
elax the unit axiom in a vector space\, the scalar multiplication by 1 bec
omes an idempotent\, splitting the space into what is preserved and what i
s annihilated. This splitting phenomenon appears in surprising places: in
the theory of motives\, where projectors decompose varieties\; in knot the
ory\, where Jones–Wenzl projectors filter diagram algebras\; and in deep
learning\, where attention mechanisms focus on relevant features. I'll in
troduce the topos-theoretic model of neural networks (Belfiore–Bennequin
) and suggest that learning difficulties like catastrophic forgetting and
generalization gaps can be viewed as homotopical obstructions to achieving
"nice" (fibrant) network states. Architectural tools like residual connec
tions and attention can then be seen as learned\, conditional idempotents
—adaptable splitters that help networks organize information. This talk
is an invitation to think structurally across disciplines. I won't present
finished theorems\, but a framework of connections that links motivic phi
losophy\, categorical algebra\, and the practice of machine learning. The
goal is to start a conversation: can tools from pure mathematics—obstruc
tion theory\, homotopy colimits\, derivators—help us design more robust\
, interpretable\, and composable learning systems? No expertise in motives
\, knots\, or AI is required—only curiosity about how ideas weave togeth
er.\n
LOCATION:https://researchseminars.org/talk/knotgraphgroup/135/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Радомир Степанов
DTSTART:20260404T140500Z
DTEND:20260404T153500Z
DTSTAMP:20260422T225701Z
UID:knotgraphgroup/136
DESCRIPTION:Title: Редукция гомологий Хованова-Рожанс
кого для бипартитных узлов\nby Радомир
Степанов as part of Knots\, graphs and groups\n\n\nAbstract\nВ р
аботах по гомологиям Хованова–Розанско
го вычисление инвариантов для узлов и за
цеплений с помощью матричных факторизац
ий было громоздким даже для простых диаг
рамм\, но для бипартитных узлов вычислен
ия существенно упрощаются. В этом случае
бикомплекс Хованова-Рожанского сводитс
я к обычному монокомплексу на векторных
пространствах и мы покажем\, как найти оп
ераторы действующие в новом комплексе.\n
LOCATION:https://researchseminars.org/talk/knotgraphgroup/136/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Louis Kauffman
DTSTART:20260228T140500Z
DTEND:20260228T153500Z
DTSTAMP:20260422T225701Z
UID:knotgraphgroup/137
DESCRIPTION:Title: Temperley-Lieb Algebra - Visualizing Meanders and Idempotents
\nby Louis Kauffman as part of Knots\, graphs and groups\n\n\nAbstract\nTh
e Temperley–Lieb algebra first arose as a matrix algebra describing tran
sfer functions in statistical mechanics models such as the Potts and Ising
models. The algebra acquired a formal definition in terms of generators a
nd relations that allowed its representations to be identified in multiple
contexts.\n\nIn the early 1980's Vaughan Jones found the algebra once aga
in in a context between mathematics and physics as an algebra of projector
s that arose in a tower construction of von Neumann algebras. For this con
text\, Jones investigated the formally defined algebra and its matrix repr
esentations\, 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 algebra). He
also discovered a representation of the Artin braid group to the TL algebr
a. By composing this representation with the trace tr\, Jones defined an i
nvariant of braids that could be modified via the Markov Theorem for braid
s\, knots\, and links to produce a polynomial invariant of knots that is n
ow known as the Jones polynomial.\n\nThe speaker discovered knot diagramma
tic and combinatorial interpretations of the Jones polynomial and the Temp
erley–Lieb algebra that allow the polynomial to be seen as part of a gen
eralized Potts model partition function defined on planar link diagrams an
d planar graphs. The combinatorial interpretation of the Temperley–Lieb
algebra allows the Jones trace to be interpreted as a loop count for closu
res of Connection Monoid representations of the Temperley–Lieb algebra.
The multiplicative structure of the Temperley–Lieb algebra is represente
d in the speaker's work by a Connection Monoid and Connection Category who
se 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 the other.
