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BEGIN:VEVENT
SUMMARY:L. Kauffman
DTSTART:20201221T153000Z
DTEND:20201221T170000Z
DTSTAMP:20260422T230719Z
UID:Knotsandtopology/1
DESCRIPTION:Title: Virtual Knots\, Index Polynomials and the Sawollek Polynomial
\nby L. Kauffman as part of Knots and representation theory\n\n\nAbstract\
nThis talk will discuss the Affine Index Polynomial and its relationship w
ith the Sawollek Polynomial for virtual knots and links.\n
LOCATION:https://researchseminars.org/talk/Knotsandtopology/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:N. Bogachev (Skoltech & MIPT)
DTSTART:20201228T153000Z
DTEND:20201228T170000Z
DTSTAMP:20260422T230719Z
UID:Knotsandtopology/2
DESCRIPTION:Title: Arithmetic and quasi-arithmetic hyperbolic reflection groups\
nby N. Bogachev (Skoltech & MIPT) as part of Knots and representation theo
ry\n\n\nAbstract\nIn 1967\, Vinberg started a systematic study of hyperbol
ic reflection groups. In particular\, he showed that Coxeter polytopes are
natural fundamental domains of hyperbolic reflection groups and developed
practically efficient methods that allow to determine compactness or volu
me finiteness of a given Coxeter polytope by looking at its Coxeter diagra
m. He also proved a (quasi-)arithmeticity criterion for hyperbolic lattice
s generated by reflections. In 1981\, Vinberg showed that there are no com
pact Coxeter polytopes in hyperbolic spaces H^n for n>29. Also\, he showed
that there are no arithmetic hyperbolic reflection groups H^n for n>29\,
either. Due to the results of Nikulin (2007) and Agol\, Belolipetsky\, Sto
rm\, and Whyte (2008) it became known that there are only finitely many ma
ximal arithmetic hyperbolic reflection groups in all dimensions. These res
ults give hope that maximal arithmetic hyperbolic reflection groups can be
classified.\n \nA very interesting moment is that compact Coxeter polytop
es are known only up to H^8\, and in H^7 and H^8 all the known examples ar
e arithmetic. Thus\, besides the problem of classification of arithmetic h
yperbolic reflection groups (which remains open since 1970-80s) we have an
other very natural question (which is again open since 1980s): do there ex
ist compact (both arithmetic and non-arithmetic) hyperbolic Coxeter polyto
pes in H^n for n>8 ?\n \nThis talk will be devoted to the discussion of th
ese two related problems. One part of the talk is based on the recent prep
rint https://arxiv.org/abs/2003.11944 where some new geometric classifica
tion method is described. The second part is based on a joint work with Al
exander Kolpakov https://arxiv.org/abs/2002.11445 where we prove that eac
h lower-dimensional face of a quasi-arithmetic Coxeter polytope\, which ha
ppens to be itself a Coxeter polytope\, is also quasi-arithmetic. We also
provide a few illustrative examples.\n
LOCATION:https://researchseminars.org/talk/Knotsandtopology/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:I.M. Nikonov
DTSTART:20210111T153000Z
DTEND:20210111T170000Z
DTSTAMP:20260422T230719Z
UID:Knotsandtopology/3
DESCRIPTION:Title: On noncommutative geometry\nby I.M. Nikonov as part of Knots
and representation theory\n\n\nAbstract\nNoncommutative (differential) geo
metry was introduced by Alain Connes about forty years ago. It is based on
the correspondence between topological and geometrical objects (manifolds
\, bundles\, differential forms etc.) and algebraic ones (algebras\, modul
es\, Hochschild homology etc.)In the talk we review the basic construction
s of noncommutative geometry: C*-algebras\, cyclic homology and Chern char
acter.\n
LOCATION:https://researchseminars.org/talk/Knotsandtopology/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Victoria Lebed
DTSTART:20210118T153000Z
DTEND:20210118T170000Z
DTSTAMP:20260422T230719Z
UID:Knotsandtopology/4
DESCRIPTION:Title: Unexpected applications of homotopical algebra to knot theory
\nby Victoria Lebed as part of Knots and representation theory\n\n\nAbstra
ct\nInteractions between knot theory and homotopical algebra are numerous
and natural. But the connections unveiled in this talk are rather unexpect
ed. Following a recent preprint with Markus Szymik\, I will explain how ho
motopy can help one to compute the full homology of racks and quandles. Th
ese are certain algebraic structures\, useful in knot theory and other are
as of mathematics. Their homology plays a key role in applications. Althou
gh very easy to define\, it is extremely difficult to compute. Complete co
mputations have been done only for a few families of racks. Our methods ad
d a new family to this list\, the family of permutation racks. The necessa
ry background on racks and quandles\, and their role in braid and knot the
ories\, will be given.\n
LOCATION:https://researchseminars.org/talk/Knotsandtopology/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:S. Kim
DTSTART:20210125T153000Z
DTEND:20210125T170000Z
DTSTAMP:20260422T230719Z
UID:Knotsandtopology/5
DESCRIPTION:Title: Links in $S_{g} \\times S^{1}$ and its lifting\nby S. Kim as
part of Knots and representation theory\n\n\nAbstract\nA virtual knot\, wh
ich is one of generalizations of knots in $\\mathbb{R}^{3}$ (or $S^{3}$)\,
is\, roughly speaking\, an embedded circle in thickened surface $S_{g} \\
times I$. In this talk we will discuss about knots in 3 dimensional $S_{g}
\\times S^{1}$. We introduce basic notions for knots in $S_{g} \\times S^
{1}$\, for example\, diagrams\, moves for diagrams and so on. For knots in
$S_{g} \\times S^{1}$ technically we lose over/under information\, but we
will have information how many times the knot rotates along $S^{1}$. We w
ill discuss the geometric meaning of the rotating information.\n
LOCATION:https://researchseminars.org/talk/Knotsandtopology/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:V.O. Manturov
DTSTART:20210201T153000Z
DTEND:20210201T170000Z
DTSTAMP:20260422T230719Z
UID:Knotsandtopology/6
DESCRIPTION:Title: Invariants of free knots valued in free groups\nby V.O. Mantu
rov as part of Knots and representation theory\n\n\nAbstract\nThis talk is
a part of the project of creating ``non-commutative'' invariants\nin topo
logy. The main idea is to replace ``characteristic classes'' of moduli spa
ces\nwith ``characteristic loops''. We discuss ``the last stage'' of the t
alk devoted to\nthe abstract objects we get in the end: the free knots\, a
n discuss their invariants\nvalued in free groups.\n \nThese invariants a
llow one to detect easily mutations\, invertibility\, and other phenomena.
\n
LOCATION:https://researchseminars.org/talk/Knotsandtopology/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Manpreet Singh (Mohali\, India)
DTSTART:20210208T153000Z
DTEND:20210208T170000Z
DTSTAMP:20260422T230719Z
UID:Knotsandtopology/7
DESCRIPTION:Title: Algebraic structures in knot theory\nby Manpreet Singh (Mohal
i\, India) as part of Knots and representation theory\n\n\nAbstract\nA vir
tual knot is a smooth\, simple closed curve in a thickened compact oriente
d surfaces considered up to ambient isotopy\, stabilisation/destabilisatio
n and orientation preserving homeomorphism of surfaces. Kuperberg proves t
hat every virtual link has a unique representative as a link up to ambient
isotopy in a thickened surface of the minimal genus. A classical knot the
ory is the study of smooth embedding of circles in the 3-sphere up to ambi
ent isotopy. Considering classical theory as the study of links in the thi
ckened 2-sphere\, the preceding result implies that classical knot theory
is embedded inside virtual knot theory. One of the fundamental problems in
knot theory is the classification of knots. In the classical case\, the f
undamental group of the knot complement space is a well known invariant. B
ut there are examples where it fails to distinguish distinct knots. Around
the 1980s\, Matveev and Joyce introduce a complete classical knot invaria
nt (up to the orientation of the knot and the ambient space) using distrib
utive groupoids (quandles)\, known as the knot quandle. \n \nIn the talk\,
I will describe the construction of knot quandle given by Matveev. I will
introduce the notion of residually finite quandles and prove that all lin
k quandles are residually finite. Using this\, I will prove that the word
problem is solvable for link quandle. I will discuss the orderability of q
uandles\, in particular for link quandles. Since all link groups are left-
orderable\, it is reasonable to expect that link quandles are left (right)
-orderable. In contrast\, I will show that orderability of link quandle be
have quite differently than that of the corresponding link groups. I will
also introduce a recent combinatorial generalisation of virtual links to w
hich we name as marked virtual links. I will associate groups and peripher
al structures to these diagrams and study their properties.\n
LOCATION:https://researchseminars.org/talk/Knotsandtopology/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Neha Nanda
DTSTART:20210215T153000Z
DTEND:20210215T170000Z
DTSTAMP:20260422T230719Z
UID:Knotsandtopology/8
DESCRIPTION:Title: An excursion on doodles on surfaces and virtual twins\nby Neh
a Nanda as part of Knots and representation theory\n\n\nAbstract\nStudy of
certain isotopy classes of a finite collection of immersed circles withou
t triple or higher intersections on closed oriented surfaces can be though
t of as a planar analogue of virtual knot theory where the genus zero case
corresponds to classical knot theory. Alexander and Markov theorems for t
he classical setting is well-known\, where the role of groups is played by
twin groups\, a class of right-angled Coxeter groups with only far commut
ativity relations. In the talk\, Alexander and Markov theorems for higher
genus case\, where the role of groups is played by a new class of groups c
alled virtual twin groups\, will be discussed which is work in collaborati
on with Dr Mahender Singh. Furthermore\, recent work on structural aspects
of these groups will be addressed which is a joint work with Dr Mahender
Singh and Dr Tushar Kanta Naik.\n
LOCATION:https://researchseminars.org/talk/Knotsandtopology/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Th. Yu. Popelensky
DTSTART:20210222T153000Z
DTEND:20210222T170000Z
DTSTAMP:20260422T230719Z
UID:Knotsandtopology/9
DESCRIPTION:Title: Quaternionic conjugation spaces\nby Th. Yu. Popelensky as par
t of Knots and representation theory\n\n\nAbstract\nThere is a considerabl
e amount of examples of spaces $X$ equipped with an involution $\\tau$\nsu
ch that the mod 2--cohomology rings $H^{2*}(X)$ and $H^*(X^\\tau)$ are iso
morphic.\nHausmann\, Holm\, and Puppe have shown that such an isomorphim i
s a part of a certain structure\non equivariant cohomology of $X$ and $X^\
\tau$\, which is called an {\\it $H$-frame}.\nThe simplest examples are co
mplex Grassmannians and flag manifolds with complex conjugation.\nWe devel
op a similar notion of $Q$-frame which appears in the situation\nwhen a sp
ace $X$ is equipped with two commuting involutions $\\tau_1\,\\tau_2$ and\
nthe mod 2-cohomology rings $H^{4*}(X)$ and $H^*(X^{\\tau_1\,\\tau_2})$ ar
e isomorphic.\nMotivating examples are quaternionic Grassmannians and quat
ernionic flag manifolds equipped with\ntwo complex involutions. We show na
turality and uniqueness of $Q$-framing.\nWe prove that $Q$-framing can be
defined for direct limits\, products\, etc. of $Q$-framed spaces.\nThis li
st of operations contains glueing a disk in $\\HH^n$ with complex involuti
ons $\\tau_1$ and $\\tau_2$ to a $Q$-framed space by an equivariant map of
boundary sphere.\n\nAn imporant part of $H$-frame structure in paper by H
.--H.--P. was so called {\\em conjugation equation}.\nFranz and Puppe calc
ulated the coefficients of the conjugation equation in terms of the Steenr
od squares.\nAs a part of a $Q$-framing we introduce corresponding structu
re\nequation and express its coefficients by explicit formula in terms of
the Steenrod operations.\n
LOCATION:https://researchseminars.org/talk/Knotsandtopology/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:M. Khovanov
DTSTART:20210301T153000Z
DTEND:20210301T170000Z
DTSTAMP:20260422T230719Z
UID:Knotsandtopology/10
DESCRIPTION:Title: Introduction to universal construction of topological theories\nby M. Khovanov as part of Knots and representation theory\n\n\nAbstrac
t\nA multiplicative function on diffeomorphism classes of n-manifolds exte
nds to a functorial assignment of state spaces to (n-1)-manifolds. Resulti
ng topological theories are interesting already in very low dimensions. We
'll explain the framework for these theories and provide a number of examp
les.\n
LOCATION:https://researchseminars.org/talk/Knotsandtopology/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Byeorhi Kim
DTSTART:20210315T153000Z
DTEND:20210315T170000Z
DTSTAMP:20260422T230719Z
UID:Knotsandtopology/11
DESCRIPTION:Title: On generalized quandle extensions of a quandle defined on a grou
p\nby Byeorhi Kim as part of Knots and representation theory\n\n\nAbst
ract\nIn 1980s\, Joyce and Matveev introduced a quandle which is an algebr
aic structure related to knot theory. In the papers\, they also showed tha
t for given a group and a group automorphism\, there is a quandle structur
e on the group\, later called ’generalized Alexander quandle’. In part
icular\, when the automorphism is an inner automorphism by a fixed element
$\\zeta$\, we denote the quandle operation by $\\triangleleft_{\\zeta}$.
In this talk\, we study a relationship between group extensions of a group
$G$ and quandle extensions of a generalized Alexander quandle $(G\,\\\\tr
iangleleft_{\\zeta})$ whose underlying set coincides with that of $G$. Thi
s is a joint work with Y.Bae and S.Carter.\n
LOCATION:https://researchseminars.org/talk/Knotsandtopology/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mahender Singh
DTSTART:20210322T153000Z
DTEND:20210322T170000Z
DTSTAMP:20260422T230719Z
UID:Knotsandtopology/12
DESCRIPTION:Title: Surface knot theory and related groups\nby Mahender Singh as
part of Knots and representation theory\n\n\nAbstract\nStudy of certain i
sotopy classes of a finite collection of immersed circles without triple o
r higher intersections on closed oriented surfaces can be thought of as a
planar analogue of virtual knot theory where the genus zero case correspon
ds to classical knot theory. It is intriguing to know which class of group
s serves the purpose that Artin braid groups serve in classical knot theor
y. Mikhail Khovanov proved that twin groups\, a class of right angled Coxe
ter groups with only far commutativity relations\, do the job for genus ze
ro case. A recent work shows that an appropriate class of groups called vi
rtual twin groups fits into the theory for higher genus cases. The talk wo
uld give an overview of some recent developments along these lines.\n
LOCATION:https://researchseminars.org/talk/Knotsandtopology/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Svjetlana Terzi ́c
DTSTART:20210329T153000Z
DTEND:20210329T170000Z
DTSTAMP:20260422T230719Z
UID:Knotsandtopology/13
DESCRIPTION:Title: Toric topology of the Grassmann manifolds\nby Svjetlana Terz
i ́c as part of Knots and representation theory\n\n\nAbstract\nbased on j
oint results with Victor M.~ Buchstaber\n\n\nIt is a classical problem
to study the canonical action of the compact torus $T^{n}$ on a Grassmann
manifold $G_{n\,2}$ which is connected to a series of problems in mod
ern algebraic topology\, algebraic geometry and mathematical physics. \n
\nThe aim of the talk is to present the recent results which are concerne
d with the description of the orbit space $G_{n\,2}/T^n$ in term of the
new notions:\n\\begin{itemize}\n\\item universal space of parameters $\\m
athcal{F}_{n}$\;\n\\item virtual spaces of parameters $\\widetilde{F}_{\
\sigma}\\subset \\mathcal{F}_{n}$ which correspond to the strata $W_{\\si
gma}$ in stratification $G_{n\,2} = \\cup _{\\sigma} W_{\\sigma}$ defin
ed in terms of the Pl\\"ucker coordinates\;\n\\item projections $\\wide
tilde{F}_{\\sigma}\\to F_{\\sigma}$ for the spaces of parameters $F_{\\s
igma}$ which correspond to the strata $W_{\\sigma}$.\n\\end{itemize}\n\n
In the course of the talk it will be described the chamber decomposition o
f the hypersimplex $\\Delta _{n\,2}$ which is defined by the special arr
angements of hyperplanes and represents one of the basic tools for the de
scription of the orbit space $G_{n\,2}/T^n$ in terms of the given noti
ons.\n
LOCATION:https://researchseminars.org/talk/Knotsandtopology/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hyeran Cho
DTSTART:20210412T153000Z
DTEND:20210412T170000Z
DTSTAMP:20260422T230719Z
UID:Knotsandtopology/14
DESCRIPTION:Title: Derivation of Schubert normal forms of 2-bridge knots from (1\,1
)-diagrams\nby Hyeran Cho as part of Knots and representation theory\n
\n\nAbstract\nA genus one 1-bridge knot (simply called a (1\, 1)-knot) is
a knot that can be decomposed into two trivial arcs embed in two solid tor
i in a genus one Heegaard splitting of a lens space. A (1\,1)-knot can be
described by a (1\,1)-diagram D(a\, b\, c\, r) determined by four integers
a\, b\, c\, and r. It is known that every 2-bride knot is a (1\, 1)-knot
and has a (1\, 1)-diagram of the form D(a\, 0\, 1\, r). In this talk\, we
give the dual diagram of D(a\, 0\, 1\, r) explicitly and present how to de
rive a Schubert normal form of a 2-bridge knot from the dual diagram. This
gives an alternative proof of the Grasselli and Mulazzani’s result asse
rting that D(a\, 0\, 1\, r) is a (1\, 1)-diagram of 2-bridge knot with a S
chubert normal form b(2a+1\, 2r).\n
LOCATION:https://researchseminars.org/talk/Knotsandtopology/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Colin Adams
DTSTART:20210419T153000Z
DTEND:20210419T170000Z
DTSTAMP:20260422T230719Z
UID:Knotsandtopology/15
DESCRIPTION:Title: Multi-crossings and Petal Number for Classical and Virtual Knots
\nby Colin Adams as part of Knots and representation theory\n\n\nAbstr
act\nInstead of considering projections of knots with two strands crossing
at every crossing\, we can ask for n strands to cross at every crossing.
We will show that every knot and link has such an n-crossing projection fo
r all integers n greater than 1 and therefore an n-crossing number. We als
o show that every knot has a projection with a single multi-crossing and n
o nested loops\, which is a petal projection and which generates a petal n
umber. We will discuss these ideas for both classical and virtual knots.
