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BEGIN:VEVENT
SUMMARY:Maggie Miller (Princeton University)
DTSTART:20200420T130000Z
DTEND:20200420T140000Z
DTSTAMP:20260422T213051Z
UID:ckvk_astrks/1
DESCRIPTION:Title: The effect of link Dehn surgery on the Thurston norm\nby Maggie Mi
ller (Princeton University) as part of Classical knots\, virtual knots\, a
nd algebraic structures related to knots\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/ckvk_astrks/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Colin Adams (Williams College)
DTSTART:20200427T130000Z
DTEND:20200427T140000Z
DTSTAMP:20260422T213051Z
UID:ckvk_astrks/2
DESCRIPTION:Title: Hyperbolicity and Turaev hyperbolicity of virtual knots\nby Colin
Adams (Williams College) as part of Classical knots\, virtual knots\, and
algebraic structures related to knots\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/ckvk_astrks/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Puttipong Pongtanapaisan (University of Iowa)
DTSTART:20200504T130000Z
DTEND:20200504T140000Z
DTSTAMP:20260422T213051Z
UID:ckvk_astrks/3
DESCRIPTION:Title: Knots with critical bridge spheres\nby Puttipong Pongtanapaisan (U
niversity of Iowa) as part of Classical knots\, virtual knots\, and algebr
aic structures related to knots\n\n\nAbstract\nDavid Bachman introduced th
e notion of critical surfaces and showed that they satisfy useful properti
es. In particular\, they behave like incompressible surfaces and strongly
irreducible surfaces. In this talk\, I will review some techniques that h
ave been used to study bridge spheres and give examples of nontrivial knot
s with critical bridge spheres. This is joint work with Daniel Rodman.\n
LOCATION:https://researchseminars.org/talk/ckvk_astrks/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Micah Chrisman (OSU)
DTSTART:20200518T130000Z
DTEND:20200518T140000Z
DTSTAMP:20260422T213051Z
UID:ckvk_astrks/4
DESCRIPTION:Title: Extending Milnor's concordance invariants to virtual knots and welded
links\nby Micah Chrisman (OSU) as part of Classical knots\, virtual kn
ots\, and algebraic structures related to knots\n\n\nAbstract\nMilnor's $\
\bar{\\mu}$-invariants for links in the 3-sphere vanish on any link concor
dant to a boundary link. In particular\, they are are trivial for any clas
sical knot. Here we define an analogue of Milnor's concordance invariants
for knots in thickened surfaces $\\Sigma \\times [0\,1]$\, where $\\Sigma$
is closed and oriented. These invariants vanish on any knot concordant to
a homologically trivial knot in $\\Sigma \\times [0\,1]$. We use them to
give new examples of non-slice virtual knots having trivial Rasmussen inva
riant\, graded genus\, affine index polynomial\, and generalized Alexander
polynomial. Moreover\, we complete the slice status classification of the
2564 virtual knots having at most five classical crossings and reduce to
four (of 90235) the number of virtual knots with six classical crossings h
aving unknown slice status. Furthermore\, we prove that in contrast to the
classical knot concordance group\, the virtual knot concordance group is
not abelian. As part of the construction of the extended $\\bar{\\mu}$-inv
ariants\, we also obtain a generalization of the $\\bar{\\mu}$-invariants
of classical links in $S^3$ to ribbon torus links in $S^4$ and welded link
s.\n
LOCATION:https://researchseminars.org/talk/ckvk_astrks/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lou Kauffman (University of Illinois\, Chicago and Novosibirsk Sta
te University)
DTSTART:20200601T130000Z
DTEND:20200601T140000Z
DTSTAMP:20260422T213051Z
UID:ckvk_astrks/5
DESCRIPTION:Title: Rotational Virtual Links\, Parity Polynomials and Quantum Link Invaria
nts\nby Lou Kauffman (University of Illinois\, Chicago and Novosibirsk
State University) as part of Classical knots\, virtual knots\, and algebr
aic structures related to knots\n\n\nAbstract\nThis talk discusses virtual
knot theory and rotational virtual knot theory. In virtual knot theory we
introduce a virtual crossing in the diagrams along with over crossings an
d under crossings. Virtual crossings are artifacts of representing knots i
n higher genus surfaces as diagrams in the plane.\n \nVirtual diagrammatic
equivalence is the same as studying knots in thickened surfaces up to amb
ient isotopy\, surface homeomorphisms and handle stabilization. At the dia
grammatic level\, virtual knot equivalence is generated by Reidemeister mo
ves plus detour moves. In rotational virtual knot theory\, the detour move
s are restricted to regular homotopy of plane curves (the self-crossings a
re virtual). Rotational virtual knot theory has the property that all clas
sical quantum link invariants extend to quantum invariants of rotational v
irtual knots and links. We explain this extension\, and we consider the qu
estion of the power of quantum invariants in this context.\n \nBy consider
ing first the bracket polynomial and its extension to a parity bracket pol
ynomial for virtual knots (Manturov) and its further extension to a rotati
onal parity bracket polynomial for knots and links (Kaestner and Kauffman)
\, we give examples of links that are detected via the parity invariants t
hat are not detectable by quantum invariants. In the course of the discuss
ion we explain a functor from the rotational tangle category to the diagra
mmatic category of a quantum algebra. We delineate significant weaknesses
in quantum invariants and how these gaps can be fulfilled by taking parity
into account.\n
LOCATION:https://researchseminars.org/talk/ckvk_astrks/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Scott Carter (University of South Alabama)
DTSTART:20200525T140000Z
DTEND:20200525T150000Z
DTSTAMP:20260422T213051Z
UID:ckvk_astrks/6
