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BEGIN:VEVENT
SUMMARY:L. Kauffman
DTSTART;VALUE=DATE-TIME:20201221T153000Z
DTEND;VALUE=DATE-TIME:20201221T170000Z
DTSTAMP;VALUE=DATE-TIME:20240522T205447Z
UID:Knotsandtopology/1
DESCRIPTION:Title: Virtual Knots\, Index Polynomials and the Sawollek Polynomial
\nby L. Kauffman as part of Knots and representation theory\n\n\nAbstract\
nThis talk will discuss the Affine Index Polynomial and its relationship w
ith the Sawollek Polynomial for virtual knots and links.\n
LOCATION:https://researchseminars.org/talk/Knotsandtopology/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:N. Bogachev (Skoltech & MIPT)
DTSTART;VALUE=DATE-TIME:20201228T153000Z
DTEND;VALUE=DATE-TIME:20201228T170000Z
DTSTAMP;VALUE=DATE-TIME:20240522T205447Z
UID:Knotsandtopology/2
DESCRIPTION:Title: Arithmetic and quasi-arithmetic hyperbolic reflection groups\
nby N. Bogachev (Skoltech & MIPT) as part of Knots and representation theo
ry\n\n\nAbstract\nIn 1967\, Vinberg started a systematic study of hyperbol
ic reflection groups. In particular\, he showed that Coxeter polytopes are
natural fundamental domains of hyperbolic reflection groups and developed
practically efficient methods that allow to determine compactness or volu
me finiteness of a given Coxeter polytope by looking at its Coxeter diagra
m. He also proved a (quasi-)arithmeticity criterion for hyperbolic lattice
s generated by reflections. In 1981\, Vinberg showed that there are no com
pact Coxeter polytopes in hyperbolic spaces H^n for n>29. Also\, he showed
that there are no arithmetic hyperbolic reflection groups H^n for n>29\,
either. Due to the results of Nikulin (2007) and Agol\, Belolipetsky\, Sto
rm\, and Whyte (2008) it became known that there are only finitely many ma
ximal arithmetic hyperbolic reflection groups in all dimensions. These res
ults give hope that maximal arithmetic hyperbolic reflection groups can be
classified.\n \nA very interesting moment is that compact Coxeter polytop
es are known only up to H^8\, and in H^7 and H^8 all the known examples ar
e arithmetic. Thus\, besides the problem of classification of arithmetic h
yperbolic reflection groups (which remains open since 1970-80s) we have an
other very natural question (which is again open since 1980s): do there ex
ist compact (both arithmetic and non-arithmetic) hyperbolic Coxeter polyto
pes in H^n for n>8 ?\n \nThis talk will be devoted to the discussion of th
ese two related problems. One part of the talk is based on the recent prep
rint https://arxiv.org/abs/2003.11944 where some new geometric classifica
tion method is described. The second part is based on a joint work with Al
exander Kolpakov https://arxiv.org/abs/2002.11445 where we prove that eac
h lower-dimensional face of a quasi-arithmetic Coxeter polytope\, which ha
ppens to be itself a Coxeter polytope\, is also quasi-arithmetic. We also
provide a few illustrative examples.\n
LOCATION:https://researchseminars.org/talk/Knotsandtopology/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:I.M. Nikonov
DTSTART;VALUE=DATE-TIME:20210111T153000Z
DTEND;VALUE=DATE-TIME:20210111T170000Z
DTSTAMP;VALUE=DATE-TIME:20240522T205447Z
UID:Knotsandtopology/3
DESCRIPTION:Title: On noncommutative geometry\nby I.M. Nikonov as part of Knots
and representation theory\n\n\nAbstract\nNoncommutative (differential) geo
metry was introduced by Alain Connes about forty years ago. It is based on
the correspondence between topological and geometrical objects (manifolds
\, bundles\, differential forms etc.) and algebraic ones (algebras\, modul
es\, Hochschild homology etc.)In the talk we review the basic construction
s of noncommutative geometry: C*-algebras\, cyclic homology and Chern char
acter.\n
LOCATION:https://researchseminars.org/talk/Knotsandtopology/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Victoria Lebed
DTSTART;VALUE=DATE-TIME:20210118T153000Z
DTEND;VALUE=DATE-TIME:20210118T170000Z
DTSTAMP;VALUE=DATE-TIME:20240522T205447Z
UID:Knotsandtopology/4
DESCRIPTION:Title: Unexpected applications of homotopical algebra to knot theory
\nby Victoria Lebed as part of Knots and representation theory\n\n\nAbstra
ct\nInteractions between knot theory and homotopical algebra are numerous
and natural. But the connections unveiled in this talk are rather unexpect
ed. Following a recent preprint with Markus Szymik\, I will explain how ho
motopy can help one to compute the full homology of racks and quandles. Th
ese are certain algebraic structures\, useful in knot theory and other are
as of mathematics. Their homology plays a key role in applications. Althou
gh very easy to define\, it is extremely difficult to compute. Complete co
mputations have been done only for a few families of racks. Our methods ad
d a new family to this list\, the family of permutation racks. The necessa
ry background on racks and quandles\, and their role in braid and knot the
ories\, will be given.\n
LOCATION:https://researchseminars.org/talk/Knotsandtopology/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:S. Kim
DTSTART;VALUE=DATE-TIME:20210125T153000Z
DTEND;VALUE=DATE-TIME:20210125T170000Z
DTSTAMP;VALUE=DATE-TIME:20240522T205447Z
UID:Knotsandtopology/5
DESCRIPTION:Title: Links in $S_{g} \\times S^{1}$ and its lifting\nby S. Kim as
part of Knots and representation theory\n\n\nAbstract\nA virtual knot\, wh
ich is one of generalizations of knots in $\\mathbb{R}^{3}$ (or $S^{3}$)\,
is\, roughly speaking\, an embedded circle in thickened surface $S_{g} \\
times I$. In this talk we will discuss about knots in 3 dimensional $S_{g}
\\times S^{1}$. We introduce basic notions for knots in $S_{g} \\times S^
{1}$\, for example\, diagrams\, moves for diagrams and so on. For knots in
$S_{g} \\times S^{1}$ technically we lose over/under information\, but we
will have information how many times the knot rotates along $S^{1}$. We w
ill discuss the geometric meaning of the rotating information.\n
LOCATION:https://researchseminars.org/talk/Knotsandtopology/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:V.O. Manturov
DTSTART;VALUE=DATE-TIME:20210201T153000Z
DTEND;VALUE=DATE-TIME:20210201T170000Z
DTSTAMP;VALUE=DATE-TIME:20240522T205447Z
UID:Knotsandtopology/6
DESCRIPTION:Title: Invariants of free knots valued in free groups\nby V.O. Mantu
rov as part of Knots and representation theory\n\n\nAbstract\nThis talk is
a part of the project of creating ``non-commutative'' invariants\nin topo
logy. The main idea is to replace ``characteristic classes'' of moduli spa
ces\nwith ``characteristic loops''. We discuss ``the last stage'' of the t
alk devoted to\nthe abstract objects we get in the end: the free knots\, a
n discuss their invariants\nvalued in free groups.\n \nThese invariants a
llow one to detect easily mutations\, invertibility\, and other phenomena.