\n
LOCATION:https://researchseminars.org/talk/Knotsandtopology/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ivan Dynnikov
DTSTART:20210426T153000Z
DTEND:20210426T170000Z
DTSTAMP:20260422T230719Z
UID:Knotsandtopology/16
DESCRIPTION:Title: A method for distingiushing Legendrian and transverse links\
nby Ivan Dynnikov as part of Knots and representation theory\n\n\nAbstract
\nLegendrian (respectively\, transverse) links are smooth links in the\nth
ree-space that are tangent (respectively\, transverse) to the standard\nco
ntact structure. Deciding whether two such links are equivalent modulo a\n
contactomorphism is a hard problem in general. Many topological invariants
\nof Legendrian and transverse links are known\, but they do not suffice f
or\na classification even in the case of knots of crossing number six.\n\n
In recent joint works with Maxim Prasolov and Vladimir Shastin we\ndevelop
ed a rectangular diagram machinery for surfaces and links in the\nthree-sp
ace. This machinery has a tight connection with contact topology\,\nnamely
with Legendrian links and Giroux's convex surfaces. We are mainly\nintere
sted in studying rectangular diagrams of links that cannot be\nmonotonical
ly simplified by means of elementary moves. It turns out that\nthis questi
on is nearly equivalent to classification of Legendrian links.\n\nThe main
outcome we have so far is an algorithm for comparing two\nLegendrian (or
transverse) links. The computational complexity of the\nalgorithm is\, of
course\, very high\, but\, in many cases\, certain parts of\nthe procedure
can be bypassed\, which allows us to distinguish quite\ncomplicated Legen
drian knots. In praticular\, we have managed to provide an\nexample of two
inequivalent Legendrian knots cobounding an annulus tangent\nto the stand
rard contact structure along the entire boundary. Such\nexamples were prev
iously unknown.\n\nThe work is supported by the Russian Science Foundation
under\ngrant 19-11-00151\n
LOCATION:https://researchseminars.org/talk/Knotsandtopology/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ivan Reshetnikov
DTSTART:20210503T153000Z
DTEND:20210503T170000Z
DTSTAMP:20260422T230719Z
UID:Knotsandtopology/17
DESCRIPTION:Title: Discontinuously basic sets and the 13th problem of Hilbert\n
by Ivan Reshetnikov as part of Knots and representation theory\n\n\nAbstra
ct\nA subset $M \\subset \\textbf{R}^3$ is called a \\emph{discontinuously
basic subset}\, if for any function $f \\colon M \\to \\textbf{R}$ there
exist such functions $f_1\; f_2\; f_3 \\colon \\textbf{R} \\to R$ that $f(
x_1\, x_2\, x_3) = f_1(x_1) + f_2(x_2) + f_3(x_3)$ for each point $(x_1\,
x_2\, x_3)\\in M$. We will prove a criterion for a discontinuous basic sub
set for some specific subsets in terms of some graph properties. We will a
lso introduce several constructions for minimal discontinuous non-basic su
bsets.\n
LOCATION:https://researchseminars.org/talk/Knotsandtopology/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Adam Lowrance
DTSTART:20210510T153000Z
DTEND:20210510T170000Z
DTSTAMP:20260422T230719Z
UID:Knotsandtopology/18
DESCRIPTION:Title: The Jones polynomial\, Khovanov homology\, and Turaev genus\
nby Adam Lowrance as part of Knots and representation theory\n\n\nAbstract
\nThe Turaev surface of a link diagram is a surface built from a cobordism
between the all-A and all-B Kauffman states of the diagram\, and the Tura
ev genus of a link is the minimum genus of the Turaev surface for any diag
ram of the link. The Turaev surface was first used to give simple versions
of the Kauffman-Mursaugi-Thistlethwaite proofs of some Tait conjectures.
\n\nIn this talk\, we first give a brief history of the Turaev surface\, t
he Turaev genus of a link\, and some related applications. We then discuss
some recent results on the extremal and near extremal terms in the Jones
polynomial and Khovanov homology of a Turaev genus one link.\n
LOCATION:https://researchseminars.org/talk/Knotsandtopology/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andriy Haydys
DTSTART:20210607T153000Z
DTEND:20210607T170000Z
DTSTAMP:20260422T230719Z
UID:Knotsandtopology/19
DESCRIPTION:Title: On Fukaya-Seidel category and Khovanov homology\nby Andriy H
aydys as part of Knots and representation theory\n\n\nAbstract\nI will tal
k about a construction of the Fukaya-Seidel category for the holomorphic C
hern-Simons functional. This involves certain gauge-theoretic equations\,
which are conjecturally related also to Khovanov homology.\n
LOCATION:https://researchseminars.org/talk/Knotsandtopology/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Scott Baldridge
DTSTART:20230717T153000Z
DTEND:20230717T170000Z
DTSTAMP:20260422T230719Z
UID:Knotsandtopology/20
DESCRIPTION:Title: Bigraded 2-color homology is not a variant of Khovanov homology!
\nby Scott Baldridge as part of Knots and representation theory\n\nAbs
tract: TBA\n
LOCATION:https://researchseminars.org/talk/Knotsandtopology/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dimitris Kodokostas
DTSTART:20230724T153000Z
DTEND:20230724T170000Z
DTSTAMP:20260422T230719Z
UID:Knotsandtopology/21
DESCRIPTION:Title: An algorithmically computable complete invariant of knots\nb
y Dimitris Kodokostas as part of Knots and representation theory\n\nAbstra
ct: TBA\n
LOCATION:https://researchseminars.org/talk/Knotsandtopology/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:TBA
DTSTART:20230731T153000Z
DTEND:20230731T170000Z
DTSTAMP:20260422T230719Z
UID:Knotsandtopology/22
DESCRIPTION:by TBA as part of Knots and representation theory\n\nAbstract:
TBA\n
LOCATION:https://researchseminars.org/talk/Knotsandtopology/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lilya A. Grunwald
DTSTART:20230807T153000Z
DTEND:20230807T170000Z
DTSTAMP:20260422T230719Z
UID:Knotsandtopology/23
DESCRIPTION:Title: The number of rooted forests in circulant graph\nby Lilya A.
Grunwald as part of Knots and representation theory\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/Knotsandtopology/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ben McCarty
DTSTART:20230814T153000Z
DTEND:20230814T170000Z
DTSTAMP:20260422T230719Z
UID:Knotsandtopology/24
DESCRIPTION:Title: n-Color Vertex Homology\nby Ben McCarty as part of Knots and
representation theory\n\n\nAbstract\nWe will show how to categorify the v
ertex bracket polynomial\, which is based upon one of Roger Penrose’s fo
rmulas for counting the number of 3-edge colorings of a planar trivalent g
raph. We produce a bigraded theory called bigraded n-color vertex homology
whose graded Euler characteristic is the vertex bracket polynomial. We th
en produce a spectral sequence whose E∞ page is a filtered theory called
filtered n-color vertex homology\, and show that it is generated by certa
in types of properly colored ribbon subgraphs. In particular for n = 2\, w
e show that the n-color vertex homology is generated by colorings that cor
respond to perfect matchings. This is joint work with Scott Baldridge.\n
LOCATION:https://researchseminars.org/talk/Knotsandtopology/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alina Pavlikova
DTSTART:20230821T153000Z
DTEND:20230821T170000Z
DTSTAMP:20260422T230719Z
UID:Knotsandtopology/26
DESCRIPTION:Title: Bipartite knots and its applications\nby Alina Pavlikova as
part of Knots and representation theory\n\n\nAbstract\nThe non-bipartite k
not conjecture\, formulated in 1987 by Józef Przytitzky\, remained open f
or 24 years\, despite the efforts of several eminent mathematicians\, incl
uding its author and J. H. Conway [3]. In 2011\, S. Duzhin found a necessa
ry condition for a knot to be bipartite and gave examples of non-bipartite
knots. Further study of bipartite knots we explore their rich combinatori
al structure and hidden connections with the four color graph theorem.\n
LOCATION:https://researchseminars.org/talk/Knotsandtopology/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dmitrii Rachenkov
DTSTART:20230904T153000Z
DTEND:20230904T170000Z
DTSTAMP:20260422T230719Z
UID:Knotsandtopology/28
DESCRIPTION:Title: Quasi-polynomial solutions of anharmonic oscillators\nby Dmi
trii Rachenkov as part of Knots and representation theory\n\n\nAbstract\nI
n 2014\, in the article “Quadratic differentials as stability condition
s” T. Bridgeland and I. Smith proved that that moduli spaces of meromorp
hic quadratic differentials with simple zeroes on compact Riemann surfaces
can be identified with spaces of stability conditions on a class of CY3 t
riangulated categories. These categories can be defined using quivers with
potential associated to triangulated surfaces.\n\nAny quadratic different
ial defines an anharmonic oscillator equation and one can ask whether it h
as as a solution quasi-polynomial (=polynomial multiplied by exponent). Th
e general answer – work in progress! – should have a nice view in term
s of the spaces of stability conditions .\n\nIn my talk I am going to pre
sent in examples Bridgeland-Smith’s construction. If time permits I will
speak about Shapiro-Tater conjecture which proof involves quasi-polynomia
l solutions of a quartic anharmonic oscillators.\n\n \n\nReferences: arXiv
:2203.16889\, arXiv:1302.7030\n
LOCATION:https://researchseminars.org/talk/Knotsandtopology/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Igor Nikonov
DTSTART:20230828T153000Z
DTEND:20230828T170000Z
DTSTAMP:20260422T230719Z
UID:Knotsandtopology/29
DESCRIPTION:Title: On biquandles for the groups $G^k_n$ and surface singular braid
monoid\nby Igor Nikonov as part of Knots and representation theory\n\n
\nAbstract\nThe groups $G^k_n$ were defined by V. O. Manturov in order to
describe dynamical systems in configuration systems. In the talk we will c
onsider two applications of this theory: we define a biquandle structure o
n the groups $G^k_n$\, and construct a homomorphism from the surface singu
lar braid monoid to the group $G^2_n$.\n
LOCATION:https://researchseminars.org/talk/Knotsandtopology/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Igor Nikonov
DTSTART:20230911T153000Z
DTEND:20230911T170000Z
DTSTAMP:20260422T230719Z
UID:Knotsandtopology/30
DESCRIPTION:Title: Photography principle\, data transmission\, and invariants of ma
nifolds\nby Igor Nikonov as part of Knots and representation theory\n\
n\nAbstract\nIn the present talk we discuss the techniques suggested in [V
. O. Manturov\, I.M. Nikonov\, The groups Гn4\, braids\, and 3-manifolds\
, arXiv: 2305.06316] and the photography principle [V.O.Manturov\, Z.Wan\,
The photography method: solving pentagon\, hexagon\, and other equations\
, arXiv:2305.11945] to open a very broad path for constructing invariants
for manifolds of dimensions greater than or equal to 4.\n
LOCATION:https://researchseminars.org/talk/Knotsandtopology/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Younes Benyahia (SISSA\, Italy)
DTSTART:20230918T153000Z
DTEND:20230918T170000Z
DTSTAMP:20260422T230719Z
UID:Knotsandtopology/31
DESCRIPTION:Title: Exotic 2-knots and 2-links in 4-manifolds.\nby Younes Benyah
ia (SISSA\, Italy) as part of Knots and representation theory\n\n\nAbstrac
t\nTwo smoothly embedded surfaces in a 4-manifold are called exotic if the
y are topologically isotopic but smoothly not. In 1997\, Fintushel and Ste
rn constructed the first examples of exotic surfaces. Since then\, there h
ave been many constructions of exotic surfaces in other settings\, in part
icular\, ones closer to the smooth unknotting conjecture. \n In this talk\
, we give a construction of infinite families of exotic 2-spheres (in some
4-manifolds) that are topologically unknotted\, and we show how to adapt
the idea to obtain infinite families of exotic 2-links. This is a joint wo
rk with Bais\, Malech and Torres (see also https://arxiv.org/abs/2206.0965
9).\n
LOCATION:https://researchseminars.org/talk/Knotsandtopology/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hongdae Yun
DTSTART:20230925T153000Z
DTEND:20230925T170000Z
DTSTAMP:20260422T230719Z
UID:Knotsandtopology/32
DESCRIPTION:Title: A note on geometric realization of extreme Khovanov homology f
or some family of links\nby Hongdae Yun as part of Knots and represent
ation theory\n\n\nAbstract\nThe Khovanov (co)homology was introduced by Mi
khail Khovanov in 2000 and Viro explained it in terms of enhanced states
of diagram. Also J. González-Meneses\, P.M.G. Manchón\, M. Silvero prov
ed (potential) extreme Khovanov homology of link is isomorphic to independ
ence simplicial complex of Lando graph from the link. In this talk\, we re
call the definition of Khovanov homology. Furthermore we investigate the g
eometric realization of extreme Khovanov homology of some family of knots
and links. This is joint work with Mark H Siggers and Seung Yeop Yang.\n
LOCATION:https://researchseminars.org/talk/Knotsandtopology/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Igor Nikonov
DTSTART:20231002T153000Z
DTEND:20231002T170000Z
DTSTAMP:20260422T230719Z
UID:Knotsandtopology/33
DESCRIPTION:Title: Examples of weight systems of framed chord diagrams\nby Igor
Nikonov as part of Knots and representation theory\n\n\nAbstract\nWe exte
nd Bar-Natan’s construction of weight systems induced by Lie algebra rep
resentations to the case of framed chord diagrams. (joint work with Denis
Ilyutko)\n
LOCATION:https://researchseminars.org/talk/Knotsandtopology/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:П. Н. Питал
DTSTART:20231023T153000Z
DTEND:20231023T170000Z
DTSTAMP:20260422T230719Z
UID:Knotsandtopology/34
DESCRIPTION:Title: Обобщенные факториалы и p-упорядоч
ения\nby П. Н. Питал as part of Knots and representation th
eory\n\n\nAbstract\nВ докладе будет рассказано об
интересном обобщении понятия факториал
а\, предложенном М. Бхаргавой для дедеки
ндовых колец.\n
LOCATION:https://researchseminars.org/talk/Knotsandtopology/34/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kevin Walker
DTSTART:20231030T153000Z
DTEND:20231030T170000Z
DTSTAMP:20260422T230719Z
UID:Knotsandtopology/35
DESCRIPTION:Title: A very general approach to TQFT state sums\nby Kevin Walker
as part of Knots and representation theory\n\n\nAbstract\nI’ll discuss a
very general (“universal”) approach to constructing TQFT state sums f
or manifolds. This will be based on https://arxiv.org/abs/2104.02101\, bu
t in contrast to that paper I’ll start with concrete examples and work t
oward the more general statements.\n
LOCATION:https://researchseminars.org/talk/Knotsandtopology/35/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hayk Sedrakyan
DTSTART:20231113T153000Z
DTEND:20231113T170000Z
DTSTAMP:20260422T230719Z
UID:Knotsandtopology/36
DESCRIPTION:Title: Distance formula for a point inside a triangle (formula for a di
agonal of any quadrilateral)\nby Hayk Sedrakyan as part of Knots and r
epresentation theory\n\n\nAbstract\nGiven a connected graph with four vert
ices and six edges (a quadrilateral and its diagonals). We obtained a nove
l formula to find the length of any of its edges using the other five edge
lengths. For example\, in the case of a convex quadrilateral we are able
to find the length of its diagonal using its side lengths and the length o
f the other diagonal. In the case of a concave quadrilateral (point inside
a triangle)\, we are able to find the distance between this point and any
of the vertices of the triangle.\n
LOCATION:https://researchseminars.org/talk/Knotsandtopology/36/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Scott Carter
DTSTART:20231127T153000Z
DTEND:20231127T170000Z
DTSTAMP:20260422T230719Z
UID:Knotsandtopology/37
DESCRIPTION:Title: Intricacies about the binary icosahedral group\nby Scott Car
ter as part of Knots and representation theory\n\n\nAbstract\nZeeman's the
orem tells us that both the 5-twist spun trefoil and the 2-twist spun toru
s knot T(3\,5) are fibered knotted spheres in 4-dimensional space where th
e fiber is the punctured Poincare homology sphere. That closed homology sp
here is the quotient of the 3-sphere under the action of the binary icosah
edral group. It is a 5-fold or 2-fold branched cover of 3-space branched o
ver the respective knot. The group is isomorphic to SL_2(Z/5). I want to u
nderstand all of the statements asserted above. To that end\, I am working
on comparing three different presentations of this group. In as much as p
ossible\, I will explicitly represent the elements in the group as strings
with quipu\, matrices\, generators\, and elements in the 3-sphere. I'll a
lso give different pictures that allow one to compute relationships among
the words in the standard presentation of the group. I'm also interested i
n braiding the homology sphere in 5-space.\n
LOCATION:https://researchseminars.org/talk/Knotsandtopology/37/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bao Vuong
DTSTART:20231120T153000Z
DTEND:20231120T170000Z
DTSTAMP:20260422T230719Z
UID:Knotsandtopology/38
DESCRIPTION:Title: Reidemeister torsion of link complements in 3-torus\nby Bao
Vuong as part of Knots and representation theory\n\n\nAbstract\nThe relati
on between Alexander polynomial of a knot and the torsion invariant of Rei
demeister\, Franz and de Rham for knot complement was first noticed by Mil
nor. As a consequence of the relation\, Milnor gave another proof for symm
etry of Alexander polynomial. Milnor applied the result to knot theory\, c
onsidering the case of classical knot\, i.e. the knot complement has the h
omology of the circle. It turns out that there are similar relations betwe
en Reidemeister torsion and twisted Alexander polynomial for the case of k
not complement in other spaces\, rather than three dimensional sphere when
the homology group contains also torsion. The technology to get explicit
relations as Milnor had created making use of simple homotopy theory for C
W-complexes and Fox free differential calculus. Those ensure a CW structur
e for the knot complement\, associated with a presentation of the fundamen
tal group\, so that the boundary maps are obtained by free derivatives. Th
e method works out fine also for the case of knots and links in three dime
nsional torus. Thus we show that the Reidemeister torsion of the link comp
lement and its twisted Alexander polynomial are equal.\n
LOCATION:https://researchseminars.org/talk/Knotsandtopology/38/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Martinez-Garcia Jesus
DTSTART:20231204T153000Z
DTEND:20231204T170000Z
DTSTAMP:20260422T230719Z
UID:Knotsandtopology/39
DESCRIPTION:Title: Moduli of Fano varieties via K-stability\nby Martinez-Garcia
Jesus as part of Knots and representation theory\n\n\nAbstract\nK-stabili
ty is a recent theory that interacts with complex and analytic geometry\,
birational geometry and moduli theory. Take a Fano variety (a complex proj
ective variety with positive Ricci curvature). Can we construct a compact
moduli space that parametrises all the ‘reasonable’ degenerations of t
his variety (including fairly singular ones) and that it is itself ‘reas
onable’ as a space? The answer is positive if the variety is K-(poly)sta
ble and this moduli space\, known as K-moduli\, parametrises all K-polysta
ble Fano varieties. From a complex viewpoint\, K-polystable Fano varieties
are precisely those which admit a Kahler-Einstein metric.\n\nSmooth Fano
varieties have been classified up to dimension 3 but until recent work by
Abban-Zhuang and others\, we did not have enough tools to decide which one
s were K-polystable\, let alone to describe the K-moduli itself. In this t
alk I will survey these notions and present recent progress in the subject
\, with special emphasis in the programme to classify Fano varieties and t
heir K-moduli in low dimensions.\n
LOCATION:https://researchseminars.org/talk/Knotsandtopology/39/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Igor M. Nikonov
DTSTART:20231211T153000Z
DTEND:20231211T170000Z
DTSTAMP:20260422T230719Z
UID:Knotsandtopology/40
DESCRIPTION:Title: Rota-Baxter operators and Hopf algebras\nby Igor M. Nikonov
as part of Knots and representation theory\n\n\nAbstract\nWe will consider
several problems related to Rota-Baxter operators and Hopf algebras:\n1)
construction of group Rota-Baxter operators of arbitrary weight on Lie gro
ups\n2) conditions under which a Rota-Baxter operator on a group is a Rota
-Baxter operator of a group algebra\n3) construction of relative Roth-Baxt
er operators for noncommutative Hopf algebras\n
LOCATION:https://researchseminars.org/talk/Knotsandtopology/40/
END:VEVENT
BEGIN:VEVENT
SUMMARY:O.G. Styrt
DTSTART:20231218T153000Z
DTEND:20231218T170000Z
DTSTAMP:20260422T230719Z
UID:Knotsandtopology/41
DESCRIPTION:Title: Elements of a Lie algebra acting nilpotently in all its represen
tations\nby O.G. Styrt as part of Knots and representation theory\n\n\
nAbstract\nAn equivalent condition for an element of a Lie algebra acting
nilpotently in all its representations is obtained. Namely\, it should bel
ong to the derived algebra and go via factoring over the radical to a nilp
otent element of the corresponding (semisimple) quotient algebra.\nThe tal
k is based on the speaker's preprint https://arxiv.org/abs/2209.13309\n
LOCATION:https://researchseminars.org/talk/Knotsandtopology/41/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Manpreet Singh
DTSTART:20240108T153000Z
DTEND:20240108T170000Z
DTSTAMP:20260422T230719Z
UID:Knotsandtopology/42
DESCRIPTION:Title: Invariants of knots from biquandles and virtual biquandles\n
