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BEGIN:VEVENT
SUMMARY:L. Kauffman
DTSTART:20201221T153000Z
DTEND:20201221T170000Z
DTSTAMP:20260404T111446Z
UID:Knotsandtopology/1
DESCRIPTION:Title: Virtual Knots\, Index Polynomials and the Sawollek Polynom
ial\nby L. Kauffman as part of Knots and representation theory\n\n\nAb
stract\nThis talk will discuss the Affine Index Polynomial and its relatio
nship with the Sawollek Polynomial for virtual knots and links.\n
LOCATION:https://stable.researchseminars.org/talk/Knotsandtopology/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:N. Bogachev (Skoltech & MIPT)
DTSTART:20201228T153000Z
DTEND:20201228T170000Z
DTSTAMP:20260404T111446Z
UID:Knotsandtopology/2
DESCRIPTION:Title: Arithmetic and quasi-arithmetic hyperbolic reflection grou
ps\nby N. Bogachev (Skoltech & MIPT) as part of Knots and representati
on theory\n\n\nAbstract\nIn 1967\, Vinberg started a systematic study of h
yperbolic reflection groups. In particular\, he showed that Coxeter polyto
pes are natural fundamental domains of hyperbolic reflection groups and de
veloped practically efficient methods that allow to determine compactness
or volume finiteness of a given Coxeter polytope by looking at its Coxeter
diagram. He also proved a (quasi-)arithmeticity criterion for hyperbolic
lattices generated by reflections. In 1981\, Vinberg showed that there are
no compact 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\, Belolipetsk
y\, Storm\, and Whyte (2008) it became known that there are only finitely
many maximal arithmetic hyperbolic reflection groups in all dimensions. Th
ese results give hope that maximal arithmetic hyperbolic reflection groups
can be classified.\n \nA very interesting moment is that compact Coxeter
polytopes are known only up to H^8\, and in H^7 and H^8 all the known exam
ples are arithmetic. Thus\, besides the problem of classification of arith
metic hyperbolic reflection groups (which remains open since 1970-80s) we
have another very natural question (which is again open since 1980s): do t
here exist compact (both arithmetic and non-arithmetic) hyperbolic Coxeter
polytopes in H^n for n>8 ?\n \nThis talk will be devoted to the discussio
n of these two related problems. One part of the talk is based on the rece
nt preprint https://arxiv.org/abs/2003.11944 where some new geometric cla
ssification method is described. The second part is based on a joint work
with Alexander Kolpakov https://arxiv.org/abs/2002.11445 where we prove t
hat each lower-dimensional face of a quasi-arithmetic Coxeter polytope\, w
hich happens to be itself a Coxeter polytope\, is also quasi-arithmetic. W
e also provide a few illustrative examples.\n
LOCATION:https://stable.researchseminars.org/talk/Knotsandtopology/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:I.M. Nikonov
DTSTART:20210111T153000Z
DTEND:20210111T170000Z
DTSTAMP:20260404T111446Z
UID:Knotsandtopology/3
DESCRIPTION:Title: On noncommutative geometry\nby I.M. Nikonov as part of
Knots and representation theory\n\n\nAbstract\nNoncommutative (differenti
al) geometry was introduced by Alain Connes about forty years ago. It is b
ased on the correspondence between topological and geometrical objects (ma
nifolds\, bundles\, differential forms etc.) and algebraic ones (algebras\
, modules\, Hochschild homology etc.)In the talk we review the basic const
ructions of noncommutative geometry: C*-algebras\, cyclic homology and Che
rn character.\n
LOCATION:https://stable.researchseminars.org/talk/Knotsandtopology/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Victoria Lebed
DTSTART:20210118T153000Z
DTEND:20210118T170000Z
DTSTAMP:20260404T111446Z
UID:Knotsandtopology/4
DESCRIPTION:Title: Unexpected applications of homotopical algebra to knot the
ory\nby Victoria Lebed as part of Knots and representation theory\n\n\
nAbstract\nInteractions between knot theory and homotopical algebra are nu
merous and natural. But the connections unveiled in this talk are rather u
nexpected. Following a recent preprint with Markus Szymik\, I will explain
how homotopy can help one to compute the full homology of racks and quand
les. These are certain algebraic structures\, useful in knot theory and ot
her areas of mathematics. Their homology plays a key role in applications.
Although very easy to define\, it is extremely difficult to compute. Comp
lete computations have been done only for a few families of racks. Our met
hods add a new family to this list\, the family of permutation racks. The
necessary background on racks and quandles\, and their role in braid and k
not theories\, will be given.\n
LOCATION:https://stable.researchseminars.org/talk/Knotsandtopology/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:S. Kim
DTSTART:20210125T153000Z
DTEND:20210125T170000Z
DTSTAMP:20260404T111446Z
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 kn
ot\, which 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 $S_{g} \\t
imes S^{1}$\, for example\, diagrams\, moves for diagrams and so on. For k
nots 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 will discuss the geometric meaning of the rotating information.\n
LOCATION:https://stable.researchseminars.org/talk/Knotsandtopology/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:V.O. Manturov
DTSTART:20210201T153000Z
DTEND:20210201T170000Z
DTSTAMP:20260404T111446Z
UID:Knotsandtopology/6
DESCRIPTION:Title: Invariants of free knots valued in free groups\nby V.O
. Manturov as part of Knots and representation theory\n\n\nAbstract\nThis
talk is a part of the project of creating ``non-commutative'' invariants\n
in topology. The main idea is to replace ``characteristic classes'' of mod
uli spaces\nwith ``characteristic loops''. We discuss ``the last stage'' o
f the talk devoted to\nthe abstract objects we get in the end: the free kn
ots\, an discuss their invariants\nvalued in free groups.\n \nThese invar
iants allow one to detect easily mutations\, invertibility\, and other phe
nomena.\n
LOCATION:https://stable.researchseminars.org/talk/Knotsandtopology/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Manpreet Singh (Mohali\, India)
DTSTART:20210208T153000Z
DTEND:20210208T170000Z
DTSTAMP:20260404T111446Z
UID:Knotsandtopology/7
DESCRIPTION:Title: Algebraic structures in knot theory\nby Manpreet Singh
(Mohali\, India) as part of Knots and representation theory\n\n\nAbstract
\nA virtual knot is a smooth\, simple closed curve in a thickened compact
oriented surfaces considered up to ambient isotopy\, stabilisation/destabi
lisation and orientation preserving homeomorphism of surfaces. Kuperberg p
roves that every virtual link has a unique representative as a link up to
ambient isotopy in a thickened surface of the minimal genus. A classical k
not theory is the study of smooth embedding of circles in the 3-sphere up
to ambient isotopy. Considering classical theory as the study of links in
the thickened 2-sphere\, the preceding result implies that classical knot
theory is embedded inside virtual knot theory. One of the fundamental prob
lems in knot theory is the classification of knots. In the classical case\
, the fundamental group of the knot complement space is a well known invar
iant. But there are examples where it fails to distinguish distinct knots.
Around the 1980s\, Matveev and Joyce introduce a complete classical knot
invariant (up to the orientation of the knot and the ambient space) using
distributive 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 link quandles are residually finite. Using this\, I will prove that th
e word problem is solvable for link quandle. I will discuss the orderabili
ty of quandles\, in particular for link quandles. Since all link groups ar
e left-orderable\, it is reasonable to expect that link quandles are left
(right)-orderable. In contrast\, I will show that orderability of link qua
ndle behave quite differently than that of the corresponding link groups.
I will also introduce a recent combinatorial generalisation of virtual lin
ks to which we name as marked virtual links. I will associate groups and p
eripheral structures to these diagrams and study their properties.\n
LOCATION:https://stable.researchseminars.org/talk/Knotsandtopology/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Neha Nanda
DTSTART:20210215T153000Z
DTEND:20210215T170000Z
DTSTAMP:20260404T111446Z
UID:Knotsandtopology/8
DESCRIPTION:Title: An excursion on doodles on surfaces and virtual twins\
nby Neha Nanda as part of Knots and representation theory\n\n\nAbstract\nS
tudy of certain isotopy classes of a finite collection of immersed circles
without triple or higher intersections on closed oriented surfaces can be
thought of as a planar analogue of virtual knot theory where the genus ze
ro case corresponds to classical knot theory. Alexander and Markov theorem
s for the classical setting is well-known\, where the role of groups is pl
ayed by twin groups\, a class of right-angled Coxeter groups with only far
commutativity relations. In the talk\, Alexander and Markov theorems for
higher genus case\, where the role of groups is played by a new class of g
roups called virtual twin groups\, will be discussed which is work in coll
aboration with Dr Mahender Singh. Furthermore\, recent work on structural
aspects of these groups will be addressed which is a joint work with Dr Ma
hender Singh and Dr Tushar Kanta Naik.\n
LOCATION:https://stable.researchseminars.org/talk/Knotsandtopology/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Th. Yu. Popelensky
DTSTART:20210222T153000Z
DTEND:20210222T170000Z
DTSTAMP:20260404T111446Z
UID:Knotsandtopology/9
DESCRIPTION:Title: Quaternionic conjugation spaces\nby Th. Yu. Popelensky
as part of Knots and representation theory\n\n\nAbstract\nThere is a cons
iderable amount of examples of spaces $X$ equipped with an involution $\\t
au$\nsuch that the mod 2--cohomology rings $H^{2*}(X)$ and $H^*(X^\\tau)$
are isomorphic.\nHausmann\, Holm\, and Puppe have shown that such an isomo
rphim is a part of a certain structure\non equivariant cohomology of $X$ a
nd $X^\\tau$\, which is called an {\\it $H$-frame}.\nThe simplest examples
are complex Grassmannians and flag manifolds with complex conjugation.\nW
e develop a similar notion of $Q$-frame which appears in the situation\nwh
en a space $X$ is equipped with two commuting involutions $\\tau_1\,\\tau_
2$ and\nthe mod 2-cohomology rings $H^{4*}(X)$ and $H^*(X^{\\tau_1\,\\tau_
2})$ are isomorphic.\nMotivating examples are quaternionic Grassmannians a
nd quaternionic flag manifolds equipped with\ntwo complex involutions. We
show naturality and uniqueness of $Q$-framing.\nWe prove that $Q$-framing
can be defined for direct limits\, products\, etc. of $Q$-framed spaces.\n
This list of operations contains glueing a disk in $\\HH^n$ with complex i
nvolutions $\\tau_1$ and $\\tau_2$ to a $Q$-framed space by an equivariant
map of boundary sphere.\n\nAn imporant part of $H$-frame structure in pap
er by H.--H.--P. was so called {\\em conjugation equation}.\nFranz and Pup
pe calculated the coefficients of the conjugation equation in terms of the
Steenrod squares.\nAs a part of a $Q$-framing we introduce corresponding
structure\nequation and express its coefficients by explicit formula in te
rms of the Steenrod operations.\n
LOCATION:https://stable.researchseminars.org/talk/Knotsandtopology/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:M. Khovanov
DTSTART:20210301T153000Z
DTEND:20210301T170000Z
DTSTAMP:20260404T111446Z
UID:Knotsandtopology/10
DESCRIPTION:Title: Introduction to universal construction of topological the
ories\nby M. Khovanov as part of Knots and representation theory\n\n\n
Abstract\nA multiplicative function on diffeomorphism classes of n-manifol
ds extends to a functorial assignment of state spaces to (n-1)-manifolds.
Resulting topological theories are interesting already in very low dimensi
ons. We'll explain the framework for these theories and provide a number o
f examples.\n
LOCATION:https://stable.researchseminars.org/talk/Knotsandtopology/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Byeorhi Kim
DTSTART:20210315T153000Z
DTEND:20210315T170000Z
DTSTAMP:20260404T111446Z
UID:Knotsandtopology/11
DESCRIPTION:Title: On generalized quandle extensions of a quandle defined on
a group\nby Byeorhi Kim as part of Knots and representation theory\n\
n\nAbstract\nIn 1980s\, Joyce and Matveev introduced a quandle which is an
algebraic structure related to knot theory. In the papers\, they also sho
wed that for given a group and a group automorphism\, there is a quandle s
tructure on the group\, later called ’generalized Alexander quandle’.
In particular\, when the automorphism is an inner automorphism by a fixed
element $\\zeta$\, we denote the quandle operation by $\\triangleleft_{\\z
eta}$. In this talk\, we study a relationship between group extensions of
a group $G$ and quandle extensions of a generalized Alexander quandle $(G\
,\\\\triangleleft_{\\zeta})$ whose underlying set coincides with that of $
G$. This is a joint work with Y.Bae and S.Carter.\n
LOCATION:https://stable.researchseminars.org/talk/Knotsandtopology/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mahender Singh
DTSTART:20210322T153000Z
DTEND:20210322T170000Z
DTSTAMP:20260404T111446Z
UID:Knotsandtopology/12
DESCRIPTION:Title: Surface knot theory and related groups\nby Mahender S
ingh as part of Knots and representation theory\n\n\nAbstract\nStudy of ce
rtain isotopy classes of a finite collection of immersed circles without t
riple or higher intersections on closed oriented surfaces can be thought o
f as a planar analogue of virtual knot theory where the genus zero case co
rresponds to classical knot theory. It is intriguing to know which class o
f groups serves the purpose that Artin braid groups serve in classical kno
t theory. Mikhail Khovanov proved that twin groups\, a class of right angl
ed Coxeter groups with only far commutativity relations\, do the job for g
enus zero case. A recent work shows that an appropriate class of groups ca
lled virtual twin groups fits into the theory for higher genus cases. The
talk would give an overview of some recent developments along these lines.
\n
LOCATION:https://stable.researchseminars.org/talk/Knotsandtopology/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Svjetlana Terzi ́c
DTSTART:20210329T153000Z
DTEND:20210329T170000Z
DTSTAMP:20260404T111446Z
UID:Knotsandtopology/13
DESCRIPTION:Title: Toric topology of the Grassmann manifolds\nby Svjetla
na Terzi ́c as part of Knots and representation theory\n\n\nAbstract\nbas
ed on joint 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 Gr
assmann manifold $G_{n\,2}$ which is connected to a series of problems
in modern algebraic topology\, algebraic geometry and mathematical physic
s. \n\nThe aim of the talk is to present the recent results which are c
oncerned 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 parameter
s $\\mathcal{F}_{n}$\;\n\\item virtual spaces of parameters $\\widetild
e{F}_{\\sigma}\\subset \\mathcal{F}_{n}$ which correspond to the strata $
W_{\\sigma}$ in stratification $G_{n\,2} = \\cup _{\\sigma} W_{\\sigma}$
defined in terms of the Pl\\"ucker coordinates\;\n\\item projections
$\\widetilde{F}_{\\sigma}\\to F_{\\sigma}$ for the spaces of parameters
$F_{\\sigma}$ which correspond to the strata $W_{\\sigma}$.\n\\end{itemi
ze}\n\nIn the course of the talk it will be described the chamber decompos
ition of the hypersimplex $\\Delta _{n\,2}$ which is defined by the spec
ial arrangements of hyperplanes and represents one of the basic tools for
the description of the orbit space $G_{n\,2}/T^n$ in terms of the giv
en notions.\n
LOCATION:https://stable.researchseminars.org/talk/Knotsandtopology/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hyeran Cho
DTSTART:20210412T153000Z
DTEND:20210412T170000Z
DTSTAMP:20260404T111446Z
UID:Knotsandtopology/14
DESCRIPTION:Title: Derivation of Schubert normal forms of 2-bridge knots fro
m (1\,1)-diagrams\nby Hyeran Cho as part of Knots and representation t
heory\n\n\nAbstract\nA genus one 1-bridge knot (simply called a (1\, 1)-kn
ot) is a knot that can be decomposed into two trivial arcs embed in two so
lid tori 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 i
ntegers 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 tal
k\, we give the dual diagram of D(a\, 0\, 1\, r) explicitly and present ho
w to derive a Schubert normal form of a 2-bridge knot from the dual diagra
m. This gives an alternative proof of the Grasselli and Mulazzani’s resu
lt asserting that D(a\, 0\, 1\, r) is a (1\, 1)-diagram of 2-bridge knot w
ith a Schubert normal form b(2a+1\, 2r).\n
LOCATION:https://stable.researchseminars.org/talk/Knotsandtopology/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Colin Adams
DTSTART:20210419T153000Z
DTEND:20210419T170000Z
DTSTAMP:20260404T111446Z
UID:Knotsandtopology/15
DESCRIPTION:Title: Multi-crossings and Petal Number for Classical and Virtua
l Knots\nby Colin Adams as part of Knots and representation theory\n\n
\nAbstract\nInstead of considering projections of knots with two strands c
rossing at every crossing\, we can ask for n strands to cross at every cro
ssing. We will show that every knot and link has such an n-crossing projec
tion for all integers n greater than 1 and therefore an n-crossing number.