\n
LOCATION:https://researchseminars.org/talk/Knotsandtopology/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Manpreet Singh (Mohali\, India)
DTSTART;VALUE=DATE-TIME:20210208T153000Z
DTEND;VALUE=DATE-TIME:20210208T170000Z
DTSTAMP;VALUE=DATE-TIME:20240522T205447Z
UID:Knotsandtopology/7
DESCRIPTION:Title: Algebraic structures in knot theory\nby Manpreet Singh (Mohal
i\, India) as part of Knots and representation theory\n\n\nAbstract\nA vir
tual knot is a smooth\, simple closed curve in a thickened compact oriente
d surfaces considered up to ambient isotopy\, stabilisation/destabilisatio
n and orientation preserving homeomorphism of surfaces. Kuperberg proves t
hat every virtual link has a unique representative as a link up to ambient
isotopy in a thickened surface of the minimal genus. A classical knot the
ory is the study of smooth embedding of circles in the 3-sphere up to ambi
ent isotopy. Considering classical theory as the study of links in the thi
ckened 2-sphere\, the preceding result implies that classical knot theory
is embedded inside virtual knot theory. One of the fundamental problems in
knot theory is the classification of knots. In the classical case\, the f
undamental group of the knot complement space is a well known invariant. B
ut there are examples where it fails to distinguish distinct knots. Around
the 1980s\, Matveev and Joyce introduce a complete classical knot invaria
nt (up to the orientation of the knot and the ambient space) using distrib
utive groupoids (quandles)\, known as the knot quandle. \n \nIn the talk\,
I will describe the construction of knot quandle given by Matveev. I will
introduce the notion of residually finite quandles and prove that all lin
k quandles are residually finite. Using this\, I will prove that the word
problem is solvable for link quandle. I will discuss the orderability of q
uandles\, in particular for link quandles. Since all link groups are left-
orderable\, it is reasonable to expect that link quandles are left (right)
-orderable. In contrast\, I will show that orderability of link quandle be
have quite differently than that of the corresponding link groups. I will
also introduce a recent combinatorial generalisation of virtual links to w
hich we name as marked virtual links. I will associate groups and peripher
al structures to these diagrams and study their properties.\n
LOCATION:https://researchseminars.org/talk/Knotsandtopology/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Neha Nanda
DTSTART;VALUE=DATE-TIME:20210215T153000Z
DTEND;VALUE=DATE-TIME:20210215T170000Z
DTSTAMP;VALUE=DATE-TIME:20240522T205447Z
UID:Knotsandtopology/8
DESCRIPTION:Title: An excursion on doodles on surfaces and virtual twins\nby Neh
a Nanda as part of Knots and representation theory\n\n\nAbstract\nStudy of
certain isotopy classes of a finite collection of immersed circles withou
t triple or higher intersections on closed oriented surfaces can be though
t of as a planar analogue of virtual knot theory where the genus zero case
corresponds to classical knot theory. Alexander and Markov theorems for t
he classical setting is well-known\, where the role of groups is played by
twin groups\, a class of right-angled Coxeter groups with only far commut
ativity relations. In the talk\, Alexander and Markov theorems for higher
genus case\, where the role of groups is played by a new class of groups c
alled virtual twin groups\, will be discussed which is work in collaborati
on with Dr Mahender Singh. Furthermore\, recent work on structural aspects
of these groups will be addressed which is a joint work with Dr Mahender
Singh and Dr Tushar Kanta Naik.\n
LOCATION:https://researchseminars.org/talk/Knotsandtopology/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Th. Yu. Popelensky
DTSTART;VALUE=DATE-TIME:20210222T153000Z
DTEND;VALUE=DATE-TIME:20210222T170000Z
DTSTAMP;VALUE=DATE-TIME:20240522T205447Z
UID:Knotsandtopology/9
DESCRIPTION:Title: Quaternionic conjugation spaces\nby Th. Yu. Popelensky as par
t of Knots and representation theory\n\n\nAbstract\nThere is a considerabl
e amount of examples of spaces $X$ equipped with an involution $\\tau$\nsu
ch that the mod 2--cohomology rings $H^{2*}(X)$ and $H^*(X^\\tau)$ are iso
morphic.\nHausmann\, Holm\, and Puppe have shown that such an isomorphim i
s a part of a certain structure\non equivariant cohomology of $X$ and $X^\
\tau$\, which is called an {\\it $H$-frame}.\nThe simplest examples are co
mplex Grassmannians and flag manifolds with complex conjugation.\nWe devel
op a similar notion of $Q$-frame which appears in the situation\nwhen a sp
ace $X$ is equipped with two commuting involutions $\\tau_1\,\\tau_2$ and\
nthe mod 2-cohomology rings $H^{4*}(X)$ and $H^*(X^{\\tau_1\,\\tau_2})$ ar
e isomorphic.\nMotivating examples are quaternionic Grassmannians and quat
ernionic flag manifolds equipped with\ntwo complex involutions. We show na
turality and uniqueness of $Q$-framing.\nWe prove that $Q$-framing can be
defined for direct limits\, products\, etc. of $Q$-framed spaces.\nThis li
st of operations contains glueing a disk in $\\HH^n$ with complex involuti
ons $\\tau_1$ and $\\tau_2$ to a $Q$-framed space by an equivariant map of
boundary sphere.\n\nAn imporant part of $H$-frame structure in paper by H
.--H.--P. was so called {\\em conjugation equation}.\nFranz and Puppe calc
ulated the coefficients of the conjugation equation in terms of the Steenr
od squares.\nAs a part of a $Q$-framing we introduce corresponding structu
re\nequation and express its coefficients by explicit formula in terms of
the Steenrod operations.\n
LOCATION:https://researchseminars.org/talk/Knotsandtopology/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:M. Khovanov
DTSTART;VALUE=DATE-TIME:20210301T153000Z
DTEND;VALUE=DATE-TIME:20210301T170000Z
DTSTAMP;VALUE=DATE-TIME:20240522T205447Z
UID:Knotsandtopology/10
DESCRIPTION:Title: Introduction to universal construction of topological theories\nby M. Khovanov as part of Knots and representation theory\n\n\nAbstrac
t\nA multiplicative function on diffeomorphism classes of n-manifolds exte
nds to a functorial assignment of state spaces to (n-1)-manifolds. Resulti
ng topological theories are interesting already in very low dimensions. We
'll explain the framework for these theories and provide a number of examp
les.\n
LOCATION:https://researchseminars.org/talk/Knotsandtopology/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Byeorhi Kim
DTSTART;VALUE=DATE-TIME:20210315T153000Z
DTEND;VALUE=DATE-TIME:20210315T170000Z
DTSTAMP;VALUE=DATE-TIME:20240522T205447Z
UID:Knotsandtopology/11
DESCRIPTION:Title: On generalized quandle extensions of a quandle defined on a grou
p\nby Byeorhi Kim as part of Knots and representation theory\n\n\nAbst
ract\nIn 1980s\, Joyce and Matveev introduced a quandle which is an algebr
aic structure related to knot theory. In the papers\, they also showed tha
t for given a group and a group automorphism\, there is a quandle structur
e on the group\, later called ’generalized Alexander quandle’. In part
icular\, when the automorphism is an inner automorphism by a fixed element
$\\zeta$\, we denote the quandle operation by $\\triangleleft_{\\zeta}$.
