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CALSCALE:GREGORIAN
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BEGIN:VEVENT
SUMMARY:A. Ya. Kanel-Belov
DTSTART;VALUE=DATE-TIME:20230715T140500Z
DTEND;VALUE=DATE-TIME:20230715T153500Z
DTSTAMP;VALUE=DATE-TIME:20241016T082739Z
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;VALUE=DATE-TIME:20230722T140500Z
DTEND;VALUE=DATE-TIME:20230722T153500Z
DTSTAMP;VALUE=DATE-TIME:20241016T082739Z
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;VALUE=DATE-TIME:20230729T140500Z
DTEND;VALUE=DATE-TIME:20230729T153500Z
DTSTAMP;VALUE=DATE-TIME:20241016T082739Z
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;VALUE=DATE-TIME:20230805T140500Z
DTEND;VALUE=DATE-TIME:20230805T153500Z
DTSTAMP;VALUE=DATE-TIME:20241016T082739Z
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;VALUE=DATE-TIME:20230812T140500Z
DTEND;VALUE=DATE-TIME:20230812T153500Z
DTSTAMP;VALUE=DATE-TIME:20241016T082739Z
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;VALUE=DATE-TIME:20230819T140500Z
DTEND;VALUE=DATE-TIME:20230819T153500Z
DTSTAMP;VALUE=DATE-TIME:20241016T082739Z
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;VALUE=DATE-TIME:20230826T140500Z
DTEND;VALUE=DATE-TIME:20230826T153500Z
DTSTAMP;VALUE=DATE-TIME:20241016T082739Z
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;VALUE=DATE-TIME:20230902T140500Z
DTEND;VALUE=DATE-TIME:20230902T153500Z
DTSTAMP;VALUE=DATE-TIME:20241016T082739Z
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;VALUE=DATE-TIME:20231007T140500Z
DTEND;VALUE=DATE-TIME:20231007T153500Z
DTSTAMP;VALUE=DATE-TIME:20241016T082739Z
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;VALUE=DATE-TIME:20230909T140500Z
DTEND;VALUE=DATE-TIME:20230909T153500Z
DTSTAMP;VALUE=DATE-TIME:20241016T082739Z
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;VALUE=DATE-TIME:20230916T140500Z
DTEND;VALUE=DATE-TIME:20230916T153500Z
DTSTAMP;VALUE=DATE-TIME:20241016T082739Z
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;VALUE=DATE-TIME:20230923T140500Z
DTEND;VALUE=DATE-TIME:20230923T153500Z
DTSTAMP;VALUE=DATE-TIME:20241016T082739Z
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;VALUE=DATE-TIME:20230930T140500Z
DTEND;VALUE=DATE-TIME:20230930T153500Z
DTSTAMP;VALUE=DATE-TIME:20241016T082739Z
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;VALUE=DATE-TIME:20231014T140500Z
DTEND;VALUE=DATE-TIME:20231014T153500Z
DTSTAMP;VALUE=DATE-TIME:20241016T082739Z
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;VALUE=DATE-TIME:20231021T140500Z
DTEND;VALUE=DATE-TIME:20231021T153500Z
DTSTAMP;VALUE=DATE-TIME:20241016T082739Z
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;VALUE=DATE-TIME:20231028T140500Z
DTEND;VALUE=DATE-TIME:20231028T153500Z
DTSTAMP;VALUE=DATE-TIME:20241016T082739Z
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;VALUE=DATE-TIME:20231111T140500Z
DTEND;VALUE=DATE-TIME:20231111T153500Z
DTSTAMP;VALUE=DATE-TIME:20241016T082739Z
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;VALUE=DATE-TIME:20231118T140500Z
DTEND;VALUE=DATE-TIME:20231118T153500Z
DTSTAMP;VALUE=DATE-TIME:20241016T082739Z
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;VALUE=DATE-TIME:20231125T140500Z
DTEND;VALUE=DATE-TIME:20231125T153500Z
DTSTAMP;VALUE=DATE-TIME:20241016T082739Z
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;VALUE=DATE-TIME:20231202T140500Z
DTEND;VALUE=DATE-TIME:20231202T153500Z
DTSTAMP;VALUE=DATE-TIME:20241016T082739Z