DESCRIPTION:Title: Diagrammatic Algebra\, Part 1\nby Scott Carter (University of Sout
h Alabama) as part of Classical knots\, virtual knots\, and algebraic stru
ctures related to knots\n\n\nAbstract\nThis talk is based upon joint work
with Seiichi Kamada.\nAbstract tensor notation for multi-linear maps uses
boxes with in-coming and out-going strings to represent structure constant
s. I judicious choice of variables for such constants leads to the diagram
matic representation: boxes are replaced by glyphs. One of the most simple
examples of a multi-category is the diagrammatic representation of embedd
ed surfaces in 3-space that we all grew up learning. The standard drawing
of a torus (an oval\, a smile and a moustache) is a representation based u
pon drawings of surface singularities. We start from a two object category
with a pair of arrows that relate them. Cups and caps are constructed eas
ily. From these\, births\, deaths\, saddles\, forks\, and cusps are create
d as triple arrows. At the top level\, there are critical cancelations\, l
ips\, beak-to-beak\, horizontal cusps\, and swallow-tails. \n\nInteresting
ly\, the structure extends inductively to describe many relations about h
andles. in higher dimensions.\n
LOCATION:https://researchseminars.org/talk/ckvk_astrks/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Scott Taylor (Colby College)
DTSTART:20200615T140000Z
DTEND:20200615T150000Z
DTSTAMP:20260422T213051Z
UID:ckvk_astrks/7
DESCRIPTION:Title: Lower bounds on the tunnel number of composite spatial graphs.\nby
Scott Taylor (Colby College) as part of Classical knots\, virtual knots\,
and algebraic structures related to knots\n\n\nAbstract\nThe tunnel numbe
r of a graph embedded in a 3-dimensional manifold is the fewest number of
arcs needed so that the union of the graph with the arcs has handlebody ex
terior. The behavior of tunnel number with respect to connected sum of kno
ts can vary dramatically\, depending on the knots involved. However\, a cl
assical theorem of Scharlemann and Schultens says that the tunnel number o
f a composite knot is at least the number of factors. For theta graphs\, t
rivalent vertex sum is the operation which most closely resembles the conn
ected sum of knots.The analogous theorem of Scharlemann and Schultens no l
onger holds\, however. I will provide a sharp lower bound for the tunnel n
umber of composite theta graphs\,using recent work on a new knot invariant
which is additive under connected sum and trivalent vertex sum. This is j
oint work with Maggy Tomova.\n
LOCATION:https://researchseminars.org/talk/ckvk_astrks/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Emanuele Zappala (University of South Florida)
DTSTART:20200622T140000Z
DTEND:20200622T150000Z
DTSTAMP:20260422T213051Z
UID:ckvk_astrks/8
DESCRIPTION:Title: Invariants of framed links from cohomology of ternary self-distributiv
e structures\nby Emanuele Zappala (University of South Florida) as par
t of Classical knots\, virtual knots\, and algebraic structures related to
knots\n\n\nAbstract\nn this talk I recall the definitions of shelf/rack/q
uandle and their cohomology theory. I also give the construction of cocycl
e invariant of links\, due to Carter\, Jelsovsky\, Kamada\, Langford and S
aito (Trans. Amer. Math. Soc. 355 (2003)\, 3947-3989). Then\, I introduce
higher arity self-distributive structures and show that an appropriate dia
grammatic interpretation of them is suitable to define a ternary version o
f the cocycle invariant for framed link invariants\, via blackboard framin
gs. I discuss the computation of cohomology of ternary structures\, as com
position of mutually distributive operations\, and a cohomology theory of
certain ternary quandles called group heaps. Furthermore I mention a categ
orical version of self-distributivity\, along with examples from Lie algeb
ras and Hopf algebras\, and the construction of ribbon categories from ter
nary operations that provide a quantum interpretation of the (ternary) coc
ycle invariant.\n
LOCATION:https://researchseminars.org/talk/ckvk_astrks/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Neslihan Gugucmcu (\, Izmir Institute of Technology and University
of Goettingen)
DTSTART:20200629T140000Z
DTEND:20200629T150000Z
DTSTAMP:20260422T213051Z
UID:ckvk_astrks/9
DESCRIPTION:Title: What is a braidoid diagram?\nby Neslihan Gugucmcu (\, Izmir Instit
ute of Technology and Universityof Goettingen) as part of Classical knots\
, virtual knots\, and algebraic structures related to knots\n\n\nAbstract\
nIn this talk we first review the basics of the theory of knotoids introdu
ced by Vladimir Turaev in 2012 [1]. A knotoid diagram is basically an open
-ended knot diagram with two open endpoints that can lie in any local regi
on complementary to the plane of the diagram. The theory of knotoids exten
ds the classical knot theory and brings up some interesting problems and f
eatures such as the height problem [1\,3] and parity notion and related in
variants such as off writhe and parity bracket polynomial [4]. It was a cu
rious problem to determine a "braid like object" corresponding to knotoid
diagrams. The second part of this talk is devoted to the theory of braidoi
ds\, introduced by the author and Sofia Lambropoulou [2]. We present the n
otion of a braidoid and analogous theorems to the classical Alexander Theo
rem and the Markov Theorem\, that relate knotoids/multi-knotoids in the pl
ane to braidoids.\n
LOCATION:https://researchseminars.org/talk/ckvk_astrks/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:J. Scott Carter (niversity of South Alabama)
DTSTART:20200713T140000Z
DTEND:20200713T150000Z
DTSTAMP:20260422T213051Z
UID:ckvk_astrks/10
DESCRIPTION:Title: Diagrammatic algebra\, part 2\nby J. Scott Carter (niversity of S
outh Alabama) as part of Classical knots\, virtual knots\, and algebraic s