by Manpreet Singh as part of Knots and representation theory\n\n\nAbstract
\nWe will prove that for a given virtual link L and a virtual biquandle (X
\,f\,R)\, the set of colorings of L by (X\,f\,R) is in bijection with the
set of colorings of L by a biquandle (X\,VR)\, where VR is a new operator
we define on X. The biquandle (X\,VR) is the 1-induced biquandle associate
d with (X\,f\,R). Moreover\, we will prove that for a virtual link L\, the
associated biquandle BQ(L) is isomorphic to the 1-induced biquandle of th
e virtual biquandle VBQ(L). Furthermore\, the 1-induced biquandle of VBQ(L
) is isomorphic to VBQ(L) as virtual biquandles. If time permits\, we will
introduce a cohomology theory for (X\,f\,R) and give its applications to
knots.\n
LOCATION:https://researchseminars.org/talk/Knotsandtopology/42/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Igor Nikonov
DTSTART:20231225T153000Z
DTEND:20231225T170000Z
DTSTAMP:20260422T230719Z
UID:Knotsandtopology/43
DESCRIPTION:Title: Virtual index cocycles and invariants of virtual links\nby I
gor Nikonov as part of Knots and representation theory\n\n\nAbstract\nVirt
ual index cocycle is the 1-cochain that counts virtual crossings in the ar
cs of a virtual link diagram. We show how this cocycle can be used to refo
rmulate and unify some known invariants of virtual links.\n
LOCATION:https://researchseminars.org/talk/Knotsandtopology/43/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Visakh Narayanan
DTSTART:20240115T153000Z
DTEND:20240115T170000Z
DTSTAMP:20260422T230719Z
UID:Knotsandtopology/44
DESCRIPTION:Title: Knots in $\\mathbb{R}P^3$\nby Visakh Narayanan as part of Kn
ots and representation theory\n\n\nAbstract\nWe will discuss some properti
es of knots in three dimensional projective space. Our technique for this
purpose is to associate a virtual link to a link in projective space so th
at equivalent projective links go to equivalent virtual links (modulo a sp
ecial flype move). We can then apply techniques in virtual knot theory to
obtain a Jones polynomial for projective links which also happens to be eq
uivalent to the Jones polynomial constructed by Drobotukhina. Then we woul
d discuss a combinatorial cobordism theory for projective links which may
be used to apply virtual Khovanov homology and the virtual Rasmussen invar
iant of Dye\, Kaestner\, and Kauffman to projective links.\n
LOCATION:https://researchseminars.org/talk/Knotsandtopology/44/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Seongjeong Kim
DTSTART:20240122T153000Z
DTEND:20240122T170000Z
DTSTAMP:20260422T230719Z
UID:Knotsandtopology/45
DESCRIPTION:Title: The groups $G_{n}^{3}$ and rhombi tilings of 2n-gons\nby Seo
ngjeong Kim as part of Knots and representation theory\n\n\nAbstract\nIn t
his talk we will consider a map from the set of rhombi tilings of 2n-gon t
o the group $G_{n}^{3}$ and will discuss our further researches.\n
LOCATION:https://researchseminars.org/talk/Knotsandtopology/45/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Christoph Schiller
DTSTART:20240226T153000Z
DTEND:20240226T170000Z
DTSTAMP:20260422T230719Z
UID:Knotsandtopology/46
DESCRIPTION:Title: From the three Reidemeister moves to the three Lie gauge groups
– with consequences for the unification of physics\nby Christoph Sc
hiller as part of Knots and representation theory\n\n\nAbstract\nQuantum t
heory suggests that the three observed gauge groups U(1)\, SU(2) and SU(3)
are related to the three Reidemeister moves of knot theory: twists\, poke
s and slides. The background for the relation is clarified: modelling \npa
rticles as fluctuating tangles of strands explains wave functions. Classif
ying tangles explains the elementary \nfermions and bosons. It is then sho
wn that twists generate U(1) and that pokes generate SU(2). The emphasis i
s put on deducing the relation between slides\, the corresponding strand d
eformations\, the Gell-Mann matrices\, and the Lie group SU(3). Consequenc
es for unification are deduced.\n
LOCATION:https://researchseminars.org/talk/Knotsandtopology/46/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Igor Nikonov
DTSTART:20240129T153000Z
DTEND:20240129T170000Z
DTSTAMP:20260422T230719Z
UID:Knotsandtopology/47
DESCRIPTION:Title: Traits of crossings and functorial maps\nby Igor Nikonov as
part of Knots and representation theory\n\n\nAbstract\nOne of the major ap
plications of parity theory are picture-valued invariants of knots such as
parity bracket. We present several examples of such invariants for links
in a fixed surface.\n
LOCATION:https://researchseminars.org/talk/Knotsandtopology/47/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Seongjeong Kim
DTSTART:20240205T153000Z
DTEND:20240205T170000Z
DTSTAMP:20260422T230719Z
UID:Knotsandtopology/48
DESCRIPTION:Title: The classification of knots in $S_{g}\\times S^{1}$ of the small
number of crossings\nby Seongjeong Kim as part of Knots and represent
ation theory\n\n\nAbstract\nIn this talk we construct invariants for knots
in $S_{g}\\times S^{1}$ and try to classify knots in $S_{g}\\times S^{1}$
with small number crossings.\n
LOCATION:https://researchseminars.org/talk/Knotsandtopology/48/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Мороз Борис Барух
DTSTART:20240212T153000Z
DTEND:20240212T170000Z
DTSTAMP:20260422T230719Z
UID:Knotsandtopology/49
DESCRIPTION:Title: Гипотеза Римана и диофантовы уравн
ения\nby Мороз Борис Барух as part of Knots and rep
resentation theory\n\n\nAbstract\nВ нашей (совместной с
А.А.Норкином) недавней работе явно выпис
ано диофантово уравнение\, неразрешимос
ть которого эквивалентна гипотезе Риман
а. Я расскажу об этой работе.\n
LOCATION:https://researchseminars.org/talk/Knotsandtopology/49/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dmitry Solovyev
DTSTART:20240304T153000Z
DTEND:20240304T170000Z
DTSTAMP:20260422T230719Z
UID:Knotsandtopology/50
DESCRIPTION:Title: Universal construction\, foams and link homology\nby Dmitry
Solovyev as part of Knots and representation theory\n\n\nAbstract\nThis ta
lk is based on a joint work with Mikhail Khovanov. In this work we review
the construction of sl(N) link homology theory coming from foams\, which c
ategorifies HOMFLY-PT link invariant and RT sl(N) quantum link invariants.
This talk is elementary\, the emphasis will be put on the theory of unori
ented SL(3) foams\, their evaluation and corresponding universal construct
ion. This version of foam theory is related to 4-color theorem and Kronhei
mer-Mrowka 3-orbifold homology theory. If time permits\, we will also talk
about how oriented SL(3) foams categorify the Kuperberg invariant.\n
LOCATION:https://researchseminars.org/talk/Knotsandtopology/50/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Igor Nikonov
DTSTART:20240219T153000Z
DTEND:20240219T170000Z
DTSTAMP:20260422T230719Z
UID:Knotsandtopology/51
DESCRIPTION:Title: On biquandles for the groups $G^k_n$ and surface singular braid
monoid\nby Igor Nikonov as part of Knots and representation theory\n\n
\nAbstract\nThe groups $G^k_n$ were defined by V. O. Manturov in order to
describe dynamical systems in configuration systems. In the talk we will c
onsider two applications of this theory: we define a biquandle structure o
n the groups Gkn\, and construct a homomorphism from the surface singular
braid monoid to the group $G^2_n$.\n
LOCATION:https://researchseminars.org/talk/Knotsandtopology/51/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Igor Nikonov
DTSTART:20240311T153000Z
DTEND:20240311T170000Z
DTSTAMP:20260422T230719Z
UID:Knotsandtopology/52
DESCRIPTION:Title: Flat-virtual knot: introduction and some invariants\nby Igor
Nikonov as part of Knots and representation theory\n\n\nAbstract\nIn atte
mpts to construct a map from classical knots to virtual ones\, we define a
series of maps from knots in the full torus (thickened torus) to flat-vir
tual knots. We give definition of flat-virtual knots and presents Alexande
r-like polynomial and Kauffman bracket for them. We also discuss a possibl
e extension of the notion of flat-virtual knots — so-called multi-flat k
nots.\n
LOCATION:https://researchseminars.org/talk/Knotsandtopology/52/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Helen Wong
DTSTART:20240325T154500Z
DTEND:20240325T171500Z
DTSTAMP:20260422T230719Z
UID:Knotsandtopology/53
DESCRIPTION:Title: Multiplication in Kauffman bracket skein algebra of a 1-hole tor
us\nby Helen Wong as part of Knots and representation theory\n\n\nAbst
ract\nThe Kauffman bracket skein algebra of a surface is a generalization
of the Jones polynomial for links and is one of few constructions from qua
ntum topology that is clearly related to hyperbolic geometry. To further u
nderstand the relationship\, it is important to understand the multiplicat
ive structure of the skein algebra. In this talk\, we present a recursion
relation and fast algorithm for multiplication in the skein algebra in the
case of a 1-hole torus.\n
LOCATION:https://researchseminars.org/talk/Knotsandtopology/53/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Oleg Styrt
DTSTART:20240318T154500Z
DTEND:20240318T171500Z
DTSTAMP:20260422T230719Z
UID:Knotsandtopology/54
DESCRIPTION:Title: Elements of a Lie algebra acting nilpotently in all its repre
sentations\nby Oleg Styrt as part of Knots and representation theory\n
\n\nAbstract\nAn equivalent condition for an element of a Lie algebra acti
ng nilpotently in all its representations is obtained. Namely\, it should
belong to the derived algebra and go via factoring over the radical to a n
ilpotent element of the corresponding (semisimple) quotient algebra.\nThe
talk is based on the preprint https://arxiv.org/abs/2209.13309\n
LOCATION:https://researchseminars.org/talk/Knotsandtopology/54/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Igor M. Nikonov
DTSTART:20240408T153000Z
DTEND:20240408T170000Z
DTSTAMP:20260422T230719Z
UID:Knotsandtopology/55
DESCRIPTION:Title: On biquandles for the groups $G^k_n$ and surface singular braid
monoid\nby Igor M. Nikonov as part of Knots and representation theory\
n\n\nAbstract\nThe groups $G^k_n$ were defined by V. O. Manturov in order
to describe dynamical systems in configuration systems. In the talk we wil
l consider two applications of this theory: we define a biquandle structur
e on the groups $G^k_n$\, and construct a homomorphism from the surface si
ngular braid monoid to the group $G^2_n$.\n
LOCATION:https://researchseminars.org/talk/Knotsandtopology/55/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Многие
DTSTART:20240415T153000Z
DTEND:20240415T170000Z
DTSTAMP:20260422T230719Z
UID:Knotsandtopology/56
DESCRIPTION:Title: Конференция "Ломоносов"\nby Многие
as part of Knots and representation theory\n\n\nAbstract\nКонфере
нция "Ломоносов"\nКонференция происходит
на русском языке.\nСписок докладчиков. (П
одробнее: https://disk.yandex.com/d/XyvJNm3i_LmjHw)\n\n1) Жиха
рева Екатерина Сергеевна (студент\, кафе
дра дифференциальной геометрии и прилож
ений\, механико-математический факульте
т\, МГУ им. М. В. Ломоносова)\, "Трехмерные а
лгебры Ли\, допускающие полупростые алге
браические операторы Нейенхейса" .\n\n2) Ле
вин Виктор Анатольевич (студент\, кафедр
а дифференциальной геометрии и приложен
ий\, механико-математический факультет\,
МГУ им. М. В. Ломоносова)\, "Слоение Лиувил
ля интегрируемых биллиардов с острыми у
глами" .\n\n3) Михайлов Иван Николаевич (сту
дент\, кафедра дифференциальной геометр
ии и приложений\, механико-математически
й факультет\, МГУ им. М. В. Ломоносова)\, "Ра
сстояние Громова-Хаусдорфа между нормир
ованными пространствами" .\n\n4) Цыганков Д
митрий Александрович (студент\, кафедра
высшей геометрии и топологии\, механико-
математический факультет\, МГУ им. М. В. Л
омоносова)\, "Гиперболические многообраз
ия\, соответствующие прямоугольным мног
огранникам\, и их расслоения над окружно
стью".\n
LOCATION:https://researchseminars.org/talk/Knotsandtopology/56/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Seongjeong Kim
DTSTART:20240422T153000Z
DTEND:20240422T170000Z
DTSTAMP:20260422T230719Z
UID:Knotsandtopology/57
DESCRIPTION:Title: Invariant of braids by using Ptolemy relation and failure for kn
ots\nby Seongjeong Kim as part of Knots and representation theory\n\n\
nAbstract\nIn this talk\, we will talk about an old work with prof. V.O. M
anturov on the construction of an invariant for braids by using Ptolemy re
lation and remind why it fails to be an invariant for links.\n
LOCATION:https://researchseminars.org/talk/Knotsandtopology/57/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Zhihao Wang
DTSTART:20240513T153000Z
DTEND:20240513T170000Z
DTSTAMP:20260422T230719Z
UID:Knotsandtopology/58
DESCRIPTION:Title: On stated $SL(n)$-skein modules\nby Zhihao Wang as part of K
nots and representation theory\n\n\nAbstract\nWe mainly focus on Classical
limit\, Splitting map\, and Frobenius homomorphism for stated $SL(n)$-s
kein modules\, and Unicity Theorem for stated $SL(n)$-skein algebras.\n\nL
et $(M\,N)$ be a marked three manifold. We use $S_n(M\,N\,v)$ to denote th
e stated $SL(n)$-skein module of $(M\,N)$ where $v$ is a nonzero complex n
umber.\nWe build a surjective algebra homomorphism from $S_n(M\,N\,1)$ to
the coordinate ring of some algebraic set\, and prove it's Kernal consists
of all nilpotents. We prove the universal representation algebra of $\\pi
_1(M)$ is isomorphic to $S_n(M\,N\,1)$ when $N$ has only one component and
$M$ is connected. Furthermore we show $S_n(M\,N^{'}\,1)$ is isomorphic t
o\n$S_n(M\,N\,1)\\otimes O(SLn)$\, where $N\\neq \\emptyset$\, $M$ is conn
ected\, and $N^{'}$ is obtained from $N$ by adding one extra marking.\n We
also prove the splitting map is injective for any marked three manifold w
hen $v=1$\, and show that the splitting map is injective (for general $v$)
if there exists at least one component of $N$ such that this component an
d the boundary of the splitting disk belong to the same component of $\\pa
rtial M$.\n\n\nWe also establish the Frobenius homomorphism for $SL(n)$\,
which is map from $S_n(M\,N\,1)$ to $S_n(M\,N\,v)$ when $v$ is a primitiv
e $m$-th root of unity with $m$ being coprime with $2n$ and every compone
nt of $M$ contains at least one marking. \nWe also show the commutativity
between Frobenius homomorphism and splitting map. When $(M\,N)$ is the thi
ckening of an essentially bordered pb surface\, we prove the Frobenius hom
omorphism is injective and it's image lives in the center. We prove the st
ated $SL(n)$-skein algebra $S_n(\\Sigma\,v)$ is\naffine almost Azumaya whe
n $\\Sigma$ is an essentially bordered pb surface and $v$ is a primitive $
m$-th root of unity with $m$ being coprime with $2n$\, which implies the
Unicity Theorem for $S_n(\\Sigma\,v)$.\n
LOCATION:https://researchseminars.org/talk/Knotsandtopology/58/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Igor Nikonov
DTSTART:20240429T153000Z
DTEND:20240429T170000Z
DTSTAMP:20260422T230719Z
UID:Knotsandtopology/59
DESCRIPTION:Title: On universal parity on free two-dimensional knots\nby Igor N
ikonov as part of Knots and representation theory\n\n\nAbstract\nIn the ta
lk we review the definition of parity on 2-knots\, and prove that the Gaus
sian parity is universal on free two-dimensional knots.\n
LOCATION:https://researchseminars.org/talk/Knotsandtopology/59/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Александр Юрьевич Буряк
DTSTART:20240506T153000Z
DTEND:20240506T170000Z
DTSTAMP:20260422T230719Z
UID:Knotsandtopology/60
DESCRIPTION:Title: DR-иерархии: от пространств модулей
кривых к интегрируемым системам.\nby Ал
ександр Юрьевич Буряк as part of Knots and representati
on theory\n\n\nAbstract\nМы постараемся продемонст
рировать как DR-иерархии\, введённые докл
адчиком в одной из работ\, позволяют очен
ь ясным образом установить связь между
топологией компактификации Делиня-Мамф
орда пространства модулей гладких алгеб
раических кривых рода g с n отмеченными т
очками и интегрируемыми системами матем
атической физики. Эта связь основываетс
я на соотношении коммутативности между
циклами двойных ветвлений (DR-циклами) в п
ространстве модулей кривых произвольно
го рода\, которое является обобщением со
отношения ассоциативности в пространст
ве модулей кривых рода 0\, которое в свою
очередь тесно связано с теорией многооб
разий Дубровина-Фробениуса.\n
LOCATION:https://researchseminars.org/talk/Knotsandtopology/60/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Scott Baldridge
DTSTART:20240520T153000Z
DTEND:20240520T170000Z
DTSTAMP:20260422T230719Z
UID:Knotsandtopology/61
DESCRIPTION:Title: Why the Vertex Polynomial counts Tait colorings of a plane triva
lent graph when evaluated at two\nby Scott Baldridge as part of Knots
and representation theory\n\n\nAbstract\nThe vertex polynomial was introdu
ced in our 2024 paper but can be inferred from Penrose’s 1971 paper on a
bstract tensor systems. In this talk\, we give a gentle introduction to th
e vertex polynomial: what it means\, how to compute it\, why it counts Tai
t colorings (3-edge colorings) of a plane trivalent graph at n=2\, and wha
t it means when evaluated at n>2. In particular\, the four color theorem i
s true if and only if the vertex polynomial is nonzero when evaluated at n
=2 for all bridgeless planar trivalent graphs. Along the way\, we will see
how the homology that it categorifies can be used to count the number of
perfect matchings of a trivalent plane graph. This is joint work with Ben
McCarty.\n
LOCATION:https://researchseminars.org/talk/Knotsandtopology/61/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Романов Николай Алексеевич
DTSTART:20240527T153000Z
DTEND:20240527T170000Z
DTSTAMP:20260422T230719Z
UID:Knotsandtopology/62
DESCRIPTION:Title: Мозаики\, замощения и их преобразов
ания\nby Романов Николай Алексеевич as par
t of Knots and representation theory\n\n\nAbstract\nОбъект вним
ания - мозаики\, замощения и их преобразо
вания. Соотношения в группе можно с помо
щью диаграмм Ван Кампена представить ка
к выкладывание мозаики\, а соотношения м
ежду соотношениями - преобразования это
й мозаики. Например\, в замощении доминош
ками прямоугольника взять квадратик 2 на
2 из двух доминошек и развернуть его на п
ол оборота. Оказывается\, для некоторого
набора фигур можно найти такой набор пре
образований (флипов)\, что любое допустим
ое замощение любой фигуры переводится э
тими флипами в любое другое допустимое з
амощение. В работе были исследованы неко
торые фигуры и наборы флипов\, получены у
ниверсальные инварианты и найдены много
мерные аналоги мозаик\, преобразований и
соотношений\, получены оценки на минима
льное количество флипов\, необходимое дл
я перевода любого состояния в любое\, а т
ак же рассмотрены обобщения на графы.\n
LOCATION:https://researchseminars.org/talk/Knotsandtopology/62/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Igor Nikonov
DTSTART:20240603T133000Z
DTEND:20240603T150000Z
DTSTAMP:20260422T230719Z
UID:Knotsandtopology/63
DESCRIPTION:Title: Virtual index cocycles and invariants of virtual links\nby I
gor Nikonov as part of Knots and representation theory\n\n\nAbstract\nVirt
ual index cocycle is the 1-cochain that counts virtual crossings in the ar
cs of a virtual link diagram. We show how this cocycle can be used to refo
rmulate and unify some known invariants of virtual links.\n
LOCATION:https://researchseminars.org/talk/Knotsandtopology/63/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Huizheng Guo(Ali) (GWU)
DTSTART:20240610T153000Z
DTEND:20240610T170000Z
DTSTAMP:20260422T230719Z
UID:Knotsandtopology/64
DESCRIPTION:Title: From GKH to Incompressible surface\nby Huizheng Guo(Ali) (GW
U) as part of Knots and representation theory\n\n\nAbstract\nFor a reduced
alternating diagram of a knot with a prime determinant $p\,$ the Kauffman
-Harary conjecture states that every non-trivial Fox $p$-coloring of the k
not assigns different colors to its arcs. In 2022\, we prove a generalizat
ion of the conjecture stated nineteen years ago by Asaeda\, Przytycki\, an
d Sikora: for every pair of distinct arcs in the reduced alternating diagr
am of a prime link with determinant $\\delta\,$ there exists a Fox $\\delt
a$-coloring that distinguishes them.\nTo explore the geometric approach of
GKH\, we attempt to extend Mensaco's meridian theorem to double branched
cover of alternating prime non-split links by extending the "bubble constr
uction". In this presentation\, we explore the behaviors of lifted loops f
rom link complement in double branched cover along branching set $L$ in $S
^3$. What is more\, we also study properties of incompressible surface\, m
eridionally incompressible surface in such double branched cover and n-cyc
lic cover of link complement in $S^3$.\n
LOCATION:https://researchseminars.org/talk/Knotsandtopology/64/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hayk Sedrakyan
DTSTART:20240617T133000Z
DTEND:20240617T150000Z
DTSTAMP:20260422T230719Z
UID:Knotsandtopology/65
DESCRIPTION:Title: Sedrakyan-Mozayeni theorem and pentagon equestion calculations\nby Hayk Sedrakyan as part of Knots and representation theory\n\n\nAbst
ract\nIn the present work\, we prove the long-standing and important open
research question: the consistency for the general case discussed in the p
aper Photography principle\, data transmission\, and invariants of manifol
ds. Ptolemy's theorem works only for a particular case and does not work f