We also show that every knot has a projection with a single multi-crossin
g and no nested loops\, which is a petal projection and which generates a
petal number. We will discuss these ideas for both classical and virtual
knots.\n
LOCATION:https://stable.researchseminars.org/talk/Knotsandtopology/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ivan Dynnikov
DTSTART:20210426T153000Z
DTEND:20210426T170000Z
DTSTAMP:20260404T111446Z
UID:Knotsandtopology/16
DESCRIPTION:Title: A method for distingiushing Legendrian and transverse lin
ks\nby Ivan Dynnikov as part of Knots and representation theory\n\n\nA
bstract\nLegendrian (respectively\, transverse) links are smooth links in
the\nthree-space that are tangent (respectively\, transverse) to the stand
ard\ncontact structure. Deciding whether two such links are equivalent mod
ulo a\ncontactomorphism is a hard problem in general. Many topological inv
ariants\nof Legendrian and transverse links are known\, but they do not su
ffice for\na classification even in the case of knots of crossing number s
ix.\n\nIn recent joint works with Maxim Prasolov and Vladimir Shastin we\n
developed a rectangular diagram machinery for surfaces and links in the\nt
hree-space. This machinery has a tight connection with contact topology\,\
nnamely with Legendrian links and Giroux's convex surfaces. We are mainly\
ninterested in studying rectangular diagrams of links that cannot be\nmono
tonically simplified by means of elementary moves. It turns out that\nthis
question is nearly equivalent to classification of Legendrian links.\n\nT
he main outcome we have so far is an algorithm for comparing two\nLegendri
an (or transverse) links. The computational complexity of the\nalgorithm i
s\, of course\, very high\, but\, in many cases\, certain parts of\nthe pr
ocedure can be bypassed\, which allows us to distinguish quite\ncomplicate
d Legendrian knots. In praticular\, we have managed to provide an\nexample
of two inequivalent Legendrian knots cobounding an annulus tangent\nto th
e standrard contact structure along the entire boundary. Such\nexamples we
re previously unknown.\n\nThe work is supported by the Russian Science Fou
ndation under\ngrant 19-11-00151\n
LOCATION:https://stable.researchseminars.org/talk/Knotsandtopology/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ivan Reshetnikov
DTSTART:20210503T153000Z
DTEND:20210503T170000Z
DTSTAMP:20260404T111446Z
UID:Knotsandtopology/17
DESCRIPTION:Title: Discontinuously basic sets and the 13th problem of Hilber
t\nby Ivan Reshetnikov as part of Knots and representation theory\n\n\
nAbstract\nA subset $M \\subset \\textbf{R}^3$ is called a \\emph{disconti
nuously basic subset}\, if for any function $f \\colon M \\to \\textbf{R}$
there exist such functions $f_1\; f_2\; f_3 \\colon \\textbf{R} \\to R$ t
hat $f(x_1\, x_2\, x_3) = f_1(x_1) + f_2(x_2) + f_3(x_3)$ for each point $
(x_1\, x_2\, x_3)\\in M$. We will prove a criterion for a discontinuous ba
sic subset for some specific subsets in terms of some graph properties. We
will also introduce several constructions for minimal discontinuous non-b
asic subsets.\n
LOCATION:https://stable.researchseminars.org/talk/Knotsandtopology/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Adam Lowrance
DTSTART:20210510T153000Z
DTEND:20210510T170000Z
DTSTAMP:20260404T111446Z
UID:Knotsandtopology/18
DESCRIPTION:Title: The Jones polynomial\, Khovanov homology\, and Turaev gen
us\nby Adam Lowrance as part of Knots and representation theory\n\n\nA
bstract\nThe Turaev surface of a link diagram is a surface built from a co
bordism between the all-A and all-B Kauffman states of the diagram\, and t
he Turaev genus of a link is the minimum genus of the Turaev surface for a
ny diagram of the link. The Turaev surface was first used to give simple v
ersions of the Kauffman-Mursaugi-Thistlethwaite proofs of some Tait conjec
tures. \n\nIn this talk\, we first give a brief history of the Turaev surf
ace\, the 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://stable.researchseminars.org/talk/Knotsandtopology/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andriy Haydys
DTSTART:20210607T153000Z
DTEND:20210607T170000Z
DTSTAMP:20260404T111446Z
UID:Knotsandtopology/19
DESCRIPTION:Title: On Fukaya-Seidel category and Khovanov homology\nby A
ndriy Haydys as part of Knots and representation theory\n\n\nAbstract\nI w
ill talk about a construction of the Fukaya-Seidel category for the holomo
rphic Chern-Simons functional. This involves certain gauge-theoretic equat
ions\, which are conjecturally related also to Khovanov homology.\n
LOCATION:https://stable.researchseminars.org/talk/Knotsandtopology/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Scott Baldridge
DTSTART:20230717T153000Z
DTEND:20230717T170000Z
DTSTAMP:20260404T111446Z
UID:Knotsandtopology/20
DESCRIPTION:Title: Bigraded 2-color homology is not a variant of Khovanov ho
mology!\nby Scott Baldridge as part of Knots and representation theory
\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/Knotsandtopology/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dimitris Kodokostas
DTSTART:20230724T153000Z
DTEND:20230724T170000Z
DTSTAMP:20260404T111446Z
UID:Knotsandtopology/21
DESCRIPTION:Title: An algorithmically computable complete invariant of knots
\nby Dimitris Kodokostas as part of Knots and representation theory\n\
nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/Knotsandtopology/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:TBA
DTSTART:20230731T153000Z
DTEND:20230731T170000Z
DTSTAMP:20260404T111446Z
UID:Knotsandtopology/22
DESCRIPTION:by TBA as part of Knots and representation theory\n\nAbstract:
TBA\n
LOCATION:https://stable.researchseminars.org/talk/Knotsandtopology/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lilya A. Grunwald
DTSTART:20230807T153000Z
DTEND:20230807T170000Z
DTSTAMP:20260404T111446Z
UID:Knotsandtopology/23
DESCRIPTION:Title: The number of rooted forests in circulant graph\nby L
ilya A. Grunwald as part of Knots and representation theory\n\nAbstract: T
BA\n
LOCATION:https://stable.researchseminars.org/talk/Knotsandtopology/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ben McCarty
DTSTART:20230814T153000Z
DTEND:20230814T170000Z
DTSTAMP:20260404T111446Z
UID:Knotsandtopology/24
DESCRIPTION:Title: n-Color Vertex Homology\nby Ben McCarty as part of Kn
ots and representation theory\n\n\nAbstract\nWe will show how to categorif
y the vertex bracket polynomial\, which is based upon one of Roger Penrose
’s formulas for counting the number of 3-edge colorings of a planar triv
alent graph. We produce a bigraded theory called bigraded n-color vertex h
omology whose graded Euler characteristic is the vertex bracket polynomial
. We then produce a spectral sequence whose E∞ page is a filtered theory
called filtered n-color vertex homology\, and show that it is generated b
y certain types of properly colored ribbon subgraphs. In particular for n
= 2\, we show that the n-color vertex homology is generated by colorings t
hat correspond to perfect matchings. This is joint work with Scott Baldri
dge.\n
LOCATION:https://stable.researchseminars.org/talk/Knotsandtopology/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alina Pavlikova
DTSTART:20230821T153000Z
DTEND:20230821T170000Z
DTSTAMP:20260404T111446Z
UID:Knotsandtopology/26
DESCRIPTION:Title: Bipartite knots and its applications\nby Alina Pavlik
ova as part of Knots and representation theory\n\n\nAbstract\nThe non-bipa
rtite knot conjecture\, formulated in 1987 by Józef Przytitzky\, remained
open for 24 years\, despite the efforts of several eminent mathematicians
\, including its author and J. H. Conway [3]. In 2011\, S. Duzhin found a
necessary condition for a knot to be bipartite and gave examples of non-bi
partite knots. Further study of bipartite knots we explore their rich comb
inatorial structure and hidden connections with the four color graph theo
rem.\n
LOCATION:https://stable.researchseminars.org/talk/Knotsandtopology/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dmitrii Rachenkov
DTSTART:20230904T153000Z
DTEND:20230904T170000Z
DTSTAMP:20260404T111446Z
UID:Knotsandtopology/28
DESCRIPTION:Title: Quasi-polynomial solutions of anharmonic oscillators\
nby Dmitrii Rachenkov as part of Knots and representation theory\n\n\nAbst
ract\nIn 2014\, in the article “Quadratic differentials as stability co
nditions” T. Bridgeland and I. Smith proved that that moduli spaces of m
eromorphic quadratic differentials with simple zeroes on compact Riemann s
urfaces can be identified with spaces of stability conditions on a class o
f CY3 triangulated categories. These categories can be defined using quive
rs with potential associated to triangulated surfaces.\n\nAny quadratic di
fferential defines an anharmonic oscillator equation and one can ask wheth
er it has as a solution quasi-polynomial (=polynomial multiplied by expone
nt). The general answer – work in progress! – should have a nice view
in terms of the spaces of stability conditions .\n\nIn my talk I am going
to present in examples Bridgeland-Smith’s construction. If time permits
I will speak about Shapiro-Tater conjecture which proof involves quasi-po
lynomial solutions of a quartic anharmonic oscillators.\n\n \n\nReferences
: arXiv:2203.16889\, arXiv:1302.7030\n
LOCATION:https://stable.researchseminars.org/talk/Knotsandtopology/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Igor Nikonov
DTSTART:20230828T153000Z
DTEND:20230828T170000Z
DTSTAMP:20260404T111446Z
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 the
ory\n\n\nAbstract\nThe groups $G^k_n$ were defined by V. O. Manturov in or
der to describe dynamical systems in configuration systems. In the talk we
will consider two applications of this theory: we define a biquandle stru
cture on the groups $G^k_n$\, and construct a homomorphism from the surfac
e singular braid monoid to the group $G^2_n$.\n
LOCATION:https://stable.researchseminars.org/talk/Knotsandtopology/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Igor Nikonov
DTSTART:20230911T153000Z
DTEND:20230911T170000Z
DTSTAMP:20260404T111446Z
UID:Knotsandtopology/30
DESCRIPTION:Title: Photography principle\, data transmission\, and invariant
s of manifolds\nby Igor Nikonov as part of Knots and representation th
eory\n\n\nAbstract\nIn the present talk we discuss the techniques suggeste
d in [V. O. Manturov\, I.M. Nikonov\, The groups Гn4\, braids\, and 3-man
ifolds\, arXiv: 2305.06316] and the photography principle [V.O.Manturov\,
Z.Wan\, The photography method: solving pentagon\, hexagon\, and other equ
ations\, arXiv:2305.11945] to open a very broad path for constructing inva
riants for manifolds of dimensions greater than or equal to 4.\n
LOCATION:https://stable.researchseminars.org/talk/Knotsandtopology/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Younes Benyahia (SISSA\, Italy)
DTSTART:20230918T153000Z
DTEND:20230918T170000Z
DTSTAMP:20260404T111446Z
UID:Knotsandtopology/31
DESCRIPTION:Title: Exotic 2-knots and 2-links in 4-manifolds.\nby Younes
Benyahia (SISSA\, Italy) as part of Knots and representation theory\n\n\n
Abstract\nTwo smoothly embedded surfaces in a 4-manifold are called exotic
if they are topologically isotopic but smoothly not. In 1997\, Fintushel
and Stern constructed the first examples of exotic surfaces. Since then\,
there have been many constructions of exotic surfaces in other settings\,
in particular\, ones closer to the smooth unknotting conjecture. \n In thi
s 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 j
oint work with Bais\, Malech and Torres (see also https://arxiv.org/abs/22
06.09659).\n
LOCATION:https://stable.researchseminars.org/talk/Knotsandtopology/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hongdae Yun
DTSTART:20230925T153000Z
DTEND:20230925T170000Z
DTSTAMP:20260404T111446Z
UID:Knotsandtopology/32
DESCRIPTION:Title: A note on geometric realization of extreme Khovanov hom
ology for some family of links\nby Hongdae Yun as part of Knots and re
presentation theory\n\n\nAbstract\nThe Khovanov (co)homology was introduce
d by Mikhail Khovanov in 2000 and Viro explained it in terms of enhanced
states of diagram. Also J. González-Meneses\, P.M.G. Manchón\, M. Silve
ro proved (potential) extreme Khovanov homology of link is isomorphic to i
ndependence simplicial complex of Lando graph from the link. In this talk\
, we recall the definition of Khovanov homology. Furthermore we investigat
e the geometric realization of extreme Khovanov homology of some family of
knots and links. This is joint work with Mark H Siggers and Seung Yeop Ya
ng.\n
LOCATION:https://stable.researchseminars.org/talk/Knotsandtopology/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Igor Nikonov
DTSTART:20231002T153000Z
DTEND:20231002T170000Z
DTSTAMP:20260404T111446Z
UID:Knotsandtopology/33
DESCRIPTION:Title: Examples of weight systems of framed chord diagrams\n
by Igor Nikonov as part of Knots and representation theory\n\n\nAbstract\n
We extend Bar-Natan’s construction of weight systems induced by Lie alge
bra representations to the case of framed chord diagrams. (joint work wit
h Denis Ilyutko)\n
LOCATION:https://stable.researchseminars.org/talk/Knotsandtopology/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:П. Н. Питал
DTSTART:20231023T153000Z
DTEND:20231023T170000Z
DTSTAMP:20260404T111446Z
UID:Knotsandtopology/34
DESCRIPTION:Title: Обобщенные факториалы и p-упоря
дочения\nby П. Н. Питал as part of Knots and representat
ion theory\n\n\nAbstract\nВ докладе будет рассказан
о об интересном обобщении понятия факто
риала\, предложенном М. Бхаргавой для де
декиндовых колец.\n
LOCATION:https://stable.researchseminars.org/talk/Knotsandtopology/34/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kevin Walker
DTSTART:20231030T153000Z
DTEND:20231030T170000Z
DTSTAMP:20260404T111446Z
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 di
scuss a very general (“universal”) approach to constructing TQFT state
sums for manifolds. This will be based on https://arxiv.org/abs/2104.021
01\, but in contrast to that paper I’ll start with concrete examples and
work toward the more general statements.\n
LOCATION:https://stable.researchseminars.org/talk/Knotsandtopology/35/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hayk Sedrakyan
DTSTART:20231113T153000Z
DTEND:20231113T170000Z
DTSTAMP:20260404T111446Z
UID:Knotsandtopology/36
DESCRIPTION:Title: Distance formula for a point inside a triangle (formula f
or a diagonal of any quadrilateral)\nby Hayk Sedrakyan as part of Knot
s and representation theory\n\n\nAbstract\nGiven a connected graph with fo
ur vertices and six edges (a quadrilateral and its diagonals). We obtained
a novel formula to find the length of any of its edges using the other fi
ve edge lengths. For example\, in the case of a convex quadrilateral we ar
e able to find the length of its diagonal using its side lengths and the l
ength of 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://stable.researchseminars.org/talk/Knotsandtopology/36/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Scott Carter
DTSTART:20231127T153000Z
DTEND:20231127T170000Z
DTSTAMP:20260404T111446Z
UID:Knotsandtopology/37
DESCRIPTION:Title: Intricacies about the binary icosahedral group\nby Sc
ott Carter as part of Knots and representation theory\n\n\nAbstract\nZeema
n's theorem tells us that both the 5-twist spun trefoil and the 2-twist sp
un torus knot T(3\,5) are fibered knotted spheres in 4-dimensional space w
here the fiber is the punctured Poincare homology sphere. That closed homo
logy sphere is the quotient of the 3-sphere under the action of the binary
icosahedral group. It is a 5-fold or 2-fold branched cover of 3-space bra
nched over the respective knot. The group is isomorphic to SL_2(Z/5). I wa
nt to understand all of the statements asserted above. To that end\, I am
working on comparing three different presentations of this group. In as mu
ch as possible\, I will explicitly represent the elements in the group as
strings with quipu\, matrices\, generators\, and elements in the 3-sphere.