tructures related to knots\n\n\nAbstract\nIn this talk\, I discuss replaci
ng axioms in a Frobenius algebra with diagrams and constructing glyphs to
represent those diagrams. The ideas are extended to considering isotopy cl
asses of knots as a 4-category. Then we discuss braids\, braided manifolds
\, braid movies\, charts\, chart movies\, curtains\, and curtain movies as
methods of braiding simple branched covers in codimension 2. As usual\, t
here are lots of diagrams.\n
LOCATION:https://researchseminars.org/talk/ckvk_astrks/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David Freund (Harvard University)
DTSTART:20200720T140000Z
DTEND:20200720T150000Z
DTSTAMP:20260422T213051Z
UID:ckvk_astrks/11
DESCRIPTION:Title: Some Algebraic Structures for Flat Virtual Links\nby David Freund
(Harvard University) as part of Classical knots\, virtual knots\, and alg
ebraic structures related to knots\n\n\nAbstract\nFlat virtual links are g
eneralizations of curves on surfaces that have come out of Kauffman's virt
ual knot theory. In particular\, we consider the curves up to homotopy and
allow the supporting surface to change via the addition or removal of emp
ty handles. Under this equivalence\, a flat virtual link obtains a complet
ely combinatorial structure.\n\nAnalogous to the classical problem of find
ing the minimal number of intersection points between two curves\, we can
ask for the minimal number of intersection points between components of a
flat virtual link. By moving between geometric and combinatorial models\,
we develop generalizations of the Andersen-Mattes-Reshetikhin Poisson brac
ket and compute it for infinite families of two-component flat virtual lin
ks using a generalization of Henrich's singular based matrix for flat virt
ual knots. Throughout the talk\, we emphasize the motivation behind differ
ent constructions.\n
LOCATION:https://researchseminars.org/talk/ckvk_astrks/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rhea Palak Bakshi (George Washington University)
DTSTART:20200727T140000Z
DTEND:20200727T150000Z
DTSTAMP:20260422T213051Z
UID:ckvk_astrks/12
DESCRIPTION:Title: Skein modules and framing changes of links in 3-manifolds\nby Rhe
a Palak Bakshi (George Washington University) as part of Classical knots\,
virtual knots\, and algebraic structures related to knots\n\n\nAbstract\n
We show that the only way of changing the framing of a link by ambient iso
topy in an oriented $3$-manifold is when the manifold admits a properly em
bedded non-separating $S^2$. This change of framing is given by the Dirac
trick\, also known as the light bulb trick. The main tool we use is based
on McCullough's work on the mapping class groups of $3$-manifolds. We also
express our results in the language of skein modules. In particular\, we
relate our results to the presence of torsion in the framing skein module.
\n
LOCATION:https://researchseminars.org/talk/ckvk_astrks/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nic Petit (Boston College)
DTSTART:20200810T140000Z
DTEND:20200810T150000Z
DTSTAMP:20260422T213051Z
UID:ckvk_astrks/13
DESCRIPTION:Title: The multi-variable Affine Index Polynomial\nby Nic Petit (Boston
College) as part of Classical knots\, virtual knots\, and algebraic struct
ures related to knots\n\n\nAbstract\nWe will be going over a recent genera
lization of the affine index polynomial to the case of virtual links. We w
ill give some background on the invariant\, present the generalization\, a
nd discuss how different colorings of the link produce different invariant
s.\n
LOCATION:https://researchseminars.org/talk/ckvk_astrks/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Homayun Karimi (McMaster University)
DTSTART:20200817T140000Z
DTEND:20200817T150000Z
DTSTAMP:20260422T213051Z
UID:ckvk_astrks/14
DESCRIPTION:Title: The Jones-Krushkal polynomial and minimal diagrams of surface links\nby Homayun Karimi (McMaster University) as part of Classical knots\, v
irtual knots\, and algebraic structures related to knots\n\n\nAbstract\nWe
prove a Kauffman-Murasugi-Thistlethwaite theorem for alternating\nlinks i
n thickened surfaces. It implies that any reduced alternating diagram of a
link\nin a thickened surface has minimal crossing number\, and any two re
duced alternating\ndiagrams of the same link have the same writhe. This re
sult is proved more generally\nfor link diagrams that are adequate\, and t
he proof involves a two-variable generalization\nof the Jones polynomial f
or surface links defined by Krushkal. The main result is\nused to establis
h the first and second Tait conjectures for links in thickened surfaces\na
nd for virtual links\n
LOCATION:https://researchseminars.org/talk/ckvk_astrks/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Allison Moore (Virginia Commonwealth University)
DTSTART:20200824T140000Z
DTEND:20200824T150000Z
DTSTAMP:20260422T213051Z
UID:ckvk_astrks/15
DESCRIPTION:Title: Triple linking and Heegaard Floer homology\nby Allison Moore (Vir
ginia Commonwealth University) as part of Classical knots\, virtual knots\
, and algebraic structures related to knots\n\n\nAbstract\nWe will describ
e several appearances of Milnor’s link invariants in the link Floer comp
lex. This will include a formula that expresses the Milnor triple linking
number in terms of the h-function. We will also show that the triple linki
ng number is involved in a structural property of the d-invariants of surg
ery on certain algebraically split links. We will apply the above properti
es toward new detection results for the Borromean and Whitehead links. Thi
s is joint work with Gorsky\, Lidman and Liu.\n
LOCATION:https://researchseminars.org/talk/ckvk_astrks/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Heather Dye and Aaron Kastner (McKendree U. and North Park U. (res
p.))