or a general case\, we prove the general case using Sedrakyan-Mozayeni the
orem and Sedrakyan-Gandhi theorem.\nDescription. The consistency for the p
articular case discussed in the paper Photography principle\, data transmi
ssion\, and invariants of manifolds is proved using Ptolemy's theorem. Pto
lemy's theorem is not a strong enough theorem to be applied to the general
case and no other stronger theorem is known that can be used to prove the
consistency for the general case. We use the novel Sedrakyan-Mozayeni the
orem and Sedrakyan-Gandhi theorem to prove the consistency for the most ge
neral case. It leads to an elegant proof of this long-standing and importa
nt open research question.\n
LOCATION:https://researchseminars.org/talk/Knotsandtopology/65/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Igor Nikonov
DTSTART:20240624T133000Z
DTEND:20240624T150000Z
DTSTAMP:20260422T230719Z
UID:Knotsandtopology/66
DESCRIPTION:Title: Parity functors\nby Igor Nikonov as part of Knots and repres
entation theory\n\n\nAbstract\nA parity is a rule to assign labels to the
crossings of knot diagrams in a way compatible with Reidemeister moves. Pa
rity functors can be viewed as parities which provide to each knot diagram
its own coefficient group that contains parities of the crossings. In the
talk we describe parity functors for free knots.\n
LOCATION:https://researchseminars.org/talk/Knotsandtopology/66/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Byeorhi Kim
DTSTART:20240701T133000Z
DTEND:20240701T150000Z
DTSTAMP:20260422T230719Z
UID:Knotsandtopology/67
DESCRIPTION:Title: On a smoothing strategy for topological surfaces in 4-manifolds<
/a>\nby Byeorhi Kim as part of Knots and representation theory\n\n\nAbstra
ct\nIn this talk\, I will talk about a new smoothing technique for topolog
ically embedded surfaces or disks in smooth 4-manifolds that provides topo
logical isotopies to smooth surfaces. This result is motivated from recent
David Gabai's Light bulb theorem. As an application\, we can get some res
ults which leading us to "topological = smooth" in dimension 4 for isotopy
classifications of certain disks and spheres. This is a joint work with J
. C. Cha.\n
LOCATION:https://researchseminars.org/talk/Knotsandtopology/67/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Igor Nikonov
DTSTART:20240708T133000Z
DTEND:20240708T150000Z
DTSTAMP:20260422T230719Z
UID:Knotsandtopology/68
DESCRIPTION:Title: Biquandloids of knots in thickened surfaces\nby Igor Nikonov
as part of Knots and representation theory\n\n\nAbstract\nWe define a mod
ification of biquandle construction for knots in a fixed thickened surface
and give several examples of the new invariant.\n
LOCATION:https://researchseminars.org/talk/Knotsandtopology/68/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Renaud Detcherry
DTSTART:20240729T133000Z
DTEND:20240729T150000Z
DTSTAMP:20260422T230719Z
UID:Knotsandtopology/69
DESCRIPTION:Title: On torsion in the Kauffman bracket skein modules of 3-manifolds<
/a>\nby Renaud Detcherry as part of Knots and representation theory\n\n\nA
bstract\nThe Kauffman bracket skein module S(M) of an oriented 3-manifold
M is an object that describes the combinatorics of links in M\, and which
is closely related to Jones polynomials of links in S^3 and to SL2(C)-char
acter varieties of 3-manifolds.\nAn old question of Przytycki asks whether
for M a 3-manifold that admits a non-boundary parallel essential surface\
, there is torsion in S(M). We will present new criterions for the presenc
e of torsion in S(M). In particular\, we give the first examples of closed
3-manifolds without spheres or tori such that S(M) has torsion. We also s
how that if a Seifert manifold M has a non-boudnary parallel essential sur
face\, then S(M) has torsion.\n
LOCATION:https://researchseminars.org/talk/Knotsandtopology/69/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hyungtae Baek
DTSTART:20240715T133000Z
DTEND:20240715T150000Z
DTSTAMP:20260422T230719Z
UID:Knotsandtopology/70
DESCRIPTION:Title: Hilbert basis theorem for $S$-Noetherian modules and $S$-strong
Mori modules\nby Hyungtae Baek as part of Knots and representation the
ory\n\n\nAbstract\nLet $R$ be a commutative ring with identity\, $D$ an in
tegral domain\, and $M$ a module over $R$ or $D$.\n\nIn 1899\, David Hilbe
rt proved the Hilbert basis theorem:\n$R$ is a Noetherian ring if and only
if\n$R[X]$ is a Noetherian ring.\nThis theorem is a fundamental result\ni
n commutative algebra and algebraic geometry.\n\nMany ring theorists have
generalized Noetherian rings\nand the Hilbert basis theorem to such genera
lizations.\n\nIn this talk\, we investigate $S$-Noetherian modules and\n$S
$-strong Mori modules\,\nand explore the Hilbert basis theorem for such mo
dules.\nTo do this\, we delve into the concept of star-operations (specifi
cally $w$-operations).\n\nThe main goal of this talk is to address the fol
lowing problems:\n\\begin{enumerate}\n\\item[(1)] When is $M$ an $S$-Noeth
erian module?\n\\item[(2)] When is $M$ an $S$-strong Mori module?\n\\end{e
numerate}\n
LOCATION:https://researchseminars.org/talk/Knotsandtopology/70/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bart Vlaar
DTSTART:20240819T133000Z
DTEND:20240819T150000Z
DTSTAMP:20260422T230719Z
UID:Knotsandtopology/71
DESCRIPTION:Title: Cylindrical structures arising from quantum symmetric pairs\
nby Bart Vlaar as part of Knots and representation theory\n\n\nAbstract\nR
-matrices (solutions of the Yang-Baxter equation) and quantum groups are i
ntimately connected and find applications in mathematical physics\, repres
entation theory\, low-dimensional topology and algebraic geometry. K-matri
ces (solutions of the reflection equation) and quantum deformations of sym
metric pairs form a vast generalization\, under development since the 1990
s. We survey this and discuss some results on the case of quantum groups a
nd quantum symmetric pairs of affine type (joint work with Andrea Appel).\
n
LOCATION:https://researchseminars.org/talk/Knotsandtopology/71/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jean-Marc Schlenker
DTSTART:20240909T153000Z
DTEND:20240909T170000Z
DTSTAMP:20260422T230719Z
UID:Knotsandtopology/72
DESCRIPTION:Title: Polyhedra inscribed in a quadric\nby Jean-Marc Schlenker as
part of Knots and representation theory\n\n\nAbstract\nSteiner asked in 18
32 what are the combinatorial types of polyhedra with vertices on a quadri
c. We will survey what is known on this question\, and show how recent res
ults are based on studying ideal polyhedra in different geometries. Hodgso
n\, Rivin and Smith characterized the combinatorics of polyhedra inscribed
in a sphere using properties of ideal hyperbolic polyhedra. More recently
we described the combinatorics of polyhedra inscribed in a one-sheeted hy
perboloid or cone\, using properties of ideal polyhedra in the anti-de Sit
ter and Half-pipe spaces. Further results describe the combinatorial types
of polyhedra "weakly inscribed" in a two-sheeted hyperboloid (that is\, w
ith their vertices on it but not entirely on one side)\, using a natural e
xtension of hyperbolic space by the de Sitter space. The same question for
the one-sheeted hyperboloid remains open.\nJoint work with Jeff Danciger
and Sara Maloni.\n
LOCATION:https://researchseminars.org/talk/Knotsandtopology/72/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jae-baek Lee
DTSTART:20240805T143000Z
DTEND:20240805T160000Z
DTSTAMP:20260422T230719Z
UID:Knotsandtopology/73
DESCRIPTION:Title: Disconnected common graphs via supersaturation and beyond\nb
y Jae-baek Lee as part of Knots and representation theory\n\n\nAbstract\nA
graph $H$ is said to be \\emph{common} if the number of labelled monochro
matic copies of $H$ in a $2$-colouring of the edges of a large complete gr
aph is asymptotically minimized by a random colouring. It is well known th
at the disjoint union of two common graphs may not be common\; e.g.\, $K_2
$ and $K_3$ are common\, but their disjoint union is not. We find the firs
t pair of uncommon graphs whose disjoint union is common and a common grap
h and an uncommon graph whose disjoint union is common. Our approach is to
reduce the problem of showing that certain disconnected graphs are common
to a constrained optimization problem\, in which the constraints are deri
ved from supersaturation bounds related to Razborov's Triangle Density The
orem. \nIn addition\, we will introduce the recent results related to Rams
ey multiplicity constant. \nThis is joint work with Joseph Hyde and Jonat
han Noel.\n
LOCATION:https://researchseminars.org/talk/Knotsandtopology/73/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Igor Nikonov
DTSTART:20240812T153000Z
DTEND:20240812T170000Z
DTSTAMP:20260422T230719Z
UID:Knotsandtopology/74
DESCRIPTION:Title: Virtual index cocycles and invariants of virtual links\nby I
gor Nikonov as part of Knots and representation theory\n\n\nAbstract\nVirt
ual index cocycle is the 1-cochain that counts virtual crossings in the ar
cs of a virtual link diagram. We show how this cocycle can be used to refo
rmulate and unify some known invariants of virtual links.\n
LOCATION:https://researchseminars.org/talk/Knotsandtopology/74/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Guowei Wei
DTSTART:20240923T153000Z
DTEND:20240923T170000Z
DTSTAMP:20260422T230719Z
UID:Knotsandtopology/75
DESCRIPTION:Title: Topological deep learning: The past\, present\, and future\n
by Guowei Wei as part of Knots and representation theory\n\n\nAbstract\nIn
the past few years\, topological deep learning (TDL)\, a term coined by u
s in 2017\, has become an emerging paradigm in artificial intelligence (AI
). TDL is built on persistent homology (PH)\, an algebraic topology techni
que that bridges the gap between complex geometry and abstract topology th
rough multiscale analysis. While TDL has made huge strides in a wide varie
ty of scientific and engineering disciplines\, its most compelling success
was observed in biosciences with intrinsically high dimensional and intri
cately complex data. I will discuss the limitations/ challenges of TDL and
new approaches based on algebraic topology\, geometric topology and diffe
rential geometry may tackle these challenges. I will also discuss how topo
logy is enabling AI and how AI is assisting topological reasoning.\n
LOCATION:https://researchseminars.org/talk/Knotsandtopology/75/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Qiuyu Ren
DTSTART:20240930T133000Z
DTEND:20240930T150000Z
DTSTAMP:20260422T230719Z
UID:Knotsandtopology/76
DESCRIPTION:by Qiuyu Ren as part of Knots and representation theory\n\nAbs
tract: TBA\n
LOCATION:https://researchseminars.org/talk/Knotsandtopology/76/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrey M. Elishev
DTSTART:20240826T133000Z
DTEND:20240826T150000Z
DTSTAMP:20260422T230719Z
UID:Knotsandtopology/77
DESCRIPTION:Title: On Automorphisms of Tame Polynomial Automorphism Ind-Schemes in
Positive Characteristic\nby Andrey M. Elishev as part of Knots and rep
resentation theory\n\n\nAbstract\nLet $n\\geq 3$ and let $K$ be an algebra
ically closed field. When the characteristic of $K$ is zero\, a classical
theorem of Anick states that tame $K$-algebra automorphisms of $K[x_1\,\\l
dots\, x_n]$ approximate polynomial endomorphisms with constant non-zero J
acobian in the power series topology. This fact has been at the center of
one of the more promising approaches to the Jacobian Conjecture and\, in a
related development (cf. https://www.worldscientific.com/doi/abs/10.1142/
S0218196718400040)\, has allowed for a description of the set $\\Aut_{Ind}
\\Aut K[x_1\,\\ldots\, x_n]$ of automorphisms of $\\Aut K[x_1\,\\ldots\, x
_n]$ preserving the Ind-scheme structure. My talk will focus on a few fine
r details of the positive-characteristic extension of the aforementioned w
ork\, compiled in https://arxiv.org/abs/2103.12784\, together with its imp
lications for some of the tougher open problems in the area. Joint work wi
th A. Kanel-Belov and J.-T. Yu.\n
LOCATION:https://researchseminars.org/talk/Knotsandtopology/77/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Igor M. Nikonov
DTSTART:20240902T133000Z
DTEND:20240902T150000Z
DTSTAMP:20260422T230719Z
UID:Knotsandtopology/78
DESCRIPTION:Title: Flat-virtual knot: introduction and some invariants\nby Igor
M. Nikonov as part of Knots and representation theory\n\n\nAbstract\nIn a
ttempts to construct a map from classical knots to virtual ones\, we defin
e a series of maps from knots in the full torus (thickened torus) to flat-
virtual knots. We give definition of flat-virtual knots and presents Alexa
nder-like polynomial and Kauffman bracket for them. We also discuss a poss
ible extension of the notion of flat-virtual knots — so-called multi-fla
t knots.\n
LOCATION:https://researchseminars.org/talk/Knotsandtopology/78/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anup Poudel
DTSTART:20240916T133000Z
DTEND:20240916T150000Z
DTSTAMP:20260422T230719Z
UID:Knotsandtopology/79
DESCRIPTION:Title: Lie Superalgebra generalizations of the JKS-invariant]{Lie Super
algebra generalizations of the Jaeger-Kauffman-Saleur Invariant\nby An
up Poudel as part of Knots and representation theory\n\n\nAbstract\nJaeger
-Kauffman-Saleur (JKS) identified the Alexander polynomial with the $U_q(
\\mathfrak{gl}(1|1))$ quantum invariant of classical links and extended t
his to a 2-variable invariant of links in thickened surfaces. Here we gen
eralize this story for every Lie superalgebra of type $\\mathfrak{gl}(m|n
)$. First\, we define a $U_q(\\mathfrak{gl}(m|n))$ Reshetikhin-Turaev inv
ariant for virtual tangles. When $m=n=1$\, this recovers the Alexander po
lynomial of almost classical knots\, as defined by Boden-Gaudreau-Harper
-Nicas-White. Next\, an extended $U_q(\\mathfrak{gl}(m|n))$ Reshetikin-Tu
raev invariant of virtual tangles is obtained by applying the Bar-Natan
Zh-construction. This is equivalent to the 2-variable JKS-invariant when
$m=n=1$\, but otherwise our invariants are new whenever $n>0$. Furthermo
re\, in contrast with the classical case\, the virtual and extended $U_q(
\\mathfrak{gl}(m|n))$ invariants are not entirely determined by the diffe
rence $m-n$. For example\, the invariants from $U_q(\\mathfrak{gl}(2|0))$
(i.e. the classical Jones polynomial) and $U_q(\\mathfrak{gl}(3|1))$ are
distinct\, as are the extended invariants from $U_q(\\mathfrak{gl}(1|1))
$ and $U_q(\\mathfrak{gl}(2|2))$. Further applications and conjectures b
ased on calculations will be discussed. This is a joint work with Micah
Chrisman.\n
LOCATION:https://researchseminars.org/talk/Knotsandtopology/79/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anton Dzhamay
DTSTART:20241014T153000Z
DTEND:20241014T170000Z
DTSTAMP:20260422T230719Z
UID:Knotsandtopology/80
DESCRIPTION:Title: Geometry of Discrete Integrable Systems: QRT Maps and Discrete P
ainlevé Equations\nby Anton Dzhamay as part of Knots and representati
on theory\n\n\nAbstract\nMany interesting examples of discrete integrable
systems can be studied from the geometric point of view. In this talk we w
ill consider two classes of examples of such system: autonomous (QRT maps)
and non-autonomous (discrete Painlevé equations). We introduce some geom
etric tools to study these systems\, such as the blowup procedure to const
ruct algebraic surfaces on which the mappings are regularized\, linearizat
ion of the mapping on the Picard lattice of the surface and\, for discrete
Painlevé equations\, the decomposition of the Picard lattice into comple
mentary pairs of the surface and symmetry sub-lattices and construction of
a birational representation of affine Weyl symmetry groups that gives a c
omplete algebraic description of our non-linear dynamic.\n\nThis talk is b
ased on joint work with Stefan Carstea (Bucharest) and Tomoyuki Takenawa (
Tokyo).\n
LOCATION:https://researchseminars.org/talk/Knotsandtopology/80/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Igor Nikonov
DTSTART:20241007T153000Z
DTEND:20241007T170000Z
DTSTAMP:20260422T230719Z
UID:Knotsandtopology/81
DESCRIPTION:Title: On universal parity on free two-dimensional knots\nby Igor N
ikonov as part of Knots and representation theory\n\n\nAbstract\nIn the ta
lk we review the definition of parity on 2-knots\, and prove that the Gaus
sian parity is universal on free two-dimensional knots.\n
LOCATION:https://researchseminars.org/talk/Knotsandtopology/81/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tumpa Mahato
DTSTART:20241021T153000Z
DTEND:20241021T170000Z
DTSTAMP:20260422T230719Z
UID:Knotsandtopology/82
DESCRIPTION:Title: Parameterization and non-triviality of knotted surfaces arising
from 1-dimensional knots\nby Tumpa Mahato as part of Knots and represe
ntation theory\n\n\nAbstract\nAlthough we study knotted surfaces using dia
grams and braids\, visualizing is very important\nto understand these abst
ract mathematical objects. Therefore\, parameterizing these\nembeddings of
2-manifolds using elementary functions becomes crucial not only for compu
ting\ninvariants but also to provide a machinery to visualize and interact
with these objects.\nIn this talk\, we will provide a concrete parameteri
zation of a few class of knotted surfaces\,\ncalled using elementary funct
ions.\nMoreover\, we will discuss the non-triviality of a specific class o
f surface knots called ribbon\ntorus knots by using its connection with we
lded knots by S. Satoh’s Tube map. We will\nexplore the non-triviality o
f welded knots by studying a welded knot invariant\, called welded\nunknot
ting number and utilize those results to examine the non-triviality of rib
bon torus\nknots.\n
LOCATION:https://researchseminars.org/talk/Knotsandtopology/82/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Seongjeong Kim
DTSTART:20241028T153000Z
DTEND:20241028T170000Z
DTSTAMP:20260422T230719Z
UID:Knotsandtopology/83
DESCRIPTION:Title: The Kauffman bracket skein module of $\\mathbf {(S^1 \\times S^2
) \\ \\# \\ (S^1 \\times S^2)}$: another counterexample of Marche’s conj
ecture\nby Seongjeong Kim as part of Knots and representation theory\n
\n\nAbstract\nDetermining the structure of the Kauffman bracket skein modu
le of all $3$-manifolds over the ring of Laurent polynomials $\\mathbb Z[A
^{\\pm 1}]$ is a big open problem in skein theory. Very little is known ab
out the skein module of non-prime manifolds over this ring. In this paper\
, we compute the Kauffman bracket skein module of the $3$-manifold $(S^1 \
\times S^2) \\ \\# \\ (S^1 \\times S^2)$ over the ring $\\mathbb Z[A^{\\pm
1}]$. We do this by analysing the submodule of handle sliding relations\,
for which we provide a suitable basis. Along the way we also compute the
Kauffman bracket skein module of $(S^1 \\times S^2) \\ \\# \\ (S^1 \\times
D^2)$. Furthermore\, we show that the skein module of $(S^1 \\times S^2)
\\ \\# \\ (S^1 \\times S^2)$ does not split into the sum of free and torsi
on submodules.\n
LOCATION:https://researchseminars.org/talk/Knotsandtopology/83/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michael Shapiro
DTSTART:20241216T153000Z
DTEND:20241216T170000Z
DTSTAMP:20260422T230719Z
UID:Knotsandtopology/85
DESCRIPTION:Title: Goldman bracket and cluster algebra\nby Michael Shapiro as p
art of Knots and representation theory\n\n\nAbstract\nWe remind the defini
tion of Goldman Poisson bracket on the space of local systems on a surface
and its relation to cluster algebras of triangulated surfaces.\n
LOCATION:https://researchseminars.org/talk/Knotsandtopology/85/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Igor Nikonov
DTSTART:20241104T153000Z
DTEND:20241104T170000Z
DTSTAMP:20260422T230719Z
UID:Knotsandtopology/86
DESCRIPTION:Title: Flat-virtual knots: an introduction and some invariants\nby
Igor Nikonov as part of Knots and representation theory\n\n\nAbstract\nWe
define a series of maps from knots in the full torus (and thickened torus)
to flat-virtual knots. We give definition of flat-virtual knots and prese
nts Alexander-like polynomial and Kauffman bracket for them. We also discu
ss a possible extension of the notion of flat-virtual knots — so-called
multi-flat knots.\n
LOCATION:https://researchseminars.org/talk/Knotsandtopology/86/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Oscar Ocampo
DTSTART:20241125T153000Z
DTEND:20241125T170000Z
DTSTAMP:20260422T230719Z
UID:Knotsandtopology/87
DESCRIPTION:Title: Characteristic subgroups and the R$_\\infty$-property for virtua
l braid groups\nby Oscar Ocampo as part of Knots and representation th
eory\n\n\nAbstract\nThere is currently a growing interest in the study of
groups having the R$_\\infty$-property (the study of their twisted conjuga
cy classes)\, it finds their origins in algebraic topology and to be more
precise in Nielsen–Reidemeister fixed point theory.\nLet $n\\geq 2$. Let
$VB_n$ (resp.\\ $VP_n$) denote the virtual braid group (resp.\\ virtual p
ure braid group)\, let $WB_n$ (resp.\\ $WP_n$) denote the welded braid gro
up (resp.\\ welded pure braid group) and let $UVB_n$ (resp.\\ $UVP_n$) den
ote the unrestricted virtual braid group (resp.\\ unrestricted virtual pur
e braid group).\nIn the first part of this talk we prove that\, for $n\\ge
q 4$\, the group $VP_n$ and for $n\\geq 3$ the groups $WP_n$ and $UVP_n$ a
re characteristic subgroups of $VB_n$\, $WB_n$ and $UVB_n$\, respectively.