In this talk\, we study a relationship between group extensions of a group
$G$ and quandle extensions of a generalized Alexander quandle $(G\,\\\\tr
iangleleft_{\\zeta})$ whose underlying set coincides with that of $G$. Thi
s is a joint work with Y.Bae and S.Carter.\n
LOCATION:https://researchseminars.org/talk/Knotsandtopology/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mahender Singh
DTSTART;VALUE=DATE-TIME:20210322T153000Z
DTEND;VALUE=DATE-TIME:20210322T170000Z
DTSTAMP;VALUE=DATE-TIME:20240522T205447Z
UID:Knotsandtopology/12
DESCRIPTION:Title: Surface knot theory and related groups\nby Mahender Singh as
part of Knots and representation theory\n\n\nAbstract\nStudy of certain i
sotopy classes of a finite collection of immersed circles without triple o
r higher intersections on closed oriented surfaces can be thought of as a
planar analogue of virtual knot theory where the genus zero case correspon
ds to classical knot theory. It is intriguing to know which class of group
s serves the purpose that Artin braid groups serve in classical knot theor
y. Mikhail Khovanov proved that twin groups\, a class of right angled Coxe
ter groups with only far commutativity relations\, do the job for genus ze
ro case. A recent work shows that an appropriate class of groups called vi
rtual twin groups fits into the theory for higher genus cases. The talk wo
uld give an overview of some recent developments along these lines.\n
LOCATION:https://researchseminars.org/talk/Knotsandtopology/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Svjetlana Terzi ́c
DTSTART;VALUE=DATE-TIME:20210329T153000Z
DTEND;VALUE=DATE-TIME:20210329T170000Z
DTSTAMP;VALUE=DATE-TIME:20240522T205447Z
UID:Knotsandtopology/13
DESCRIPTION:Title: Toric topology of the Grassmann manifolds\nby Svjetlana Terz
i ́c as part of Knots and representation theory\n\n\nAbstract\nbased on j
oint results with Victor M.~ Buchstaber\n\n\nIt is a classical problem
to study the canonical action of the compact torus $T^{n}$ on a Grassmann
manifold $G_{n\,2}$ which is connected to a series of problems in mod
ern algebraic topology\, algebraic geometry and mathematical physics. \n
\nThe aim of the talk is to present the recent results which are concerne
d with the description of the orbit space $G_{n\,2}/T^n$ in term of the
new notions:\n\\begin{itemize}\n\\item universal space of parameters $\\m
athcal{F}_{n}$\;\n\\item virtual spaces of parameters $\\widetilde{F}_{\
\sigma}\\subset \\mathcal{F}_{n}$ which correspond to the strata $W_{\\si
gma}$ in stratification $G_{n\,2} = \\cup _{\\sigma} W_{\\sigma}$ defin
ed in terms of the Pl\\"ucker coordinates\;\n\\item projections $\\wide
tilde{F}_{\\sigma}\\to F_{\\sigma}$ for the spaces of parameters $F_{\\s
igma}$ which correspond to the strata $W_{\\sigma}$.\n\\end{itemize}\n\n
In the course of the talk it will be described the chamber decomposition o
f the hypersimplex $\\Delta _{n\,2}$ which is defined by the special arr
angements of hyperplanes and represents one of the basic tools for the de
scription of the orbit space $G_{n\,2}/T^n$ in terms of the given noti
ons.\n
LOCATION:https://researchseminars.org/talk/Knotsandtopology/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hyeran Cho
DTSTART;VALUE=DATE-TIME:20210412T153000Z
DTEND;VALUE=DATE-TIME:20210412T170000Z
DTSTAMP;VALUE=DATE-TIME:20240522T205447Z
UID:Knotsandtopology/14
DESCRIPTION:Title: Derivation of Schubert normal forms of 2-bridge knots from (1\,1
)-diagrams\nby Hyeran Cho as part of Knots and representation theory\n
\n\nAbstract\nA genus one 1-bridge knot (simply called a (1\, 1)-knot) is
a knot that can be decomposed into two trivial arcs embed in two solid tor
i in a genus one Heegaard splitting of a lens space. A (1\,1)-knot can be
described by a (1\,1)-diagram D(a\, b\, c\, r) determined by four integers
a\, b\, c\, and r. It is known that every 2-bride knot is a (1\, 1)-knot
and has a (1\, 1)-diagram of the form D(a\, 0\, 1\, r). In this talk\, we
give the dual diagram of D(a\, 0\, 1\, r) explicitly and present how to de
rive a Schubert normal form of a 2-bridge knot from the dual diagram. This
gives an alternative proof of the Grasselli and Mulazzani’s result asse
rting that D(a\, 0\, 1\, r) is a (1\, 1)-diagram of 2-bridge knot with a S
chubert normal form b(2a+1\, 2r).\n
LOCATION:https://researchseminars.org/talk/Knotsandtopology/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Colin Adams
DTSTART;VALUE=DATE-TIME:20210419T153000Z
DTEND;VALUE=DATE-TIME:20210419T170000Z
DTSTAMP;VALUE=DATE-TIME:20240522T205447Z
UID:Knotsandtopology/15
DESCRIPTION:Title: Multi-crossings and Petal Number for Classical and Virtual Knots
\nby Colin Adams as part of Knots and representation theory\n\n\nAbstr
act\nInstead of considering projections of knots with two strands crossing
at every crossing\, we can ask for n strands to cross at every crossing.
We will show that every knot and link has such an n-crossing projection fo
r all integers n greater than 1 and therefore an n-crossing number. We als
o show that every knot has a projection with a single multi-crossing and n
o nested loops\, which is a petal projection and which generates a petal n
umber. We will discuss these ideas for both classical and virtual knots.
\n
LOCATION:https://researchseminars.org/talk/Knotsandtopology/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ivan Dynnikov
DTSTART;VALUE=DATE-TIME:20210426T153000Z
DTEND;VALUE=DATE-TIME:20210426T170000Z
DTSTAMP;VALUE=DATE-TIME:20240522T205447Z
UID:Knotsandtopology/16
DESCRIPTION:Title: A method for distingiushing Legendrian and transverse links\
nby Ivan Dynnikov as part of Knots and representation theory\n\n\nAbstract
\nLegendrian (respectively\, transverse) links are smooth links in the\nth
ree-space that are tangent (respectively\, transverse) to the standard\nco
ntact structure. Deciding whether two such links are equivalent modulo a\n
contactomorphism is a hard problem in general. Many topological invariants
\nof Legendrian and transverse links are known\, but they do not suffice f
or\na classification even in the case of knots of crossing number six.\n\n
In recent joint works with Maxim Prasolov and Vladimir Shastin we\ndevelop
ed a rectangular diagram machinery for surfaces and links in the\nthree-sp
ace. This machinery has a tight connection with contact topology\,\nnamely
with Legendrian links and Giroux's convex surfaces. We are mainly\nintere
sted in studying rectangular diagrams of links that cannot be\nmonotonical
ly simplified by means of elementary moves. It turns out that\nthis questi
on is nearly equivalent to classification of Legendrian links.\n\nThe main
outcome we have so far is an algorithm for comparing two\nLegendrian (or
transverse) links. The computational complexity of the\nalgorithm is\, of
course\, very high\, but\, in many cases\, certain parts of\nthe procedure
can be bypassed\, which allows us to distinguish quite\ncomplicated Legen
drian knots. In praticular\, we have managed to provide an\nexample of two
inequivalent Legendrian knots cobounding an annulus tangent\nto the stand
rard contact structure along the entire boundary. Such\nexamples were prev
iously unknown.\n\nThe work is supported by the Russian Science Foundation
under\ngrant 19-11-00151\n
LOCATION:https://researchseminars.org/talk/Knotsandtopology/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ivan Reshetnikov
DTSTART;VALUE=DATE-TIME:20210503T153000Z
DTEND;VALUE=DATE-TIME:20210503T170000Z
DTSTAMP;VALUE=DATE-TIME:20240522T205447Z
UID:Knotsandtopology/17
DESCRIPTION:Title: Discontinuously basic sets and the 13th problem of Hilbert\n
by Ivan Reshetnikov as part of Knots and representation theory\n\n\nAbstra
ct\nA subset $M \\subset \\textbf{R}^3$ is called a \\emph{discontinuously
basic subset}\, if for any function $f \\colon M \\to \\textbf{R}$ there
exist such functions $f_1\; f_2\; f_3 \\colon \\textbf{R} \\to R$ that $f(
x_1\, x_2\, x_3) = f_1(x_1) + f_2(x_2) + f_3(x_3)$ for each point $(x_1\,
x_2\, x_3)\\in M$. We will prove a criterion for a discontinuous basic sub
set for some specific subsets in terms of some graph properties. We will a
lso introduce several constructions for minimal discontinuous non-basic su
bsets.\n
LOCATION:https://researchseminars.org/talk/Knotsandtopology/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Adam Lowrance
DTSTART;VALUE=DATE-TIME:20210510T153000Z
DTEND;VALUE=DATE-TIME:20210510T170000Z
DTSTAMP;VALUE=DATE-TIME:20240522T205447Z
UID:Knotsandtopology/18
DESCRIPTION:Title: The Jones polynomial\, Khovanov homology\, and Turaev genus\
nby Adam Lowrance as part of Knots and representation theory\n\n\nAbstract
\nThe Turaev surface of a link diagram is a surface built from a cobordism
between the all-A and all-B Kauffman states of the diagram\, and the Tura
ev genus of a link is the minimum genus of the Turaev surface for any diag
ram of the link. The Turaev surface was first used to give simple versions
of the Kauffman-Mursaugi-Thistlethwaite proofs of some Tait conjectures.