DTSTART:20200914T130000Z
DTEND:20200914T140000Z
DTSTAMP:20260422T213051Z
UID:ckvk_astrks/16
DESCRIPTION:Title: Using virtual knots to define groups\nby Heather Dye and Aaron Ka
stner (McKendree U. and North Park U. (resp.)) as part of Classical knots\
, virtual knots\, and algebraic structures related to knots\n\n\nAbstract\
nIn the paper Virtual Alexander Polynomials\, we defined a virtual knot gr
oup that used information about the parity of the classical crossings. Thi
s virtual knot group was defined using ad-hoc methods. In the paper\, Virt
ual knot groups and almost classical knots\, Boden et al describes several
different knot groups obtained from virtual knots. These knot groups are
related and specializations lead to the classical knot group. Here\, we co
nstruct a formal structure for virtual knot groups and examine specializat
ions and extensions of the groups.\n
LOCATION:https://researchseminars.org/talk/ckvk_astrks/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Scott Baldridge (LSU)
DTSTART:20200922T130000Z
DTEND:20200922T140000Z
DTSTAMP:20260422T213051Z
UID:ckvk_astrks/17
DESCRIPTION:Title: Why unoriented Khovanov homology is useful in graph theory\nby Sc
ott Baldridge (LSU) as part of Classical knots\, virtual knots\, and algeb
raic structures related to knots\n\n\nAbstract\nThe Jones polynomial and K
hovanov homology of a classical link are oriented link invariants—they d
epend upon an initial choice of orientation for the link. In this talk\, w
e describe a Jones polynomial and Khovanov homology theory for unoriented
virtual links. We then show how to transfer these unoriented versions over
to graph theory to construct the Tait polynomial of a trivalent graph. Th
is invariant polynomial counts the number of 3-edge colorings of a graph w
hen evaluated at 1. If this count is nonzero for all bridgeless planar tri
valent graphs\, then the famous four color theorem is true. Thus\, we show
how topological ideas can be used to have an impact in graph theory. This
is joint work with Lou Kauffman and Ben McCarty.\n
LOCATION:https://researchseminars.org/talk/ckvk_astrks/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Matthew Harper (OSU)
DTSTART:20200928T130000Z
DTEND:20200928T140000Z
DTSTAMP:20260422T213051Z
UID:ckvk_astrks/18
DESCRIPTION:Title: A generalization of the Alexander Polynomial from Higher Rank Quantum
Groups\nby Matthew Harper (OSU) as part of Classical knots\, virtual
knots\, and algebraic structures related to knots\n\n\nAbstract\nMurakami
and Ohtsuki have shown that the Alexander polynomial is an $R$-matrix inva
riant associated with representations $V(t)$ of unrolled restricted quantu
m $\\mathfrak{sl}_2$ at a fourth root of unity. In this context\, the high
est weight $t\\in\\mathbb{C}^\\times$ of the representation determines the
polynomial variable. In this talk\, we discuss an extension of their cons
truction to a link invariant $\\Delta_{\\mathfrak{g}}$\, which takes value
s in $n$-variable Laurent polynomials\, where $n$ is the rank of $\\mathfr
ak{g}$. We begin with an overview of computing quantum invariants and of t
he $\\mathfrak{sl}_2$ case. Our focus will then shift to $\\mathfrak{g}=\\
mathfrak{sl}_{3}$. After going through the construction\, we briefly sketc
h the proof of the following theorem: For any knot $K$\, evaluating $\\Del
ta_{\\mathfrak{sl}_3}$ at ${t_1=\\pm1}$\, ${t_2=\\pm1}$\, or ${t_2=\\pm it
_1^{-1}}$ recovers the Alexander polynomial of $K$. We also compare $\\Del
ta_{\\mathfrak{sl}_3}$ with other invariants by giving specific examples.
In particular\, this invariant can detect mutation and is non-trivial on W
hitehead doubles.\n
LOCATION:https://researchseminars.org/talk/ckvk_astrks/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mustafa Hajij (Santa Clara University)
DTSTART:20201019T140000Z
DTEND:20201019T150000Z
DTSTAMP:20260422T213051Z
UID:ckvk_astrks/19
DESCRIPTION:Title: Topological Deep Learning\nby Mustafa Hajij (Santa Clara Universi
ty) as part of Classical knots\, virtual knots\, and algebraic structures
related to knots\n\n\nAbstract\nIn this work\, we introduce topological de
ep learning\, a formalism that is aimed at two goals (1) Introducing topol
ogical language to deep learning for the purpose of utilizing the minimal
mathematical structures to formalize problems that arise in a generic deep
learning problem and (2) augment\, enhance and create novel deep learning
models utilizing tools available in topology. To this end\, we define and
study the classification problem in machine learning in a topological set
ting. Using this topological framework\, we show that the classification p
roblem in machine learning is always solvable under very mild conditions.