\nIn the second part of the talk we show that\, for $n\\geq 2$\, the virtu
al braid group $VB_n$\, the unrestricted virtual pure braid group $UVP_n$\
, and the unrestricted virtual braid group $UVB_n$ have the R$_\\infty$-pr
operty.\nJoint work with Daciberg Lima Gonçalves and Karel Dekimpe.\n
LOCATION:https://researchseminars.org/talk/Knotsandtopology/87/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Fedor Nilov
DTSTART:20241111T153000Z
DTEND:20241111T170000Z
DTSTAMP:20260422T230719Z
UID:Knotsandtopology/88
DESCRIPTION:Title: Webs from lines and circles\nby Fedor Nilov as part of Knots
and representation theory\n\n\nAbstract\nThree sets of curves in a domain
is a hexagonal 3-web\, if there is a diffeomorphism f which takes the s
ets of segments parallel to the sides of a fixed triangle. In 1938 \nW. Bl
aschke and G. Bol stated the problem of classification of all hexagonal 3
-webs from lines and circles. This problem is still open. We will discuss
the current status of the problem and related questions.\n
LOCATION:https://researchseminars.org/talk/Knotsandtopology/88/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ben Mccarty
DTSTART:20241223T153000Z
DTEND:20241223T170000Z
DTSTAMP:20260422T230719Z
UID:Knotsandtopology/89
DESCRIPTION:Title: What does the Penrose polynomial actually count?\nby Ben Mcc
arty as part of Knots and representation theory\n\n\nAbstract\nThe Penrose
polynomial P(G\,n) famously counts 3-edge colorings when G is a planar tr
ivalent graph and the polynomial is evaluated at n=3. However\, for graph
s that are not trivalent\, and for other values of n\, what it counts has
been harder to describe. In this talk we show that a shift in perspective
toward face colorings on a set of ribbon graphs allows one to obtain a co
mplete characterization of the Penrose polynomial for n>0. This character
ization utilizes an understanding of the filtered n-color homology\, which
will be briefly described in the talk.\n\nThis is joint work with Scott B
aldridge.\n
LOCATION:https://researchseminars.org/talk/Knotsandtopology/89/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tumpa Mahato
DTSTART:20241202T153000Z
DTEND:20241202T170000Z
DTSTAMP:20260422T230719Z
UID:Knotsandtopology/90
DESCRIPTION:Title: Isolated-region number of a link projection\nby Tumpa Mahato
as part of Knots and representation theory\n\n\nAbstract\nA set of region
s of a link projection is said to be isolated if any pair of regions in th
e set share no crossings. The isolate-region number of a link projection i
s the maximum value of the cardinality for isolated sets of regions of the
link projection.\nThis talk involves various results for computing isolat
e-region number and its relation with warping degree and welded unknotting
number of a knot.\n
LOCATION:https://researchseminars.org/talk/Knotsandtopology/90/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Seongjeong Kim
DTSTART:20241118T153000Z
DTEND:20241118T170000Z
DTSTAMP:20260422T230719Z
UID:Knotsandtopology/91
DESCRIPTION:Title: The groups $G_{n}^{k}$\, $2n$-gon tilings\, and stacking of cube
s\nby Seongjeong Kim as part of Knots and representation theory\n\n\nA
bstract\nIn the present talk we discuss three ways of looking at rhombile
tilings: stacking 3-dimensional cubes\, elements of groups\, and configura
tions of lines and points.\n
LOCATION:https://researchseminars.org/talk/Knotsandtopology/91/
END:VEVENT
BEGIN:VEVENT
SUMMARY:André Henriques
DTSTART:20241209T153000Z
DTEND:20241209T170000Z
DTSTAMP:20260422T230719Z
UID:Knotsandtopology/92
DESCRIPTION:Title: What kind of thing is... Rep(G)?\nby André Henriques as par
t of Knots and representation theory\n\n\nAbstract\nWhat kind of mathemati
cal object is the category of representations of a group? The answer depen
ds on what kind of group we're considering: finite / algebraic / topologic
al / etc... In all cases\, after having axiomatised the kind of categorie
s that look like Rep(G)\, a surprisingly fruitful question is to ask wheth
er there are other categories that satisfy all the same axioms\, but are n
ot of the form Rep(G).\n
LOCATION:https://researchseminars.org/talk/Knotsandtopology/92/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sandip Samanta
DTSTART:20241230T153000Z
DTEND:20241230T170000Z
DTSTAMP:20260422T230719Z
UID:Knotsandtopology/93
DESCRIPTION:Title: Associahedra and Its Combinatorial Isomorphism to Three Other Mo
dels\nby Sandip Samanta as part of Knots and representation theory\n\n
\nAbstract\nAssociahedra (or Stasheff polytopes) were first introduced by
Stasheff in his thesis to define the notion of A_n-spaces. Over time\, the
se polytopes have continued to appear in various studies\, including A_n-m
aps and moduli spaces\, due to their rich combinatorial structures. In thi
s talk\, we will explore three additional models of these polytopes: Loday
's cone construction\, collapsed multiplihedra\, and graph cubeahedra\, an
d examine the combinatorial isomorphism between them.\nThis is based on a
joint work with Dr. Somnath Basu.\n
LOCATION:https://researchseminars.org/talk/Knotsandtopology/93/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Protasov Vladimir (University of L’Aquila (Italy)\, Moscow State
University (Russia))
DTSTART:20250113T153000Z
DTEND:20250113T170000Z
DTSTAMP:20260422T230719Z
UID:Knotsandtopology/94
DESCRIPTION:Title: The Newton aerodynamic problem: after 300 years all over again
\nby Protasov Vladimir (University of L’Aquila (Italy)\, Moscow Stat
e University (Russia)) as part of Knots and representation theory\n\n\nAbs
tract\nIn 1687 Isaac Newton in his main work ``Principia'' posed the follo
wing Aerodynamic Problem: find the convex surface of the minimal front
al resistance during its uniform motion through an inviscid and incompr
essible medium. The surface must contain a given disc orthogonal to the ve
ctor of velocity and have a given altitude. The solution of Newton bec
ame a classical example in the calculus of variations. However\, in early
1990s G.Butazzo\, D.Kawohl\, and P.Guasoni presented a surface of a sm
aller resistance. They showed that the optimality of Newtons's surface con
cerns only a special case (although\, considered to be general by most
of specialists). The aerodynamic problem had to be solved again under g
eneral assumptions\, which turned out to be a hard task. The solution
is still unknown\, although some properties of the optimal surface have be
en established. \n \nWe give a survey of some of the known results inc
luding construction of non-convex surfaces of arbitrary small resistance
and of invisible surfaces. Then we present a new approach to analyze the
optimal convex surface by using inequalities between derivatives. Some
of these inequalities are\, probably\, of independent interest. \n \nTh
is is a joint work with A.Plakhov (University of Aveiro\, Portugal)\n
LOCATION:https://researchseminars.org/talk/Knotsandtopology/94/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Igor Nikonov
DTSTART:20250106T153000Z
DTEND:20250106T170000Z
DTSTAMP:20260422T230719Z
UID:Knotsandtopology/95
DESCRIPTION:Title: On skein invariants\nby Igor Nikonov as part of Knots and re
presentation theory\n\n\nAbstract\nIt is known that some knot invariants c
an be defined by relations (called skein relations) on diagrams which diff
er at a local site. Among skein invariants one can mention Alexander and J
ones polynomials\, Arf invariant and writhe polynomial. In the talk we wil
l remind these and other examples of skein invariants and introduce a new
skein invariant for links in a fixed thickened surface.\n
LOCATION:https://researchseminars.org/talk/Knotsandtopology/95/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mark Powell
DTSTART:20250127T153000Z
DTEND:20250127T170000Z
DTSTAMP:20260422T230719Z
UID:Knotsandtopology/96
DESCRIPTION:Title: Classification of 4-manifolds with infinite dihedral fundamental
group.\nby Mark Powell as part of Knots and representation theory\n\n
\nAbstract\nI will discuss the homotopy classification of 4-manifolds with
certain fundamental groups\, before focusing on the case of infinite dihe
dral fundamental group.\nIn this case we have been able to upgrade the hom
otopy classification to a homeomorphism classification. \nAfter explainin
g these classifications\, I will then discuss\, in detail\, a key pair of
examples that are homotopy equivalent but not homeomorphic.\n
LOCATION:https://researchseminars.org/talk/Knotsandtopology/96/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Николай Романов
DTSTART:20250120T153000Z
DTEND:20250120T170000Z
DTSTAMP:20260422T230719Z
UID:Knotsandtopology/97
DESCRIPTION:Title: Хеширование и антихеширование.\nb
y Николай Романов as part of Knots and representation theory
\n\n\nAbstract\nНа занятии рассмотрим разные ме
тоды хеширования\, вероятностные и генер
ационные способы поиска коллизий и спос
обы (относительно) быстрого расхеширова
ния и общие методы взлома хешей. Затем по
грузимся в вычислительную геометрию\, оп
тимизацию\, посмотрим\, как хеширование п
омогает реализовывать быстрые поисковы
е алгоритмы в динамических системах и то
как эти динамические системы вредят хеш
ированию.\n
LOCATION:https://researchseminars.org/talk/Knotsandtopology/97/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pramod Padmanabhan
DTSTART:20250210T153000Z
DTEND:20250210T170000Z
DTSTAMP:20260422T230719Z
UID:Knotsandtopology/98
DESCRIPTION:Title: Universal methods to solve higher simplex equations\nby Pram
od Padmanabhan as part of Knots and representation theory\n\n\nAbstract\nA
brief introduction to the Yang-Baxter\, tetrahedron and other higher simp
lex equations in physics and mathematics will be given\, especially from t
he point of view of exactly solvable statistical mechanical models. Follow
ing this we will explain different methods developed to solve all of these
higher simplex equations. The methods are algebraic and they yield repres
entation independent solutions to these operator equations. Some of the al
gebras include Clifford algebras\, the algebra of Majorana fermions and th
e algebra of complex Dirac fermions.\n\nThe talk will mostly be based on h
ttps://arxiv.org/abs/2404.11501 and https://arxiv.org/abs/2410.20328.\n
LOCATION:https://researchseminars.org/talk/Knotsandtopology/98/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrew Bartholomew
DTSTART:20250217T153000Z
DTEND:20250217T170000Z
DTSTAMP:20260422T230719Z
UID:Knotsandtopology/99
DESCRIPTION:Title: Using biracks to extract invariants of knots\nby Andrew Bart
holomew as part of Knots and representation theory\n\n\nAbstract\nWe prese
nt a polynomial invariant based on labelling a knot diagram with a birack
rather than a biquandle as is the usual case. The polynomial is an invari
ant of a class of knot theories amenable to a generalisation of theorem of
Trace on regular homotopy\, which we describe. We also take the opportun
ity to reprise the relevant generalised knot theory and the theory of gene
ralised biracks in the light of this work and recent developments.\n
LOCATION:https://researchseminars.org/talk/Knotsandtopology/99/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mikhail Khovanov
DTSTART:20250331T153000Z
DTEND:20250331T170000Z
DTSTAMP:20260422T230719Z
UID:Knotsandtopology/100
DESCRIPTION:Title: Webs and foams in historical perspective\nby Mikhail Khovan
ov as part of Knots and representation theory\n\n\nAbstract\nWe will revie
w webs\, starting with the work of Kauffman and Murakami-Ohtsuki-Yamada an
d\nexplain how categorification of webs led to foams. A sketch of the cons
truction of a TQFT for foams from the Robert-Wagner evaluation and from ma
trix factorizations will be given\, as well as application to the construc
tion of link homology.\n
LOCATION:https://researchseminars.org/talk/Knotsandtopology/100/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mukilraj K
DTSTART:20250224T153000Z
DTEND:20250224T170000Z
DTSTAMP:20260422T230719Z
UID:Knotsandtopology/102
DESCRIPTION:Title: Loop homology of some highly connected manifold\nby Mukilra
j K as part of Knots and representation theory\n\n\nAbstract\nChas and Sul
livan showed that $H_*(LM)$ of a closed oriented manifold forms Batalin-Vi
lkovisky algebra. It is also well known that $H_*(LX)$ is in many ways con
nected to the Hochshchild (co)homology. We will use one of such connection
s to compute $H_*(LX)$ where $X$ is a $S^2$ bundle over $S^2$. We will als
o try to visualize some homology classes of $L(S^2)$.\n
LOCATION:https://researchseminars.org/talk/Knotsandtopology/102/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Manpreet Singh
DTSTART:20250317T153000Z
DTEND:20250317T170000Z
DTSTAMP:20260422T230719Z
UID:Knotsandtopology/103
DESCRIPTION:Title: On the Cohomology Theory of Twisted Yang-Baxter Sets\nby Ma
npreet Singh as part of Knots and representation theory\n\n\nAbstract\nIn
this talk\, I will introduce twisted set-theoretic Yang-Baxter solutions a
nd develop a corresponding cohomology theory. This extends the standard co
homology theory of Yang-Baxter solutions. Moreover\, I will explain how th
ese structures and their cocycles can be used to study knots. This is join
t work with Professor Mohamed Elhamdadi.\n
LOCATION:https://researchseminars.org/talk/Knotsandtopology/103/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Igor Nikonov
DTSTART:20250303T153000Z
DTEND:20250303T170000Z
DTSTAMP:20260422T230719Z
UID:Knotsandtopology/104
DESCRIPTION:Title: Flat-virtual knot: introduction and some invariants\nby Igo
r Nikonov as part of Knots and representation theory\n\n\nAbstract\nIn att
empts to construct a map from classical knots to virtual ones\, we define
a series of maps from knots in the full torus (thickened torus) to flat-vi
rtual knots. We give definition of flat-virtual knots and presents Alexand
er-like polynomial and Kauffman bracket for them. We also discuss a possib
le extension of the notion of flat-virtual knots — so-called multi-flat
knots.\n
LOCATION:https://researchseminars.org/talk/Knotsandtopology/104/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Seongjeong Kim
DTSTART:20250310T153000Z
DTEND:20250310T170000Z
DTSTAMP:20260422T230719Z
UID:Knotsandtopology/105
DESCRIPTION:Title: On the Kauffman bracket skein module of $\\mathbf {(S^1 \\time
s S^2) \\ \\# \\ (S^1 \\times S^2)}$\nby Seongjeong Kim as part of Kno
ts and representation theory\n\n\nAbstract\nDetermining the structure of t
he Kauffman bracket skein module of all $3$-manifolds over the ring of Lau
rent polynomials $\\mathbb Z[A^{\\pm 1}]$ is a big open problem in skein t
heory. Very little is known about the skein module of non-prime manifolds
over this ring. In this paper\, we compute the Kauffman bracket skein modu
le of the $3$-manifold $(S^1 \\times S^2) \\ \\# \\ (S^1 \\times S^2)$ ove
r the ring $\\mathbb Z[A^{\\pm 1}]$. We do this by analysing the submodule
of handle sliding relations\, for which we provide a suitable basis. Alon
g the way we compute the Kauffman bracket skein module of $(S^1 \\times S^
2) \\ \\# \\ (S^1 \\times D^2)$. We also show that the skein module of $(S
^1 \\times S^2) \\ \\# \\ (S^1 \\times S^2)$ does not split into the sum o
f free and torsion submodules. Furthermore\, we illustrate two families of
torsion elements in this skein module.\n\nThis is joint work with Rhea Pa
lak Bakshi\, Shangjun Shi\, and Xiao Wang.\n
LOCATION:https://researchseminars.org/talk/Knotsandtopology/105/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Igor Nikonov
DTSTART:20250324T153000Z
DTEND:20250324T170000Z
DTSTAMP:20260422T230719Z
UID:Knotsandtopology/106
DESCRIPTION:Title: Invariants of links through Gnk\nby Igor Nikonov as part of
Knots and representation theory\n\n\nAbstract\nV.O. Manturov introduced a
family of groups $G^k_n$ for two positive integers $n\, k$ and formulated
the following principle:\n \nIf dynamical systems describing a motion of
n particles has a nice codimension 1 property governed exactly by $k$ part
icles then these dynamical systems have a topological invariant valued in
$G^k_n$.\n \nThe first main example is an invariant of braids valued in $G
^3_n$. A very attractive question is how to construct invariants of knots
or links\, objects which can not be described by a motion of fixed number
of points\, which do not form a group. To solve this question for links\,
we look at links as equivalence classes of braids modulo Markov moves and
apply this consideration to the construction of MN-indices on the groups $
G^k_n$.\n
LOCATION:https://researchseminars.org/talk/Knotsandtopology/106/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anna Taranenko
DTSTART:20250407T153000Z
DTEND:20250407T170000Z
DTSTAMP:20260422T230719Z
UID:Knotsandtopology/107
DESCRIPTION:Title: Multidimensional matrices in algebraic hypergraph theory\nb
y Anna Taranenko as part of Knots and representation theory\n\n\nAbstract\
nThe main goal of the presented study is to develop methods for working wi
th multidimensional matrices that can be applied to problems of existence
and enumeration of various structures in hypergraphs. Many results in the
search for substructures in graphs are based on certain correspondences be
tween graphs and matrices and the application of linear algebra methods. A
mong the most important topics in the combinatorial matrix theory are the
representation of graphs using adjacency and incidence matrices\, the Koni
g-Hall theorem for systems of distinct representatives\, the permanents of
doubly stochastic matrices\, and Latin squares. We generalize these direc
tions to multidimensional matrices and hypergraphs and lay the foundations
of the combinatorial theory of multidimensional matrices.\n
LOCATION:https://researchseminars.org/talk/Knotsandtopology/107/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Seongjeong Kim
DTSTART:20250414T153000Z
DTEND:20250414T170000Z
DTSTAMP:20260422T230719Z
UID:Knotsandtopology/108
DESCRIPTION:Title: Group $G_{n}^{3}$ and hidden crossings from braids\nby Seon
gjeong Kim as part of Knots and representation theory\n\n\nAbstract\nIn th
is talk\, we remind basic motivations of the group $G_{n}^{3}$ and $G_{n}^
{k}$. We introduce a modification of group $G_{n}^{3}$\, denoted by $\\til
de{G_{n}^{3}}$. We construct a homomorphism from the pure braid group $PB_
{n}$ to $\\tilde{G_{n}^{3}}$\, which introduce hidden crossings between cl
assical crossings of braids. This talk is based on https://arxiv.org/abs/1
612.03486 in 2016 and Chapter 9.4 of the book “Invariants and pictures
”.\n
LOCATION:https://researchseminars.org/talk/Knotsandtopology/108/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dmitry Melnikov (International Institute of Physics)
DTSTART:20250421T153000Z
DTEND:20250421T170000Z
DTSTAMP:20260422T230719Z
UID:Knotsandtopology/109
DESCRIPTION:Title: Knots\, emerging spaces and quantum correlators\nby Dmitry
Melnikov (International Institute of Physics) as part of Knots and represe
ntation theory\n\n\nAbstract\nAtiyah's axioms of topological quantum field
theory (TQFT) provide a very intuitive description of quantum mechanics.