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;VALUE=DATE-TIME:20231216T140500Z
DTEND;VALUE=DATE-TIME:20231216T153500Z
DTSTAMP;VALUE=DATE-TIME:20241016T082739Z
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;VALUE=DATE-TIME:20231209T140500Z
DTEND;VALUE=DATE-TIME:20231209T153500Z
DTSTAMP;VALUE=DATE-TIME:20241016T082739Z
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;VALUE=DATE-TIME:20231223T140500Z
DTEND;VALUE=DATE-TIME:20231223T153500Z
DTSTAMP;VALUE=DATE-TIME:20241016T082739Z
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;VALUE=DATE-TIME:20231230T140500Z
DTEND;VALUE=DATE-TIME:20231230T153500Z
DTSTAMP;VALUE=DATE-TIME:20241016T082739Z
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;VALUE=DATE-TIME:20240120T140500Z
DTEND;VALUE=DATE-TIME:20240120T153500Z
DTSTAMP;VALUE=DATE-TIME:20241016T082739Z
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;VALUE=DATE-TIME:20240127T140500Z
DTEND;VALUE=DATE-TIME:20240127T153500Z
DTSTAMP;VALUE=DATE-TIME:20241016T082739Z
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;VALUE=DATE-TIME:20240309T140500Z
DTEND;VALUE=DATE-TIME:20240309T153500Z
DTSTAMP;VALUE=DATE-TIME:20241016T082739Z
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;VALUE=DATE-TIME:20240203T140500Z
DTEND;VALUE=DATE-TIME:20240203T153500Z
DTSTAMP;VALUE=DATE-TIME:20241016T082739Z
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;VALUE=DATE-TIME:20240302T140500Z
DTEND;VALUE=DATE-TIME:20240302T153500Z
DTSTAMP;VALUE=DATE-TIME:20241016T082739Z
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;VALUE=DATE-TIME:20240210T140500Z
DTEND;VALUE=DATE-TIME:20240210T153500Z
DTSTAMP;VALUE=DATE-TIME:20241016T082739Z
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;VALUE=DATE-TIME:20240224T140500Z
DTEND;VALUE=DATE-TIME:20240224T153500Z
DTSTAMP;VALUE=DATE-TIME:20241016T082739Z
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;VALUE=DATE-TIME:20240316T140500Z
DTEND;VALUE=DATE-TIME:20240316T153500Z
DTSTAMP;VALUE=DATE-TIME:20241016T082739Z
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;VALUE=DATE-TIME:20240323T140500Z
DTEND;VALUE=DATE-TIME:20240323T153500Z
DTSTAMP;VALUE=DATE-TIME:20241016T082739Z
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;VALUE=DATE-TIME:20240330T140500Z
DTEND;VALUE=DATE-TIME:20240330T153500Z
DTSTAMP;VALUE=DATE-TIME:20241016T082739Z
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;VALUE=DATE-TIME:20240406T140500Z
DTEND;VALUE=DATE-TIME:20240406T153500Z
DTSTAMP;VALUE=DATE-TIME:20241016T082739Z
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;VALUE=DATE-TIME:20240413T140500Z
DTEND;VALUE=DATE-TIME:20240413T153500Z
DTSTAMP;VALUE=DATE-TIME:20241016T082739Z
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;VALUE=DATE-TIME:20240420T140500Z
DTEND;VALUE=DATE-TIME:20240420T153500Z
DTSTAMP;VALUE=DATE-TIME:20241016T082739Z
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;VALUE=DATE-TIME:20240427T140500Z
DTEND;VALUE=DATE-TIME:20240427T153500Z
DTSTAMP;VALUE=DATE-TIME:20241016T082739Z
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;VALUE=DATE-TIME:20240504T140500Z
DTEND;VALUE=DATE-TIME:20240504T153500Z
DTSTAMP;VALUE=DATE-TIME:20241016T082739Z
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;VALUE=DATE-TIME:20240511T140500Z
DTEND;VALUE=DATE-TIME:20240511T153500Z
DTSTAMP;VALUE=DATE-TIME:20241016T082739Z
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;VALUE=DATE-TIME:20240518T140500Z
DTEND;VALUE=DATE-TIME:20240518T153500Z