I'll also give different pictures that allow one to compute relationships
among the words in the standard presentation of the group. I'm also inter
ested in braiding the homology sphere in 5-space.\n
LOCATION:https://stable.researchseminars.org/talk/Knotsandtopology/37/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bao Vuong
DTSTART:20231120T153000Z
DTEND:20231120T170000Z
DTSTAMP:20260404T111446Z
UID:Knotsandtopology/38
DESCRIPTION:Title: Reidemeister torsion of link complements in 3-torus\n
by Bao Vuong as part of Knots and representation theory\n\n\nAbstract\nThe
relation between Alexander polynomial of a knot and the torsion invariant
of Reidemeister\, Franz and de Rham for knot complement was first noticed
by Milnor. As a consequence of the relation\, Milnor gave another proof f
or symmetry of Alexander polynomial. Milnor applied the result to knot the
ory\, considering the case of classical knot\, i.e. the knot complement ha
s the homology of the circle. It turns out that there are similar relation
s between Reidemeister torsion and twisted Alexander polynomial for the ca
se of knot complement in other spaces\, rather than three dimensional sphe
re when the homology group contains also torsion. The technology to get ex
plicit relations as Milnor had created making use of simple homotopy theor
y for CW-complexes and Fox free differential calculus. Those ensure a CW s
tructure for the knot complement\, associated with a presentation of the f
undamental group\, so that the boundary maps are obtained by free derivati
ves. The method works out fine also for the case of knots and links in thr
ee dimensional torus. Thus we show that the Reidemeister torsion of the li
nk complement and its twisted Alexander polynomial are equal.\n
LOCATION:https://stable.researchseminars.org/talk/Knotsandtopology/38/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Martinez-Garcia Jesus
DTSTART:20231204T153000Z
DTEND:20231204T170000Z
DTSTAMP:20260404T111446Z
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-
stability is a recent theory that interacts with complex and analytic geom
etry\, birational geometry and moduli theory. Take a Fano variety (a compl
ex projective variety with positive Ricci curvature). Can we construct a c
ompact moduli space that parametrises all the ‘reasonable’ degeneratio
ns of this variety (including fairly singular ones) and that it is itself
‘reasonable’ as a space? The answer is positive if the variety is K-(p
oly)stable and this moduli space\, known as K-moduli\, parametrises all K-
polystable Fano varieties. From a complex viewpoint\, K-polystable Fano va
rieties are precisely those which admit a Kahler-Einstein metric.\n\nSmoot
h Fano varieties have been classified up to dimension 3 but until recent w
ork by Abban-Zhuang and others\, we did not have enough tools to decide wh
ich ones were K-polystable\, let alone to describe the K-moduli itself. In
this talk I will survey these notions and present recent progress in the
subject\, with special emphasis in the programme to classify Fano varietie
s and their K-moduli in low dimensions.\n
LOCATION:https://stable.researchseminars.org/talk/Knotsandtopology/39/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Igor M. Nikonov
DTSTART:20231211T153000Z
DTEND:20231211T170000Z
DTSTAMP:20260404T111446Z
UID:Knotsandtopology/40
DESCRIPTION:Title: Rota-Baxter operators and Hopf algebras\nby Igor M. N
ikonov as part of Knots and representation theory\n\n\nAbstract\nWe will c
onsider several problems related to Rota-Baxter operators and Hopf algebra
s:\n1) construction of group Rota-Baxter operators of arbitrary weight on
Lie groups\n2) conditions under which a Rota-Baxter operator on a group is
a Rota-Baxter operator of a group algebra\n3) construction of relative Ro
th-Baxter operators for noncommutative Hopf algebras\n
LOCATION:https://stable.researchseminars.org/talk/Knotsandtopology/40/
END:VEVENT
BEGIN:VEVENT
SUMMARY:O.G. Styrt
DTSTART:20231218T153000Z
DTEND:20231218T170000Z
DTSTAMP:20260404T111446Z
UID:Knotsandtopology/41
DESCRIPTION:Title: Elements of a Lie algebra acting nilpotently in all its r
epresentations\nby O.G. Styrt as part of Knots and representation theo
ry\n\n\nAbstract\nAn equivalent condition for an element of a Lie algebra
acting nilpotently in all its representations is obtained. Namely\, it sho
uld belong to the derived algebra and go via factoring over the radical to
a nilpotent element of the corresponding (semisimple) quotient algebra.\n
The talk is based on the speaker's preprint https://arxiv.org/abs/2209.133
09\n
LOCATION:https://stable.researchseminars.org/talk/Knotsandtopology/41/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Manpreet Singh
DTSTART:20240108T153000Z
DTEND:20240108T170000Z
DTSTAMP:20260404T111446Z
UID:Knotsandtopology/42
DESCRIPTION:Title: Invariants of knots from biquandles and virtual biquandle
s\nby Manpreet Singh as part of Knots and representation theory\n\n\nA
bstract\nWe will prove that for a given virtual link L and a virtual biqua
ndle (X\,f\,R)\, the set of colorings of L by (X\,f\,R) is in bijection wi
th the set of colorings of L by a biquandle (X\,VR)\, where VR is a new op
erator we define on X. The biquandle (X\,VR) is the 1-induced biquandle as
sociated 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 biquandl
e of the virtual biquandle VBQ(L). Furthermore\, the 1-induced biquandle o
f 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 applicati
ons to knots.\n
LOCATION:https://stable.researchseminars.org/talk/Knotsandtopology/42/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Igor Nikonov
DTSTART:20231225T153000Z
DTEND:20231225T170000Z
DTSTAMP:20260404T111446Z
UID:Knotsandtopology/43
DESCRIPTION:Title: Virtual index cocycles and invariants of virtual links\nby Igor Nikonov as part of Knots and representation theory\n\n\nAbstrac
t\nVirtual index cocycle is the 1-cochain that counts virtual crossings in
the arcs of a virtual link diagram. We show how this cocycle can be used
to reformulate and unify some known invariants of virtual links.\n
LOCATION:https://stable.researchseminars.org/talk/Knotsandtopology/43/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Visakh Narayanan
DTSTART:20240115T153000Z
DTEND:20240115T170000Z
DTSTAMP:20260404T111446Z
UID:Knotsandtopology/44
DESCRIPTION:Title: Knots in $\\mathbb{R}P^3$\nby Visakh Narayanan as par
t of Knots and representation theory\n\n\nAbstract\nWe will discuss some p
roperties of knots in three dimensional projective space. Our technique fo
r this purpose is to associate a virtual link to a link in projective spac
e so that equivalent projective links go to equivalent virtual links (modu
lo a special flype move). We can then apply techniques in virtual knot the
ory to obtain a Jones polynomial for projective links which also happens t
o be equivalent to the Jones polynomial constructed by Drobotukhina. Then
we would discuss a combinatorial cobordism theory for projective links whi
ch may be used to apply virtual Khovanov homology and the virtual Rasmusse
n invariant of Dye\, Kaestner\, and Kauffman to projective links.\n
LOCATION:https://stable.researchseminars.org/talk/Knotsandtopology/44/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Seongjeong Kim
DTSTART:20240122T153000Z
DTEND:20240122T170000Z
DTSTAMP:20260404T111446Z
UID:Knotsandtopology/45
DESCRIPTION:Title: The groups $G_{n}^{3}$ and rhombi tilings of 2n-gons\
nby Seongjeong Kim as part of Knots and representation theory\n\n\nAbstrac
t\nIn this talk we will consider a map from the set of rhombi tilings of 2
n-gon to the group $G_{n}^{3}$ and will discuss our further researches.\n
LOCATION:https://stable.researchseminars.org/talk/Knotsandtopology/45/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Christoph Schiller
DTSTART:20240226T153000Z
DTEND:20240226T170000Z
DTSTAMP:20260404T111446Z
UID:Knotsandtopology/46
DESCRIPTION:Title: From the three Reidemeister moves to the three Lie gauge
groups – with consequences for the unification of physics\nby Chris
toph Schiller as part of Knots and representation theory\n\n\nAbstract\nQu
antum theory suggests that the three observed gauge groups U(1)\, SU(2) an
d SU(3) are related to the three Reidemeister moves of knot theory: twists
\, pokes and slides. The background for the relation is clarified: modelli
ng \nparticles as fluctuating tangles of strands explains wave functions.
Classifying tangles explains the elementary \nfermions and bosons. It is t
hen shown that twists generate U(1) and that pokes generate SU(2). The emp
hasis is put on deducing the relation between slides\, the corresponding s
trand deformations\, the Gell-Mann matrices\, and the Lie group SU(3). Con
sequences for unification are deduced.\n
LOCATION:https://stable.researchseminars.org/talk/Knotsandtopology/46/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Igor Nikonov
DTSTART:20240129T153000Z
DTEND:20240129T170000Z
DTSTAMP:20260404T111446Z
UID:Knotsandtopology/47
DESCRIPTION:Title: Traits of crossings and functorial maps\nby Igor Niko
nov as part of Knots and representation theory\n\n\nAbstract\nOne of the m
ajor applications 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://stable.researchseminars.org/talk/Knotsandtopology/47/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Seongjeong Kim
DTSTART:20240205T153000Z
DTEND:20240205T170000Z
DTSTAMP:20260404T111446Z
UID:Knotsandtopology/48
DESCRIPTION:Title: The classification of knots in $S_{g}\\times S^{1}$ of th
e small number of crossings\nby Seongjeong Kim as part of Knots and re
presentation theory\n\n\nAbstract\nIn this talk we construct invariants fo
r 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://stable.researchseminars.org/talk/Knotsandtopology/48/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Мороз Борис Барух
DTSTART:20240212T153000Z
DTEND:20240212T170000Z
DTSTAMP:20260404T111446Z
UID:Knotsandtopology/49
DESCRIPTION:Title: Гипотеза Римана и диофантовы у
равнения\nby Мороз Борис Барух as part of Knots
and representation theory\n\n\nAbstract\nВ нашей (совместн
ой с А.А.Норкином) недавней работе явно в
ыписано диофантово уравнение\, неразреш
имость которого эквивалентна гипотезе Р
имана. Я расскажу об этой работе.\n
LOCATION:https://stable.researchseminars.org/talk/Knotsandtopology/49/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dmitry Solovyev
DTSTART:20240304T153000Z
DTEND:20240304T170000Z
DTSTAMP:20260404T111446Z
UID:Knotsandtopology/50
DESCRIPTION:Title: Universal construction\, foams and link homology\nby
Dmitry Solovyev as part of Knots and representation theory\n\n\nAbstract\n
This talk 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 categorifies HOMFLY-PT link invariant and RT sl(N) quantum link inva
riants. This talk is elementary\, the emphasis will be put on the theory o
f unoriented SL(3) foams\, their evaluation and corresponding universal co
nstruction. This version of foam theory is related to 4-color theorem and
Kronheimer-Mrowka 3-orbifold homology theory. If time permits\, we will al
so talk about how oriented SL(3) foams categorify the Kuperberg invariant.
\n
LOCATION:https://stable.researchseminars.org/talk/Knotsandtopology/50/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Igor Nikonov
DTSTART:20240219T153000Z
DTEND:20240219T170000Z
DTSTAMP:20260404T111446Z
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 the
ory\n\n\nAbstract\nThe groups $G^k_n$ were defined by V. O. Manturov in or
der to describe dynamical systems in configuration systems. In the talk we
will consider two applications of this theory: we define a biquandle stru
cture on the groups Gkn\, and construct a homomorphism from the surface si
ngular braid monoid to the group $G^2_n$.\n
LOCATION:https://stable.researchseminars.org/talk/Knotsandtopology/51/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Igor Nikonov
DTSTART:20240311T153000Z
DTEND:20240311T170000Z
DTSTAMP:20260404T111446Z
UID:Knotsandtopology/52
DESCRIPTION:Title: Flat-virtual knot: introduction and some invariants\n
by Igor Nikonov as part of Knots and representation theory\n\n\nAbstract\n
In attempts to construct a map from classical knots to virtual ones\, we d
efine a series of maps from knots in the full torus (thickened torus) to f
lat-virtual knots. We give definition of flat-virtual knots and presents A
lexander-like polynomial and Kauffman bracket for them. We also discuss a
possible extension of the notion of flat-virtual knots — so-called multi
-flat knots.\n
LOCATION:https://stable.researchseminars.org/talk/Knotsandtopology/52/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Helen Wong
DTSTART:20240325T154500Z
DTEND:20240325T171500Z
DTSTAMP:20260404T111446Z
UID:Knotsandtopology/53
DESCRIPTION:Title: Multiplication in Kauffman bracket skein algebra of a 1-h
ole torus\nby Helen Wong as part of Knots and representation theory\n\
n\nAbstract\nThe Kauffman bracket skein algebra of a surface is a generali
zation of the Jones polynomial for links and is one of few constructions f
rom quantum topology that is clearly related to hyperbolic geometry. To fu
rther understand the relationship\, it is important to understand the mult
iplicative structure of the skein algebra. In this talk\, we present a rec
ursion relation and fast algorithm for multiplication in the skein algebra
in the case of a 1-hole torus.\n
LOCATION:https://stable.researchseminars.org/talk/Knotsandtopology/53/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Oleg Styrt
DTSTART:20240318T154500Z
DTEND:20240318T171500Z
DTSTAMP:20260404T111446Z
UID:Knotsandtopology/54
DESCRIPTION:Title: Elements of a Lie algebra acting nilpotently in all it
s representations\nby Oleg Styrt as part of Knots and representation t
heory\n\n\nAbstract\nAn equivalent condition for an element of a Lie algeb
ra acting nilpotently in all its representations is obtained. Namely\, it
should belong to the derived algebra and go via factoring over the radical
to a nilpotent element of the corresponding (semisimple) quotient algebra
.\nThe talk is based on the preprint https://arxiv.org/abs/2209.13309\n
LOCATION:https://stable.researchseminars.org/talk/Knotsandtopology/54/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Igor M. Nikonov
DTSTART:20240408T153000Z
DTEND:20240408T170000Z
DTSTAMP:20260404T111446Z
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 will consider two applications of this theory: we define a biquandle s
tructure on the groups $G^k_n$\, and construct a homomorphism from the sur
face singular braid monoid to the group $G^2_n$.\n
LOCATION:https://stable.researchseminars.org/talk/Knotsandtopology/55/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Многие
DTSTART:20240415T153000Z
DTEND:20240415T170000Z
DTSTAMP:20260404T111446Z
UID:Knotsandtopology/56
DESCRIPTION:Title: Конференция "Ломоносов"\nby Мн
огие as part of Knots and representation theory\n\n\nAbstract\nКон
ференция "Ломоносов"\nКонференция происх
одит на русском языке.\nСписок докладчик
ов. (Подробнее: https://disk.yandex.com/d/XyvJNm3i_LmjHw)\n\n1)
Жихарева Екатерина Сергеевна (студент\,
кафедра дифференциальной геометрии и пр
иложений\, механико-математический факу
льтет\, МГУ им. М. В. Ломоносова)\, "Трехмер
ные алгебры Ли\, допускающие полупростые
алгебраические операторы Нейенхейса" .\n
\n2) Левин Виктор Анатольевич (студент\, ка
федра дифференциальной геометрии и прил
ожений\, механико-математический факуль
тет\, МГУ им. М. В. Ломоносова)\, "Слоение Ли
увилля интегрируемых биллиардов с остры
ми углами" .\n\n3) Михайлов Иван Николаевич
(студент\, кафедра дифференциальной геом
етрии и приложений\, механико-математиче
ский факультет\, МГУ им. М. В. Ломоносова)\,
"Расстояние Громова-Хаусдорфа между нор
мированными пространствами" .\n\n4) Цыганк
ов Дмитрий Александрович (студент\, кафе
дра высшей геометрии и топологии\, механ
ико-математический факультет\, МГУ им. М.
В. Ломоносова)\, "Гиперболические многооб
разия\, соответствующие прямоугольным м
ногогранникам\, и их расслоения над окру
жностью".\n
LOCATION:https://stable.researchseminars.org/talk/Knotsandtopology/56/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Seongjeong Kim
DTSTART:20240422T153000Z
DTEND:20240422T170000Z
DTSTAMP:20260404T111446Z
UID:Knotsandtopology/57
DESCRIPTION:Title: Invariant of braids by using Ptolemy relation and failure
for knots\nby Seongjeong Kim as part of Knots and representation theo
ry\n\n\nAbstract\nIn this talk\, we will talk about an old work with prof.