At the core of this description are topological spaces emerging as a ''phy
sical'' realization of quantum correlations. In the first part of my talk
I will review a simple realization of the TQFT axioms\, with correlation f
unctions encoded by the Jones polynomials of knots and links. In the secon
d part\, I will reflect on the role of emerging space and topology in our
understanding of quantum mechanical features\, such as quantum entanglemen
t.\n
LOCATION:https://researchseminars.org/talk/Knotsandtopology/109/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Theodore Popelensky
DTSTART:20250428T153000Z
DTEND:20250428T170000Z
DTSTAMP:20260422T230719Z
UID:Knotsandtopology/110
DESCRIPTION:Title: On the cohomology of Hopf algebras\nby Theodore Popelensky
as part of Knots and representation theory\n\n\nAbstract\nI will talk abou
t the structure on the cohomology of Hopf algebras\, which is determined b
y the spectral sequence introduced by Buchstaber. As an example\, the coho
mology of the Steenrod algebra will be considered\n
LOCATION:https://researchseminars.org/talk/Knotsandtopology/110/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Igor M. Nikonov
DTSTART:20250505T153000Z
DTEND:20250505T170000Z
DTSTAMP:20260422T230719Z
UID:Knotsandtopology/111
DESCRIPTION:Title: Biquandloids of knots in thickened surfaces\nby Igor M. Nik
onov as part of Knots and representation theory\n\n\nAbstract\nWe define a
modification of biquandle construction for knots in a fixed thickened sur
face and give several examples of the new invariant.\n
LOCATION:https://researchseminars.org/talk/Knotsandtopology/111/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vladlen Timorin
DTSTART:20250602T153000Z
DTEND:20250602T170000Z
DTSTAMP:20260422T230719Z
UID:Knotsandtopology/112
DESCRIPTION:Title: Valuations on convex polytopes and reciprocity laws\nby Vla
dlen Timorin as part of Knots and representation theory\n\n\nAbstract\nVal
uations on convex polytopes and reciprocity laws\n(based on a joint work i
n progress with A. Khovanskii and V. Kiritchenko)\n\nValuations on polytop
es\, including their special classes (say\, translation invariant or latti
ce invariant valuations) are an old research topic. We propose a new appro
ach to classification of valuations\; it is topological in nature and yiel
ds generators and relations with some natural properties. Namely\, we impo
se that generators are functorial with respect to the collections of defin
ing support hyperplanes and as local as possible. Relations reveal remarka
ble connections with complex hyperplane arrangements (even though real pol
ytopes are considered) and Parshin’s reciprocity laws.\n
LOCATION:https://researchseminars.org/talk/Knotsandtopology/112/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Р.В. Шамин (Университет Правительств
а Москвы)
DTSTART:20250512T153000Z
DTEND:20250512T170000Z
DTSTAMP:20260422T230719Z
UID:Knotsandtopology/113
DESCRIPTION:Title: Пространства начальных данных для
абстрактных параболических уравнений и
проблема Като\nby Р.В. Шамин (Университе
т Правительства Москвы) as part of Knots and represent
ation theory\n\n\nAbstract\nДоклад посвящен описанию
пространств начальных данных для абстр
актных параболических уравнений. Извест
но\, что описание пространств начальных
данных может быть получено в результате
интерполяции гильбертовых пространств (
основного пространства и области опреде
ления эллиптического оператора). Констр
уктивное описание этих пространств связ
ано в проблемой Т. Като (1961).\nВ докладе бу
дет приведен класс функционально-диффер
енциальных параболических уравнений\, д
ля которых удается конструктивно постро
ить пространства начальных данных. Таки
м образом\, был найден новый класс операт
оров\, которые удовлетворяют проблеме Ка
то. В полной мере проблема Като не решена
по сей день.\n
LOCATION:https://researchseminars.org/talk/Knotsandtopology/113/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marko Stošić
DTSTART:20250526T153000Z
DTEND:20250526T170000Z
DTSTAMP:20260422T230719Z
UID:Knotsandtopology/114
DESCRIPTION:Title: Generalized knots-quivers correspondence\nby Marko Stošić
as part of Knots and representation theory\n\n\nAbstract\nIn this talk I
will start with introducing knots-quivers correspondence that relates colo
red HOMFLY-PT invariants (or LMOV/BPS invariants) of knots\, and the Donal
dson-Thomas invariants of the corresponding quiver. After discussing diffe
rent approaches\, explanations\, and extensions of such relationships to o
ther knot and 3-manifold invariants\, I will present the generalized versi
on of knots-quivers correspondence. Under that correspondence\, the genera
tors of the quiver generating series can have higher levels\, enabling suc
cessful computations for large classes of knots (and conjecturally for all
knots)\, including the knots with the super-exponential growth property o
f the colored HOMFLY-PT invariants.\n
LOCATION:https://researchseminars.org/talk/Knotsandtopology/114/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pavel Putrov
DTSTART:20250616T153000Z
DTEND:20250616T170000Z
DTSTAMP:20260422T230719Z
UID:Knotsandtopology/115
DESCRIPTION:Title: 3-manifolds and q-series\nby Pavel Putrov as part of Knots
and representation theory\n\n\nAbstract\nIn my talk\, I will describe inva
riants of 3-manifolds valued in q-series with integral coefficients. The i
nvariants originate from physics and are expected to have a categorificati
on analogous to the categorification of the Jones polynomial of a knot by
Khovanov homology. The talk is based on the joint works with Gukov\, Pei a
nd Vafa.\n
LOCATION:https://researchseminars.org/talk/Knotsandtopology/115/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Seonghyun Yu
DTSTART:20250519T153000Z
DTEND:20250519T170000Z
DTSTAMP:20260422T230719Z
UID:Knotsandtopology/116
DESCRIPTION:Title: Full subcomplexes of Bier spheres and their topological applic
ation\nby Seonghyun Yu as part of Knots and representation theory\n\n\
nAbstract\nFull subcomplexes of a simplicial complex often determine its t
opological invariants as well as those of its associated topological space
s. In 1992\, Thomas Bier introduced combinatorial construction that yield
s a huge family of simplicial $(m-2)$-spheres on $2m$ vertices. In this ta
lk\, I will talk about several full subcomplexes of Bier spheres\, and the
ir topological application to the real toric spaces associated with Bier s
pheres.\n
LOCATION:https://researchseminars.org/talk/Knotsandtopology/116/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Завесов Александр Львович -
DTSTART:20250609T153000Z
DTEND:20250609T170000Z
DTSTAMP:20260422T230719Z
UID:Knotsandtopology/117
DESCRIPTION:Title: Теория соседства (продолжение)\nb
y Завесов Александр Львович - as part of Knots and
representation theory\n\n\nAbstract\nТеория соседства по
священа описанию и решению следующих за
дач: - Вместимость графовых систем или си
стем с квазирасстоянием в семейство Евк
лидовых пространств\; - Разделение систе
мы на пересекающиеся подсистемы по прин
ципу близости точек\; - Оптимальная струк
туризация системы через критерий соседс
тва\; - Сила связи и взаимного влияния меж
ду соседними точками\; - Внутренние и гра
ничные точки\; - Квазиметрика соседства к
ак минимальная длина ломаной (геодезиче
ская)\, идущей через соседние точки\; - Кри
визна\, разностные (дифференциальные) оп
ераторы\, области Вороного\, соседние сфе
рические слои\, плотность геодезических.
.. - Байесовская вероятностная модель\, ин
терпретирующая априорную меру как геоме
трическое пространство\, а апостериорну
ю — как набор событий во времени\; - Разме
рность\, объем и мера для априорного геом
етрического пространства\; - Энтропия дл
я Байесовской вероятностной модели как
функционал системы\; - Задача регрессии и
классификации\; - Локальная макроскопич
еская область\, которая с приемлемой точ
ностью определяет структуру соседства д
ля выбранной точки\; - Распределение плот
ности\, количества соседних точек и разм
ерности\; - Уравнение диффузии\; - Эволюци
я потоков Риччи\; - Задача кластеризации
на основе коэффициента связности (внутр
енняя кластеризация)\; - Задача кластериз
ации на основе того\, в какой степени точ
ки являются внутренними или граничными (
внешняя кластеризация)\; - Параметризаци
я расстояний в системах\; - Модели мульти
множеств и строк\; - Генеративная модель\;
- Квазилинейное программирование\; - Обо
бщенная транспортная задача\; - Диффузио
нная модель\; - Распознавание образов\; - В
ероятность и время\; - Комплексные Марков
ские цепи и граф влияния\; - Геометрии на
системах с квазиметрикой. (in Russian)\n
LOCATION:https://researchseminars.org/talk/Knotsandtopology/117/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Галахов Дмитрий Максимович
DTSTART:20250623T153000Z
DTEND:20250623T170000Z
DTSTAMP:20260422T230719Z
UID:Knotsandtopology/118
DESCRIPTION:Title: On geometric link bases for A-polynomials\nby Галахо
в Дмитрий Максимович as part of Knots and representation
theory\n\n\nAbstract\nA simple geometric way is suggested to derive the W
ard identities in the Chern-Simons theory\, also known as quantum A-polyno
mials for knots. We treat A-polynomials as relations between different lin
ks\, obtained by hanging additional "simple" components on the original kn
ot. Depending on the choice of this "decoration"\, the knot polynomial is
either multiplied by a number or decomposes into a sum over "surrounding"
representations by a cabling procedure. What happens is that these two of
decorations\, when complicated enough\, become dependent -- and this provi
des an equation. To make these geometric methods somewhat simpler we sugge
st to use an arcade formalism/representation of the braid group to simplif
y decorating links universally.\nHowever\, in this framework the eventual
equivalence of links is not a topological property -- it follows from rela
tions among R-matrices\, and depends on the choice the gauge group and inc
orporates specific link graph relations known as brackets: in practice we
will consider only the Kauffman bracket for SU(2) and the Kuberberg bracke
t for SU(3)\, however a generalization to SU(n) is potentially available.\
nIn a quasi-classical limit it is closely related to the well publicized a
ugmentation theory and contact geometry.\nThe talk is based on papers 2408
.08181 and 2505.20260 with A.Morozov.\n
LOCATION:https://researchseminars.org/talk/Knotsandtopology/118/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Matthew Harper
DTSTART:20250811T153000Z
DTEND:20250811T170000Z
DTSTAMP:20260422T230719Z
UID:Knotsandtopology/119
DESCRIPTION:Title: Coincidences of Links-Gould and other quantum invariants\nb
y Matthew Harper as part of Knots and representation theory\n\n\nAbstract\
nI will survey several recent results on the Links-Gould polynomial\, inva
riants of Garoufalidis-Kashaev\, and the quantum invariant associated to U
_q(sl_3) at a fourth root of unity. This includes the affirmation of a con
jecture of GK which proves their invariants recover the Links-Gould and sl
3 invariants. We also prove a conjecture of Geer and Patureau-Mirand that
the Links-Gould invariant admits a specialization to ADO_3 (U_q(sl_2) at a
sixth root of unity). Finally\, we'll discuss some cabling results for Li
nks-Gould and other non-semisimple quantum invariants. These results are j
oint with subsets of Stavros Garoufalidis\, Rinat Kashaev\, Ben-Michael Ko
hli\, Jiebo Song\, Guillame Tahar\, and Emmanuel Wagner.\n
LOCATION:https://researchseminars.org/talk/Knotsandtopology/119/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Igor M. Nikonov
DTSTART:20250630T130000Z
DTEND:20250630T143000Z
DTSTAMP:20260422T230719Z
UID:Knotsandtopology/120
DESCRIPTION:Title: Partial tribrackets of knots in thickened surfaces\nby Igor
M. Nikonov as part of Knots and representation theory\n\n\nAbstract\nWe d
efine a modification of Niebrzydowski tribracket construction for knots in
a fixed thickened surface and give several examples of this invariant.\n
LOCATION:https://researchseminars.org/talk/Knotsandtopology/120/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Seongjeong Kim
DTSTART:20250707T153000Z
DTEND:20250707T170000Z
DTSTAMP:20260422T230719Z
UID:Knotsandtopology/121
DESCRIPTION:Title: A characterization of virtual knots as knots in $S_{g} \\times
S^{1}$\nby Seongjeong Kim as part of Knots and representation theory\n
\n\nAbstract\nIn this talk we will show that virtual knots are embedded in
the set of knots in $S_{g} \\times S^{1}$. We will also provide a suffici
ent condition for knots in $S_{g} \\times S^{1}$ to have virtual knot diag
rams. Based on this\, we derive a sufficient condition for 2-component cla
ssical links to be separable.\n
LOCATION:https://researchseminars.org/talk/Knotsandtopology/121/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sergey Fomin (University of Michigan)
DTSTART:20250714T153000Z
DTEND:20250714T170000Z
DTSTAMP:20260422T230719Z
UID:Knotsandtopology/122
DESCRIPTION:Title: Expressive curves\nby Sergey Fomin (University of Michigan)
as part of Knots and representation theory\n\n\nAbstract\nA real plane al
gebraic curve C is called expressive if its defining polynomial has the sm
allest number of critical points allowed by the topology of the set of rea
l points of C. We give a necessary and sufficient criterion for expressivi
ty (subject to a mild technical condition)\, describe several construction
s that produce expressive curves\, and relate their study to the combinato
rics of plabic graphs\, their quivers\, and links. \n\nThis is joint work
with Eugenii Shustin (Tel Aviv University).\n
LOCATION:https://researchseminars.org/talk/Knotsandtopology/122/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Igor M. Nikonov
DTSTART:20250721T153000Z
DTEND:20250721T170000Z
DTSTAMP:20260422T230719Z
UID:Knotsandtopology/123
DESCRIPTION:Title: On skein invariants\nby Igor M. Nikonov as part of Knots an
d representation theory\n\n\nAbstract\nAfter J.H. Conway\, it is known tha
t some knot invariants can be defined by relations (called skein relations
) on diagrams which differ at a local site. Among skein invariants one can
mention Alexander and Jones polynomials\, Arf invariant and writhe polyno
mial. In the talk we will remind these and other examples of skein invaria
nts and introduce a new skein invariant for links in a fixed thickened sur
face.\n
LOCATION:https://researchseminars.org/talk/Knotsandtopology/123/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anderson Vera
DTSTART:20250804T153000Z
DTEND:20250804T170000Z
DTSTAMP:20260422T230719Z
UID:Knotsandtopology/124
DESCRIPTION:Title: Lecture series on the Le-Murakami Ohtsuki Invariant\nby And
erson Vera as part of Knots and representation theory\n\n\nAbstract\nThe L
e-Murakami-Ohtsuki invariant is a powerful invariant of 3-manifolds (unive
rsal among quantum invariants and finite-type invariants)\, in particular
it dominates all the Reshetikhin-Turaev invariants. The LMO invariant take
s values in a space of graphs called Jacobi diagrams or Feynman diagrams.
Its original definition uses the Kontsevich integral of links\, the so-cal
led iota maps and several projection maps between different quotients of s
paces of Jacobi diagrams. In this series of two talks we survey the origin
al construction of this invariant.\n
LOCATION:https://researchseminars.org/talk/Knotsandtopology/124/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anderson Vera
DTSTART:20250818T153000Z
DTEND:20250818T170000Z
DTSTAMP:20260422T230719Z
UID:Knotsandtopology/125
DESCRIPTION:Title: Lecture series on the Le-Murakami Ohtsuki Invariant\nby And
erson Vera as part of Knots and representation theory\n\n\nAbstract\nThe L
e-Murakami-Ohtsuki invariant is a powerful invariant of 3-manifolds (unive
rsal among quantum invariants and finite-type invariants)\, in particular
it dominates all the Reshetikhin-Turaev invariants. The LMO invariant take
s values in a space of graphs called Jacobi diagrams or Feynman diagrams.
Its original definition uses the Kontsevich integral of links\, the so-cal
led iota maps and several projection maps between different quotients of s
paces of Jacobi diagrams. In this series of two talks we survey the origin
al construction of this invariant.\n
LOCATION:https://researchseminars.org/talk/Knotsandtopology/125/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Дениско В.В.