DTSTAMP;VALUE=DATE-TIME:20241016T082739Z
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;VALUE=DATE-TIME:20240525T140500Z
DTEND;VALUE=DATE-TIME:20240525T153500Z
DTSTAMP;VALUE=DATE-TIME:20241016T082739Z
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;VALUE=DATE-TIME:20240601T140500Z
DTEND;VALUE=DATE-TIME:20240601T153500Z
DTSTAMP;VALUE=DATE-TIME:20241016T082739Z
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;VALUE=DATE-TIME:20240608T130500Z
DTEND;VALUE=DATE-TIME:20240608T143500Z
DTSTAMP;VALUE=DATE-TIME:20241016T082739Z
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;VALUE=DATE-TIME:20240622T130500Z
DTEND;VALUE=DATE-TIME:20240622T143500Z
DTSTAMP;VALUE=DATE-TIME:20241016T082739Z
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;VALUE=DATE-TIME:20240615T130500Z
DTEND;VALUE=DATE-TIME:20240615T143500Z
DTSTAMP;VALUE=DATE-TIME:20241016T082739Z
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;VALUE=DATE-TIME:20240629T130500Z
DTEND;VALUE=DATE-TIME:20240629T143500Z
DTSTAMP;VALUE=DATE-TIME:20241016T082739Z
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;VALUE=DATE-TIME:20240706T130500Z
DTEND;VALUE=DATE-TIME:20240706T143500Z
DTSTAMP;VALUE=DATE-TIME:20241016T082739Z
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;VALUE=DATE-TIME:20240713T100500Z
DTEND;VALUE=DATE-TIME:20240713T113500Z
DTSTAMP;VALUE=DATE-TIME:20241016T082739Z
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;VALUE=DATE-TIME:20240720T100500Z
DTEND;VALUE=DATE-TIME:20240720T113500Z
DTSTAMP;VALUE=DATE-TIME:20241016T082739Z
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;VALUE=DATE-TIME:20240817T100500Z
DTEND;VALUE=DATE-TIME:20240817T113500Z
DTSTAMP;VALUE=DATE-TIME:20241016T082739Z
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;VALUE=DATE-TIME:20240727T100500Z
DTEND;VALUE=DATE-TIME:20240727T113500Z
DTSTAMP;VALUE=DATE-TIME:20241016T082739Z
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;VALUE=DATE-TIME:20240803T100500Z
DTEND;VALUE=DATE-TIME:20240803T113500Z
DTSTAMP;VALUE=DATE-TIME:20241016T082739Z
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;VALUE=DATE-TIME:20240810T100500Z
DTEND;VALUE=DATE-TIME:20240810T113500Z
DTSTAMP;VALUE=DATE-TIME:20241016T082739Z
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;VALUE=DATE-TIME:20240824T130500Z
DTEND;VALUE=DATE-TIME:20240824T143500Z
DTSTAMP;VALUE=DATE-TIME:20241016T082739Z
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;VALUE=DATE-TIME:20240907T140500Z
DTEND;VALUE=DATE-TIME:20240907T153500Z
DTSTAMP;VALUE=DATE-TIME:20241016T082739Z
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;VALUE=DATE-TIME:20240914T140500Z
DTEND;VALUE=DATE-TIME:20240914T153500Z
DTSTAMP;VALUE=DATE-TIME:20241016T082739Z
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;VALUE=DATE-TIME:20240921T140500Z
DTEND;VALUE=DATE-TIME:20240921T153500Z
DTSTAMP;VALUE=DATE-TIME:20241016T082739Z
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;VALUE=DATE-TIME:20240928T140500Z
DTEND;VALUE=DATE-TIME:20240928T153500Z
DTSTAMP;VALUE=DATE-TIME:20241016T082739Z
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;VALUE=DATE-TIME:20241005T140500Z
DTEND;VALUE=DATE-TIME:20241005T153500Z
DTSTAMP;VALUE=DATE-TIME:20241016T082739Z
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;VALUE=DATE-TIME:20241012T140500Z
DTEND;VALUE=DATE-TIME:20241012T153500Z
DTSTAMP;VALUE=DATE-TIME:20241016T082739Z
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
END:VCALENDAR