V.O. Manturov on the construction of an invariant for braids by using Pto
lemy relation and remind why it fails to be an invariant for links.\n
LOCATION:https://stable.researchseminars.org/talk/Knotsandtopology/57/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Zhihao Wang
DTSTART:20240513T153000Z
DTEND:20240513T170000Z
DTSTAMP:20260404T111446Z
UID:Knotsandtopology/58
DESCRIPTION:Title: On stated $SL(n)$-skein modules\nby Zhihao Wang as pa
rt of Knots and representation theory\n\n\nAbstract\nWe mainly focus on Cl
assical limit\, Splitting map\, and Frobenius homomorphism for stated $S
L(n)$-skein modules\, and Unicity Theorem for stated $SL(n)$-skein algebra
s.\n\nLet $(M\,N)$ be a marked three manifold. We use $S_n(M\,N\,v)$ to de
note the stated $SL(n)$-skein module of $(M\,N)$ where $v$ is a nonzero co
mplex number.\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 c
onsists of all nilpotents. We prove the universal representation algebra o
f $\\pi_1(M)$ is isomorphic to $S_n(M\,N\,1)$ when $N$ has only one compon
ent and $M$ is connected. Furthermore we show $S_n(M\,N^{'}\,1)$ is isomo
rphic to\n$S_n(M\,N\,1)\\otimes O(SLn)$\, where $N\\neq \\emptyset$\, $M$
is connected\, and $N^{'}$ is obtained from $N$ by adding one extra markin
g.\n We also prove the splitting map is injective for any marked three man
ifold when $v=1$\, and show that the splitting map is injective (for gener
al $v$) if there exists at least one component of $N$ such that this compo
nent and the boundary of the splitting disk belong to the same component o
f $\\partial M$.\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 p
rimitive $m$-th root of unity with $m$ being coprime with $2n$ and every
component of $M$ contains at least one marking. \nWe also show the commuta
tivity between Frobenius homomorphism and splitting map. When $(M\,N)$ is
the thickening of an essentially bordered pb surface\, we prove the Froben
ius homomorphism is injective and it's image lives in the center. We prove
the stated $SL(n)$-skein algebra $S_n(\\Sigma\,v)$ is\naffine almost Azum
aya when $\\Sigma$ is an essentially bordered pb surface and $v$ is a prim
itive $m$-th root of unity with $m$ being coprime with $2n$\, which impli
es the Unicity Theorem for $S_n(\\Sigma\,v)$.\n
LOCATION:https://stable.researchseminars.org/talk/Knotsandtopology/58/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Igor Nikonov
DTSTART:20240429T153000Z
DTEND:20240429T170000Z
DTSTAMP:20260404T111446Z
UID:Knotsandtopology/59
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 talk we review the definition of parity on 2-knots\, and prove that t
he Gaussian parity is universal on free two-dimensional knots.\n
LOCATION:https://stable.researchseminars.org/talk/Knotsandtopology/59/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Александр Юрьевич Буряк
DTSTART:20240506T153000Z
DTEND:20240506T170000Z
DTSTAMP:20260404T111446Z
UID:Knotsandtopology/60
DESCRIPTION:Title: DR-иерархии: от пространств моду
лей кривых к интегрируемым системам.\nb
y Александр Юрьевич Буряк as part of Knots and repres
entation theory\n\n\nAbstract\nМы постараемся продемо
нстрировать как DR-иерархии\, введённые д
окладчиком в одной из работ\, позволяют о
чень ясным образом установить связь ме
жду топологией компактификации Делиня-М
амфорда пространства модулей гладких ал
гебраических кривых рода g с n отмеченным
и точками и интегрируемыми системами ма
тематической физики. Эта связь основыва
ется на соотношении коммутативности меж
ду циклами двойных ветвлений (DR-циклами)
в пространстве модулей кривых произволь
ного рода\, которое является обобщением
соотношения ассоциативности в простран
стве модулей кривых рода 0\, которое в сво
ю очередь тесно связано с теорией много
образий Дубровина-Фробениуса.\n
LOCATION:https://stable.researchseminars.org/talk/Knotsandtopology/60/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Scott Baldridge
DTSTART:20240520T153000Z
DTEND:20240520T170000Z
DTSTAMP:20260404T111447Z
UID:Knotsandtopology/61
DESCRIPTION:Title: Why the Vertex Polynomial counts Tait colorings of a plan
e trivalent graph when evaluated at two\nby Scott Baldridge as part of
Knots and representation theory\n\n\nAbstract\nThe vertex polynomial was
introduced in our 2024 paper but can be inferred from Penrose’s 1971 pap
er on abstract tensor systems. In this talk\, we give a gentle introductio
n to the vertex polynomial: what it means\, how to compute it\, why it cou
nts Tait colorings (3-edge colorings) of a plane trivalent graph at n=2\,
and what it means when evaluated at n>2. In particular\, the four color th
eorem is true if and only if the vertex polynomial is nonzero when evaluat
ed at n=2 for all bridgeless planar trivalent graphs. Along the way\, we w
ill see how the homology that it categorifies can be used to count the num
ber of perfect matchings of a trivalent plane graph. This is joint work wi
th Ben McCarty.\n
LOCATION:https://stable.researchseminars.org/talk/Knotsandtopology/61/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Романов Николай Алексеевич
DTSTART:20240527T153000Z
DTEND:20240527T170000Z
DTSTAMP:20260404T111447Z
UID:Knotsandtopology/62
DESCRIPTION:Title: Мозаики\, замощения и их преобр
азования\nby Романов Николай Алексееви
ч as part of Knots and representation theory\n\n\nAbstract\nОбъект
внимания - мозаики\, замощения и их преоб
разования. Соотношения в группе можно с
помощью диаграмм Ван Кампена представит
ь как выкладывание мозаики\, а соотношен
ия между соотношениями - преобразования
этой мозаики. Например\, в замощении доми
ношками прямоугольника взять квадратик
2 на 2 из двух доминошек и развернуть его
на пол оборота. Оказывается\, для некотор
ого набора фигур можно найти такой набор
преобразований (флипов)\, что любое допу
стимое замощение любой фигуры переводит
ся этими флипами в любое другое допустим
ое замощение. В работе были исследованы
некоторые фигуры и наборы флипов\, получ
ены универсальные инварианты и найдены
многомерные аналоги мозаик\, преобразов
аний и соотношений\, получены оценки на м
инимальное количество флипов\, необходи
мое для перевода любого состояния в любо
е\, а так же рассмотрены обобщения на гра
фы.\n
LOCATION:https://stable.researchseminars.org/talk/Knotsandtopology/62/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Igor Nikonov
DTSTART:20240603T133000Z
DTEND:20240603T150000Z
DTSTAMP:20260404T111447Z
UID:Knotsandtopology/63
DESCRIPTION:Title: Virtual index cocycles and invariants of virtual links\nby Igor Nikonov as part of Knots and representation theory\n\n\nAbstrac
t\nVirtual index cocycle is the 1-cochain that counts virtual crossings in
the arcs of a virtual link diagram. We show how this cocycle can be used
to reformulate and unify some known invariants of virtual links.\n
LOCATION:https://stable.researchseminars.org/talk/Knotsandtopology/63/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Huizheng Guo(Ali) (GWU)
DTSTART:20240610T153000Z
DTEND:20240610T170000Z
DTSTAMP:20260404T111447Z
UID:Knotsandtopology/64
DESCRIPTION:Title: From GKH to Incompressible surface\nby Huizheng Guo(A
li) (GWU) as part of Knots and representation theory\n\n\nAbstract\nFor a
reduced alternating diagram of a knot with a prime determinant $p\,$ the K
auffman-Harary conjecture states that every non-trivial Fox $p$-coloring o
f the knot assigns different colors to its arcs. In 2022\, we prove a gene
ralization of the conjecture stated nineteen years ago by Asaeda\, Przytyc
ki\, and Sikora: for every pair of distinct arcs in the reduced alternatin
g diagram of a prime link with determinant $\\delta\,$ there exists a Fox
$\\delta$-coloring that distinguishes them.\nTo explore the geometric appr
oach of GKH\, we attempt to extend Mensaco's meridian theorem to double br
anched cover of alternating prime non-split links by extending the "bubble
construction". In this presentation\, we explore the behaviors of lifted
loops from link complement in double branched cover along branching set $L
$ in $S^3$. What is more\, we also study properties of incompressible surf
ace\, meridionally incompressible surface in such double branched cover an
d n-cyclic cover of link complement in $S^3$.\n
LOCATION:https://stable.researchseminars.org/talk/Knotsandtopology/64/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hayk Sedrakyan
DTSTART:20240617T133000Z
DTEND:20240617T150000Z
DTSTAMP:20260404T111447Z
UID:Knotsandtopology/65
DESCRIPTION:Title: Sedrakyan-Mozayeni theorem and pentagon equestion calcula
tions\nby Hayk Sedrakyan as part of Knots and representation theory\n\
n\nAbstract\nIn the present work\, we prove the long-standing and importan
t open research question: the consistency for the general case discussed i
n the paper Photography principle\, data transmission\, and invariants of
manifolds. Ptolemy's theorem works only for a particular case and does not
work for a general case\, we prove the general case using Sedrakyan-Mozay
eni theorem and Sedrakyan-Gandhi theorem.\nDescription. The consistency fo
r the particular case discussed in the paper Photography principle\, data
transmission\, and invariants of manifolds is proved using Ptolemy's theor
em. Ptolemy'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 pr
ove the consistency for the general case. We use the novel Sedrakyan-Mozay
eni theorem and Sedrakyan-Gandhi theorem to prove the consistency for the
most general case. It leads to an elegant proof of this long-standing and
important open research question.\n
LOCATION:https://stable.researchseminars.org/talk/Knotsandtopology/65/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Igor Nikonov
DTSTART:20240624T133000Z
DTEND:20240624T150000Z
DTSTAMP:20260404T111447Z
UID:Knotsandtopology/66
DESCRIPTION:Title: Parity functors\nby Igor Nikonov as part of Knots and
representation theory\n\n\nAbstract\nA parity is a rule to assign labels
to the crossings of knot diagrams in a way compatible with Reidemeister mo
ves. Parity 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://stable.researchseminars.org/talk/Knotsandtopology/66/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Byeorhi Kim
DTSTART:20240701T133000Z
DTEND:20240701T150000Z
DTSTAMP:20260404T111447Z
UID:Knotsandtopology/67
DESCRIPTION:Title: On a smoothing strategy for topological surfaces in 4-man
ifolds\nby Byeorhi Kim as part of Knots and representation theory\n\n\
nAbstract\nIn this talk\, I will talk about a new smoothing technique for
topologically embedded surfaces or disks in smooth 4-manifolds that provid
es topological isotopies to smooth surfaces. This result is motivated from
recent David Gabai's Light bulb theorem. As an application\, we can get s
ome results 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://stable.researchseminars.org/talk/Knotsandtopology/67/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Igor Nikonov
DTSTART:20240708T133000Z
DTEND:20240708T150000Z
DTSTAMP:20260404T111447Z
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 defin
e a modification of biquandle construction for knots in a fixed thickened
surface and give several examples of the new invariant.\n
LOCATION:https://stable.researchseminars.org/talk/Knotsandtopology/68/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Renaud Detcherry
DTSTART:20240729T133000Z
DTEND:20240729T150000Z
DTSTAMP:20260404T111447Z
UID:Knotsandtopology/69
DESCRIPTION:Title: On torsion in the Kauffman bracket skein modules of 3-man
ifolds\nby Renaud Detcherry as part of Knots and representation theory
\n\n\nAbstract\nThe Kauffman bracket skein module S(M) of an oriented 3-ma
nifold 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)-character varieties of 3-manifolds.\nAn old question of Przytycki asks
whether for M a 3-manifold that admits a non-boundary parallel essential s
urface\, there is torsion in S(M). We will present new criterions for the
presence 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 show that if a Seifert manifold M has a non-boudnary parallel essent
ial surface\, then S(M) has torsion.\n
LOCATION:https://stable.researchseminars.org/talk/Knotsandtopology/69/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hyungtae Baek
DTSTART:20240715T133000Z
DTEND:20240715T150000Z
DTSTAMP:20260404T111447Z
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 representat
ion theory\n\n\nAbstract\nLet $R$ be a commutative ring with identity\, $D
$ an integral domain\, and $M$ a module over $R$ or $D$.\n\nIn 1899\, Davi
d Hilbert proved the Hilbert basis theorem:\n$R$ is a Noetherian ring if a
nd only if\n$R[X]$ is a Noetherian ring.\nThis theorem is a fundamental re
sult\nin commutative algebra and algebraic geometry.\n\nMany ring theorist
s have generalized Noetherian rings\nand the Hilbert basis theorem to such
generalizations.\n\nIn this talk\, we investigate $S$-Noetherian modules
and\n$S$-strong Mori modules\,\nand explore the Hilbert basis theorem for
such modules.\nTo do this\, we delve into the concept of star-operations (
specifically $w$-operations).\n\nThe main goal of this talk is to address
the following problems:\n\\begin{enumerate}\n\\item[(1)] When is $M$ an $S
$-Noetherian module?\n\\item[(2)] When is $M$ an $S$-strong Mori module?\n
\\end{enumerate}\n
LOCATION:https://stable.researchseminars.org/talk/Knotsandtopology/70/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bart Vlaar
DTSTART:20240819T133000Z
DTEND:20240819T150000Z
DTSTAMP:20260404T111447Z
UID:Knotsandtopology/71
DESCRIPTION:Title: Cylindrical structures arising from quantum symmetric pai
rs\nby Bart Vlaar as part of Knots and representation theory\n\n\nAbst
ract\nR-matrices (solutions of the Yang-Baxter equation) and quantum group
s are intimately connected and find applications in mathematical physics\,
representation theory\, low-dimensional topology and algebraic geometry.
K-matrices (solutions of the reflection equation) and quantum deformations
of symmetric pairs form a vast generalization\, under development since t
he 1990s. We survey this and discuss some results on the case of quantum g
roups and quantum symmetric pairs of affine type (joint work with Andrea A
ppel).\n
LOCATION:https://stable.researchseminars.org/talk/Knotsandtopology/71/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jean-Marc Schlenker
DTSTART:20240909T153000Z
DTEND:20240909T170000Z
DTSTAMP:20260404T111447Z
UID:Knotsandtopology/72
DESCRIPTION:Title: Polyhedra inscribed in a quadric\nby Jean-Marc Schlen
ker as part of Knots and representation theory\n\n\nAbstract\nSteiner aske
d in 1832 what are the combinatorial types of polyhedra with vertices on a
quadric. We will survey what is known on this question\, and show how rec
ent results are based on studying ideal polyhedra in different geometries.
Hodgson\, Rivin and Smith characterized the combinatorics of polyhedra in
scribed in a sphere using properties of ideal hyperbolic polyhedra. More r
ecently we described the combinatorics of polyhedra inscribed in a one-she
eted hyperboloid or cone\, using properties of ideal polyhedra in the anti
-de Sitter and Half-pipe spaces. Further results describe the combinatoria
l types of polyhedra "weakly inscribed" in a two-sheeted hyperboloid (that
is\, with their vertices on it but not entirely on one side)\, using a na
tural extension of hyperbolic space by the de Sitter space. The same quest
ion for the one-sheeted hyperboloid remains open.\nJoint work with Jeff Da
nciger and Sara Maloni.\n
LOCATION:https://stable.researchseminars.org/talk/Knotsandtopology/72/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jae-baek Lee
DTSTART:20240805T143000Z
DTEND:20240805T160000Z
DTSTAMP:20260404T111447Z
UID:Knotsandtopology/73
DESCRIPTION:Title: Disconnected common graphs via supersaturation and beyond
\nby Jae-baek Lee as part of Knots and representation theory\n\n\nAbst
ract\nA graph $H$ is said to be \\emph{common} if the number of labelled m
onochromatic copies of $H$ in a $2$-colouring of the edges of a large comp
lete graph is asymptotically minimized by a random colouring. It is well k
nown that 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 t
he first pair of uncommon graphs whose disjoint union is common and a comm
on graph and an uncommon graph whose disjoint union is common. Our approac
h is to reduce the problem of showing that certain disconnected graphs are
common to a constrained optimization problem\, in which the constraints a
re derived from supersaturation bounds related to Razborov's Triangle Dens
ity Theorem. \nIn addition\, we will introduce the recent results related
to Ramsey multiplicity constant. \nThis is joint work with Joseph Hyde an
d Jonathan Noel.\n
LOCATION:https://stable.researchseminars.org/talk/Knotsandtopology/73/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Igor Nikonov
DTSTART:20240812T153000Z
DTEND:20240812T170000Z
DTSTAMP:20260404T111447Z
UID:Knotsandtopology/74
DESCRIPTION:Title: Virtual index cocycles and invariants of virtual links\nby Igor Nikonov as part of Knots and representation theory\n\n\nAbstrac
t\nVirtual index cocycle is the 1-cochain that counts virtual crossings in
the arcs of a virtual link diagram. We show how this cocycle can be used
to reformulate and unify some known invariants of virtual links.\n
LOCATION:https://stable.researchseminars.org/talk/Knotsandtopology/74/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Guowei Wei
DTSTART:20240923T153000Z
DTEND:20240923T170000Z
DTSTAMP:20260404T111447Z
UID:Knotsandtopology/75
DESCRIPTION:Title: Topological deep learning: The past\, present\, and futur
e\nby Guowei Wei as part of Knots and representation theory\n\n\nAbstr
act\nIn the past few years\, topological deep learning (TDL)\, a term coin
ed by us in 2017\, has become an emerging paradigm in artificial intellige
nce (AI). TDL is built on persistent homology (PH)\, an algebraic topology
technique that bridges the gap between complex geometry and abstract topo
logy through multiscale analysis. While TDL has made huge strides in a wid
e variety of scientific and engineering disciplines\, its most compelling
success was observed in biosciences with intrinsically high dimensional an
d intricately complex data. I will discuss the limitations/ challenges of
TDL and new approaches based on algebraic topology\, geometric topology an
d differential geometry may tackle these challenges. I will also discuss h
ow topology is enabling AI and how AI is assisting topological reasoning.\
n
LOCATION:https://stable.researchseminars.org/talk/Knotsandtopology/75/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Qiuyu Ren
DTSTART:20240930T133000Z
DTEND:20240930T150000Z
DTSTAMP:20260404T111447Z
UID:Knotsandtopology/76
DESCRIPTION:by Qiuyu Ren as part of Knots and representation theory\n\nAbs
tract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/Knotsandtopology/76/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrey M. Elishev
DTSTART:20240826T133000Z
DTEND:20240826T150000Z
DTSTAMP:20260404T111447Z
UID:Knotsandtopology/77
DESCRIPTION:Title: On Automorphisms of Tame Polynomial Automorphism Ind-Sche
mes in Positive Characteristic\nby Andrey M. Elishev as part of Knots