\n\nIn this talk\, we first give a brief history of the Turaev surface\, t
he Turaev genus of a link\, and some related applications. We then discuss
some recent results on the extremal and near extremal terms in the Jones
polynomial and Khovanov homology of a Turaev genus one link.\n
LOCATION:https://researchseminars.org/talk/Knotsandtopology/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andriy Haydys
DTSTART;VALUE=DATE-TIME:20210607T153000Z
DTEND;VALUE=DATE-TIME:20210607T170000Z
DTSTAMP;VALUE=DATE-TIME:20240522T205447Z
UID:Knotsandtopology/19
DESCRIPTION:Title: On Fukaya-Seidel category and Khovanov homology\nby Andriy H
aydys as part of Knots and representation theory\n\n\nAbstract\nI will tal
k about a construction of the Fukaya-Seidel category for the holomorphic C
hern-Simons functional. This involves certain gauge-theoretic equations\,
which are conjecturally related also to Khovanov homology.\n
LOCATION:https://researchseminars.org/talk/Knotsandtopology/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Scott Baldridge
DTSTART;VALUE=DATE-TIME:20230717T153000Z
DTEND;VALUE=DATE-TIME:20230717T170000Z
DTSTAMP;VALUE=DATE-TIME:20240522T205447Z
UID:Knotsandtopology/20
DESCRIPTION:Title: Bigraded 2-color homology is not a variant of Khovanov homology!
\nby Scott Baldridge as part of Knots and representation theory\n\nAbs
tract: TBA\n
LOCATION:https://researchseminars.org/talk/Knotsandtopology/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dimitris Kodokostas
DTSTART;VALUE=DATE-TIME:20230724T153000Z
DTEND;VALUE=DATE-TIME:20230724T170000Z
DTSTAMP;VALUE=DATE-TIME:20240522T205447Z
UID:Knotsandtopology/21
DESCRIPTION:Title: An algorithmically computable complete invariant of knots\nb
y Dimitris Kodokostas as part of Knots and representation theory\n\nAbstra
ct: TBA\n
LOCATION:https://researchseminars.org/talk/Knotsandtopology/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:TBA
DTSTART;VALUE=DATE-TIME:20230731T153000Z
DTEND;VALUE=DATE-TIME:20230731T170000Z
DTSTAMP;VALUE=DATE-TIME:20240522T205447Z
UID:Knotsandtopology/22
DESCRIPTION:by TBA as part of Knots and representation theory\n\nAbstract:
TBA\n
LOCATION:https://researchseminars.org/talk/Knotsandtopology/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lilya A. Grunwald
DTSTART;VALUE=DATE-TIME:20230807T153000Z
DTEND;VALUE=DATE-TIME:20230807T170000Z
DTSTAMP;VALUE=DATE-TIME:20240522T205447Z
UID:Knotsandtopology/23
DESCRIPTION:Title: The number of rooted forests in circulant graph\nby Lilya A.
Grunwald as part of Knots and representation theory\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/Knotsandtopology/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ben McCarty
DTSTART;VALUE=DATE-TIME:20230814T153000Z
DTEND;VALUE=DATE-TIME:20230814T170000Z
DTSTAMP;VALUE=DATE-TIME:20240522T205447Z
UID:Knotsandtopology/24
DESCRIPTION:Title: n-Color Vertex Homology\nby Ben McCarty as part of Knots and
representation theory\n\n\nAbstract\nWe will show how to categorify the v
ertex bracket polynomial\, which is based upon one of Roger Penrose’s fo
rmulas for counting the number of 3-edge colorings of a planar trivalent g
raph. We produce a bigraded theory called bigraded n-color vertex homology
whose graded Euler characteristic is the vertex bracket polynomial. We th
en produce a spectral sequence whose E∞ page is a filtered theory called
filtered n-color vertex homology\, and show that it is generated by certa
in types of properly colored ribbon subgraphs. In particular for n = 2\, w
e show that the n-color vertex homology is generated by colorings that cor
respond to perfect matchings. This is joint work with Scott Baldridge.\n
LOCATION:https://researchseminars.org/talk/Knotsandtopology/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alina Pavlikova
DTSTART;VALUE=DATE-TIME:20230821T153000Z
DTEND;VALUE=DATE-TIME:20230821T170000Z
DTSTAMP;VALUE=DATE-TIME:20240522T205447Z
UID:Knotsandtopology/26
DESCRIPTION:Title: Bipartite knots and its applications\nby Alina Pavlikova as
part of Knots and representation theory\n\n\nAbstract\nThe non-bipartite k
not conjecture\, formulated in 1987 by Józef Przytitzky\, remained open f
or 24 years\, despite the efforts of several eminent mathematicians\, incl
uding its author and J. H. Conway [3]. In 2011\, S. Duzhin found a necessa
ry condition for a knot to be bipartite and gave examples of non-bipartite
knots. Further study of bipartite knots we explore their rich combinatori
al structure and hidden connections with the four color graph theorem.\n
LOCATION:https://researchseminars.org/talk/Knotsandtopology/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dmitrii Rachenkov
DTSTART;VALUE=DATE-TIME:20230904T153000Z
DTEND;VALUE=DATE-TIME:20230904T170000Z
DTSTAMP;VALUE=DATE-TIME:20240522T205447Z
UID:Knotsandtopology/28
DESCRIPTION:Title: Quasi-polynomial solutions of anharmonic oscillators\nby Dmi
trii Rachenkov as part of Knots and representation theory\n\n\nAbstract\nI
n 2014\, in the article “Quadratic differentials as stability condition
s” T. Bridgeland and I. Smith proved that that moduli spaces of meromorp
hic quadratic differentials with simple zeroes on compact Riemann surfaces
can be identified with spaces of stability conditions on a class of CY3 t
riangulated categories. These categories can be defined using quivers with
potential associated to triangulated surfaces.\n\nAny quadratic different
ial defines an anharmonic oscillator equation and one can ask whether it h
as as a solution quasi-polynomial (=polynomial multiplied by exponent). Th
e general answer – work in progress! – should have a nice view in term
s of the spaces of stability conditions .\n\nIn my talk I am going to pre
sent in examples Bridgeland-Smith’s construction. If time permits I will
speak about Shapiro-Tater conjecture which proof involves quasi-polynomia
l solutions of a quartic anharmonic oscillators.\n\n \n\nReferences: arXiv
:2203.16889\, arXiv:1302.7030\n
LOCATION:https://researchseminars.org/talk/Knotsandtopology/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Igor Nikonov
DTSTART;VALUE=DATE-TIME:20230828T153000Z
DTEND;VALUE=DATE-TIME:20230828T170000Z
DTSTAMP;VALUE=DATE-TIME:20240522T205447Z
UID:Knotsandtopology/29
DESCRIPTION:Title: On biquandles for the groups $G^k_n$ and surface singular braid
monoid\nby Igor Nikonov as part of Knots and representation theory\n\n
\nAbstract\nThe groups $G^k_n$ were defined by V. O. Manturov in order to
describe dynamical systems in configuration systems. In the talk we will c
onsider two applications of this theory: we define a biquandle structure o
n the groups $G^k_n$\, and construct a homomorphism from the surface singu
lar braid monoid to the group $G^2_n$.\n
LOCATION:https://researchseminars.org/talk/Knotsandtopology/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Igor Nikonov
DTSTART;VALUE=DATE-TIME:20230911T153000Z
DTEND;VALUE=DATE-TIME:20230911T170000Z
DTSTAMP;VALUE=DATE-TIME:20240522T205447Z
UID:Knotsandtopology/30
DESCRIPTION:Title: Photography principle\, data transmission\, and invariants of ma
nifolds\nby Igor Nikonov as part of Knots and representation theory\n\
n\nAbstract\nIn the present talk we discuss the techniques suggested in [V
. O. Manturov\, I.M. Nikonov\, The groups Гn4\, braids\, and 3-manifolds\
, arXiv: 2305.06316] and the photography principle [V.O.Manturov\, Z.Wan\,
The photography method: solving pentagon\, hexagon\, and other equations\