DTSTART:20250728T153000Z
DTEND:20250728T170000Z
DTSTAMP:20260422T230719Z
UID:Knotsandtopology/126
DESCRIPTION:by Дениско В.В. as part of Knots and representation t
heory\n\n\nAbstract\nРабота посвящена исследован
ию методов защиты статистических баз да
нных с количественными свойствами сущно
стей. Рассматриваются два основных подх
ода к обеспечению конфиденциальности да
нных: метод добавления шума и метод огра
ничения запросов. На основе анализа риск
ов утечки информации при статистических
вычислениях\, таких как сумма\, среднее и
максимум\, разработана математическая м
одель\, описывающая угрозу выделения зап
иси из набора данных с помощью предиката
.\nПоказано\, что механизмы\, обеспечивающ
ие дифференциальную конфиденциальность
\, эффективно защищают данные от идентиф
икации\, сохраняя полезность информации.
Также анализируется применимость метод
а ограничения запросов\, выявляются его
ограничения и предлагается альтернатив
ный фреймворк для оценки безопасности р
азличных статистических метрик.\nПракти
ческая часть работы включает описание в
недрения предложенной модели в программ
но-аппаратный комплекс «Анклав»\, предна
значенный для безопасной обработки данн
ых и обучения моделей машинного обучени
я. Рассмотрены основные этапы жизненног
о цикла данных и процессы подготовки\, об
работки и валидации в рамках защищённой
среды.\nРезультаты работы могут быть исп
ользованы при разработке систем защищён
ной аналитики и машинного обучения на ко
нфиденциальных данных.\n
LOCATION:https://researchseminars.org/talk/Knotsandtopology/126/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Thomas Fiedler
DTSTART:20250825T153000Z
DTEND:20250825T170000Z
DTSTAMP:20260422T230719Z
UID:Knotsandtopology/127
DESCRIPTION:Title: Tangle equations for knots\nby Thomas Fiedler as part of Kn
ots and representation theory\n\n\nAbstract\nWe make a connection between
"Tangle-valued 1-cocycles" and "Quantum equations" for knots.To each coupl
e of knot diagrams we can associate linear systems of tangle-valued equati
ons with integer coefficients. If one of the systems has no solution\, tha
n the knot diagrams represent different knots. In the opposit\, each solut
ion of a system gives a non-trivial restriction on the Reidemeister moves
for each knot isotopy which relates the two diagrams. This is an essentia
l step for a solution of the most difficult problem in knot theory: given
two diagrams\, show in an efficient manner that they represent the same kn
ot.\n
LOCATION:https://researchseminars.org/talk/Knotsandtopology/127/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Igor M. Nikonov
DTSTART:20250901T153000Z
DTEND:20250901T170000Z
DTSTAMP:20260422T230719Z
UID:Knotsandtopology/128
DESCRIPTION:Title: On crossoid structure on knots\nby Igor M. Nikonov as part
of Knots and representation theory\n\n\nAbstract\nWe define a structure ca
lled crossoid for description of colorings of the crossings in knots diagr
ams. Crossoids generalize parities in knot theory introduced by V.O. Mantu
rov. On the other hand\, any biquandle induces a crossoid structure. We gi
ve a topological description of the fundamental crossoid of a knot\, and d
efine a crossoid cocycle invariant of knots valued in crossoid cohomology.
\n
LOCATION:https://researchseminars.org/talk/Knotsandtopology/128/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vladislav Kibkalo (Lomonosov Moscow State University)
DTSTART:20250908T154000Z
DTEND:20250908T171000Z
DTSTAMP:20260422T230719Z
UID:Knotsandtopology/129
DESCRIPTION:Title: Integrable Hamiltonian systems with noncompact foliations and b
ifurcations\nby Vladislav Kibkalo (Lomonosov Moscow State University)
as part of Knots and representation theory\n\n\nAbstract\nTopological clas
sification of integrable Hamiltonian systems developed by A. Fomenko and h
is school was applied to a wide class of geometrical\, mechanical and phys
ical systems. Compactness of fibers of their Liouville foliations is an im
portant assumption here. Else new effects arise: incomplete Hamiltonian fl
ows\, non-critical bifurcations (bifurcation value preimage doesn’t cont
ain critical points of the momentum map\, moreover\, it can be empty). We
will discuss several results on such systems (see survey by A. Fomenko\, D
. Fedoseev\, 2020 J.Math.Sc.). Note that effects related to "noncompactnes
s" appeared in a more general context of dynamical systems\, more precisel
y\, as connections between nonautonomous vector fields and diffeomorphisms
(V.Grines\, L.Lerman\, 2022-2023).\n \nPseudo-Euclidean analogues of rigi
d body dynamics (see A. Borisov\, I. Mamaev\, 2016) turn out to be an impo
rtant class of systems with noncompact foliations. New our results on topo
logy of Liouville foliations of pseudo-Euclidean Euler\, Lagrange and Kova
levskaya tops\, Zhukovsky and Klebsch systems will be presented. Both comp
act and non-compact fibers\, their bifurcations (including non-critical on
e) appear in such systems. Bifurcations and Liouville foliations bases (an
alogs of Fomenko graphs) are also determined.\n
LOCATION:https://researchseminars.org/talk/Knotsandtopology/129/
END:VEVENT
BEGIN:VEVENT
SUMMARY:M. Ivanov
DTSTART:20250915T153000Z
DTEND:20250915T170000Z
DTSTAMP:20260422T230719Z
UID:Knotsandtopology/130
DESCRIPTION:Title: Invariants of virtual knots and links\nby M. Ivanov as part
of Knots and representation theory\n\n\nAbstract\nIn this talk\, I will p
resent invariants of virtual knots and links\, as well as their properties
. In particular\, I will discuss polynomial invariants\, a recursive metho
d for constructing new invariants\, and their application to the study of
connected sums of virtual knots. I will also address groups of virtual kno
ts and an approach to investigating the orderability of such groups.\n
LOCATION:https://researchseminars.org/talk/Knotsandtopology/130/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Danish Ali
DTSTART:20250929T153000Z
DTEND:20250929T170000Z
DTSTAMP:20260422T230719Z
UID:Knotsandtopology/131
DESCRIPTION:Title: A Generating Set of Reidemeister Moves of Oriented Virtual Knot
s\nby Danish Ali as part of Knots and representation theory\n\n\nAbstr
act\nIn oriented knot theory\, verifying a quantity is an invariant involv
es checking its invariance under all oriented Reidemeister moves\, a proce
ss that can be intricate and time-consuming. A generating set of oriented
moves simplifies this by requiring verification for only a minimal subset
from which all other moves can be derived. While generating sets for class
ical oriented Reidemeister moves are well-established\, their virtual coun
terparts are less explored. In this study\, we enumerate the oriented virt
ual Reidemeister moves\, identifying seventeen distinct moves after accoun
ting for redundancies due to rotational and combinatorial symmetries. We p
rove that a four-element subset serves as a generating set for these moves
. This result offers a streamlined approach to verifying invariants of ori
ented virtual knots and lays the groundwork for future advancements in vir
tual knot theory\, particularly in the study of invariants and their compu
tational properties.\n
LOCATION:https://researchseminars.org/talk/Knotsandtopology/131/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Igor Nikonov
DTSTART:20251006T153000Z
DTEND:20251006T170000Z
DTSTAMP:20260422T230719Z
UID:Knotsandtopology/132
DESCRIPTION:Title: On biquandles for the groups $G^k_n$ and surface singular braid
monoid\nby Igor Nikonov as part of Knots and representation theory\n\
n\nAbstract\nThe groups $G^k_n$ were defined by V. O. Manturov in order to
describe dynamical systems in configuration systems. In the talk we will
consider two applications of this theory: we define a biquandle structure
on the groups $G^k_n$\, and construct a homomorphism from the surface sing
ular braid monoid to the group $G^2_n$.\n
LOCATION:https://researchseminars.org/talk/Knotsandtopology/132/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Qi Wang
DTSTART:20251013T153000Z
DTEND:20251013T170000Z
DTSTAMP:20260422T230719Z
UID:Knotsandtopology/133
DESCRIPTION:Title: Representation type of cyclotomic quiver Hecke algebras\nby
Qi Wang as part of Knots and representation theory\n\n\nAbstract\nDetermi
ning the representation type of an algebra is a fundamental problem in rep
resentation theory. In this talk\, we address this problem for cyclotomic
quiver Hecke algebras\, also known as cyclotomic Khovanov–Lauda–Rouqui
er algebras\, in affine type A. Our approach consists of two main steps. F
irst\, we reduce the high-level problem to lower-level cases using a quive
r model. Second\, we construct explicit quiver presentations for these low
er-level cases and classify their representation types. This talk will mai
nly focus on the second step and serve as an introduction to quiver repres
entation theory.\n
LOCATION:https://researchseminars.org/talk/Knotsandtopology/133/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Oğuz Öner
DTSTART:20251110T153000Z
DTEND:20251110T170000Z
DTSTAMP:20260422T230719Z
UID:Knotsandtopology/134
DESCRIPTION:Title: Orientation Reversal and Resurgent Crossing of the Natural Boun
dary\nby Oğuz Öner as part of Knots and representation theory\n\n\nA
bstract\nIn this talk\, I will introduce a resurgent method that crosses t
he $|q|=1$ natural boundary for the $q$-series invariants $\\widehat{Z}$ o
f 3-manifolds (Gukov-Pei-Putrov-Vafa) and\, at the level of individual fal
se theta building blocks. In our setup\, crossing the natural boundary cor
responds to the orientation reversal of the 3-manifold $M_3$. Under this o
peration\, the $q$-series invariants for $M_3$ and $\\overline{M_3}$ are v
ery different\, and usually one of them is much harder to compute. The res
urgence approach proposes a solution to systematically computing these inv
ariants and their individual building blocks for a large class of new exam
ples. The talk is based on joint work with Adams\, Costin\, Dunne\, and Gu
kov.\n
LOCATION:https://researchseminars.org/talk/Knotsandtopology/134/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mrunmay Jagadale
DTSTART:20251020T153000Z
DTEND:20251020T170000Z
DTSTAMP:20260422T230719Z
UID:Knotsandtopology/135
DESCRIPTION:Title: TQFT for $\\hat{Z}$ invariants\nby Mrunmay Jagadale as part
of Knots and representation theory\n\n\nAbstract\nThe $\\hat{Z}$-invarian
ts of three-manifolds introduced by Gukov\, Pei\, Putrov\, and Vafa have i
nfluenced many areas of mathematics and physics. However\, their TQFT stru
cture is not yet fully understood. In this talk\, I will present a framewo
rk for decorated Spin-TQFTs and construct one based on Atiyah–Segal-like
axioms that computes the $\\hat{Z}$-invariants. This TQFT framework provi
des a new perspective on the structural properties and gluing formulas for
$\\hat{Z}$-invariants.\n
LOCATION:https://researchseminars.org/talk/Knotsandtopology/135/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Olga Frolkina
DTSTART:20251117T153000Z
DTEND:20251117T170000Z
DTSTAMP:20260422T230719Z
UID:Knotsandtopology/136
DESCRIPTION:Title: Properties of a compact set in $R^n$ and its projections\nb
y Olga Frolkina as part of Knots and representation theory\n\n\nAbstract\n
Properties of projections of zero-dimensional sets were considered already
at the end of 19th century. In 1884 G.Cantor described a surjection of th
e middle-thirds Cantor set onto the unit segment. Cantor sets in plane all
of whose projections are segments were constructed by L.Antoine (1924)\
, H.Otto (1933)\, A.Flores (1933)\, G.Noebeling (1933). In 1947\, K.Borsu
k described a Cantor set in $R^n$ such that its projection into any $(n-1
)$-plane contains an $(n-1)$-ball. As a corollary\, Borsuk obtained a knot
in $R^n$ such that its projection into any $(n-1)$-plane contains an $(n-
1)$-ball.\n \nThere are many later results in this field. The author rema
rked that for any Cantor set\n$K\\subset R^n$ there exists an arbitrarily
small isotopy $\\{ f_t \\} :R^n\\cong R^n$ such that the projection of
$f_1(K)$ into any $(n−1)$-plane has dimension $(n−1)$\; and there exi
sts an arbitrarily small isotopy $\\{ g_t \\} : R^n \\cong R^n$ such t
hat the projection of $ g_1(K)$ into any $(n−1)$-plane has dimension $(n
−2)$.\n\nIn the talk\, we will discuss these and other similar results
using the Baire category approach. The questions on typical behaviour (in
the sense of Baire category) are classic. A typical continuous function i
s nowhere differentiable (S.Banach-S.Mazurkiewicz 1931). A typical knot
is wild (J.Milnor 1964) and moreover wild at any of its points (H.G.Bot
he 1966). A typical compactum in Rn is a Cantor set (K.Kuratowski 1973
). We will discuss the behavior of projections of a compactum $X\\subset
R^n$ under a typical isotopy of $R^n$\, and as a corollary we will strengt
hen a theorem of J.Vaisala (1979).\n
LOCATION:https://researchseminars.org/talk/Knotsandtopology/136/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Josef Svoboda
DTSTART:20251027T153000Z
DTEND:20251027T170000Z
DTSTAMP:20260422T230719Z
UID:Knotsandtopology/137
DESCRIPTION:Title: Inverted Habiro series\nby Josef Svoboda as part of Knots a
nd representation theory\n\n\nAbstract\nQuantum algebra provides an import
ant source of invariants of knots and 3-manifolds. Using Verma modules of
the algebra $U_q(sl_2)$\, Park defined a new quantum knot invariant (build
ing on a previous work of Gukov--Manolescu) and observed that it can be wr
itten in a very peculiar form\, which he called inverted Habiro series. I
will describe a commutative ring $\\Lambda$ that contains these series and
explain how $\\Lambda$ could arise as the center of some form of $U_q(sl_
2)$. Then I will show how $q$-series identities of Euler\, Hecke--Rogers a
nd Ramanujan follow from the study of residues of the inverted Habiro seri
es for the simplest knots. Finally\, I will present some recent developmen
ts about the topological significance of these invariants.\n
LOCATION:https://researchseminars.org/talk/Knotsandtopology/137/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Qiuyu Ren
DTSTART:20251201T153000Z
DTEND:20251201T170000Z
DTSTAMP:20260422T230719Z
UID:Knotsandtopology/138
DESCRIPTION:Title: Khovanov skein lasagna modules with 1-dimensional inputs\nb
y Qiuyu Ren as part of Knots and representation theory\n\n\nAbstract\nSkei
n lasagna modules (with $0$-dimensional inputs) are $4$-manifold invariant
s introduced by Morrison-Walker-Wedrich. In this context\, a skein is a pr
operly embedded surface in a $4$-manifold minus a disjoint union of $4$-ba
lls\, and the lasagna comes from a TQFT for links in $S^3$ (satisfying mil
d conditions). In this talk\, we introduce skein lasagna modules with $1$-
dimensional inputs\, where a skein is a properly embedded surface in a $4$
-manifold minus a tubular neighborhood of an embedded graph\, and the lasa
gna comes from a TQFT for links in $\\#(S^1\\times S^2)$ and link cobordis
ms between them in a particular class of $4$-manifolds. We show that the K
hovanov homology of links in $\\#(S^1\\times S^2)$\, as defined by Rozansk
y and Willis\, has excellent functoriality properties sufficient to supply
the lasagna inputs. We touch upon the three key ingredients of the proof:
a lasagna interpretation of Rozansky-Willis homology by Sullivan-Zhang\;
Gabai's $4$-dimensional lightbulb theorem\; and certain Khovanov lasagna n
aturality properties of the Gluck twist operation. This is joint work with
I. Sullivan\, P. Wedrich\, M. Willis\, M. Zhang.\n
LOCATION:https://researchseminars.org/talk/Knotsandtopology/138/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Igor M. Nikonov
DTSTART:20251103T153000Z
DTEND:20251103T170000Z
DTSTAMP:20260422T230719Z
UID:Knotsandtopology/139
DESCRIPTION:Title: Homotopical multicrossing complex\nby Igor M. Nikonov as pa
rt of Knots and representation theory\n\n\nAbstract\nWe introduce the mult
icrossing complex of a tangle and define the crossing homology class. In
a sense\, the multicrossing complex unifies tribracket\, biquandle and cr
ossoid homologies\; and the tribracket\, biquandle and crossoid cycle inv
ariants are actually the result of pairing a tribracket (biquandle\, cros
soid) cocycle with the crossing homology class.\n
LOCATION:https://researchseminars.org/talk/Knotsandtopology/139/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Paul Wedrich
DTSTART:20251215T153000Z
DTEND:20251215T170000Z
DTSTAMP:20260422T230719Z
UID:Knotsandtopology/140
DESCRIPTION:Title: Perverse schobers of type A and categorified bialgebras\nby
Paul Wedrich as part of Knots and representation theory\n\n\nAbstract\nTh
is talk\, based on joint work with Dyckerhoff\, connects the concept of\np
erverse schobers - a categorification of perverse sheaves envisioned by Ka
pranov and Schechtman - with structures in quantum topology and link homol
ogy theory. We propose a definition of perverse schobers on symmetric prod
ucts of the complex line\, with respect to the discriminant stratification
\, and construct a nontrivial example using complexes of singular Soergel
bimodules of type A. Our approach centers on a stable categorification of
Kapranov-Schechtman's classification data for perverse sheaves in terms of
graded bialgebras. In particular\, we show that singular Soergel bimodule
s give rise to a categorified graded bialgebra\, which sheds new light on
the geometric foundations of the Rouquier–Rickard braiding and the role
of webs and foams in link homology theory\n
LOCATION:https://researchseminars.org/talk/Knotsandtopology/140/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vassily O. Manturov
DTSTART:20251208T153000Z
DTEND:20251208T170000Z
DTSTAMP:20260422T230719Z
UID:Knotsandtopology/141
DESCRIPTION:Title: Parity\, Vassiliev Invariants\, Framed Chord diagrams\, Legendr
ian Knots\, and Flat-Virtual Knots\nby Vassily O. Manturov as part of
Knots and representation theory\n\n\nAbstract\nIn the present talk\, I wil
l mention the following two topics:\n \n1) How to get parity for classica
l knots.\n \nFor a classical knot K we take its double-cabling L_{2}(K)=
K_{1}\\sqcup K_{2} and consider the knot K_{2} lying in the complement to
K_{1}.\n \nThe space R^{3}\\backslash K_{1} has non-trivial homology\, h
ence the theory of Vassiliev invariants for K_{1} in the complement to K_
{2} has some features of ``parity''\; we formulate many problems concerni
ng framed chord diagram\, framed Vassiliev invariants\, Kontsevich integra
l\, etc.\n \n2) In 2022\, in two joint papers with I.M.Nikonov\, we const
ructed a map from classical knot theory in the full torus S_{1}\\times R^
{2} to the so-called ``flat-virtual knot theory'' which has many ``virtua
l features.''\n\nPlane curves and fronts naturally lift to Legendrian knot
s in the spherized bundle S_{*} T R^{2} which is topologically a torus.\n
\nThis leads to a nice interplay between the theory of Legendrian knots\
, fronts\, virtual knots\, and flat-virtual knots.\n
LOCATION:https://researchseminars.org/talk/Knotsandtopology/141/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Igor M. Nikonov
DTSTART:20251222T153000Z
DTEND:20251222T170000Z
DTSTAMP:20260422T230719Z
UID:Knotsandtopology/142
DESCRIPTION:Title: On knot invariants induced by skein relations\nby Igor M. N
ikonov as part of Knots and representation theory\n\n\nAbstract\nSince 197
0s\, it is known that some knot invariants can be defined by relations (ca
lled skein relations) on diagrams which differ at a local site. Among skei