and representation theory\n\n\nAbstract\nLet $n\\geq 3$ and let $K$ be an
algebraically closed field. When the characteristic of $K$ is zero\, a cla
ssical theorem of Anick states that tame $K$-algebra automorphisms of $K[x
_1\,\\ldots\, x_n]$ approximate polynomial endomorphisms with constant non
-zero Jacobian in the power series topology. This fact has been at the cen
ter of one of the more promising approaches to the Jacobian Conjecture and
\, in a related development (cf. https://www.worldscientific.com/doi/abs/1
0.1142/S0218196718400040)\, has allowed for a description of the set $\\Au
t_{Ind}\\Aut K[x_1\,\\ldots\, x_n]$ of automorphisms of $\\Aut K[x_1\,\\ld
ots\, x_n]$ preserving the Ind-scheme structure. My talk will focus on a f
ew finer details of the positive-characteristic extension of the aforement
ioned work\, compiled in https://arxiv.org/abs/2103.12784\, together with
its implications for some of the tougher open problems in the area. Joint
work with A. Kanel-Belov and J.-T. Yu.\n
LOCATION:https://stable.researchseminars.org/talk/Knotsandtopology/77/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Igor M. Nikonov
DTSTART:20240902T133000Z
DTEND:20240902T150000Z
DTSTAMP:20260404T111447Z
UID:Knotsandtopology/78
DESCRIPTION:Title: Flat-virtual knot: introduction and some invariants\n
by Igor M. Nikonov as part of Knots and representation theory\n\n\nAbstrac
t\nIn attempts to construct a map from classical knots to virtual ones\, w
e define a series of maps from knots in the full torus (thickened torus) t
o flat-virtual knots. We give definition of flat-virtual knots and present
s Alexander-like polynomial and Kauffman bracket for them. We also discuss
a possible extension of the notion of flat-virtual knots — so-called mu
lti-flat knots.\n
LOCATION:https://stable.researchseminars.org/talk/Knotsandtopology/78/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anup Poudel
DTSTART:20240916T133000Z
DTEND:20240916T150000Z
DTSTAMP:20260404T111447Z
UID:Knotsandtopology/79
DESCRIPTION:Title: Lie Superalgebra generalizations of the JKS-invariant]{Li
e Superalgebra generalizations of the Jaeger-Kauffman-Saleur Invariant
\nby Anup Poudel as part of Knots and representation theory\n\n\nAbstract\
nJaeger-Kauffman-Saleur (JKS) identified the Alexander polynomial with th
e $U_q(\\mathfrak{gl}(1|1))$ quantum invariant of classical links and ext
ended this to a 2-variable invariant of links in thickened surfaces. Here
we generalize this story for every Lie superalgebra of type $\\mathfrak{
gl}(m|n)$. First\, we define a $U_q(\\mathfrak{gl}(m|n))$ Reshetikhin-Tur
aev invariant for virtual tangles. When $m=n=1$\, this recovers the Alexa
nder polynomial of almost classical knots\, as defined by Boden-Gaudreau
-Harper-Nicas-White. Next\, an extended $U_q(\\mathfrak{gl}(m|n))$ Reshet
ikin-Turaev invariant of virtual tangles is obtained by applying the Bar-
Natan Zh-construction. This is equivalent to the 2-variable JKS-invarian
t when $m=n=1$\, but otherwise our invariants are new whenever $n>0$. Fu
rthermore\, in contrast with the classical case\, the virtual and extende
d $U_q(\\mathfrak{gl}(m|n))$ invariants are not entirely determined by th
e difference $m-n$. 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 conjec
tures based on calculations will be discussed. This is a joint work with
Micah Chrisman.\n
LOCATION:https://stable.researchseminars.org/talk/Knotsandtopology/79/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anton Dzhamay
DTSTART:20241014T153000Z
DTEND:20241014T170000Z
DTSTAMP:20260404T111447Z
UID:Knotsandtopology/80
DESCRIPTION:Title: Geometry of Discrete Integrable Systems: QRT Maps and Dis
crete Painlevé Equations\nby Anton Dzhamay as part of Knots and repre
sentation theory\n\n\nAbstract\nMany interesting examples of discrete inte
grable systems can be studied from the geometric point of view. In this ta
lk we will consider two classes of examples of such system: autonomous (QR
T maps) and non-autonomous (discrete Painlevé equations). We introduce so
me geometric tools to study these systems\, such as the blowup procedure t
o construct algebraic surfaces on which the mappings are regularized\, lin
earization of the mapping on the Picard lattice of the surface and\, for d
iscrete Painlevé equations\, the decomposition of the Picard lattice into
complementary pairs of the surface and symmetry sub-lattices and construc
tion of a birational representation of affine Weyl symmetry groups that gi
ves a complete algebraic description of our non-linear dynamic.\n\nThis ta
lk is based on joint work with Stefan Carstea (Bucharest) and Tomoyuki Tak
enawa (Tokyo).\n
LOCATION:https://stable.researchseminars.org/talk/Knotsandtopology/80/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Igor Nikonov
DTSTART:20241007T153000Z
DTEND:20241007T170000Z
DTSTAMP:20260404T111447Z
UID:Knotsandtopology/81
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 talk we review the definition of parity on 2-knots\, and prove that t
he Gaussian parity is universal on free two-dimensional knots.\n
LOCATION:https://stable.researchseminars.org/talk/Knotsandtopology/81/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tumpa Mahato
DTSTART:20241021T153000Z
DTEND:20241021T170000Z
DTSTAMP:20260404T111447Z
UID:Knotsandtopology/82
DESCRIPTION:Title: Parameterization and non-triviality of knotted surfaces a
rising from 1-dimensional knots\nby Tumpa Mahato as part of Knots and
representation theory\n\n\nAbstract\nAlthough we study knotted surfaces us
ing diagrams and braids\, visualizing is very important\nto understand the
se abstract mathematical objects. Therefore\, parameterizing these\nembedd
ings of 2-manifolds using elementary functions becomes crucial not only fo
r computing\ninvariants but also to provide a machinery to visualize and i
nteract with these objects.\nIn this talk\, we will provide a concrete par
ameterization of a few class of knotted surfaces\,\ncalled using elementar
y functions.\nMoreover\, we will discuss the non-triviality of a specific
class of surface knots called ribbon\ntorus knots by using its connection
with welded knots by S. Satoh’s Tube map. We will\nexplore the non-trivi
ality of welded knots by studying a welded knot invariant\, called welded\
nunknotting number and utilize those results to examine the non-triviality
of ribbon torus\nknots.\n
LOCATION:https://stable.researchseminars.org/talk/Knotsandtopology/82/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Seongjeong Kim
DTSTART:20241028T153000Z
DTEND:20241028T170000Z
DTSTAMP:20260404T111447Z
UID:Knotsandtopology/83
DESCRIPTION:Title: The Kauffman bracket skein module of $\\mathbf {(S^1 \\ti
mes S^2) \\ \\# \\ (S^1 \\times S^2)}$: another counterexample of Marche
’s conjecture\nby Seongjeong Kim as part of Knots and representation
theory\n\n\nAbstract\nDetermining the structure of the Kauffman bracket s
kein module of all $3$-manifolds over the ring of Laurent polynomials $\\m
athbb Z[A^{\\pm 1}]$ is a big open problem in skein theory. Very little is
known about the skein module of non-prime manifolds over this ring. In th
is paper\, we compute the Kauffman bracket skein module of the $3$-manifol
d $(S^1 \\times S^2) \\ \\# \\ (S^1 \\times S^2)$ over the ring $\\mathbb
Z[A^{\\pm 1}]$. We do this by analysing the submodule of handle sliding re
lations\, for which we provide a suitable basis. Along the way we also com
pute the Kauffman bracket skein module of $(S^1 \\times S^2) \\ \\# \\ (S^
1 \\times D^2)$. Furthermore\, we show that the skein module of $(S^1 \\ti
mes S^2) \\ \\# \\ (S^1 \\times S^2)$ does not split into the sum of free
and torsion submodules.\n
LOCATION:https://stable.researchseminars.org/talk/Knotsandtopology/83/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michael Shapiro
DTSTART:20241216T153000Z
DTEND:20241216T170000Z
DTSTAMP:20260404T111447Z
UID:Knotsandtopology/85
DESCRIPTION:Title: Goldman bracket and cluster algebra\nby Michael Shapi
ro as part of Knots and representation theory\n\n\nAbstract\nWe remind the
definition 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://stable.researchseminars.org/talk/Knotsandtopology/85/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Igor Nikonov
DTSTART:20241104T153000Z
DTEND:20241104T170000Z
DTSTAMP:20260404T111447Z
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\nAbstra
ct\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 an
d presents Alexander-like polynomial and Kauffman bracket for them. We als
o discuss a possible extension of the notion of flat-virtual knots — so-
called multi-flat knots.\n
LOCATION:https://stable.researchseminars.org/talk/Knotsandtopology/86/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Oscar Ocampo
DTSTART:20241125T153000Z
DTEND:20241125T170000Z
DTSTAMP:20260404T111447Z
UID:Knotsandtopology/87
DESCRIPTION:Title: Characteristic subgroups and the R$_\\infty$-property for
virtual braid groups\nby Oscar Ocampo as part of Knots and representa
tion theory\n\n\nAbstract\nThere is currently a growing interest in the st
udy of groups having the R$_\\infty$-property (the study of their twisted
conjugacy classes)\, it finds their origins in algebraic topology and to b
e more precise in Nielsen–Reidemeister fixed point theory.\nLet $n\\geq
2$. Let $VB_n$ (resp.\\ $VP_n$) denote the virtual braid group (resp.\\ vi
rtual pure braid group)\, let $WB_n$ (resp.\\ $WP_n$) denote the welded br
aid group (resp.\\ welded pure braid group) and let $UVB_n$ (resp.\\ $UVP_
n$) denote the unrestricted virtual braid group (resp.\\ unrestricted virt
ual pure braid group).\nIn the first part of this talk we prove that\, for
$n\\geq 4$\, the group $VP_n$ and for $n\\geq 3$ the groups $WP_n$ and $U
VP_n$ are characteristic subgroups of $VB_n$\, $WB_n$ and $UVB_n$\, respec
tively.\nIn the second part of the talk we show that\, for $n\\geq 2$\, th
e virtual braid group $VB_n$\, the unrestricted virtual pure braid group $
UVP_n$\, and the unrestricted virtual braid group $UVB_n$ have the R$_\\in
fty$-property.\nJoint work with Daciberg Lima Gonçalves and Karel Dekimpe
.\n
LOCATION:https://stable.researchseminars.org/talk/Knotsandtopology/87/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Fedor Nilov
DTSTART:20241111T153000Z
DTEND:20241111T170000Z
DTSTAMP:20260404T111447Z
UID:Knotsandtopology/88
DESCRIPTION:Title: Webs from lines and circles\nby Fedor Nilov as part o
f 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 take
s the sets of segments parallel to the sides of a fixed triangle. In 1938
\nW. Blaschke and G. Bol stated the problem of classification of all hexa
gonal 3-webs from lines and circles. This problem is still open. We will d
iscuss the current status of the problem and related questions.\n
LOCATION:https://stable.researchseminars.org/talk/Knotsandtopology/88/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ben Mccarty
DTSTART:20241223T153000Z
DTEND:20241223T170000Z
DTSTAMP:20260404T111447Z
UID:Knotsandtopology/89
DESCRIPTION:Title: What does the Penrose polynomial actually count?\nby
Ben Mccarty 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 pl
anar trivalent graph and the polynomial is evaluated at n=3. However\, fo
r graphs that are not trivalent\, and for other values of n\, what it coun
ts has been harder to describe. In this talk we show that a shift in pers
pective toward face colorings on a set of ribbon graphs allows one to obta
in a complete characterization of the Penrose polynomial for n>0. This ch
aracterization utilizes an understanding of the filtered n-color homology\
, which will be briefly described in the talk.\n\nThis is joint work with
Scott Baldridge.\n
LOCATION:https://stable.researchseminars.org/talk/Knotsandtopology/89/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tumpa Mahato
DTSTART:20241202T153000Z
DTEND:20241202T170000Z
DTSTAMP:20260404T111447Z
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
regions of a link projection is said to be isolated if any pair of region
s in the set share no crossings. The isolate-region number of a link proje
ction is the maximum value of the cardinality for isolated sets of regions
of the link projection.\nThis talk involves various results for computing
isolate-region number and its relation with warping degree and welded unk
notting number of a knot.\n
LOCATION:https://stable.researchseminars.org/talk/Knotsandtopology/90/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Seongjeong Kim
DTSTART:20241118T153000Z
DTEND:20241118T170000Z
DTSTAMP:20260404T111447Z
UID:Knotsandtopology/91
DESCRIPTION:Title: The groups $G_{n}^{k}$\, $2n$-gon tilings\, and stacking
of cubes\nby Seongjeong Kim as part of Knots and representation theory
\n\n\nAbstract\nIn the present talk we discuss three ways of looking at rh
ombile tilings: stacking 3-dimensional cubes\, elements of groups\, and co
nfigurations of lines and points.\n
LOCATION:https://stable.researchseminars.org/talk/Knotsandtopology/91/
END:VEVENT
BEGIN:VEVENT
SUMMARY:André Henriques
DTSTART:20241209T153000Z
DTEND:20241209T170000Z
DTSTAMP:20260404T111447Z
UID:Knotsandtopology/92
DESCRIPTION:Title: What kind of thing is... Rep(G)?\nby André Henriques
as part of Knots and representation theory\n\n\nAbstract\nWhat kind of ma
thematical object is the category of representations of a group? The answe
r depends on what kind of group we're considering: finite / algebraic / to
pological / etc... In all cases\, after having axiomatised the kind of ca
tegories that look like Rep(G)\, a surprisingly fruitful question is to as
k whether there are other categories that satisfy all the same axioms\, bu
t are not of the form Rep(G).\n
LOCATION:https://stable.researchseminars.org/talk/Knotsandtopology/92/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sandip Samanta
DTSTART:20241230T153000Z
DTEND:20241230T170000Z
DTSTAMP:20260404T111447Z
UID:Knotsandtopology/93
DESCRIPTION:Title: Associahedra and Its Combinatorial Isomorphism to Three O
ther Models\nby Sandip Samanta as part of Knots and representation the
ory\n\n\nAbstract\nAssociahedra (or Stasheff polytopes) were first introdu
ced by Stasheff in his thesis to define the notion of A_n-spaces. Over tim
e\, these polytopes have continued to appear in various studies\, includin
g A_n-maps and moduli spaces\, due to their rich combinatorial structures.
In this talk\, we will explore three additional models of these polytopes
: Loday's cone construction\, collapsed multiplihedra\, and graph cubeahed
ra\, and examine the combinatorial isomorphism between them.\nThis is base
d on a joint work with Dr. Somnath Basu.\n
LOCATION:https://stable.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:20260404T111447Z
UID:Knotsandtopology/94
DESCRIPTION:Title: The Newton aerodynamic problem: after 300 years all ove
r again\nby Protasov Vladimir (University of L’Aquila (Italy)\, Mosc
ow State University (Russia)) as part of Knots and representation theory\n
\n\nAbstract\nIn 1687 Isaac Newton in his main work ``Principia'' posed th
e following Aerodynamic Problem: find the convex surface of the minima
l frontal resistance during its uniform motion through an inviscid and
incompressible medium. The surface must contain a given disc orthogonal to
the vector of velocity and have a given altitude. The solution of Newto
n became a classical example in the calculus of variations. However\, in
early 1990s G.Butazzo\, D.Kawohl\, and P.Guasoni presented a surface
of a smaller resistance. They showed that the optimality of Newtons's surf
ace concerns only a special case (although\, considered to be general
by most of specialists). The aerodynamic problem had to be solved again
under general assumptions\, which turned out to be a hard task. The so
lution is still unknown\, although some properties of the optimal surface
have been established. \n \nWe give a survey of some of the known resu
lts including construction of non-convex surfaces of arbitrary small res
istance and of invisible surfaces. Then we present a new approach to analy
ze the optimal convex surface by using inequalities between derivatives.
Some of these inequalities are\, probably\, of independent interest. \
n \nThis is a joint work with A.Plakhov (University of Aveiro\, Portugal)
\n
LOCATION:https://stable.researchseminars.org/talk/Knotsandtopology/94/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Igor Nikonov
DTSTART:20250106T153000Z
DTEND:20250106T170000Z
DTSTAMP:20260404T111447Z
UID:Knotsandtopology/95
DESCRIPTION:Title: On skein invariants\nby Igor Nikonov as part of Knots
and representation theory\n\n\nAbstract\nIt is known that some knot invar
iants can be defined by relations (called skein relations) on diagrams whi
ch differ at a local site. Among skein invariants one can mention Alexande
r and Jones polynomials\, Arf invariant and writhe polynomial. In the talk
we will remind these and other examples of skein invariants and introduce
a new skein invariant for links in a fixed thickened surface.\n
LOCATION:https://stable.researchseminars.org/talk/Knotsandtopology/95/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mark Powell
DTSTART:20250127T153000Z
DTEND:20250127T170000Z
DTSTAMP:20260404T111447Z
UID:Knotsandtopology/96
DESCRIPTION:Title: Classification of 4-manifolds with infinite dihedral fund
amental group.\nby Mark Powell as part of Knots and representation the
ory\n\n\nAbstract\nI will discuss the homotopy classification of 4-manifol
ds with certain fundamental groups\, before focusing on the case of infini
te dihedral fundamental group.\nIn this case we have been able to upgrade
the homotopy classification to a homeomorphism classification. \nAfter ex
plaining these classifications\, I will then discuss\, in detail\, a key p
air of examples that are homotopy equivalent but not homeomorphic.\n
LOCATION:https://stable.researchseminars.org/talk/Knotsandtopology/96/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Николай Романов
DTSTART:20250120T153000Z
DTEND:20250120T170000Z
DTSTAMP:20260404T111447Z
UID:Knotsandtopology/97
DESCRIPTION:Title: Хеширование и антихеширование.
\nby Николай Романов as part of Knots and representation
theory\n\n\nAbstract\nНа занятии рассмотрим разны
е методы хеширования\, вероятностные и г
енерационные способы поиска коллизий и
способы (относительно) быстрого расхеши
рования и общие методы взлома хешей. Зат
ем погрузимся в вычислительную геометри
ю\, оптимизацию\, посмотрим\, как хеширова
ние помогает реализовывать быстрые поис
ковые алгоритмы в динамических системах
и то как эти динамические системы вредя
т хешированию.\n
LOCATION:https://stable.researchseminars.org/talk/Knotsandtopology/97/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pramod Padmanabhan
DTSTART:20250210T153000Z
DTEND:20250210T170000Z
DTSTAMP:20260404T111447Z
UID:Knotsandtopology/98
DESCRIPTION:Title: Universal methods to solve higher simplex equations\n
by Pramod Padmanabhan as part of Knots and representation theory\n\n\nAbst
ract\nA brief introduction to the Yang-Baxter\, tetrahedron and other high
er simplex equations in physics and mathematics will be given\, especially
from the point of view of exactly solvable statistical mechanical models.