Furthermore\, we show that a softmax classification network acts on an inp
ut topological space by a finite sequence of topological moves to achieve
the classification task. To demonstrate these results\, we provide exampl
e datasets and show how they are acted upon by neural nets from this topol
ogical perspective.\n
LOCATION:https://researchseminars.org/talk/ckvk_astrks/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Joshua Edge (Denison University)
DTSTART:20201026T140000Z
DTEND:20201026T150000Z
DTSTAMP:20260422T213051Z
UID:ckvk_astrks/20
DESCRIPTION:Title: Classifying small virtual skein theories\nby Joshua Edge (Denison
University) as part of Classical knots\, virtual knots\, and algebraic st
ructures related to knots\n\n\nAbstract\nA skein theory for the virtual Jo
nes polynomial can be obtained from its original version with the addition
of a virtual crossing that satisfies the virtual Reidemeister moves as we
ll as a naturality condition. In general\, though\, knot polynomials will
not have virtual counterparts. In this talk\, we classify all skein-theore
tic virtual knot polynomials with certain smallness conditions. In particu
lar\, we classify all virtual knot polynomials giving non-trivial invarian
ts strictly smaller than the one given by the Higman-Sims spin model by cl
assifying the planar algebras associated with them. This classification in
cludes a family of skein theories coming from $\\text{Rep}(O(2))$ with an
interesting braiding. This talk is given in memory of Vaughan Jones.\n
LOCATION:https://researchseminars.org/talk/ckvk_astrks/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Thomas Kindred (University of Nebraska Lincoln)
DTSTART:20201109T150000Z
DTEND:20201109T160000Z
DTSTAMP:20260422T213051Z
UID:ckvk_astrks/21
DESCRIPTION:Title: The geometric content of Tait's conjectures\nby Thomas Kindred (U
niversity of Nebraska Lincoln) as part of Classical knots\, virtual knots\
, and algebraic structures related to knots\n\n\nAbstract\nIn 1898\, Tait
asserted several properties of alternating knot diagrams\, which remained
unproven until the discovery of the Jones polynomial in 1985. During that
time\, Fox asked\, ``What [geometrically] is an alternating knot?" By 1993
\, the Jones polynomial had led to proofs of all of Tait's conjectures\, b
ut the geometric content of these new results remained mysterious.\n\nIn 2
017\, Howie and Greene independently answered Fox's question\, and Greene
used his characterization to give the first purely geometric proof of part
of Tait's conjectures. Recently\, I used Greene and Howie's characterizat
ions\, among other techniques\, to give the first entirely geometric proof
of Tait's flyping conjecture (first proven in 1993 by Menasco and Thistle
thwaite). I will describe these recent developments and sketch approaches
to other parts of Tait's conjectures\, and related facts about tangles and
adequate knots\, which remain unproven by purely geometric means.\n
LOCATION:https://researchseminars.org/talk/ckvk_astrks/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Cornelia van Cott (University of San Francisco)
DTSTART:20201116T150000Z
DTEND:20201116T160000Z
DTSTAMP:20260422T213051Z
UID:ckvk_astrks/22
DESCRIPTION:Title: Two-bridge knots and their crosscap numbers\nby Cornelia van Cott
(University of San Francisco) as part of Classical knots\, virtual knots\
, and algebraic structures related to knots\n\n\nAbstract\nBegin with two
knots $K$ and $J$. Simon conjectured that if the knot group of $K$ surject
s onto that of $J$\, then the genera of the orientable surfaces that the t
wo knots bound are constrained. Specifically\, he conjectured $g(K) \\geq
g(J)$\, where $g(K)$ denotes the genus of $K$. This conjecture has been pr
oved for alternating knots and can be strengthened to an even stronger res
ult in the case of two-bridge knots. In this talk\, we consider the same s
orts of questions\, but in the world of nonorientable surfaces. We focus o
n two-bridge knots and find relationships among their crosscap numbers. Th
is is joint work with Jim Hoste and Pat Shanahan.\n
LOCATION:https://researchseminars.org/talk/ckvk_astrks/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Samantha Allen (Dartmouth College)
DTSTART:20201012T140000Z
DTEND:20201012T150000Z
DTSTAMP:20260422T213051Z
UID:ckvk_astrks/23
DESCRIPTION:Title: Unknotting with a single twist\nby Samantha Allen (Dartmouth Coll
ege) as part of Classical knots\, virtual knots\, and algebraic structures
related to knots\n\n\nAbstract\nOhyama showed that any knot can be unknot
ted by performing two full twists\, each on a set of parallel strands. We
consider the question of whether or not a given knot can be unknotted with
a single full twist\, and if so\, what are the possible linking numbers a
ssociated to such a twist. It is observed that if a knot can be unknotted
with a single twist\, then some surgery on the knot bounds a rational homo
logy ball. Using tools such as classical invariants and invariants arising
from Heegaard Floer theory\, we give obstructions for a knot to be unknot
ted with a single twist of a given linking number. In this talk\, I will d
iscuss some of these obstructions\, their implications (especially for alt
ernating knots)\, many examples\, and some unanswered questions. This talk
is based on joint work with Charles Livingston.\n
LOCATION:https://researchseminars.org/talk/ckvk_astrks/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hans Boden (McMaster University)
DTSTART:20201123T130000Z
DTEND:20201123T140000Z
DTSTAMP:20260422T213051Z
UID:ckvk_astrks/24
DESCRIPTION:Title: The Gordon-Litherland pairing for knots and links in thickened surfac
es\nby Hans Boden (McMaster University) as part of Classical knots\, v
irtual knots\, and algebraic structures related to knots\n\n\nAbstract\nWe
introduce the Gordon-Litherland pairing for knots and links in thickened
surfaces that bound unoriented spanning surfaces. Using the GL pairing\, w
e define signature and determinant invariants for such links. We relate th
e invariants to those derived from the Tait graph and Goeritz matrices. Th
ese invariants depend only on the $S^*$ equivalence class of the spanning
surface\, and the determinants give a simple criterion to check if the kno
t or link is minimal genus. This is joint work with M. Chrisman and H. Kar
imi. In further joint work with H. Karimi\, we apply the GL pairing to giv
e a topological characterization of alternating links in thickened surface
s\, extending the results of J. Greene and J. Howie.\n
LOCATION:https://researchseminars.org/talk/ckvk_astrks/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Christopher Davis (University of Wisconsin-Eau Claire)
DTSTART:20210208T150000Z
DTEND:20210208T160000Z
DTSTAMP:20260422T213051Z
UID:ckvk_astrks/25
DESCRIPTION:Title: Links in homology spheres are homotopic to slice links - an applicati
on of the relative Whitney trick.\nby Christopher Davis (University of
Wisconsin-Eau Claire) as part of Classical knots\, virtual knots\, and al
gebraic structures related to knots\n\n\nAbstract\nGeneralizing the notion
of sliceness for links in $S^3$\, a link in a homology sphere is called s
lice if it bounds a disjoint union of locally flat embedded disks in a con
tractible 4-manifold. It is trivial to see that any link in $S^3$ can be
changed by a homotopy to a slice link\, indeed any link is homotopic to th
e unlink. We prove that the same is true for links in homology spheres.