, arXiv:2305.11945] to open a very broad path for constructing invariants
for manifolds of dimensions greater than or equal to 4.\n
LOCATION:https://researchseminars.org/talk/Knotsandtopology/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Younes Benyahia (SISSA\, Italy)
DTSTART;VALUE=DATE-TIME:20230918T153000Z
DTEND;VALUE=DATE-TIME:20230918T170000Z
DTSTAMP;VALUE=DATE-TIME:20240522T205447Z
UID:Knotsandtopology/31
DESCRIPTION:Title: Exotic 2-knots and 2-links in 4-manifolds.\nby Younes Benyah
ia (SISSA\, Italy) as part of Knots and representation theory\n\n\nAbstrac
t\nTwo smoothly embedded surfaces in a 4-manifold are called exotic if the
y are topologically isotopic but smoothly not. In 1997\, Fintushel and Ste
rn constructed the first examples of exotic surfaces. Since then\, there h
ave been many constructions of exotic surfaces in other settings\, in part
icular\, ones closer to the smooth unknotting conjecture. \n In this talk\
, we give a construction of infinite families of exotic 2-spheres (in some
4-manifolds) that are topologically unknotted\, and we show how to adapt
the idea to obtain infinite families of exotic 2-links. This is a joint wo
rk with Bais\, Malech and Torres (see also https://arxiv.org/abs/2206.0965
9).\n
LOCATION:https://researchseminars.org/talk/Knotsandtopology/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hongdae Yun
DTSTART;VALUE=DATE-TIME:20230925T153000Z
DTEND;VALUE=DATE-TIME:20230925T170000Z
DTSTAMP;VALUE=DATE-TIME:20240522T205447Z
UID:Knotsandtopology/32
DESCRIPTION:Title: A note on geometric realization of extreme Khovanov homology f
or some family of links\nby Hongdae Yun as part of Knots and represent
ation theory\n\n\nAbstract\nThe Khovanov (co)homology was introduced by Mi
khail Khovanov in 2000 and Viro explained it in terms of enhanced states
of diagram. Also J. González-Meneses\, P.M.G. Manchón\, M. Silvero prov
ed (potential) extreme Khovanov homology of link is isomorphic to independ
ence simplicial complex of Lando graph from the link. In this talk\, we re
call the definition of Khovanov homology. Furthermore we investigate the g
eometric realization of extreme Khovanov homology of some family of knots
and links. This is joint work with Mark H Siggers and Seung Yeop Yang.\n
LOCATION:https://researchseminars.org/talk/Knotsandtopology/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Igor Nikonov
DTSTART;VALUE=DATE-TIME:20231002T153000Z
DTEND;VALUE=DATE-TIME:20231002T170000Z
DTSTAMP;VALUE=DATE-TIME:20240522T205447Z
UID:Knotsandtopology/33
DESCRIPTION:Title: Examples of weight systems of framed chord diagrams\nby Igor
Nikonov as part of Knots and representation theory\n\n\nAbstract\nWe exte
nd Bar-Natan’s construction of weight systems induced by Lie algebra rep
resentations to the case of framed chord diagrams. (joint work with Denis
Ilyutko)\n
LOCATION:https://researchseminars.org/talk/Knotsandtopology/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:П. Н. Питал
DTSTART;VALUE=DATE-TIME:20231023T153000Z
DTEND;VALUE=DATE-TIME:20231023T170000Z
DTSTAMP;VALUE=DATE-TIME:20240522T205447Z
UID:Knotsandtopology/34
DESCRIPTION:Title: Обобщенные факториалы и p-упорядоч
ения\nby П. Н. Питал as part of Knots and representation th
eory\n\n\nAbstract\nВ докладе будет рассказано об
интересном обобщении понятия факториал
а\, предложенном М. Бхаргавой для дедеки
ндовых колец.\n
LOCATION:https://researchseminars.org/talk/Knotsandtopology/34/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kevin Walker
DTSTART;VALUE=DATE-TIME:20231030T153000Z
DTEND;VALUE=DATE-TIME:20231030T170000Z
DTSTAMP;VALUE=DATE-TIME:20240522T205447Z
UID:Knotsandtopology/35
DESCRIPTION:Title: A very general approach to TQFT state sums\nby Kevin Walker
as part of Knots and representation theory\n\n\nAbstract\nI’ll discuss a
very general (“universal”) approach to constructing TQFT state sums f
or manifolds. This will be based on https://arxiv.org/abs/2104.02101\, bu
t in contrast to that paper I’ll start with concrete examples and work t
oward the more general statements.\n
LOCATION:https://researchseminars.org/talk/Knotsandtopology/35/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hayk Sedrakyan
DTSTART;VALUE=DATE-TIME:20231113T153000Z
DTEND;VALUE=DATE-TIME:20231113T170000Z
DTSTAMP;VALUE=DATE-TIME:20240522T205447Z
UID:Knotsandtopology/36
DESCRIPTION:Title: Distance formula for a point inside a triangle (formula for a di
agonal of any quadrilateral)\nby Hayk Sedrakyan as part of Knots and r
epresentation theory\n\n\nAbstract\nGiven a connected graph with four vert
ices and six edges (a quadrilateral and its diagonals). We obtained a nove
l formula to find the length of any of its edges using the other five edge
lengths. For example\, in the case of a convex quadrilateral we are able
to find the length of its diagonal using its side lengths and the length o
f the other diagonal. In the case of a concave quadrilateral (point inside
a triangle)\, we are able to find the distance between this point and any
of the vertices of the triangle.\n
LOCATION:https://researchseminars.org/talk/Knotsandtopology/36/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Scott Carter
DTSTART;VALUE=DATE-TIME:20231127T153000Z
DTEND;VALUE=DATE-TIME:20231127T170000Z
DTSTAMP;VALUE=DATE-TIME:20240522T205447Z
UID:Knotsandtopology/37
DESCRIPTION:Title: Intricacies about the binary icosahedral group\nby Scott Car
ter as part of Knots and representation theory\n\n\nAbstract\nZeeman's the
orem tells us that both the 5-twist spun trefoil and the 2-twist spun toru
s knot T(3\,5) are fibered knotted spheres in 4-dimensional space where th
e fiber is the punctured Poincare homology sphere. That closed homology sp
here is the quotient of the 3-sphere under the action of the binary icosah
edral group. It is a 5-fold or 2-fold branched cover of 3-space branched o
ver the respective knot. The group is isomorphic to SL_2(Z/5). I want to u
nderstand all of the statements asserted above. To that end\, I am working
on comparing three different presentations of this group. In as much as p
ossible\, I will explicitly represent the elements in the group as strings
with quipu\, matrices\, generators\, and elements in the 3-sphere. I'll a
lso give different pictures that allow one to compute relationships among
the words in the standard presentation of the group. I'm also interested i
n braiding the homology sphere in 5-space.\n
LOCATION:https://researchseminars.org/talk/Knotsandtopology/37/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bao Vuong
DTSTART;VALUE=DATE-TIME:20231120T153000Z
DTEND;VALUE=DATE-TIME:20231120T170000Z
DTSTAMP;VALUE=DATE-TIME:20240522T205447Z
UID:Knotsandtopology/38
DESCRIPTION:Title: Reidemeister torsion of link complements in 3-torus\nby Bao
Vuong as part of Knots and representation theory\n\n\nAbstract\nThe relati
on between Alexander polynomial of a knot and the torsion invariant of Rei
demeister\, Franz and de Rham for knot complement was first noticed by Mil
nor. As a consequence of the relation\, Milnor gave another proof for symm
etry of Alexander polynomial. Milnor applied the result to knot theory\, c
onsidering the case of classical knot\, i.e. the knot complement has the h
omology of the circle. It turns out that there are similar relations betwe
en Reidemeister torsion and twisted Alexander polynomial for the case of k
not complement in other spaces\, rather than three dimensional sphere when
the homology group contains also torsion. The technology to get explicit