Following this we will explain different methods developed to solve all o
f these higher simplex equations. The methods are algebraic and they yield
representation independent solutions to these operator equations. Some of
the algebras include Clifford algebras\, the algebra of Majorana fermions
and the algebra of complex Dirac fermions.\n\nThe talk will mostly be bas
ed on https://arxiv.org/abs/2404.11501 and https://arxiv.org/abs/2410.2032
8.\n
LOCATION:https://stable.researchseminars.org/talk/Knotsandtopology/98/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrew Bartholomew
DTSTART:20250217T153000Z
DTEND:20250217T170000Z
DTSTAMP:20260404T111447Z
UID:Knotsandtopology/99
DESCRIPTION:Title: Using biracks to extract invariants of knots\nby Andr
ew Bartholomew as part of Knots and representation theory\n\n\nAbstract\nW
e present 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
invariant of a class of knot theories amenable to a generalisation of the
orem of Trace on regular homotopy\, which we describe. We also take the o
pportunity to reprise the relevant generalised knot theory and the theory
of generalised biracks in the light of this work and recent developments.\
n
LOCATION:https://stable.researchseminars.org/talk/Knotsandtopology/99/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mikhail Khovanov
DTSTART:20250331T153000Z
DTEND:20250331T170000Z
DTSTAMP:20260404T111447Z
UID:Knotsandtopology/100
DESCRIPTION:Title: Webs and foams in historical perspective\nby Mikhail
Khovanov as part of Knots and representation theory\n\n\nAbstract\nWe wil
l review webs\, starting with the work of Kauffman and Murakami-Ohtsuki-Ya
mada and\nexplain how categorification of webs led to foams. A sketch of t
he construction of a TQFT for foams from the Robert-Wagner evaluation and
from matrix factorizations will be given\, as well as application to the c
onstruction of link homology.\n
LOCATION:https://stable.researchseminars.org/talk/Knotsandtopology/100/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mukilraj K
DTSTART:20250224T153000Z
DTEND:20250224T170000Z
DTSTAMP:20260404T111447Z
UID:Knotsandtopology/102
DESCRIPTION:Title: Loop homology of some highly connected manifold\nby
Mukilraj K as part of Knots and representation theory\n\n\nAbstract\nChas
and Sullivan showed that $H_*(LM)$ of a closed oriented manifold forms Bat
alin-Vilkovisky algebra. It is also well known that $H_*(LX)$ is in many w
ays connected to the Hochshchild (co)homology. We will use one of such con
nections to compute $H_*(LX)$ where $X$ is a $S^2$ bundle over $S^2$. We w
ill also try to visualize some homology classes of $L(S^2)$.\n
LOCATION:https://stable.researchseminars.org/talk/Knotsandtopology/102/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Manpreet Singh
DTSTART:20250317T153000Z
DTEND:20250317T170000Z
DTSTAMP:20260404T111447Z
UID:Knotsandtopology/103
DESCRIPTION:Title: On the Cohomology Theory of Twisted Yang-Baxter Sets
\nby Manpreet Singh as part of Knots and representation theory\n\n\nAbstra
ct\nIn this talk\, I will introduce twisted set-theoretic Yang-Baxter solu
tions and develop a corresponding cohomology theory. This extends the stan
dard cohomology theory of Yang-Baxter solutions. Moreover\, I will explain
how these structures and their cocycles can be used to study knots. This
is joint work with Professor Mohamed Elhamdadi.\n
LOCATION:https://stable.researchseminars.org/talk/Knotsandtopology/103/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Igor Nikonov
DTSTART:20250303T153000Z
DTEND:20250303T170000Z
DTSTAMP:20260404T111447Z
UID:Knotsandtopology/104
DESCRIPTION:Title: Flat-virtual knot: introduction and some invariants\
nby Igor Nikonov as part of Knots and representation theory\n\n\nAbstract\
nIn attempts 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-virtual knots. We give definition of flat-virtual knots and presents
Alexander-like polynomial and Kauffman bracket for them. We also discuss a
possible extension of the notion of flat-virtual knots — so-called mult
i-flat knots.\n
LOCATION:https://stable.researchseminars.org/talk/Knotsandtopology/104/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Seongjeong Kim
DTSTART:20250310T153000Z
DTEND:20250310T170000Z
DTSTAMP:20260404T111447Z
UID:Knotsandtopology/105
DESCRIPTION:Title: On the Kauffman bracket skein module of $\\mathbf {(S^1
\\times S^2) \\ \\# \\ (S^1 \\times S^2)}$\nby Seongjeong Kim as part
of Knots and representation theory\n\n\nAbstract\nDetermining the structu
re of the Kauffman bracket skein module 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 about the skein module of non-prime man
ifolds over this ring. In this paper\, we compute the Kauffman bracket ske
in 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 su
bmodule of handle sliding relations\, for which we provide a suitable basi
s. Along the way we compute the Kauffman bracket skein module of $(S^1 \\t
imes S^2) \\ \\# \\ (S^1 \\times D^2)$. We also show that the skein module
of $(S^1 \\times S^2) \\ \\# \\ (S^1 \\times S^2)$ does not split into th
e sum of free and torsion submodules. Furthermore\, we illustrate two fami
lies of torsion elements in this skein module.\n\nThis is joint work with
Rhea Palak Bakshi\, Shangjun Shi\, and Xiao Wang.\n
LOCATION:https://stable.researchseminars.org/talk/Knotsandtopology/105/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Igor Nikonov
DTSTART:20250324T153000Z
DTEND:20250324T170000Z
DTSTAMP:20260404T111447Z
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 intro
duced a family of groups $G^k_n$ for two positive integers $n\, k$ and for
mulated the following principle:\n \nIf dynamical systems describing a mot
ion of n particles has a nice codimension 1 property governed exactly by $
k$ particles then these dynamical systems have a topological invariant val
ued in $G^k_n$.\n \nThe first main example is an invariant of braids value
d 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 l
inks\, we look at links as equivalence classes of braids modulo Markov mov
es and apply this consideration to the construction of MN-indices on the g
roups $G^k_n$.\n
LOCATION:https://stable.researchseminars.org/talk/Knotsandtopology/106/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anna Taranenko
DTSTART:20250407T153000Z
DTEND:20250407T170000Z
DTSTAMP:20260404T111447Z
UID:Knotsandtopology/107
DESCRIPTION:Title: Multidimensional matrices in algebraic hypergraph theory
\nby Anna Taranenko as part of Knots and representation theory\n\n\nAb
stract\nThe main goal of the presented study is to develop methods for wor
king with multidimensional matrices that can be applied to problems of exi
stence and enumeration of various structures in hypergraphs. Many results
in the search for substructures in graphs are based on certain corresponde
nces between graphs and matrices and the application of linear algebra met
hods. Among the most important topics in the combinatorial matrix theory a
re the representation of graphs using adjacency and incidence matrices\, t
he Konig-Hall theorem for systems of distinct representatives\, the perman
ents of doubly stochastic matrices\, and Latin squares. We generalize thes
e directions to multidimensional matrices and hypergraphs and lay the foun
dations of the combinatorial theory of multidimensional matrices.\n
LOCATION:https://stable.researchseminars.org/talk/Knotsandtopology/107/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Seongjeong Kim
DTSTART:20250414T153000Z
DTEND:20250414T170000Z
DTSTAMP:20260404T111447Z
UID:Knotsandtopology/108
DESCRIPTION:Title: Group $G_{n}^{3}$ and hidden crossings from braids\n
by Seongjeong Kim as part of Knots and representation theory\n\n\nAbstract
\nIn this 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
$\\tilde{G_{n}^{3}}$. We construct a homomorphism from the pure braid gro
up $PB_{n}$ to $\\tilde{G_{n}^{3}}$\, which introduce hidden crossings bet
ween classical crossings of braids. This talk is based on https://arxiv.or
g/abs/1612.03486 in 2016 and Chapter 9.4 of the book “Invariants and pic
tures”.\n
LOCATION:https://stable.researchseminars.org/talk/Knotsandtopology/108/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dmitry Melnikov (International Institute of Physics)
DTSTART:20250421T153000Z
DTEND:20250421T170000Z
DTSTAMP:20260404T111447Z
UID:Knotsandtopology/109
DESCRIPTION:Title: Knots\, emerging spaces and quantum correlators\nby
Dmitry Melnikov (International Institute of Physics) as part of Knots and
representation theory\n\n\nAbstract\nAtiyah's axioms of topological quantu
m field theory (TQFT) provide a very intuitive description of quantum mech
anics. At the core of this description are topological spaces emerging as
a ''physical'' realization of quantum correlations. In the first part of m
y talk I will review a simple realization of the TQFT axioms\, with correl
ation functions encoded by the Jones polynomials of knots and links. In th
e second part\, I will reflect on the role of emerging space and topology
in our understanding of quantum mechanical features\, such as quantum enta
nglement.\n
LOCATION:https://stable.researchseminars.org/talk/Knotsandtopology/109/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Theodore Popelensky
DTSTART:20250428T153000Z
DTEND:20250428T170000Z
DTSTAMP:20260404T111447Z
UID:Knotsandtopology/110
DESCRIPTION:Title: On the cohomology of Hopf algebras\nby Theodore Pope
lensky as part of Knots and representation theory\n\n\nAbstract\nI will ta
lk about the structure on the cohomology of Hopf algebras\, which is deter
mined by the spectral sequence introduced by Buchstaber. As an example\, t
he cohomology of the Steenrod algebra will be considered\n
LOCATION:https://stable.researchseminars.org/talk/Knotsandtopology/110/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Igor M. Nikonov
DTSTART:20250505T153000Z
DTEND:20250505T170000Z
DTSTAMP:20260404T111447Z
UID:Knotsandtopology/111
DESCRIPTION:Title: Biquandloids 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 biquandle construction for knots in a fixed thicke
ned surface and give several examples of the new invariant.\n
LOCATION:https://stable.researchseminars.org/talk/Knotsandtopology/111/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vladlen Timorin
DTSTART:20250602T153000Z
DTEND:20250602T170000Z
DTSTAMP:20260404T111447Z
UID:Knotsandtopology/112
DESCRIPTION:Title: Valuations on convex polytopes and reciprocity laws\
nby Vladlen Timorin as part of Knots and representation theory\n\n\nAbstra
ct\nValuations on convex polytopes and reciprocity laws\n(based on a joint
work in progress with A. Khovanskii and V. Kiritchenko)\n\nValuations on
polytopes\, including their special classes (say\, translation invariant o
r lattice invariant valuations) are an old research topic. We propose a ne
w approach to classification of valuations\; it is topological in nature a
nd yields generators and relations with some natural properties. Namely\,
we impose that generators are functorial with respect to the collections o
f defining support hyperplanes and as local as possible. Relations reveal
remarkable connections with complex hyperplane arrangements (even though r
eal polytopes are considered) and Parshin’s reciprocity laws.\n
LOCATION:https://stable.researchseminars.org/talk/Knotsandtopology/112/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Р.В. Шамин (Университет Правительств
а Москвы)
DTSTART:20250512T153000Z
DTEND:20250512T170000Z
DTSTAMP:20260404T111447Z
UID:Knotsandtopology/113
DESCRIPTION:Title: Пространства начальных данных
для абстрактных параболических уравнен
ий и проблема Като\nby Р.В. Шамин (Универ
ситет Правительства Москвы) as part of Knots and r
epresentation theory\n\n\nAbstract\nДоклад посвящен опис
анию пространств начальных данных для а
бстрактных параболических уравнений. Из
вестно\, что описание пространств началь
ных данных может быть получено в результ
ате интерполяции гильбертовых простран
ств (основного пространства и области оп
ределения эллиптического оператора). Ко
нструктивное описание этих пространств
связано в проблемой Т. Като (1961).\nВ доклад
е будет приведен класс функционально-ди
фференциальных параболических уравнени
й\, для которых удается конструктивно по
строить пространства начальных данных.
Таким образом\, был найден новый класс оп
ераторов\, которые удовлетворяют пробле
ме Като. В полной мере проблема Като не р
ешена по сей день.\n
LOCATION:https://stable.researchseminars.org/talk/Knotsandtopology/113/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marko Stošić
DTSTART:20250526T153000Z
DTEND:20250526T170000Z
DTSTAMP:20260404T111447Z
UID:Knotsandtopology/114
DESCRIPTION:Title: Generalized knots-quivers correspondence\nby Marko S
tošić as part of Knots and representation theory\n\n\nAbstract\nIn this
talk I will start with introducing knots-quivers correspondence that relat
es colored HOMFLY-PT invariants (or LMOV/BPS invariants) of knots\, and th
e Donaldson-Thomas invariants of the corresponding quiver. After discussin
g different approaches\, explanations\, and extensions of such relationshi
ps to other knot and 3-manifold invariants\, I will present the generalize
d version of knots-quivers correspondence. Under that correspondence\, the
generators of the quiver generating series can have higher levels\, enabl
ing successful computations for large classes of knots (and conjecturally
for all knots)\, including the knots with the super-exponential growth pro
perty of the colored HOMFLY-PT invariants.\n
LOCATION:https://stable.researchseminars.org/talk/Knotsandtopology/114/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pavel Putrov
DTSTART:20250616T153000Z
DTEND:20250616T170000Z
DTSTAMP:20260404T111447Z
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 descri
be invariants of 3-manifolds valued in q-series with integral coefficients
. The invariants originate from physics and are expected to have a categor
ification analogous to the categorification of the Jones polynomial of a k
not by Khovanov homology. The talk is based on the joint works with Gukov\
, Pei and Vafa.\n
LOCATION:https://stable.researchseminars.org/talk/Knotsandtopology/115/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Seonghyun Yu
DTSTART:20250519T153000Z
DTEND:20250519T170000Z
DTSTAMP:20260404T111447Z
UID:Knotsandtopology/116
DESCRIPTION:Title: Full subcomplexes of Bier spheres and their topological
application\nby Seonghyun Yu as part of Knots and representation theo
ry\n\n\nAbstract\nFull subcomplexes of a simplicial complex often determin
e its topological invariants as well as those of its associated topologica
l spaces. In 1992\, Thomas Bier introduced combinatorial construction tha
t yields a huge family of simplicial $(m-2)$-spheres on $2m$ vertices. In
this talk\, I will talk about several full subcomplexes of Bier spheres\,
and their topological application to the real toric spaces associated with
Bier spheres.\n
LOCATION:https://stable.researchseminars.org/talk/Knotsandtopology/116/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Завесов Александр Львович -
DTSTART:20250609T153000Z
DTEND:20250609T170000Z
DTSTAMP:20260404T111447Z
UID:Knotsandtopology/117
DESCRIPTION:Title: Теория соседства (продолжение)
\nby Завесов Александр Львович - as part of Kno
ts and representation theory\n\n\nAbstract\nТеория соседств
а посвящена описанию и решению следующи
х задач: - Вместимость графовых систем ил
и систем с квазирасстоянием в семейство
Евклидовых пространств\; - Разделение си
стемы на пересекающиеся подсистемы по п
ринципу близости точек\; - Оптимальная ст
руктуризация системы через критерий сос
едства\; - Сила связи и взаимного влияния
между соседними точками\; - Внутренние и
граничные точки\; - Квазиметрика соседст
ва как минимальная длина ломаной (геодез
ическая)\, идущей через соседние точки\; -
Кривизна\, разностные (дифференциальные)
операторы\, области Вороного\, соседние
сферические слои\, плотность геодезичес
ких... - Байесовская вероятностная модель
\, интерпретирующая априорную меру как г
еометрическое пространство\, а апостери
орную — как набор событий во времени\; - Р
азмерность\, объем и мера для априорного
геометрического пространства\; - Энтропи
я для Байесовской вероятностной модели
как функционал системы\; - Задача регресс
ии и классификации\; - Локальная макроско
пическая область\, которая с приемлемой
точностью определяет структуру соседст
ва для выбранной точки\; - Распределение
плотности\, количества соседних точек и
размерности\; - Уравнение диффузии\; - Эво
люция потоков Риччи\; - Задача кластериза
ции на основе коэффициента связности (вн
утренняя кластеризация)\; - Задача класте
ризации на основе того\, в какой степени
точки являются внутренними или граничны
ми (внешняя кластеризация)\; - Параметриз
ация расстояний в системах\; - Модели мул
ьтимножеств и строк\; - Генеративная моде
ль\; - Квазилинейное программирование\; -
Обобщенная транспортная задача\; - Диффу
зионная модель\; - Распознавание образов\
; - Вероятность и время\; - Комплексные Мар
ковские цепи и граф влияния\; - Геометрии
на системах с квазиметрикой. (in Russian)\n
LOCATION:https://stable.researchseminars.org/talk/Knotsandtopology/117/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Галахов Дмитрий Максимович
DTSTART:20250623T153000Z
DTEND:20250623T170000Z
DTSTAMP:20260404T111447Z
UID:Knotsandtopology/118
DESCRIPTION:Title: On geometric link bases for A-polynomials\nby Гал
ахов Дмитрий Максимович as part of Knots and represen
tation theory\n\n\nAbstract\nA simple geometric way is suggested to derive
the Ward identities in the Chern-Simons theory\, also known as quantum A-
polynomials for knots. We treat A-polynomials as relations between differe
nt links\, obtained by hanging additional "simple" components on the origi
nal knot. Depending on the choice of this "decoration"\, the knot polynomi
al is either multiplied by a number or decomposes into a sum over "surroun
ding" representations by a cabling procedure. What happens is that these t
wo of decorations\, when complicated enough\, become dependent -- and this
provides an equation. To make these geometric methods somewhat simpler we
suggest to use an arcade formalism/representation of the braid group to s
implify decorating links universally.\nHowever\, in this framework the eve
ntual equivalence of links is not a topological property -- it follows fro
m relations among R-matrices\, and depends on the choice the gauge group a
nd incorporates specific link graph relations known as brackets: in practi
ce we will consider only the Kauffman bracket for SU(2) and the Kuberberg
bracket for SU(3)\, however a generalization to SU(n) is potentially avail
able.\nIn a quasi-classical limit it is closely related to the well public
ized augmentation theory and contact geometry.\nThe talk is based on paper
s 2408.08181 and 2505.20260 with A.Morozov.\n
LOCATION:https://stable.researchseminars.org/talk/Knotsandtopology/118/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Matthew Harper
DTSTART:20250811T153000Z
DTEND:20250811T170000Z
DTSTAMP:20260404T111447Z
UID:Knotsandtopology/119
DESCRIPTION:Title: Coincidences of Links-Gould and other quantum invariants
\nby Matthew Harper as part of Knots and representation theory\n\n\nAb
stract\nI will survey several recent results on the Links-Gould polynomial
\, invariants of Garoufalidis-Kashaev\, and the quantum invariant associat
ed to U_q(sl_3) at a fourth root of unity. This includes the affirmation o
f a conjecture of GK which proves their invariants recover the Links-Gould
and sl3 invariants. We also prove a conjecture of Geer and Patureau-Miran
d 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 Links-Gould and other non-semisimple quantum invariants. These result
s are joint with subsets of Stavros Garoufalidis\, Rinat Kashaev\, Ben-Mic
hael Kohli\, Jiebo Song\, Guillame Tahar\, and Emmanuel Wagner.\n
LOCATION:https://stable.researchseminars.org/talk/Knotsandtopology/119/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Igor M. Nikonov
DTSTART:20250630T130000Z
DTEND:20250630T143000Z
DTSTAMP:20260404T111447Z
UID:Knotsandtopology/120
DESCRIPTION:Title: Partial tribrackets of knots in thickened surfaces\n
by Igor M. Nikonov as part of Knots and representation theory\n\n\nAbstrac
t\nWe define a modification of Niebrzydowski tribracket construction for k
nots in a fixed thickened surface and give several examples of this invari
ant.\n
LOCATION:https://stable.researchseminars.org/talk/Knotsandtopology/120/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Seongjeong Kim
DTSTART:20250707T153000Z
DTEND:20250707T170000Z
DTSTAMP:20260404T111447Z
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 t
heory\n\n\nAbstract\nIn this talk we will show that virtual knots are embe
dded in the set of knots in $S_{g} \\times S^{1}$. We will also provide a
sufficient condition for knots in $S_{g} \\times S^{1}$ to have virtual kn
ot diagrams. Based on this\, we derive a sufficient condition for 2-compon
ent classical links to be separable.\n
LOCATION:https://stable.researchseminars.org/talk/Knotsandtopology/121/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sergey Fomin (University of Michigan)
DTSTART:20250714T153000Z
DTEND:20250714T170000Z
DTSTAMP:20260404T111447Z
UID:Knotsandtopology/122
DESCRIPTION:Title: Expressive curves\nby Sergey Fomin (University of Mi
chigan) as part of Knots and representation theory\n\n\nAbstract\nA real p
lane algebraic curve C is called expressive if its defining polynomial has
the smallest number of critical points allowed by the topology of the set
of real points of C. We give a necessary and sufficient criterion for exp
ressivity (subject to a mild technical condition)\, describe several const
ructions that produce expressive curves\, and relate their study to the co
mbinatorics of plabic graphs\, their quivers\, and links. \n\nThis is join
t work with Eugenii Shustin (Tel Aviv University).\n
LOCATION:https://stable.researchseminars.org/talk/Knotsandtopology/122/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Igor M. Nikonov
DTSTART:20250721T153000Z
DTEND:20250721T170000Z
DTSTAMP:20260404T111447Z
UID:Knotsandtopology/123
DESCRIPTION:Title: On skein invariants\nby Igor M. Nikonov as part of K
nots and representation theory\n\n\nAbstract\nAfter J.H. Conway\, it is kn
own that some knot invariants can be defined by relations (called skein re
lations) on diagrams which differ at a local site. Among skein invariants
one can mention Alexander and Jones polynomials\, Arf invariant and writhe
polynomial. In the talk we will remind these and other examples of skein
invariants and introduce a new skein invariant for links in a fixed thicke
ned surface.\n
LOCATION:https://stable.researchseminars.org/talk/Knotsandtopology/123/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anderson Vera
DTSTART:20250804T153000Z
DTEND:20250804T170000Z
DTSTAMP:20260404T111447Z
UID:Knotsandtopology/124
DESCRIPTION:Title: Lecture series on the Le-Murakami Ohtsuki Invariant\
nby Anderson Vera as part of Knots and representation theory\n\n\nAbstract
\nThe Le-Murakami-Ohtsuki invariant is a powerful invariant of 3-manifolds
(universal among quantum invariants and finite-type invariants)\, in part
icular it dominates all the Reshetikhin-Turaev invariants. The LMO invaria
nt takes values in a space of graphs called Jacobi diagrams or Feynman dia
grams. Its original definition uses the Kontsevich integral of links\, the
so-called iota maps and several projection maps between different quotien
ts of spaces of Jacobi diagrams. In this series of two talks we survey the
original construction of this invariant.\n
LOCATION:https://stable.researchseminars.org/talk/Knotsandtopology/124/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anderson Vera
DTSTART:20250818T153000Z
DTEND:20250818T170000Z
DTSTAMP:20260404T111447Z
UID:Knotsandtopology/125
DESCRIPTION:Title: Lecture series on the Le-Murakami Ohtsuki Invariant\
nby Anderson Vera as part of Knots and representation theory\n\n\nAbstract
\nThe Le-Murakami-Ohtsuki invariant is a powerful invariant of 3-manifolds
(universal among quantum invariants and finite-type invariants)\, in part
icular it dominates all the Reshetikhin-Turaev invariants. The LMO invaria
nt takes values in a space of graphs called Jacobi diagrams or Feynman dia
grams. Its original definition uses the Kontsevich integral of links\, the
so-called iota maps and several projection maps between different quotien
ts of spaces of Jacobi diagrams. In this series of two talks we survey the
original construction of this invariant.\n
LOCATION:https://stable.researchseminars.org/talk/Knotsandtopology/125/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Дениско В.В.