Our argument passes through a novel geometric construction which we call t
he relative Whitney trick. If time permits we will explore an application
of the relative Whitney trick to the existence of Whitney towers.\n
LOCATION:https://researchseminars.org/talk/ckvk_astrks/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Benjamin Audoux (Aix-Marseille Université)
DTSTART:20210222T150000Z
DTEND:20210222T160000Z
DTSTAMP:20260422T213051Z
UID:ckvk_astrks/26
DESCRIPTION:Title: Cut-diagrams and a Chen--Milnor presentation result for knotted surfa
ces\nby Benjamin Audoux (Aix-Marseille Université) as part of Classic
al knots\, virtual knots\, and algebraic structures related to knots\n\n\n
Abstract\nIn this talk\, I will introduce cut-diagrams\, a combinatorial d
ata which generalizes welded links to higher dimensions. Using them\, I wi
ll give and discuss then Chen-Milnor presentations for the nilpotent and r
educed fundamental groups of knotted surfaces. This is joint work in progr
ess with J-B. Meilhan and A. Yasuhara.\n
LOCATION:https://researchseminars.org/talk/ckvk_astrks/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Carmen Caprau (California State University-Fresno)
DTSTART:20210301T150000Z
DTEND:20210301T160000Z
DTSTAMP:20260422T213051Z
UID:ckvk_astrks/27
DESCRIPTION:Title: Movie moves for singular link cobordisms in 4-dimensional space\n
by Carmen Caprau (California State University-Fresno) as part of Classical
knots\, virtual knots\, and algebraic structures related to knots\n\n\nAb
stract\nTwo singular links are cobordant if one can be obtained from the o
ther by singular link isotopy together with a combination of births or dea
ths of simple unknotted curves\, and saddle point transformations. A movie
description of a singular link cobordism in 4-space is a sequence of sing
ular link diagrams obtained from a projection of the cobordism into 3-spac
e by taking 2-dimensional cross sections perpendicular to a fixed directio
n. We present a set of movie moves that are sufficient to connect any two
movies of isotopic singular link cobordisms.\n
LOCATION:https://researchseminars.org/talk/ckvk_astrks/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Miriam Kuzbary (Georgia Tech)
DTSTART:20210308T150000Z
DTEND:20210308T160000Z
DTSTAMP:20260422T213051Z
UID:ckvk_astrks/28
DESCRIPTION:Title: Pure Braids and Link Concordance\nby Miriam Kuzbary (Georgia Tech
) as part of Classical knots\, virtual knots\, and algebraic structures re
lated to knots\n\n\nAbstract\nThe knot concordance group can be contextual
ized as organizing problems about 3- and 4-dimensional spaces and the rela
tionships between them. Every 3-manifold is surgery on some link\, not nec
essarily a knot\, and thus it is natural to ask about such a group for lin
ks. In 1988\, Le Dimet constructed the string link concordance groups and
in 1998\, Habegger and Lin precisely characterized these groups as quotien
ts of the link concordance sets using a group action. Notably\, the knot c
oncordance group is abelian while\, for each n\, the string link concordan
ce group on n strands is non-abelian as it contains the pure braid group o
n n strands as a subgroup. In this talk\, I will discuss my result the quo
tient of each string link concordance group by its pure braid subgroup is
still non-abelian.\n
LOCATION:https://researchseminars.org/talk/ckvk_astrks/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jean-Babtiste Meilhan (Université Grenoble Alpes)
DTSTART:20210322T140000Z
DTEND:20210322T150000Z
DTSTAMP:20260422T213051Z
UID:ckvk_astrks/29
DESCRIPTION:Title: Characterization(s) of the Reduced Peripheral System\nby Jean-Bab
tiste Meilhan (Université Grenoble Alpes) as part of Classical knots\, vi
rtual knots\, and algebraic structures related to knots\n\n\nAbstract\nThe
reduced peripheral system was introduced by Milnor in the 50’s\nfor the
study of links up to link-homotopy\, i.e. up to homotopies\nleaving disti
nct components disjoint. This invariant\, however\, fails\nto classify lin
ks up to link-homotopy for links of 4 or more\ncomponents. The purpose of
this paper is to show that the topological\ninformation which is detected
by Milnor’s reduced peripheral system is\nactually 4-dimensional. We giv
e a topological characterization in\nterms of ribbon solid tori in 4-space
up to link-homotopy\, using a\nversion of Artin’s Spun construction. T
he proof relies heavily on an\nintermediate characterization\, in terms of
welded links up to\nself-virtualization\, providing hence a purely topolo
gical application\nof the combinatorial theory of welded links.\n
LOCATION:https://researchseminars.org/talk/ckvk_astrks/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ayaka Shimizu (National Institute of Technology\, Gunma College\,
Japan)
DTSTART:20210405T140000Z
DTEND:20210405T150000Z
DTSTAMP:20260422T213051Z
UID:ckvk_astrks/31
DESCRIPTION:Title: The reductivity of a knot projection\nby Ayaka Shimizu (National
Institute of Technology\, Gunma College\, Japan) as part of Classical knot
s\, virtual knots\, and algebraic structures related to knots\n\n\nAbstrac
t\nThe reductivity of a knot projection is defined to be the minimum numbe
r of splices required to make the projection reducible\, where the splices
are applied to a knot projection resulting in another knot projection. It
has been shown that the reductivity is four or less for any knot projecti
on and shown that there are infinitely many knot projections with reductiv
ity 0\, 1\, 2\, and 3. The "reductivity problem" is a problem asking the e
xistence of a knot projection whose reductivity is four. In this talk\, we