relations as Milnor had created making use of simple homotopy theory for C
W-complexes and Fox free differential calculus. Those ensure a CW structur
e for the knot complement\, associated with a presentation of the fundamen
tal group\, so that the boundary maps are obtained by free derivatives. Th
e method works out fine also for the case of knots and links in three dime
nsional torus. Thus we show that the Reidemeister torsion of the link comp
lement and its twisted Alexander polynomial are equal.\n
LOCATION:https://researchseminars.org/talk/Knotsandtopology/38/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Martinez-Garcia Jesus
DTSTART;VALUE=DATE-TIME:20231204T153000Z
DTEND;VALUE=DATE-TIME:20231204T170000Z
DTSTAMP;VALUE=DATE-TIME:20240522T205447Z
UID:Knotsandtopology/39
DESCRIPTION:Title: Moduli of Fano varieties via K-stability\nby Martinez-Garcia
Jesus as part of Knots and representation theory\n\n\nAbstract\nK-stabili
ty is a recent theory that interacts with complex and analytic geometry\,
birational geometry and moduli theory. Take a Fano variety (a complex proj
ective variety with positive Ricci curvature). Can we construct a compact
moduli space that parametrises all the ‘reasonable’ degenerations of t
his variety (including fairly singular ones) and that it is itself ‘reas
onable’ as a space? The answer is positive if the variety is K-(poly)sta
ble and this moduli space\, known as K-moduli\, parametrises all K-polysta
ble Fano varieties. From a complex viewpoint\, K-polystable Fano varieties
are precisely those which admit a Kahler-Einstein metric.\n\nSmooth Fano
varieties have been classified up to dimension 3 but until recent work by
Abban-Zhuang and others\, we did not have enough tools to decide which one
s were K-polystable\, let alone to describe the K-moduli itself. In this t
alk I will survey these notions and present recent progress in the subject
\, with special emphasis in the programme to classify Fano varieties and t
heir K-moduli in low dimensions.\n
LOCATION:https://researchseminars.org/talk/Knotsandtopology/39/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Igor M. Nikonov
DTSTART;VALUE=DATE-TIME:20231211T153000Z
DTEND;VALUE=DATE-TIME:20231211T170000Z
DTSTAMP;VALUE=DATE-TIME:20240522T205447Z
UID:Knotsandtopology/40
DESCRIPTION:Title: Rota-Baxter operators and Hopf algebras\nby Igor M. Nikonov
as part of Knots and representation theory\n\n\nAbstract\nWe will consider
several problems related to Rota-Baxter operators and Hopf algebras:\n1)
construction of group Rota-Baxter operators of arbitrary weight on Lie gro
ups\n2) conditions under which a Rota-Baxter operator on a group is a Rota
-Baxter operator of a group algebra\n3) construction of relative Roth-Baxt
er operators for noncommutative Hopf algebras\n
LOCATION:https://researchseminars.org/talk/Knotsandtopology/40/
END:VEVENT
BEGIN:VEVENT
SUMMARY:O.G. Styrt
DTSTART;VALUE=DATE-TIME:20231218T153000Z
DTEND;VALUE=DATE-TIME:20231218T170000Z
DTSTAMP;VALUE=DATE-TIME:20240522T205447Z
UID:Knotsandtopology/41
DESCRIPTION:Title: Elements of a Lie algebra acting nilpotently in all its represen
tations\nby O.G. Styrt as part of Knots and representation theory\n\n\
nAbstract\nAn equivalent condition for an element of a Lie algebra acting
nilpotently in all its representations is obtained. Namely\, it should bel
ong to the derived algebra and go via factoring over the radical to a nilp
otent element of the corresponding (semisimple) quotient algebra.\nThe tal
k is based on the speaker's preprint https://arxiv.org/abs/2209.13309\n
LOCATION:https://researchseminars.org/talk/Knotsandtopology/41/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Manpreet Singh
DTSTART;VALUE=DATE-TIME:20240108T153000Z
DTEND;VALUE=DATE-TIME:20240108T170000Z
DTSTAMP;VALUE=DATE-TIME:20240522T205447Z
UID:Knotsandtopology/42
DESCRIPTION:Title: Invariants of knots from biquandles and virtual biquandles\n
by Manpreet Singh as part of Knots and representation theory\n\n\nAbstract
\nWe will prove that for a given virtual link L and a virtual biquandle (X
\,f\,R)\, the set of colorings of L by (X\,f\,R) is in bijection with the
set of colorings of L by a biquandle (X\,VR)\, where VR is a new operator
we define on X. The biquandle (X\,VR) is the 1-induced biquandle associate
d with (X\,f\,R). Moreover\, we will prove that for a virtual link L\, the
associated biquandle BQ(L) is isomorphic to the 1-induced biquandle of th
e virtual biquandle VBQ(L). Furthermore\, the 1-induced biquandle of VBQ(L
) is isomorphic to VBQ(L) as virtual biquandles. If time permits\, we will
introduce a cohomology theory for (X\,f\,R) and give its applications to
knots.\n
LOCATION:https://researchseminars.org/talk/Knotsandtopology/42/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Igor Nikonov
DTSTART;VALUE=DATE-TIME:20231225T153000Z
DTEND;VALUE=DATE-TIME:20231225T170000Z
DTSTAMP;VALUE=DATE-TIME:20240522T205447Z
UID:Knotsandtopology/43
DESCRIPTION:Title: Virtual index cocycles and invariants of virtual links\nby I
gor Nikonov as part of Knots and representation theory\n\n\nAbstract\nVirt
ual index cocycle is the 1-cochain that counts virtual crossings in the ar
cs of a virtual link diagram. We show how this cocycle can be used to refo
rmulate and unify some known invariants of virtual links.\n
LOCATION:https://researchseminars.org/talk/Knotsandtopology/43/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Visakh Narayanan
DTSTART;VALUE=DATE-TIME:20240115T153000Z
DTEND;VALUE=DATE-TIME:20240115T170000Z
DTSTAMP;VALUE=DATE-TIME:20240522T205447Z
UID:Knotsandtopology/44
DESCRIPTION:Title: Knots in $\\mathbb{R}P^3$\nby Visakh Narayanan as part of Kn
ots and representation theory\n\n\nAbstract\nWe will discuss some properti
es of knots in three dimensional projective space. Our technique for this
purpose is to associate a virtual link to a link in projective space so th
at equivalent projective links go to equivalent virtual links (modulo a sp
ecial flype move). We can then apply techniques in virtual knot theory to
obtain a Jones polynomial for projective links which also happens to be eq
uivalent to the Jones polynomial constructed by Drobotukhina. Then we woul
d discuss a combinatorial cobordism theory for projective links which may
be used to apply virtual Khovanov homology and the virtual Rasmussen invar
iant of Dye\, Kaestner\, and Kauffman to projective links.\n
LOCATION:https://researchseminars.org/talk/Knotsandtopology/44/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Seongjeong Kim
DTSTART;VALUE=DATE-TIME:20240122T153000Z
DTEND;VALUE=DATE-TIME:20240122T170000Z
DTSTAMP;VALUE=DATE-TIME:20240522T205447Z
UID:Knotsandtopology/45
DESCRIPTION:Title: The groups $G_{n}^{3}$ and rhombi tilings of 2n-gons\nby Seo
ngjeong Kim as part of Knots and representation theory\n\n\nAbstract\nIn t
his talk we will consider a map from the set of rhombi tilings of 2n-gon t
o the group $G_{n}^{3}$ and will discuss our further researches.\n
LOCATION:https://researchseminars.org/talk/Knotsandtopology/45/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Christoph Schiller
DTSTART;VALUE=DATE-TIME:20240226T153000Z
DTEND;VALUE=DATE-TIME:20240226T170000Z
DTSTAMP;VALUE=DATE-TIME:20240522T205447Z
UID:Knotsandtopology/46
DESCRIPTION:Title: From the three Reidemeister moves to the three Lie gauge groups
– with consequences for the unification of physics\nby Christoph Sc
hiller as part of Knots and representation theory\n\n\nAbstract\nQuantum t