DTSTART:20250728T153000Z
DTEND:20250728T170000Z
DTSTAMP:20260404T111447Z
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://stable.researchseminars.org/talk/Knotsandtopology/126/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Thomas Fiedler
DTSTART:20250825T153000Z
DTEND:20250825T170000Z
DTSTAMP:20260404T111447Z
UID:Knotsandtopology/127
DESCRIPTION:Title: Tangle equations for knots\nby Thomas Fiedler as par
t of Knots and representation theory\n\n\nAbstract\nWe make a connection b
etween "Tangle-valued 1-cocycles" and "Quantum equations" for knots.To eac
h couple of knot diagrams we can associate linear systems of tangle-valued
equations with integer coefficients. If one of the systems has no solutio
n\, than the knot diagrams represent different knots. In the opposit\, eac
h solution of a system gives a non-trivial restriction on the Reidemeister
moves for each knot isotopy which relates the two diagrams. This is an e
ssential 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 knot.\n
LOCATION:https://stable.researchseminars.org/talk/Knotsandtopology/127/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Igor M. Nikonov
DTSTART:20250901T153000Z
DTEND:20250901T170000Z
DTSTAMP:20260404T111447Z
UID:Knotsandtopology/128
DESCRIPTION:Title: On crossoid structure on knots\nby Igor M. Nikonov a
s part of Knots and representation theory\n\n\nAbstract\nWe define a struc
ture called crossoid for description of colorings of the crossings in knot
s diagrams. Crossoids generalize parities in knot theory introduced by V.O
. Manturov. On the other hand\, any biquandle induces a crossoid structure
. We give a topological description of the fundamental crossoid of a knot\
, and define a crossoid cocycle invariant of knots valued in crossoid coho
mology.\n
LOCATION:https://stable.researchseminars.org/talk/Knotsandtopology/128/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vladislav Kibkalo (Lomonosov Moscow State University)
DTSTART:20250908T154000Z
DTEND:20250908T171000Z
DTSTAMP:20260404T111447Z
UID:Knotsandtopology/129
DESCRIPTION:Title: Integrable Hamiltonian systems with noncompact foliation
s and bifurcations\nby Vladislav Kibkalo (Lomonosov Moscow State Unive
rsity) as part of Knots and representation theory\n\n\nAbstract\nTopologic
al classification of integrable Hamiltonian systems developed by A. Fomenk
o and his school was applied to a wide class of geometrical\, mechanical a
nd physical systems. Compactness of fibers of their Liouville foliations i
s an important assumption here. Else new effects arise: incomplete Hamilto
nian flows\, non-critical bifurcations (bifurcation value preimage doesn
’t contain critical points of the momentum map\, moreover\, it can be em
pty). We will discuss several results on such systems (see survey by A. Fo
menko\, D. Fedoseev\, 2020 J.Math.Sc.). Note that effects related to "nonc
ompactness" appeared in a more general context of dynamical systems\, more
precisely\, as connections between nonautonomous vector fields and diffeo
morphisms (V.Grines\, L.Lerman\, 2022-2023).\n \nPseudo-Euclidean analogue
s of rigid body dynamics (see A. Borisov\, I. Mamaev\, 2016) turn out to b
e an important class of systems with noncompact foliations. New our result
s on topology of Liouville foliations of pseudo-Euclidean Euler\, Lagrange
and Kovalevskaya tops\, Zhukovsky and Klebsch systems will be presented.
Both compact and non-compact fibers\, their bifurcations (including non-cr
itical one) appear in such systems. Bifurcations and Liouville foliations
bases (analogs of Fomenko graphs) are also determined.\n
LOCATION:https://stable.researchseminars.org/talk/Knotsandtopology/129/
END:VEVENT
BEGIN:VEVENT
SUMMARY:M. Ivanov
DTSTART:20250915T153000Z
DTEND:20250915T170000Z
DTSTAMP:20260404T111447Z
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 present invariants of virtual knots and links\, as well as their pro
perties. In particular\, I will discuss polynomial invariants\, a recursiv
e method for constructing new invariants\, and their application to the st
udy of connected sums of virtual knots. I will also address groups of virt
ual knots and an approach to investigating the orderability of such groups
.\n
LOCATION:https://stable.researchseminars.org/talk/Knotsandtopology/130/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Danish Ali
DTSTART:20250929T153000Z
DTEND:20250929T170000Z
DTSTAMP:20260404T111447Z
UID:Knotsandtopology/131
DESCRIPTION:Title: A Generating Set of Reidemeister Moves of Oriented Virtu
al Knots\nby Danish Ali as part of Knots and representation theory\n\n
\nAbstract\nIn oriented knot theory\, verifying a quantity is an invariant
involves checking its invariance under all oriented Reidemeister moves\,
a process that can be intricate and time-consuming. A generating set of or
iented moves simplifies this by requiring verification for only a minimal
subset from which all other moves can be derived. While generating sets fo
r classical oriented Reidemeister moves are well-established\, their virtu
al counterparts are less explored. In this study\, we enumerate the orient
ed virtual Reidemeister moves\, identifying seventeen distinct moves after
accounting for redundancies due to rotational and combinatorial symmetrie
s. We prove that a four-element subset serves as a generating set for thes
e moves. This result offers a streamlined approach to verifying invariants
of oriented virtual knots and lays the groundwork for future advancements
in virtual knot theory\, particularly in the study of invariants and thei
r computational properties.\n
LOCATION:https://stable.researchseminars.org/talk/Knotsandtopology/131/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Igor Nikonov
DTSTART:20251006T153000Z
DTEND:20251006T170000Z
DTSTAMP:20260404T111447Z
UID:Knotsandtopology/132
DESCRIPTION:Title: On biquandles for the groups $G^k_n$ and surface singula
r braid monoid\nby Igor Nikonov as part of Knots and representation th
eory\n\n\nAbstract\nThe groups $G^k_n$ were defined by V. O. Manturov in o
rder to describe dynamical systems in configuration systems. In the talk w
e will consider two applications of this theory: we define a biquandle str
ucture on the groups $G^k_n$\, and construct a homomorphism from the surfa
ce singular braid monoid to the group $G^2_n$.\n
LOCATION:https://stable.researchseminars.org/talk/Knotsandtopology/132/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Qi Wang
DTSTART:20251013T153000Z
DTEND:20251013T170000Z
DTSTAMP:20260404T111447Z
UID:Knotsandtopology/133
DESCRIPTION:Title: Representation type of cyclotomic quiver Hecke algebras<
/a>\nby Qi Wang as part of Knots and representation theory\n\n\nAbstract\n
Determining the representation type of an algebra is a fundamental problem
in representation theory. In this talk\, we address this problem for cycl
otomic quiver Hecke algebras\, also known as cyclotomic Khovanov–Lauda
–Rouquier algebras\, in affine type A. Our approach consists of two main
steps. First\, we reduce the high-level problem to lower-level cases usin
g a quiver model. Second\, we construct explicit quiver presentations for
these lower-level cases and classify their representation types. This talk
will mainly focus on the second step and serve as an introduction to quiv
er representation theory.\n
LOCATION:https://stable.researchseminars.org/talk/Knotsandtopology/133/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Oğuz Öner
DTSTART:20251110T153000Z
DTEND:20251110T170000Z
DTSTAMP:20260404T111447Z
UID:Knotsandtopology/134
DESCRIPTION:Title: Orientation Reversal and Resurgent Crossing of the Natur
al Boundary\nby Oğuz Öner as part of Knots and representation theory
\n\n\nAbstract\nIn this talk\, I will introduce a resurgent method that cr
osses the $|q|=1$ natural boundary for the $q$-series invariants $\\wideha
t{Z}$ of 3-manifolds (Gukov-Pei-Putrov-Vafa) and\, at the level of individ
ual false theta building blocks. In our setup\, crossing the natural bound
ary corresponds to the orientation reversal of the 3-manifold $M_3$. Under
this operation\, the $q$-series invariants for $M_3$ and $\\overline{M_3}
$ are very different\, and usually one of them is much harder to compute.
The resurgence approach proposes a solution to systematically computing th
ese invariants and their individual building blocks for a large class of n
ew examples. The talk is based on joint work with Adams\, Costin\, Dunne\,
and Gukov.\n
LOCATION:https://stable.researchseminars.org/talk/Knotsandtopology/134/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mrunmay Jagadale
DTSTART:20251020T153000Z
DTEND:20251020T170000Z
DTSTAMP:20260404T111447Z
UID:Knotsandtopology/135
DESCRIPTION:Title: TQFT for $\\hat{Z}$ invariants\nby Mrunmay Jagadale
as part of Knots and representation theory\n\n\nAbstract\nThe $\\hat{Z}$-i
nvariants of three-manifolds introduced by Gukov\, Pei\, Putrov\, and Vafa
have influenced many areas of mathematics and physics. However\, their TQ
FT structure is not yet fully understood. In this talk\, I will present a
framework for decorated Spin-TQFTs and construct one based on Atiyah–Seg
al-like axioms that computes the $\\hat{Z}$-invariants. This TQFT framewor
k provides a new perspective on the structural properties and gluing formu
las for $\\hat{Z}$-invariants.\n
LOCATION:https://stable.researchseminars.org/talk/Knotsandtopology/135/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Olga Frolkina
DTSTART:20251117T153000Z
DTEND:20251117T170000Z
DTSTAMP:20260404T111447Z
UID:Knotsandtopology/136
DESCRIPTION:Title: Properties of a compact set in $R^n$ and its projections
\nby Olga Frolkina as part of Knots and representation theory\n\n\nAbs
tract\nProperties of projections of zero-dimensional sets were considered
already at the end of 19th century. In 1884 G.Cantor described a surjectio
n of the middle-thirds Cantor set onto the unit segment. Cantor sets in pl
ane all of whose projections are segments were constructed by L.Antoine
(1924)\, H.Otto (1933)\, A.Flores (1933)\, G.Noebeling (1933). In 1947\,
K.Borsuk described a Cantor set in $R^n$ such that its projection into an
y $(n-1)$-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 auth
or remarked that for any Cantor set\n$K\\subset R^n$ there exists an arbi
trarily small isotopy $\\{ f_t \\} :R^n\\cong R^n$ such that the projec
tion of $f_1(K)$ into any $(n−1)$-plane has dimension $(n−1)$\; and th
ere exists an arbitrarily small isotopy $\\{ g_t \\} : R^n \\cong R^n$
such that the projection of $ g_1(K)$ into any $(n−1)$-plane has dimens
ion $(n−2)$.\n\nIn the talk\, we will discuss these and other similar r
esults using the Baire category approach. The questions on typical behavi
our (in the sense of Baire category) are classic. A typical continuous fun
ction is nowhere differentiable (S.Banach-S.Mazurkiewicz 1931). A typica
l knot is wild (J.Milnor 1964) and moreover wild at any of its points (
H.G.Bothe 1966). A typical compactum in Rn is a Cantor set (K.Kuratowsk
i 1973). We will discuss the behavior of projections of a compactum $X\\s
ubset R^n$ under a typical isotopy of $R^n$\, and as a corollary we will
strengthen a theorem of J.Vaisala (1979).\n
LOCATION:https://stable.researchseminars.org/talk/Knotsandtopology/136/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Josef Svoboda
DTSTART:20251027T153000Z
DTEND:20251027T170000Z
DTSTAMP:20260404T111447Z
UID:Knotsandtopology/137
DESCRIPTION:Title: Inverted Habiro series\nby Josef Svoboda as part of
Knots and representation theory\n\n\nAbstract\nQuantum algebra provides an
important source of invariants of knots and 3-manifolds. Using Verma modu
les of the algebra $U_q(sl_2)$\, Park defined a new quantum knot invariant
(building on a previous work of Gukov--Manolescu) and observed that it ca
n be written in a very peculiar form\, which he called inverted Habiro ser
ies. I will describe a commutative ring $\\Lambda$ that contains these ser
ies 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--R
ogers and Ramanujan follow from the study of residues of the inverted Habi
ro series for the simplest knots. Finally\, I will present some recent dev
elopments about the topological significance of these invariants.\n
LOCATION:https://stable.researchseminars.org/talk/Knotsandtopology/137/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Qiuyu Ren
DTSTART:20251201T153000Z
DTEND:20251201T170000Z
DTSTAMP:20260404T111447Z
UID:Knotsandtopology/138
DESCRIPTION:Title: Khovanov skein lasagna modules with 1-dimensional inputs
\nby Qiuyu Ren as part of Knots and representation theory\n\n\nAbstrac
t\nSkein lasagna modules (with $0$-dimensional inputs) are $4$-manifold in
variants introduced by Morrison-Walker-Wedrich. In this context\, a skein
is a properly embedded surface in a $4$-manifold minus a disjoint union of
$4$-balls\, and the lasagna comes from a TQFT for links in $S^3$ (satisfy
ing mild conditions). In this talk\, we introduce skein lasagna modules wi
th $1$-dimensional inputs\, where a skein is a properly embedded surface i
n a $4$-manifold minus a tubular neighborhood of an embedded graph\, and t
he lasagna comes from a TQFT for links in $\\#(S^1\\times S^2)$ and link c
obordisms between them in a particular class of $4$-manifolds. We show tha
t the Khovanov homology of links in $\\#(S^1\\times S^2)$\, as defined by
Rozansky 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-Z
hang\; Gabai's $4$-dimensional lightbulb theorem\; and certain Khovanov la
sagna naturality properties of the Gluck twist operation. This is joint wo
rk with I. Sullivan\, P. Wedrich\, M. Willis\, M. Zhang.\n
LOCATION:https://stable.researchseminars.org/talk/Knotsandtopology/138/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Igor M. Nikonov
DTSTART:20251103T153000Z
DTEND:20251103T170000Z
DTSTAMP:20260404T111447Z
UID:Knotsandtopology/139
DESCRIPTION:Title: Homotopical multicrossing complex\nby Igor M. Nikono
v as part of Knots and representation theory\n\n\nAbstract\nWe introduce t
he multicrossing complex of a tangle and define the crossing homology cla
ss. In a sense\, the multicrossing complex unifies tribracket\, biquandle
and crossoid homologies\; and the tribracket\, biquandle and crossoid cy
cle invariants are actually the result of pairing a tribracket (biquandle
\, crossoid) cocycle with the crossing homology class.\n
LOCATION:https://stable.researchseminars.org/talk/Knotsandtopology/139/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Paul Wedrich
DTSTART:20251215T153000Z
DTEND:20251215T170000Z
DTSTAMP:20260404T111447Z
UID:Knotsandtopology/140
DESCRIPTION:Title: Perverse schobers of type A and categorified bialgebras<
/a>\nby Paul Wedrich as part of Knots and representation theory\n\n\nAbstr
act\nThis talk\, based on joint work with Dyckerhoff\, connects the concep
t of\nperverse schobers - a categorification of perverse sheaves envisione
d by Kapranov and Schechtman - with structures in quantum topology and lin
k homology theory. We propose a definition of perverse schobers on symmetr
ic products of the complex line\, with respect to the discriminant stratif
ication\, and construct a nontrivial example using complexes of singular S
oergel bimodules of type A. Our approach centers on a stable categorificat
ion of Kapranov-Schechtman's classification data for perverse sheaves in t
erms of graded bialgebras. In particular\, we show that singular Soergel b
imodules give rise to a categorified graded bialgebra\, which sheds new li
ght on the geometric foundations of the Rouquier–Rickard braiding and th
e role of webs and foams in link homology theory\n
LOCATION:https://stable.researchseminars.org/talk/Knotsandtopology/140/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vassily O. Manturov
DTSTART:20251208T153000Z
DTEND:20251208T170000Z
DTSTAMP:20260404T111447Z
UID:Knotsandtopology/141
DESCRIPTION:Title: Parity\, Vassiliev Invariants\, Framed Chord diagrams\,
Legendrian Knots\, and Flat-Virtual Knots\nby Vassily O. Manturov as p
art of Knots and representation theory\n\n\nAbstract\nIn the present talk\
, I will mention the following two topics:\n \n1) How to get parity for c
lassical 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 comple
ment to K_{1}.\n \nThe space R^{3}\\backslash K_{1} has non-trivial homol
ogy\, hence the theory of Vassiliev invariants for K_{1} in the complemen
t to K_{2} has some features of ``parity''\; we formulate many problems c
oncerning framed chord diagram\, framed Vassiliev invariants\, Kontsevich
integral\, etc.\n \n2) In 2022\, in two joint papers with I.M.Nikonov\, w
e constructed a map from classical knot theory in the full torus S_{1}\\t
imes R^{2} to the so-called ``flat-virtual knot theory'' which has many `