will discuss some strategies for the reductivity problem focusing on the
region of a knot projection.\n
LOCATION:https://researchseminars.org/talk/ckvk_astrks/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michael Klug (UC-Berkeley)
DTSTART:20210315T140000Z
DTEND:20210315T150000Z
DTSTAMP:20260422T213051Z
UID:ckvk_astrks/32
DESCRIPTION:Title: Arf invariants in low dimensions\nby Michael Klug (UC-Berkeley) a
s part of Classical knots\, virtual knots\, and algebraic structures relat
ed to knots\n\n\nAbstract\nI will briefly discuss some work in progress re
garding a relationship between several different mod 2 invariants in dimen
sions 2\, 3\, and 4. In particular\, I will relate the Arf invariant of a
knot\, the Arf invariant of a characteristic surface\, the Rochlin invaria
nt of a homology sphere\, and the Kirby-Siebenmann invariant of a 4-manifo
ld.\n
LOCATION:https://researchseminars.org/talk/ckvk_astrks/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ilya Kofman (CUNY)
DTSTART:20201130T150000Z
DTEND:20201130T160000Z
DTSTAMP:20260422T213051Z
UID:ckvk_astrks/33
DESCRIPTION:Title: A volumish theorem for virtual links\nby Ilya Kofman (CUNY) as pa
rt of Classical knots\, virtual knots\, and algebraic structures related t
o knots\n\n\nAbstract\nDasbach and Lin proved a “volumish theorem” for
alternating links. We prove the analogue for alternating link diagrams on
surfaces\, which provides bounds on the hyperbolic volume of a link in a
thickened surface in terms of coefficients of its reduced Jones-Krushkal p
olynomial. Joint work with Abhijit Champanerkar.\n
LOCATION:https://researchseminars.org/talk/ckvk_astrks/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Akira Yasuhara (Waseda University)
DTSTART:20210419T140000Z
DTEND:20210419T150000Z
DTSTAMP:20260422T213051Z
UID:ckvk_astrks/34
DESCRIPTION:Title: Arrow calculus for welded links\nby Akira Yasuhara (Waseda Univer
sity) as part of Classical knots\, virtual knots\, and algebraic structure
s related to knots\n\n\nAbstract\nWe develop a calculus for diagrams of kn
otted objects. We define arrow presentations\, which encode the crossing i
nformation of a diagram into arrows in a way somewhat similar to Gauss dia
grams\, and more generally w–tree presentations\, which can be seen as
“higher-order Gauss diagrams”. This arrow calculus is used to develop
an analogue of Habiro’s clasper theory for welded knotted objects\, whic
h contain classical link diagrams as a subset. This provides a “realizat
ion” of Polyak’s algebra of arrow diagrams at the welded level\, and l
eads to a characterization of finite- type invariants of welded knots and
long knots. \nThis is a joint work with Jean-Baptiste Meilhan (University
of Grenoble Alpes).\n
LOCATION:https://researchseminars.org/talk/ckvk_astrks/34/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kodai Wada (Kobe University)
DTSTART:20210531T140000Z
DTEND:20210531T150000Z
DTSTAMP:20260422T213051Z
UID:ckvk_astrks/35
DESCRIPTION:Title: Classification of string links up to $2n$-moves and link-homotopy
\nby Kodai Wada (Kobe University) as part of Classical knots\, virtual kno
ts\, and algebraic structures related to knots\n\n\nAbstract\nIn this talk
\, we give a necessary and sufficient condition for two string links to be
equivalent up to $2n$-moves and link-homotopy in terms of Milnor invarian
ts. This reveals a relation between Milnor invariants and $2n$-moves. This
is a joint work with Haruko Miyazawa and Akira Yasuhara.\n
LOCATION:https://researchseminars.org/talk/ckvk_astrks/35/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Boris Colombari (Aix-Marseille Université)
DTSTART:20210607T140000Z
DTEND:20210607T150000Z
DTSTAMP:20260422T213051Z
UID:ckvk_astrks/36
DESCRIPTION:Title: Classification of welded links and welded string links up to $w_q$-co
ncordance\nby Boris Colombari (Aix-Marseille Université) as part of C
lassical knots\, virtual knots\, and algebraic structures related to knots
\n\n\nAbstract\nThe notion of $w_q$-concordance has been introduced by J-B
. Meilhan and A. Yasuhara through the use of arrow calculus. It is a welde
d analogue of the $C_k$-concordance on classical links coming from the cla
sper calculus introduced by K. Habiro. In this talk I will present a class
ification of welded string links (resp. welded links) up to $w_q$-concorda
nce by their Milnor invariants (resp. by their q-nilpotent peripheral syst
em). I will compare these results to the classification of classical links
up to $C_k$-concordance obtained by J. Conant\, R. Schneiderman and P. Te
ichner before introducing the relevant invariants on welded objects. I wil
l give elements of the proof of my results using a version of arrow calcul
us adapted to the representation of welded objects by Gauss diagrams.\n
LOCATION:https://researchseminars.org/talk/ckvk_astrks/36/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sam Nelson (Claremont McKenna University)
DTSTART:20210517T140000Z
DTEND:20210517T150000Z
DTSTAMP:20260422T213051Z
UID:ckvk_astrks/37
DESCRIPTION:Title: Region coloring invariants for knots\nby Sam Nelson (Claremont Mc
Kenna University) as part of Classical knots\, virtual knots\, and algebra
ic structures related to knots\n\n\nAbstract\nIn this talk we will survey
some region-coloring structures for knots (Niebrzydowski tribrackets\, vir
tual tribrackets\, multitribrackets and psybrackets) and related structure
s and see applications to counting invariants and enhancement as well as s
ome applications to music.\n
LOCATION:https://researchseminars.org/talk/ckvk_astrks/37/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Zhiyun Cheng (Beijing Normal University)
DTSTART:20210726T140000Z