heory suggests that the three observed gauge groups U(1)\, SU(2) and SU(3)
are related to the three Reidemeister moves of knot theory: twists\, poke
s and slides. The background for the relation is clarified: modelling \npa
rticles as fluctuating tangles of strands explains wave functions. Classif
ying tangles explains the elementary \nfermions and bosons. It is then sho
wn that twists generate U(1) and that pokes generate SU(2). The emphasis i
s put on deducing the relation between slides\, the corresponding strand d
eformations\, the Gell-Mann matrices\, and the Lie group SU(3). Consequenc
es for unification are deduced.\n
LOCATION:https://researchseminars.org/talk/Knotsandtopology/46/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Igor Nikonov
DTSTART;VALUE=DATE-TIME:20240129T153000Z
DTEND;VALUE=DATE-TIME:20240129T170000Z
DTSTAMP;VALUE=DATE-TIME:20240522T205447Z
UID:Knotsandtopology/47
DESCRIPTION:Title: Traits of crossings and functorial maps\nby Igor Nikonov as
part of Knots and representation theory\n\n\nAbstract\nOne of the major ap
plications of parity theory are picture-valued invariants of knots such as
parity bracket. We present several examples of such invariants for links
in a fixed surface.\n
LOCATION:https://researchseminars.org/talk/Knotsandtopology/47/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Seongjeong Kim
DTSTART;VALUE=DATE-TIME:20240205T153000Z
DTEND;VALUE=DATE-TIME:20240205T170000Z
DTSTAMP;VALUE=DATE-TIME:20240522T205447Z
UID:Knotsandtopology/48
DESCRIPTION:Title: The classification of knots in $S_{g}\\times S^{1}$ of the small
number of crossings\nby Seongjeong Kim as part of Knots and represent
ation theory\n\n\nAbstract\nIn this talk we construct invariants for knots
in $S_{g}\\times S^{1}$ and try to classify knots in $S_{g}\\times S^{1}$
with small number crossings.\n
LOCATION:https://researchseminars.org/talk/Knotsandtopology/48/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Мороз Борис Барух
DTSTART;VALUE=DATE-TIME:20240212T153000Z
DTEND;VALUE=DATE-TIME:20240212T170000Z
DTSTAMP;VALUE=DATE-TIME:20240522T205447Z
UID:Knotsandtopology/49
DESCRIPTION:Title: Гипотеза Римана и диофантовы уравн
ения\nby Мороз Борис Барух as part of Knots and rep
resentation theory\n\n\nAbstract\nВ нашей (совместной с
А.А.Норкином) недавней работе явно выпис
ано диофантово уравнение\, неразрешимос
ть которого эквивалентна гипотезе Риман
а. Я расскажу об этой работе.\n
LOCATION:https://researchseminars.org/talk/Knotsandtopology/49/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dmitry Solovyev
DTSTART;VALUE=DATE-TIME:20240304T153000Z
DTEND;VALUE=DATE-TIME:20240304T170000Z
DTSTAMP;VALUE=DATE-TIME:20240522T205447Z
UID:Knotsandtopology/50
DESCRIPTION:Title: Universal construction\, foams and link homology\nby Dmitry
Solovyev as part of Knots and representation theory\n\n\nAbstract\nThis ta
lk is based on a joint work with Mikhail Khovanov. In this work we review
the construction of sl(N) link homology theory coming from foams\, which c
ategorifies HOMFLY-PT link invariant and RT sl(N) quantum link invariants.
This talk is elementary\, the emphasis will be put on the theory of unori
ented SL(3) foams\, their evaluation and corresponding universal construct
ion. This version of foam theory is related to 4-color theorem and Kronhei
mer-Mrowka 3-orbifold homology theory. If time permits\, we will also talk
about how oriented SL(3) foams categorify the Kuperberg invariant.\n
LOCATION:https://researchseminars.org/talk/Knotsandtopology/50/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Igor Nikonov
DTSTART;VALUE=DATE-TIME:20240219T153000Z
DTEND;VALUE=DATE-TIME:20240219T170000Z
DTSTAMP;VALUE=DATE-TIME:20240522T205447Z
UID:Knotsandtopology/51
DESCRIPTION:Title: On biquandles for the groups $G^k_n$ and surface singular braid
monoid\nby Igor Nikonov as part of Knots and representation theory\n\n
\nAbstract\nThe groups $G^k_n$ were defined by V. O. Manturov in order to
describe dynamical systems in configuration systems. In the talk we will c
onsider two applications of this theory: we define a biquandle structure o
n the groups Gkn\, and construct a homomorphism from the surface singular
braid monoid to the group $G^2_n$.\n
LOCATION:https://researchseminars.org/talk/Knotsandtopology/51/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Igor Nikonov
DTSTART;VALUE=DATE-TIME:20240311T153000Z
DTEND;VALUE=DATE-TIME:20240311T170000Z
DTSTAMP;VALUE=DATE-TIME:20240522T205447Z
UID:Knotsandtopology/52
DESCRIPTION:Title: Flat-virtual knot: introduction and some invariants\nby Igor
Nikonov as part of Knots and representation theory\n\n\nAbstract\nIn atte
mpts to construct a map from classical knots to virtual ones\, we define a
series of maps from knots in the full torus (thickened torus) to flat-vir
tual knots. We give definition of flat-virtual knots and presents Alexande
r-like polynomial and Kauffman bracket for them. We also discuss a possibl
e extension of the notion of flat-virtual knots — so-called multi-flat k
nots.\n
LOCATION:https://researchseminars.org/talk/Knotsandtopology/52/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Helen Wong
DTSTART;VALUE=DATE-TIME:20240325T154500Z
DTEND;VALUE=DATE-TIME:20240325T171500Z
DTSTAMP;VALUE=DATE-TIME:20240522T205447Z
UID:Knotsandtopology/53
DESCRIPTION:Title: Multiplication in Kauffman bracket skein algebra of a 1-hole tor
us\nby Helen Wong as part of Knots and representation theory\n\n\nAbst
ract\nThe Kauffman bracket skein algebra of a surface is a generalization
of the Jones polynomial for links and is one of few constructions from qua
ntum topology that is clearly related to hyperbolic geometry. To further u
nderstand the relationship\, it is important to understand the multiplicat
ive structure of the skein algebra. In this talk\, we present a recursion
relation and fast algorithm for multiplication in the skein algebra in the
case of a 1-hole torus.\n
LOCATION:https://researchseminars.org/talk/Knotsandtopology/53/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Oleg Styrt
DTSTART;VALUE=DATE-TIME:20240318T154500Z
DTEND;VALUE=DATE-TIME:20240318T171500Z
DTSTAMP;VALUE=DATE-TIME:20240522T205447Z
UID:Knotsandtopology/54
DESCRIPTION:Title: Elements of a Lie algebra acting nilpotently in all its repre
sentations\nby Oleg Styrt as part of Knots and representation theory\n
\n\nAbstract\nAn equivalent condition for an element of a Lie algebra acti
ng nilpotently in all its representations is obtained. Namely\, it should
belong to the derived algebra and go via factoring over the radical to a n
ilpotent element of the corresponding (semisimple) quotient algebra.\nThe
talk is based on the preprint https://arxiv.org/abs/2209.13309\n
LOCATION:https://researchseminars.org/talk/Knotsandtopology/54/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Igor M. Nikonov
DTSTART;VALUE=DATE-TIME:20240408T153000Z
DTEND;VALUE=DATE-TIME:20240408T170000Z
DTSTAMP;VALUE=DATE-TIME:20240522T205447Z
UID:Knotsandtopology/55
DESCRIPTION:Title: On biquandles for the groups $G^k_n$ and surface singular braid
monoid\nby Igor M. Nikonov as part of Knots and representation theory\
n\n\nAbstract\nThe groups $G^k_n$ were defined by V. O. Manturov in order
to describe dynamical systems in configuration systems. In the talk we wil
l consider two applications of this theory: we define a biquandle structur
e on the groups $G^k_n$\, and construct a homomorphism from the surface si