`virtual features.''\n\nPlane curves and fronts naturally lift to Legendri
an knots in the spherized bundle S_{*} T R^{2} which is topologically a t
orus.\n \nThis leads to a nice interplay between the theory of Legendrian
knots\, fronts\, virtual knots\, and flat-virtual knots.\n
LOCATION:https://stable.researchseminars.org/talk/Knotsandtopology/141/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Igor M. Nikonov
DTSTART:20251222T153000Z
DTEND:20251222T170000Z
DTSTAMP:20260404T111447Z
UID:Knotsandtopology/142
DESCRIPTION:Title: On knot invariants induced by skein relations\nby Ig
or M. Nikonov as part of Knots and representation theory\n\n\nAbstract\nSi
nce 1970s\, it is known that some knot invariants can be defined by relati
ons (called skein relations) on diagrams which differ at a local site. Amo
ng skein invariants one can mention Alexander and Jones polynomials\, Arf
invariant and writhe polynomial. In the talk we will remind these and othe
r examples of skein invariants and introduce a new skein invariant for lin
ks in a fixed thickened surface.\n
LOCATION:https://stable.researchseminars.org/talk/Knotsandtopology/142/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Louis Kauffman
DTSTART:20251229T153000Z
DTEND:20251229T170000Z
DTSTAMP:20260404T111447Z
UID:Knotsandtopology/143
DESCRIPTION:Title: Topological Quantum Computing - Fibonacci Model and Majo
rana Fermions Knots and representation theory\nby Louis Kauffman as pa
rt of Knots and representation theory\n\n\nAbstract\nWe will discuss topol
ogical quantum computing from the point of view of the Fibonacci model (vi
a Temperley-Lieb recoupling theory based on Kauffman bracket polynomial) a
nd also in terms of braid group representations associated with Majorana F
ermions. The talk will be self-contained and we will quickly review what w
e discussed in the previous talks in this series.\n
LOCATION:https://stable.researchseminars.org/talk/Knotsandtopology/143/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dmitriy Khudoteplov
DTSTART:20260112T153000Z
DTEND:20260112T170000Z
DTSTAMP:20260404T111447Z
UID:Knotsandtopology/144
DESCRIPTION:Title: Vogel classification of Lie algebras\nby Dmitriy Khu
doteplov as part of Knots and representation theory\n\n\nAbstract\nIn the
early stage of the development of Vassiliev knot invariants there was a co
njecture that all Vassiliev invariants come from simple Lie algebras. Pier
re Vogel disproved this conjecture\, constructing a Jacobi diagram lying i
n the kernels of all Lie algebra weight systems. Originally\, Vogel though
t that there exists some generalization of Lie algebra involving three par
ameters so that the simple Lie algebras are obtained by specialization of
these parameters. Later it was discovered that these parameters must satis
fy an additional relation\, which is contrary to the initial idea. On the
other side\, this discovery enables to classify Lie algebras in an elegant
way\, rooted in the knot theory.\n
LOCATION:https://stable.researchseminars.org/talk/Knotsandtopology/144/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Igor Nikonov
DTSTART:20260105T153000Z
DTEND:20260105T170000Z
DTSTAMP:20260404T111447Z
UID:Knotsandtopology/145
DESCRIPTION:Title: On biquandles for the groups $G^k_n$ and surface singula
r braid monoid\nby Igor Nikonov as part of Knots and representation th
eory\n\n\nAbstract\nThe groups $G^k_n$ were defined by V. O. Manturov in o
rder to describe dynamical systems in configuration systems. In the talk w
e will consider two applications of this theory: we define a biquandle str
ucture on the groups $G^k_n$\, and construct a homomorphism from the surfa
ce singular braid monoid to the group $G^2_n$.\n
LOCATION:https://stable.researchseminars.org/talk/Knotsandtopology/145/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Seongjeong Kim
DTSTART:20260119T153000Z
DTEND:20260119T170000Z
DTSTAMP:20260404T111447Z
UID:Knotsandtopology/146
DESCRIPTION:Title: On braids for Knots in $S_{g} \\times S^{1}$\nby Seo
ngjeong Kim as part of Knots and representation theory\n\n\nAbstract\nIn \
\cite{Kim} for an oriented surface $S_{g}$ of genus $g$ it is shown that l
inks in $S_{g} \\times S^{1}$ can be presented by virtual diagrams with a
decoration\, so called\, {\\em double lines}. In this paper\, first we def
ine braids with double lines for links in $S_{g}\\times S^{1}$. We denote
the group of braids with double lines by $VB_{n}^{dl}$. Alexander and Mark
ov theorem 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 double lines\, but without virtual crossings\, then the Hecke algebr
a of $B_{n}^{dl}$ is isomorphic to affine Hecke algebra.\n
LOCATION:https://stable.researchseminars.org/talk/Knotsandtopology/146/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Igor Nikonov
DTSTART:20260126T153000Z
DTEND:20260126T170000Z
DTSTAMP:20260404T111447Z
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 crossings of knot diagrams which is compatible with Reidemeister moves
. We define the notion of parity for based matrices -- algebraic objects i
ntroduced 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 par
ity of virtual knots.\n
LOCATION:https://stable.researchseminars.org/talk/Knotsandtopology/147/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Phillip Choi
DTSTART:20260309T153000Z
DTEND:20260309T170000Z
DTSTAMP:20260404T111447Z
UID:Knotsandtopology/148
DESCRIPTION:Title: Colored Jones Polynomials of 4-Plats\nby Phillip Cho
i as part of Knots and representation theory\n\n\nAbstract\nUsing the diag
rammatic formulation of the Jones polynomial given by the Kauffman bracket
\, we review the standard construction of the N-colored Jones polynomial.
We then consider the case of 4-plat diagrams (2-bridge knots/links) and sh
ow that the diagrammatic formula simplifies when interpreted through the r
epresentation theory of quantum groups.\n
LOCATION:https://stable.researchseminars.org/talk/Knotsandtopology/148/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Igor M. Nikonov
DTSTART:20260202T153000Z
DTEND:20260202T170000Z
DTSTAMP:20260404T111447Z
UID:Knotsandtopology/149
DESCRIPTION:Title: On a representation of the group Gn3\nby Igor M. Nik
onov as part of Knots and representation theory\n\n\nAbstract\nWe consider
a certain modification of the group $G^3_n$ which describes dynamics of p
oint configurations\, in particular braids\, and define a representation o
f the modified $G^3_n$. The braid representation induced by it is powerful
enough to detect the kernel of the Burau representation.\n
LOCATION:https://stable.researchseminars.org/talk/Knotsandtopology/149/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Fedor Nilov
DTSTART:20260209T153000Z
DTEND:20260209T170000Z
DTSTAMP:20260404T111447Z
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\nAbstrac
t\nThe classical Steiner problem consists in finding the number of non-deg
enerate conics (second-order curves) tangent to 5 given conics in the plan
e. We will construct several configurations of four circles such that ther
e is a family of similar conics tangent to these circles.\n
LOCATION:https://stable.researchseminars.org/talk/Knotsandtopology/150/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexander Zheglov
DTSTART:20260216T153000Z
DTEND:20260216T170000Z
DTSTAMP:20260404T111447Z
UID:Knotsandtopology/151
DESCRIPTION:Title: The Krichever correspondence and the theory of commuting
ordinary differential operators\nby Alexander Zheglov as part of Knot
s and representation theory\n\n\nAbstract\nIn the 1970s\, a method was dev
ised to use Jacobians of algebraic curves and the corresponding theta func
tions to write out exact solutions to some well-known equations of mathema
tical physics\, namely those obtained from the Kadomtsev–Petviashvili hi
erarchy (an infinite system of partial differential equations)\, in partic
ular\, the Korteweg–de Vries and Kadomtsev–Petviashvili equations. The
se solutions are based on the geometry of algebraic curves and line bundle
s on them (or\, more generally\, torsion-free sheaves)\, rings of commutin
g ordinary differential operators\, and the Krichever map\, which associat
es certain algebraic-geometric data associated with a projective curve and
a line bundle on it with a point in an infinite-dimensional algebraic var
iety\, the Sato Grassmannian. This correspondence (known as the Krichever
correspondence) was subsequently refined and developed by many renowned ma
thematicians (W. Drinfeld\, D. Mumford\, J. Verdier\, G. Segal\, D. Wilson
\, M. Mulase\, T. Shiota)\, and played an important role in solving the Sc
hottky problem.\nIn my talk I will attempt to outline the basic definition
s and constructions of this theory.\n
LOCATION:https://stable.researchseminars.org/talk/Knotsandtopology/151/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vassily Manturov
DTSTART:20260302T152500Z
DTEND:20260302T170000Z
DTSTAMP:20260404T111447Z
UID:Knotsandtopology/152
DESCRIPTION:Title: The photography method: how to solve equations without w
riting them\nby Vassily Manturov as part of Knots and representation t
heory\n\n\nAbstract\nWe shall talk about a universal method which allows o
ne to guess solutions\nof different equations which can be written differe
ntly.\n \n Very often it leads to solutions of equations coming from physi
cs and\napplicable to topology.\n \n The simplest but structurally very im
portant is the proof (without calculations)\nthat the Ptolemy transformati
on satisfies the pentagon identity (in other words\,\nbeing applied five t
imes it gives the identity map).\n \n Then we will tell how to "draw equat
ions" and solve them by using\n"proper sense" arguments (соображе
ния здравого смысла).\n\n Usual logical considerations wi
ll lead to various generalisations \n(for example
\, tropical ones). The photography method is related to\nvarious branches
of mathematics: cluster algebras\, braids\, Conway-Coxeter\nfriezes\, Stas
heff polytopes\, associators ets.\n \n We shall describe some direct
ions of further research and list the papers where\nthis was initiated and
colleagues and students working on them.\n
LOCATION:https://stable.researchseminars.org/talk/Knotsandtopology/152/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Igor Nikonov
DTSTART:20260223T153000Z
DTEND:20260223T170000Z
DTSTAMP:20260404T111447Z
UID:Knotsandtopology/153
DESCRIPTION:Title: On universal parity on free two-dimensional knots\nb
y Igor Nikonov as part of Knots and representation theory\n\n\nAbstract\nI
n the talk we review the definition of parity on 2-knots\, and prove that
the Gaussian parity is universal on free two-dimensional knots.\n
LOCATION:https://stable.researchseminars.org/talk/Knotsandtopology/153/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Du Pei
DTSTART:20260316T153000Z
DTEND:20260316T170000Z
DTSTAMP:20260404T111447Z
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 studying skein modules of 3-manifolds by embedding them into the Hilbe
rt spaces of four-dimensional supersymmetric gauge theories. When the 3-ma
nifold has reduced holonomy\, this approach leads to an algorithm for the
dimension of the skein module for a general gauge group\, expressed as a s
um over nilpotent orbits in the Lie algebra. Surprisingly\, the dimensions
often differ between Langlands-dual pairs\, for which I will provide a ph
ysical explanation. This perspective helps to clarify the relation between
the gauge-theoretic framework of Kapustin and Witten and other versions o
f the geometric Langlands program\, and explains why the dimensions of ske
in modules do not exhibit a TQFT-like behavior.\n
LOCATION:https://stable.researchseminars.org/talk/Knotsandtopology/154/
END:VEVENT
BEGIN:VEVENT
SUMMARY:G.V. Belozerov
DTSTART:20260323T153000Z
DTEND:20260323T170000Z
DTSTAMP:20260404T111447Z
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\nAbstr
act\nThe most illustrative integrable Hamiltonian systems are billiards bo
unded by confocal quadrics. The integrability of these systems follows fro
m the classical Jacobi--Chasles theorem. Recall that according to this the
orem\, \\textit{tangent lines drawn to a geodesic on an $n$-axial ellipsoi
d in Euclidean $\\mathbb{R}^n$ touch\, in addition to this ellipsoid\, $n-
2$ confocal quadrics common to all points of the given geodesic}. This the
orem implies the integrability of the geodesic flow on the ellipsoid.\n\nV
.A. Kibkalo investigated the issue of integrability of the geodesic flow o
n the intersection of several confocal quadrics. He showed that the geodes
ic flow on the intersection of $(n-2)$ confocal quadrics is a completely i
ntegrable Hamiltonian system. It turns out that the result remains valid i
f we consider the geodesic flow on the intersection of an arbitrary number
of non-degenerate confocal quadrics. Moreover\, the following theorem hol
ds.\n\n\\begin{theorem}[Belozerov]\nLet $Q_1\, \\ldots\, Q_k$ be non-degen
erate confocal quadrics of different types in $\\mathbb{R}^n$ and $Q = \\b
igcap_{i=1}^k Q_i$. Then:\n\\begin{enumerate}\n \\item the geodesic flo
w on $Q$ is quadratically integrable\;\n \\item tangent lines drawn to
all points of a geodesic on $Q$\, in addition to $Q_1\, \\ldots\, Q_k$\, t
ouch $n-k-1$ quadrics confocal with $Q_1\, \\ldots\, Q_k$ and common to al
l points of this geodesic.\n\\end{enumerate}\n\\end{theorem}\n\n\\textbf{R
emark.} Geodesics on the intersection of non-degenerate confocal quadrics\
, in general\, are not geodesics on any of the quadrics $Q_1\, \\ldots\, Q
_k$. Therefore\, Theorem 1 is not a consequence of the classical Jacobi-Ch
asles theorem.\n\nAccording to Theorem 1 and the result of V.V. Kozlov on
integrable geodesic flows on two-dimensional surfaces\, the connected comp
onent of the compact intersection of $(n-2)$ quadrics is homeomorphic eith
er to a torus $T^2$ or to a sphere $S^2$. Both cases are realized. Neverth
eless\, it is possible to describe the class of homeomorphism of any compa
ct intersection of non-degenerate confocal quadrics. It turns out that it
is homeomorphic to a direct product of spheres.\n\nIt also turned out that
the classical Jacobi-Chasles theorem can be generalized not only for Eucl
idean spaces\, but also for pseudo-Euclidean spaces and spaces of constant
curvature. These generalizations significantly enrich the class of integr
able billiards.\n\nStudying the trajectory properties of multidimensional
billiards bounded by ellipsoids\, the author and his scientific advisor A.
T. Fomenko 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 a
n ellipse 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 tur
ns out that this fact has a multidimensional generalization\, so ellipsoid
s of arbitrary dimension can be constructed using a thread.\n
LOCATION:https://stable.researchseminars.org/talk/Knotsandtopology/155/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Theodore Popelensky
DTSTART:20260504T153000Z
DTEND:20260504T170000Z
DTSTAMP:20260404T111447Z
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://stable.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:20260404T111447Z
UID:Knotsandtopology/158
DESCRIPTION:Title: On the construction of foldings of branched covers along
knots\nby Byeorhi Kim as part of Knots and representation theory\n\nI
nteractive livestream: https://us02web.zoom.us/j/81866745751?pwd=bEFqUUlZM
1hVV0tvN0xWdXRsV2pnQT09\n\nAbstract\nIn this talk\, we study braiding and
folding of branched covers of the 3-sphere along knots\, focusing on const
ructions derived from quandle colorings of knots and quipu diagrams for fi
nite groups. These techniques were developed in earlier work. We present a
detailed folding of the dihedral cover of \\(S^3\\) branched along the to
rus knot \\(T(2\,5)\\)\, and describe a related example for the trefoil kn
ot using the alternating group \\(A_4\\). These constructions provide e
xplicit geometric models for branched covers and suggest potential extensi
ons to surface-knot branch sets in \\(S^4\\).\n
LOCATION:https://stable.researchseminars.org/talk/Knotsandtopology/158/
URL:https://us02web.zoom.us/j/81866745751?pwd=bEFqUUlZM1hVV0tvN0xWdXRsV2pn
QT09
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yangzhou Liu
DTSTART:20260330T153000Z
DTEND:20260330T170000Z
DTSTAMP:20260404T111447Z
UID:Knotsandtopology/159
DESCRIPTION:Title: Secant-quandle: an invariant of braids and knots\nby
Yangzhou Liu as part of Knots and representation theory\n\n\nAbstract\nWe
construct a novel invariant of braids and knots\, secant-quandle (SQ)\,wi
th generic secants serving as generators and generic horizontal trisecants
serving as relations\, i.e.\, SQ=Γ⟨S_M | S_T\,E_M⟩\, where M is a br
aid or link.\n
LOCATION:https://stable.researchseminars.org/talk/Knotsandtopology/159/
END:VEVENT
END:VCALENDAR