\n\nThe talk will begin with the formal definition of the TL monoid and wi
ll show how it is modeled by the Connection Monoid and similarly with the
TL Category and a Connection Category. This interpretation allows us to se
e answers to algebra questions about the Temperley–Lieb Monoid that woul
d be invisible without the combinatorial interpretation. In particular we
will show how the structure of repeated powers of elements in TL appears a
nd how idempotents correspond to generalized meanders. A meander is a Jord
an curve in the plane cut through transversely by a straight line. The fas
cinating and highly visual combinatorics of the meanders informs the struc
ture of the TL algebra via the way meanders correspond to factorizations o
f the identity in the Temperley–Lieb Category.\n\nWe continue the discus
sion to include generalized meanders in relation to idempotents in the Bra
uer Monoid and in Tangle Categories and other Monoidal Categories.\n
LOCATION:https://researchseminars.org/talk/knotgraphgroup/137/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sviatoslav Dzhenzher
DTSTART:20260307T140500Z
DTEND:20260307T153500Z
DTSTAMP:20260422T225701Z
UID:knotgraphgroup/138
DESCRIPTION:Title: Kolmogorov--Arnold Stability\nby Sviatoslav Dzhenzher as part
of Knots\, graphs and groups\n\n\nAbstract\nRegarding the representation
theorem of Kolmogorov and Arnold (KA) as an algorithm for representing or
<> functions\, we test its robustness by analyzing its stabili
ty to withstand re-parameterizations of the hidden space.\nOne may think o
f such re-parameterizations as the work of an adversary attempting to foil
the construction of the KA outer function.\nWe find KA to be stable under
countable collections of continuous re-parameterizations\, but unearth a
question about the equi-continuity of the outer functions that\, so far\,
obstructs taking limits and defeating continuous groups of re-parameteriza
tions.\nThis question on the regularity of the outer functions is relevant
to the debate over the applicability of KA to the general theory of NNs.\
n
LOCATION:https://researchseminars.org/talk/knotgraphgroup/138/
END:VEVENT
BEGIN:VEVENT
SUMMARY:A. Allemand
DTSTART:20260214T140500Z
DTEND:20260214T153500Z
DTSTAMP:20260422T225701Z
UID:knotgraphgroup/139
DESCRIPTION:Title: Topological Galois Theory\nby A. Allemand as part of Knots\,
graphs and groups\n\n\nAbstract\nWe will discuss Vladimir Arnold's elegant
method for proving the unsolvability of many equations in elementary func
tions.\n
LOCATION:https://researchseminars.org/talk/knotgraphgroup/139/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hayk Sedrakyan
DTSTART:20260221T140500Z
DTEND:20260221T153500Z
DTSTAMP:20260422T225701Z
UID:knotgraphgroup/140
DESCRIPTION:Title: Novel Generalizations of Sedrakyan's inequality and equality cond
itions\nby Hayk Sedrakyan as part of Knots\, graphs and groups\n\n\nAb
stract\nNovel Generalizations of Sedrakyan's inequality are foundational c
omparison principles that establish sharp lower bounds for structured sums
. Beyond its classical role in algebraic inequality theory\, they serve as
a methodological tool for estimating quantities that arise in diverse mat
hematical sciences. In topology and knot theory\, it can support bounding
arguments for invariants and energy-type functionals. In group theory\, an
alogous inequality structures appear in estimates involving weights\, meas
ures\, and representation norms. In discrete geometry\, it assists in opti
mizing configurations and proving extremal properties of finite point sets
and graphs. More broadly\, its conceptual framework—transforming comple
x weighted relationships into simpler global bounds—makes it valuable in
theoretical physics\, optimization\, and information science\, where cont
rolling aggregate behavior from local data is essential.\n
LOCATION:https://researchseminars.org/talk/knotgraphgroup/140/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tumpa Mahato
DTSTART:20260328T140500Z
DTEND:20260328T153500Z
DTSTAMP:20260422T225701Z
UID:knotgraphgroup/141
DESCRIPTION:Title: Arc shift move and region arc shift move for twisted knots\nb
y Tumpa Mahato as part of Knots\, graphs and groups\n\n\nAbstract\nIn this
paper\, we study the unknotting operation for twisted knots\, called arc
shift move. First\, we find a family of twisted knots with arc shift numbe
r n for any given $n \\in \\mathbb{N}$. Then we define a new unknotting
operation\, called the region arc shift move for twisted knots and find f
amily of twisted knots whose region arc shift number is less than or equal
to n for any given $n \\in \\mathbb{N}$. Later\, we explore bounds for
region arc shift number and forbidden number.\n
LOCATION:https://researchseminars.org/talk/knotgraphgroup/141/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ivan Remizov
DTSTART:20260321T123000Z
DTEND:20260321T140000Z
DTSTAMP:20260422T225701Z
UID:knotgraphgroup/142
DESCRIPTION:Title: The Rate of Convergence of Chernoff Approximations to Operator Se
migroups and Approximate Solution of Differential Equations\nby Ivan R
emizov as part of Knots\, graphs and groups\n\n\nAbstract\nWe will discuss
a (surprisingly simple) proof of a theorem on the rate of convergence 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 Chernoff's t
heorem in 1968. Colleagues from all over the world used a wide range of to