n invariants one can mention Alexander and Jones polynomials\, Arf invaria
nt and writhe polynomial. In the talk we will remind these and other examp
les of skein invariants and introduce a new skein invariant for links in a
fixed thickened surface.\n
LOCATION:https://researchseminars.org/talk/Knotsandtopology/142/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Louis Kauffman
DTSTART:20251229T153000Z
DTEND:20251229T170000Z
DTSTAMP:20260422T230719Z
UID:Knotsandtopology/143
DESCRIPTION:Title: Topological Quantum Computing - Fibonacci Model and Majorana Fe
rmions Knots and representation theory\nby Louis Kauffman as part of K
nots and representation theory\n\n\nAbstract\nWe will discuss topological
quantum computing from the point of view of the Fibonacci model (via Tempe
rley-Lieb recoupling theory based on Kauffman bracket polynomial) and also
in terms of braid group representations associated with Majorana Fermions
. The talk will be self-contained and we will quickly review what we discu
ssed in the previous talks in this series.\n
LOCATION:https://researchseminars.org/talk/Knotsandtopology/143/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dmitriy Khudoteplov
DTSTART:20260112T153000Z
DTEND:20260112T170000Z
DTSTAMP:20260422T230719Z
UID:Knotsandtopology/144
DESCRIPTION:Title: Vogel classification of Lie algebras\nby Dmitriy Khudoteplo
v as part of Knots and representation theory\n\n\nAbstract\nIn the early s
tage of the development of Vassiliev knot invariants there was a conjectur
e that all Vassiliev invariants come from simple Lie algebras. Pierre Voge
l disproved this conjecture\, constructing a Jacobi diagram lying in the k
ernels of all Lie algebra weight systems. Originally\, Vogel thought that
there exists some generalization of Lie algebra involving three parameters
so that the simple Lie algebras are obtained by specialization of these p
arameters. Later it was discovered that these parameters must satisfy an a
dditional relation\, which is contrary to the initial idea. On the other s
ide\, this discovery enables to classify Lie algebras in an elegant way\,
rooted in the knot theory.\n
LOCATION:https://researchseminars.org/talk/Knotsandtopology/144/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Igor Nikonov
DTSTART:20260105T153000Z
DTEND:20260105T170000Z
DTSTAMP:20260422T230719Z
UID:Knotsandtopology/145
DESCRIPTION:Title: On biquandles for the groups $G^k_n$ and surface singular braid
monoid\nby Igor Nikonov as part of Knots and representation theory\n\
n\nAbstract\nThe groups $G^k_n$ were defined by V. O. Manturov in order to
describe dynamical systems in configuration systems. In the talk we will
consider two applications of this theory: we define a biquandle structure
on the groups $G^k_n$\, and construct a homomorphism from the surface sing
ular braid monoid to the group $G^2_n$.\n
LOCATION:https://researchseminars.org/talk/Knotsandtopology/145/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Seongjeong Kim
DTSTART:20260119T153000Z
DTEND:20260119T170000Z
DTSTAMP:20260422T230719Z
UID:Knotsandtopology/146
DESCRIPTION:Title: On braids for Knots in $S_{g} \\times S^{1}$\nby Seongjeong
Kim as part of Knots and representation theory\n\n\nAbstract\nIn \\cite{K
im} for an oriented surface $S_{g}$ of genus $g$ it is shown that links in
$S_{g} \\times S^{1}$ can be presented by virtual diagrams with a decorat
ion\, so called\, {\\em double lines}. In this paper\, first we define bra
ids with double lines for links in $S_{g}\\times S^{1}$. We denote the gro
up of braids with double lines by $VB_{n}^{dl}$. Alexander and Markov theo
rem for links in $S_{g}\\times S^{1}$ can be proved. We show that\, if we
restrict our interest to the group $B_{n}^{dl}$ generated by braids with d
ouble lines\, but without virtual crossings\, then the Hecke algebra of $B
_{n}^{dl}$ is isomorphic to affine Hecke algebra.\n
LOCATION:https://researchseminars.org/talk/Knotsandtopology/146/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Igor Nikonov
DTSTART:20260126T153000Z
DTEND:20260126T170000Z
DTSTAMP:20260422T230719Z
UID:Knotsandtopology/147
DESCRIPTION:Title: Parity on based matrices\nby Igor Nikonov as part of Knots
and representation theory\n\n\nAbstract\nA parity is a labeling of the cro
ssings of knot diagrams which is compatible with Reidemeister moves. We de
fine the notion of parity for based matrices -- algebraic objects introduc
ed by V. Turaev in his research of virtual strings. We present the reduced
stable parity on based matrices which gives a new example of a parity of
virtual knots.\n
LOCATION:https://researchseminars.org/talk/Knotsandtopology/147/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Phillip Choi
DTSTART:20260309T153000Z
DTEND:20260309T170000Z
DTSTAMP:20260422T230719Z
UID:Knotsandtopology/148
DESCRIPTION:Title: Colored Jones Polynomials of 4-Plats\nby Phillip Choi as pa
rt of Knots and representation theory\n\n\nAbstract\nUsing the diagrammati
c formulation of the Jones polynomial given by the Kauffman bracket\, we r
eview the standard construction of the N-colored Jones polynomial. We then
consider the case of 4-plat diagrams (2-bridge knots/links) and show that
the diagrammatic formula simplifies when interpreted through the represen
tation theory of quantum groups.\n
LOCATION:https://researchseminars.org/talk/Knotsandtopology/148/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Igor M. Nikonov
DTSTART:20260202T153000Z
DTEND:20260202T170000Z
DTSTAMP:20260422T230719Z
UID:Knotsandtopology/149
DESCRIPTION:Title: On a representation of the group Gn3\nby Igor M. Nikonov as
part of Knots and representation theory\n\n\nAbstract\nWe consider a cert
ain modification of the group $G^3_n$ which describes dynamics of point co
nfigurations\, in particular braids\, and define a representation of the m
odified $G^3_n$. The braid representation induced by it is powerful enough
to detect the kernel of the Burau representation.\n
LOCATION:https://researchseminars.org/talk/Knotsandtopology/149/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Fedor Nilov
DTSTART:20260209T153000Z
DTEND:20260209T170000Z
DTSTAMP:20260422T230719Z
UID:Knotsandtopology/150
DESCRIPTION:Title: On families of similar conics tangent to four circles.\nby
Fedor Nilov as part of Knots and representation theory\n\n\nAbstract\nThe
classical Steiner problem consists in finding the number of non-degenerate
conics (second-order curves) tangent to 5 given conics in the plane. We w
ill construct several configurations of four circles such that there is a
family of similar conics tangent to these circles.\n
LOCATION:https://researchseminars.org/talk/Knotsandtopology/150/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexander Zheglov
DTSTART:20260216T153000Z
DTEND:20260216T170000Z
DTSTAMP:20260422T230719Z
UID:Knotsandtopology/151
DESCRIPTION:Title: The Krichever correspondence and the theory of commuting ordina
ry differential operators\nby Alexander Zheglov as part of Knots and r
epresentation theory\n\n\nAbstract\nIn the 1970s\, a method was devised to
use Jacobians of algebraic curves and the corresponding theta functions t
o write out exact solutions to some well-known equations of mathematical p
hysics\, namely those obtained from the Kadomtsev–Petviashvili hierarchy
(an infinite system of partial differential equations)\, in particular\,
the Korteweg–de Vries and Kadomtsev–Petviashvili equations. These solu
tions are based on the geometry of algebraic curves and line bundles on th
em (or\, more generally\, torsion-free sheaves)\, rings of commuting ordin
ary differential operators\, and the Krichever map\, which associates cert
ain algebraic-geometric data associated with a projective curve and a line
bundle on it with a point in an infinite-dimensional algebraic variety\,
the Sato Grassmannian. This correspondence (known as the Krichever corresp
ondence) was subsequently refined and developed by many renowned mathemati
cians (W. Drinfeld\, D. Mumford\, J. Verdier\, G. Segal\, D. Wilson\, M. M
ulase\, T. Shiota)\, and played an important role in solving the Schottky
problem.\nIn my talk I will attempt to outline the basic definitions and c
onstructions of this theory.\n
LOCATION:https://researchseminars.org/talk/Knotsandtopology/151/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vassily Manturov
DTSTART:20260302T152500Z
DTEND:20260302T170000Z
DTSTAMP:20260422T230719Z
UID:Knotsandtopology/152
DESCRIPTION:Title: The photography method: how to solve equations without writing
them\nby Vassily Manturov as part of Knots and representation theory\n
\n\nAbstract\nWe shall talk about a universal method which allows one to g
uess solutions\nof different equations which can be written differently.\n
\n Very often it leads to solutions of equations coming from physics and\
napplicable to topology.\n \n The simplest but structurally very important
is the proof (without calculations)\nthat the Ptolemy transformation sati
sfies the pentagon identity (in other words\,\nbeing applied five times it
gives the identity map).\n \n Then we will tell how to "draw equations" a
nd solve them by using\n"proper sense" arguments (соображения
здравого смысла).\n\n Usual logical considerations will lead
to various generalisations \n(for example\, trop
ical ones). The photography method is related to\nvarious branches of math
ematics: cluster algebras\, braids\, Conway-Coxeter\nfriezes\, Stasheff po
lytopes\, associators ets.\n \n We shall describe some directions of
further research and list the papers where\nthis was initiated and collea
gues and students working on them.\n
LOCATION:https://researchseminars.org/talk/Knotsandtopology/152/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Igor Nikonov
DTSTART:20260223T153000Z
DTEND:20260223T170000Z
DTSTAMP:20260422T230719Z
UID:Knotsandtopology/153
DESCRIPTION:Title: On universal parity on free two-dimensional knots\nby Igor
Nikonov as part of Knots and representation theory\n\n\nAbstract\nIn the t
alk we review the definition of parity on 2-knots\, and prove that the Gau
ssian parity is universal on free two-dimensional knots.\n
LOCATION:https://researchseminars.org/talk/Knotsandtopology/153/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Du Pei
DTSTART:20260316T153000Z
DTEND:20260316T170000Z
DTSTAMP:20260422T230719Z
UID:Knotsandtopology/154
DESCRIPTION:Title: Gauge theory and skein modules\nby Du Pei as part of Knots
and representation theory\n\n\nAbstract\nI will outline an approach to stu
dying skein modules of 3-manifolds by embedding them into the Hilbert spac
es of four-dimensional supersymmetric gauge theories. When the 3-manifold
has reduced holonomy\, this approach leads to an algorithm for the dimensi
on of the skein module for a general gauge group\, expressed as a sum over
nilpotent orbits in the Lie algebra. Surprisingly\, the dimensions often
differ between Langlands-dual pairs\, for which I will provide a physical
explanation. This perspective helps to clarify the relation between the ga
uge-theoretic framework of Kapustin and Witten and other versions of the g
eometric Langlands program\, and explains why the dimensions of skein modu
les do not exhibit a TQFT-like behavior.\n
LOCATION:https://researchseminars.org/talk/Knotsandtopology/154/
END:VEVENT
BEGIN:VEVENT
SUMMARY:G.V. Belozerov
DTSTART:20260323T153000Z
DTEND:20260323T170000Z
DTSTAMP:20260422T230719Z
UID:Knotsandtopology/155
DESCRIPTION:Title: Generalizations of Jacobi-Chasles and Graves Theorems\nby G
.V. Belozerov as part of Knots and representation theory\n\n\nAbstract\nTh
e most illustrative integrable Hamiltonian systems are billiards bounded b
y confocal quadrics. The integrability of these systems follows from the c
lassical Jacobi--Chasles theorem. Recall that according to this theorem\,
\\textit{tangent lines drawn to a geodesic on an $n$-axial ellipsoid in Eu
clidean $\\mathbb{R}^n$ touch\, in addition to this ellipsoid\, $n-2$ conf
ocal quadrics common to all points of the given geodesic}. This theorem im
plies the integrability of the geodesic flow on the ellipsoid.\n\nV.A. Kib
kalo investigated the issue of integrability of the geodesic flow on the i
ntersection of several confocal quadrics. He showed that the geodesic flow
on the intersection of $(n-2)$ confocal quadrics is a completely integrab
le Hamiltonian system. It turns out that the result remains valid if we co
nsider the geodesic flow on the intersection of an arbitrary number of non
-degenerate confocal quadrics. Moreover\, the following theorem holds.\n\n
\\begin{theorem}[Belozerov]\nLet $Q_1\, \\ldots\, Q_k$ be non-degenerate c
onfocal quadrics of different types in $\\mathbb{R}^n$ and $Q = \\bigcap_{
i=1}^k Q_i$. Then:\n\\begin{enumerate}\n \\item the geodesic flow on $Q
$ is quadratically integrable\;\n \\item tangent lines drawn to all poi
nts of a geodesic on $Q$\, in addition to $Q_1\, \\ldots\, Q_k$\, touch $n
-k-1$ quadrics confocal with $Q_1\, \\ldots\, Q_k$ and common to all point
s of this geodesic.\n\\end{enumerate}\n\\end{theorem}\n\n\\textbf{Remark.}
Geodesics on the intersection of non-degenerate confocal quadrics\, in ge
neral\, are not geodesics on any of the quadrics $Q_1\, \\ldots\, Q_k$. Th
erefore\, Theorem 1 is not a consequence of the classical Jacobi-Chasles t
heorem.\n\nAccording to Theorem 1 and the result of V.V. Kozlov on integra
ble geodesic flows on two-dimensional surfaces\, the connected component o
f the compact intersection of $(n-2)$ quadrics is homeomorphic either to a
torus $T^2$ or to a sphere $S^2$. Both cases are realized. Nevertheless\,
it is possible to describe the class of homeomorphism of any compact inte
rsection of non-degenerate confocal quadrics. It turns out that it is home
omorphic to a direct product of spheres.\n\nIt also turned out that the cl
assical Jacobi-Chasles theorem can be generalized not only for Euclidean s
paces\, but also for pseudo-Euclidean spaces and spaces of constant curvat
ure. These generalizations significantly enrich the class of integrable bi
lliards.\n\nStudying the trajectory properties of multidimensional billiar
ds bounded by ellipsoids\, the author and his scientific advisor A.T. Fome
nko obtained a generalization of two more classical results — the focal
property of quadrics and Graves' theorem. Recall that the classical Graves
' theorem states that \\textit{if you put an inextensible loop on an ellip
se and\, stretching the thread with a pencil to the limit\, draw a curve\,
the result will be an ellipse confocal with the given one}. It turns out
that this fact has a multidimensional generalization\, so ellipsoids of ar
bitrary dimension can be constructed using a thread.\n
LOCATION:https://researchseminars.org/talk/Knotsandtopology/155/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Theodore Popelensky
DTSTART:20260504T153000Z
DTEND:20260504T170000Z
DTSTAMP:20260422T230719Z
UID:Knotsandtopology/156
DESCRIPTION:by Theodore Popelensky as part of Knots and representation the
ory\n\nInteractive livestream: https://us02web.zoom.us/j/81866745751?pwd=b
EFqUUlZM1hVV0tvN0xWdXRsV2pnQT09\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/Knotsandtopology/156/
URL:https://us02web.zoom.us/j/81866745751?pwd=bEFqUUlZM1hVV0tvN0xWdXRsV2pn
QT09
END:VEVENT
BEGIN:VEVENT
SUMMARY:Byeorhi Kim
DTSTART:20260406T153000Z
DTEND:20260406T170000Z
DTSTAMP:20260422T230719Z
UID:Knotsandtopology/158
DESCRIPTION:Title: On the construction of foldings of branched covers along knots<
/a>\nby Byeorhi Kim as part of Knots and representation theory\n\n\nAbstra
ct\nIn this talk\, we study braiding and folding of branched covers of the
3-sphere along knots\, focusing on constructions derived from quandle col
orings of knots and quipu diagrams for finite groups. These techniques wer
e developed in earlier work. We present a detailed folding of the dihedral
cover of \\(S^3\\) branched along the torus knot \\(T(2\,5)\\)\, and desc
ribe a related example for the trefoil knot using the alternating group \\
(A_4\\). These constructions provide explicit geometric models for bran
ched covers and suggest potential extensions to surface-knot branch sets i
n \\(S^4\\).\n
LOCATION:https://researchseminars.org/talk/Knotsandtopology/158/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yangzhou Liu
DTSTART:20260330T153000Z
DTEND:20260330T170000Z
DTSTAMP:20260422T230719Z
UID:Knotsandtopology/159
DESCRIPTION:Title: Secant-quandle: an invariant of braids and knots\nby Yangzh
ou Liu as part of Knots and representation theory\n\n\nAbstract\nWe constr
uct a novel invariant of braids and knots\, secant-quandle (SQ)\,with gene
ric secants serving as generators and generic horizontal trisecants servin
g as relations\, i.e.\, SQ=Γ⟨S_M | S_T\,E_M⟩\, where M is a braid or
link.\n
LOCATION:https://researchseminars.org/talk/Knotsandtopology/159/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kâzim İlhab İkeda
DTSTART:20260420T153000Z
DTEND:20260420T170000Z
DTSTAMP:20260422T230719Z
UID:Knotsandtopology/160
DESCRIPTION:Title: On the Langlands reciprocity and functoriality principles\n
by Kâzim İlhab İkeda as part of Knots and representation theory\n\n\nAb
stract\nPlease find the abstract here: https://disk.yandex.com/d/C93I7Hc9L
tnEXQ\n
LOCATION:https://researchseminars.org/talk/Knotsandtopology/160/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Various speakers
DTSTART:20260413T153000Z
DTEND:20260413T170000Z
DTSTAMP:20260422T230719Z
UID:Knotsandtopology/161
DESCRIPTION:Title: Конференции Ломоносов-2026\nby Various
speakers as part of Knots and representation theory\n\n\nAbstract\n1. О
бщая топологическая классификация грав
итационных биллиардов\, ограниченных ду
гами семейств софокусных парабол\nЗайце
ва Анастасия Владимировна\nМосковский г
осударственный университет имени М.В.Ло
моносова\, Механико-математический факу
льтет\n \nРассмотрим все возможные облас
ти на плоскости\, ограниченные дугами со
фокусных парабол. Биллиард с гравитацио
нным потенциалом в данных областях — ин
тегрируем [2\, 3]. Интегрируемость позволя
ет вычислить инварианты Фоменко–Цишанг
а [1]. Всего таких областей 9. Проведена об
щая топологическая классификация грави
тационных биллиардов\, ограниченных дуг
ами софокусных парабол [4\, 5]. Получены 3 т
ипа неэквивалентных слоений Лиувилля. Д
ля каждого из 9 случаев исследованы обла
сти возможного движения\, построены бифу
ркационные диаграммы и вычислены метки.
Получена следующая теорема:\nТеорема 1. Д
ля гравитационных биллиардов в областях
Ω1–Ω9 существуют всего три типа неэкви
валентных слоений Лиувилля неособых изо
энергетических поверхностей.\nИсточники
и литература\n1. Болсинов А.В.\, Фоменко А.
Т. Интегрируемые гамильтоновы системы. Г
еометрия\, топология\, классификация. Иже
вск\, 1999. Т. I.\n2. Кобцев И.Ф. Эллиптический
биллиард в поле потенциальных сил: класс
ификация движений\, топологический анал
из // Математический сборник. М.\, 2020. С. 93-12
0.\n3. Козлов В.В. Некоторые интегрируемые
обобщения задачи Якоби о геодезических
на эллипсоиде // Прикладная математика и
механика. М.\, 1995. Том 59\, выпуск 1.\n4. Фокиче
ва В.В. Топологическая классификация бил
лиардов в локально плоских областях\, ог
раниченных дугами софокусных квадрик //
Математический сборник. М.\, 2015. С. 127-176.\n5.
Харламов М.П. Топологический анализ и бу
левы функции: I. Методы и приближения к кл
ассическим системам // Нелинейная динами
ка. М.\, 2010. Том 6\, №4. С. 769-805.\n
LOCATION:https://researchseminars.org/talk/Knotsandtopology/161/
END:VEVENT
END:VCALENDAR