ngular braid monoid to the group $G^2_n$.\n
LOCATION:https://researchseminars.org/talk/Knotsandtopology/55/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Многие
DTSTART;VALUE=DATE-TIME:20240415T153000Z
DTEND;VALUE=DATE-TIME:20240415T170000Z
DTSTAMP;VALUE=DATE-TIME:20240522T205447Z
UID:Knotsandtopology/56
DESCRIPTION:Title: Конференция "Ломоносов"\nby Многие
as part of Knots and representation theory\n\n\nAbstract\nКонфере
нция "Ломоносов"\nКонференция происходит
на русском языке.\nСписок докладчиков. (П
одробнее: https://disk.yandex.com/d/XyvJNm3i_LmjHw)\n\n1) Жиха
рева Екатерина Сергеевна (студент\, кафе
дра дифференциальной геометрии и прилож
ений\, механико-математический факульте
т\, МГУ им. М. В. Ломоносова)\, "Трехмерные а
лгебры Ли\, допускающие полупростые алге
браические операторы Нейенхейса" .\n\n2) Ле
вин Виктор Анатольевич (студент\, кафедр
а дифференциальной геометрии и приложен
ий\, механико-математический факультет\,
МГУ им. М. В. Ломоносова)\, "Слоение Лиувил
ля интегрируемых биллиардов с острыми у
глами" .\n\n3) Михайлов Иван Николаевич (сту
дент\, кафедра дифференциальной геометр
ии и приложений\, механико-математически
й факультет\, МГУ им. М. В. Ломоносова)\, "Ра
сстояние Громова-Хаусдорфа между нормир
ованными пространствами" .\n\n4) Цыганков Д
митрий Александрович (студент\, кафедра
высшей геометрии и топологии\, механико-
математический факультет\, МГУ им. М. В. Л
омоносова)\, "Гиперболические многообраз
ия\, соответствующие прямоугольным мног
огранникам\, и их расслоения над окружно
стью".\n
LOCATION:https://researchseminars.org/talk/Knotsandtopology/56/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Seongjeong Kim
DTSTART;VALUE=DATE-TIME:20240422T153000Z
DTEND;VALUE=DATE-TIME:20240422T170000Z
DTSTAMP;VALUE=DATE-TIME:20240522T205447Z
UID:Knotsandtopology/57
DESCRIPTION:Title: Invariant of braids by using Ptolemy relation and failure for kn
ots\nby Seongjeong Kim as part of Knots and representation theory\n\n\
nAbstract\nIn this talk\, we will talk about an old work with prof. V.O. M
anturov on the construction of an invariant for braids by using Ptolemy re
lation and remind why it fails to be an invariant for links.\n
LOCATION:https://researchseminars.org/talk/Knotsandtopology/57/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Zhihao Wang
DTSTART;VALUE=DATE-TIME:20240513T153000Z
DTEND;VALUE=DATE-TIME:20240513T170000Z
DTSTAMP;VALUE=DATE-TIME:20240522T205447Z
UID:Knotsandtopology/58
DESCRIPTION:Title: On stated $SL(n)$-skein modules\nby Zhihao Wang as part of K
nots and representation theory\n\n\nAbstract\nWe mainly focus on Classical
limit\, Splitting map\, and Frobenius homomorphism for stated $SL(n)$-s
kein modules\, and Unicity Theorem for stated $SL(n)$-skein algebras.\n\nL
et $(M\,N)$ be a marked three manifold. We use $S_n(M\,N\,v)$ to denote th
e stated $SL(n)$-skein module of $(M\,N)$ where $v$ is a nonzero complex n
umber.\nWe build a surjective algebra homomorphism from $S_n(M\,N\,1)$ to
the coordinate ring of some algebraic set\, and prove it's Kernal consists
of all nilpotents. We prove the universal representation algebra of $\\pi
_1(M)$ is isomorphic to $S_n(M\,N\,1)$ when $N$ has only one component and
$M$ is connected. Furthermore we show $S_n(M\,N^{'}\,1)$ is isomorphic t
o\n$S_n(M\,N\,1)\\otimes O(SLn)$\, where $N\\neq \\emptyset$\, $M$ is conn
ected\, and $N^{'}$ is obtained from $N$ by adding one extra marking.\n We
also prove the splitting map is injective for any marked three manifold w
hen $v=1$\, and show that the splitting map is injective (for general $v$)
if there exists at least one component of $N$ such that this component an
d the boundary of the splitting disk belong to the same component of $\\pa
rtial M$.\n\n\nWe also establish the Frobenius homomorphism for $SL(n)$\,
which is map from $S_n(M\,N\,1)$ to $S_n(M\,N\,v)$ when $v$ is a primitiv
e $m$-th root of unity with $m$ being coprime with $2n$ and every compone
nt of $M$ contains at least one marking. \nWe also show the commutativity
between Frobenius homomorphism and splitting map. When $(M\,N)$ is the thi
ckening of an essentially bordered pb surface\, we prove the Frobenius hom
omorphism is injective and it's image lives in the center. We prove the st
ated $SL(n)$-skein algebra $S_n(\\Sigma\,v)$ is\naffine almost Azumaya whe
n $\\Sigma$ is an essentially bordered pb surface and $v$ is a primitive $
m$-th root of unity with $m$ being coprime with $2n$\, which implies the
Unicity Theorem for $S_n(\\Sigma\,v)$.\n
LOCATION:https://researchseminars.org/talk/Knotsandtopology/58/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Igor Nikonov
DTSTART;VALUE=DATE-TIME:20240429T153000Z
DTEND;VALUE=DATE-TIME:20240429T170000Z
DTSTAMP;VALUE=DATE-TIME:20240522T205447Z
UID:Knotsandtopology/59
DESCRIPTION:Title: On universal parity on free two-dimensional knots\nby Igor N
ikonov as part of Knots and representation theory\n\n\nAbstract\nIn the ta
lk we review the definition of parity on 2-knots\, and prove that the Gaus
sian parity is universal on free two-dimensional knots.\n
LOCATION:https://researchseminars.org/talk/Knotsandtopology/59/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Александр Юрьевич Буряк
DTSTART;VALUE=DATE-TIME:20240506T153000Z
DTEND;VALUE=DATE-TIME:20240506T170000Z
DTSTAMP;VALUE=DATE-TIME:20240522T205447Z
UID:Knotsandtopology/60
DESCRIPTION:Title: DR-иерархии: от пространств модулей
кривых к интегрируемым системам.\nby Ал
ександр Юрьевич Буряк as part of Knots and representati
on theory\n\n\nAbstract\nМы постараемся продемонст
рировать как DR-иерархии\, введённые докл
адчиком в одной из работ\, позволяют очен
ь ясным образом установить связь между
топологией компактификации Делиня-Мамф
орда пространства модулей гладких алгеб
раических кривых рода g с n отмеченными т
очками и интегрируемыми системами матем
атической физики. Эта связь основываетс
я на соотношении коммутативности между
циклами двойных ветвлений (DR-циклами) в п
ространстве модулей кривых произвольно
го рода\, которое является обобщением со
отношения ассоциативности в пространст
ве модулей кривых рода 0\, которое в свою
очередь тесно связано с теорией многооб
разий Дубровина-Фробениуса.\n
LOCATION:https://researchseminars.org/talk/Knotsandtopology/60/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Scott Baldridge
DTSTART;VALUE=DATE-TIME:20240520T153000Z
DTEND;VALUE=DATE-TIME:20240520T170000Z
DTSTAMP;VALUE=DATE-TIME:20240522T205447Z
UID:Knotsandtopology/61
DESCRIPTION:Title: Why the Vertex Polynomial counts Tait colorings of a plane triva
lent graph when evaluated at two\nby Scott Baldridge as part of Knots
and representation theory\n\n\nAbstract\nThe vertex polynomial was introdu
ced in our 2024 paper but can be inferred from Penrose’s 1971 paper on a
bstract tensor systems. In this talk\, we give a gentle introduction to th
e vertex polynomial: what it means\, how to compute it\, why it counts Tai
t colorings (3-edge colorings) of a plane trivalent graph at n=2\, and wha
t it means when evaluated at n>2. In particular\, the four color theorem i
s true if and only if the vertex polynomial is nonzero when evaluated at n
=2 for all bridgeless planar trivalent graphs. Along the way\, we will see
how the homology that it categorifies can be used to count the number of
perfect matchings of a trivalent plane graph. This is joint work with Ben
McCarty.\n
LOCATION:https://researchseminars.org/talk/Knotsandtopology/61/
END:VEVENT
END:VCALENDAR