ols of functional analysis to find it\, but a result was only recently obt
ained\, and with very simple techniques.\n \nThe one-dimensional analogue
of Chernoff's theorem states the following: if S is a real-valued function
of a real variable\, S(0) = 1\, S'(0) = L\, then for every real number t\
, the numbers (S(t/n))^n tend to exp(tL) as n tends to infinity. This simp
le fact is easily proven using the "second remarkable limit theorem" from
a course in mathematical analysis. The infinite-dimensional version of thi
s statement is called Chernoff's theorem. In it\, L is a closed\, densely
defined linear operator on a Banach space\, exp(tL) is a C0-semigroup of o
perators with generator L\, and S is called the Chernoff function for L. T
hus\, to approximately find a semigroup\, it suffices to find at least one
Chernoff function for the semigroup's generator. This simplifies the prob
lem\, as it is much easier to find a Chernoff function than\, for example\
, the generator's resolvent. This is because if an operator is the generat
or of a semigroup\, then this semigroup is unique\, and this operator's re
solvent is also uniwue. However\, there are always many Chernoff functions
for the generator\, so finding one of the Chernoff functions is easier th
an finding a unique semigroup or a unique resolvent. Given this Chernoff f
unction\, we can use Chernoff's theorem to first obtain a semigroup and th
en a resolvent — since the resolvent is obtained from the semigroup usin
g the Laplace transform.\n \nChernoff's original theorem doesn't specify a
ny properties of the Chernoff function that influence the rate of converge
nce of Chernoff approximations as n tends to infinity\, and even in the on
e-dimensional case\, this is a nontrivial problem. The general solution to
this problem will be discussed in the talk.\n \nWe will also discuss how
to use Chernoff approximations to find the resolvent of a semigroup genera
tor\, and how to use it to find solutions to differential equations with v
ariable coefficients — ordinary and elliptic partial differential equati
ons.\n \nNote that the theory of operator semigroups initially arose from
the need to express solutions to linear evolution partial differential equ
ations (parabolic and Schrödinger) in the language of operator theory. Ch
ernoff's theorem allows\, in many cases\, to express arbitrarily accurate
approximations to the solution of the Cauchy problem in terms of the coeff
icients of these equations and the initial condition\, as well as to mathe
matically justify the correctness of representing the solution as a Feynma
n integral. Many works and results in this area are attributed to the dist
inguished professor of Moscow State University Oleg Georgievich Smolyanov\
, the teacher of the report's co-authors\, who introduced them to this top
ic.\n
LOCATION:https://researchseminars.org/talk/knotgraphgroup/142/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ivan Remizov
DTSTART:20260411T123000Z
DTEND:20260411T140000Z
DTSTAMP:20260422T225701Z
UID:knotgraphgroup/143
DESCRIPTION:Title: The Rate of Convergence of Chernoff Approximations to Operator Se
migroups and Approximate Solution of Differential Equations\nby Ivan R
emizov as part of Knots\, graphs and groups\n\n\nAbstract\nВвиду бо
льшого интереса к подробностям доклад б
ыло решено разбить на два выступления. П
ервое выступление состоялось 21 марта\, н
а нём было дано определение С0-полугрупп
ы операторов и были показаны некоторые п
риложения этих полугрупп. Во втором выст
уплении 11 апреля мы обсудим черновские а
ппроксимации С0-полугрупп и скорость их
сходимости.\n
LOCATION:https://researchseminars.org/talk/knotgraphgroup/143/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Raphael Pinarbasi
DTSTART:20260502T140500Z
DTEND:20260502T153500Z
DTSTAMP:20260422T225701Z
UID:knotgraphgroup/144
DESCRIPTION:by Raphael Pinarbasi as part of Knots\, graphs and groups\n\nA
bstract: TBA\n
LOCATION:https://researchseminars.org/talk/knotgraphgroup/144/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Arno Mikaelyan
DTSTART:20260509T140500Z
DTEND:20260509T153500Z
DTSTAMP:20260422T225701Z
UID:knotgraphgroup/145
DESCRIPTION:Title: Generalizations and some particular cases of Ptolemy type formula
s\nby Arno Mikaelyan as part of Knots\, graphs and groups\n\n\nAbstrac
t\nThis presentation introduces the Sedrakyan–Mozayeni formula\, offerin
g an alternative to classical transformations based on Ptolemy’s theorem
. The talk will present the general form of the formula\, explore its geom
etric significance\, and examine several notable special cases that illust
rate its versatility and applications.\n
LOCATION:https://researchseminars.org/talk/knotgraphgroup/145/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yangzhou Liu
DTSTART:20260418T140500Z
DTEND:20260418T153500Z
DTSTAMP:20260422T225701Z
UID:knotgraphgroup/146
DESCRIPTION:Title: Secant-quandle: an invariant of braids and knots\nby Yangzhou
Liu as part of Knots\, graphs and groups\n\n\nAbstract\nWe construct a no
vel invariant of braids and knots\, called the \\textbf{secant-quandle} (\
\textbf{SQ})\, derived from homotopy classes of generic secants and generi
c horizontal trisecants. This invariant provides a natural generalization
of the usual knot quandle\, capturing richer topological information.\n
LOCATION:https://researchseminars.org/talk/knotgraphgroup/146/
END:VEVENT
END:VCALENDAR