DTEND:20210726T150000Z
DTSTAMP:20260422T213051Z
UID:ckvk_astrks/39
DESCRIPTION:Title: Chord index type invariants of virtual knots\nby Zhiyun Cheng (Be
ijing Normal University) as part of Classical knots\, virtual knots\, and
algebraic structures related to knots\n\n\nAbstract\nAs an extension of cl
assical knot theory\, virtual knot theory studies the embeddings of one sp
here in thickened surfaces up to stable equivalence. Roughly speaking\, th
ere are two kinds of virtual knot invariants\, the first kind comes from k
not invariants of classical knots but the second kind usually vanishes on
classical knots. Most of the second kind of virtual knot invariants are de
fined by using the chord parity or chord index. In this talk\, I will repo
rt some recent progress on virtual knot invariants derived from various ch
ord indices.\n
LOCATION:https://researchseminars.org/talk/ckvk_astrks/39/
END:VEVENT
BEGIN:VEVENT
SUMMARY:William Rushworth (McMaster University)
DTSTART:20210705T140000Z
DTEND:20210705T150000Z
DTSTAMP:20260422T213051Z
UID:ckvk_astrks/41
DESCRIPTION:Title: Minimal crossing number implies minimal supporting genus\nby Will
iam Rushworth (McMaster University) as part of Classical knots\, virtual k
nots\, and algebraic structures related to knots\n\n\nAbstract\nWe prove t
hat a minimal crossing virtual link diagram is a minimal genus diagram. Th
at is\, the genus of its Carter surface realizes the supporting genus of t
he virtual link represented by the diagram. The result is obtained by intr
oducing a new parity theory for virtual links. This answers a basic questi
on in virtual knot theory\, and recovers the corresponding result of Mantu
rov in the case of virtual knots. Joint work with Hans Boden.\n
LOCATION:https://researchseminars.org/talk/ckvk_astrks/41/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Zsuzsanna Dancso (The University of Sydney)
DTSTART:20210921T140000Z
DTEND:20210921T150000Z
DTSTAMP:20260422T213051Z
UID:ckvk_astrks/42
DESCRIPTION:Title: Welded Tangles and the Kashiwara-Vergne Groups\nby Zsuzsanna Danc
so (The University of Sydney) as part of Classical knots\, virtual knots\,
and algebraic structures related to knots\n\n\nAbstract\nIn this talk I w
ill explain a general method of "translating" between a certain type of pr
oblem in topology\, and solving equations in graded spaces in (quantum) al
gebra. I'll talk through several applications of this method from the 90's
to today: Drinfel'd associators and parenthesised braids\, Grothendieck-T
eichmuller groups\, welded tangles and the Alekseev-Enriquez-Torossian for
mulation of the Kashiwara-Vergne equations\, and most recently\, a topolog
ical description of the Kashiwara-Vergne groups. The "recent" portion of t
he talk is based on joint work with Iva Halacheva and Marcy Robertson (arX
iv: 2106.02373)\, and joint work with Dror Bar-Natan (arXiv: 1405.1955).\n
LOCATION:https://researchseminars.org/talk/ckvk_astrks/42/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eva Horvat (University of Ljubljana)
DTSTART:20211005T140000Z
DTEND:20211005T150000Z
DTSTAMP:20260422T213051Z
UID:ckvk_astrks/43
DESCRIPTION:Title: Flattening knotted surfaces\nby Eva Horvat (University of Ljublja
na) as part of Classical knots\, virtual knots\, and algebraic structures
related to knots\n\n\nAbstract\nA knotted surface $\\mathcal{K}$ in the 4-
sphere admits a projection to a 2-sphere\, whose set of critical points co
incides with a hyperbolic diagram of $\\mathcal{K}$. We apply such project
ions\, called flattenings\, to define three invariants of embedded surface
s: the width\, the trunk and the partition number. These invariants are st
udied for some families of embedded surfaces.\n
LOCATION:https://researchseminars.org/talk/ckvk_astrks/43/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ben McCarty (University of Memphis)
DTSTART:20211102T140000Z
DTEND:20211102T150000Z
DTSTAMP:20260422T213051Z
UID:ckvk_astrks/44
DESCRIPTION:Title: Khovanov homology for virtual links\nby Ben McCarty (University o
f Memphis) as part of Classical knots\, virtual knots\, and algebraic stru
ctures related to knots\n\n\nAbstract\nShortly after Khovanov homology for
classical knots and links was developed in the late 90s\, Bar-Natan produ
ced a Mathematica program for computing it from a planar diagram. Yet when
Manturov defined Khovanov homology for virtual links in 2007\, a program
for computing it did not appear until Tubbenhauer's 2012 paper. Even then\
, the theoretical framework used was quite different from the one Manturov
described. In this talk\, we describe a theoretical framework for computi
ng the Khovanov homology of a virtual link\, synthesized from work by Mant
urov\, Dye-Kaestner-Kauffman and others. We also show how to use this fram
ework to create a program for computing the Khovanov homology of a virtual
link\, which is directly based upon Bar-Natan's original program for clas
sical links. This program is joint work with Scott Baldridge\, Heather Dy
e\, Aaron Kaestner\, and Lou Kauffman.\n
LOCATION:https://researchseminars.org/talk/ckvk_astrks/44/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Melissa Zhang (University of Georgia)
DTSTART:20211117T150000Z
DTEND:20211117T160000Z
DTSTAMP:20260422T213051Z
UID:ckvk_astrks/45
DESCRIPTION:Title: Constructions toward topological applications of U(1) x U(1) equivari
ant Khovanov homology\nby Melissa Zhang (University of Georgia) as par
t of Classical knots\, virtual knots\, and algebraic structures related to
knots\n\n\nAbstract\nIn 2018\, Khovanov and Robert introduced a version o
f Khovanov homology over a larger ground ring\, termed U(1)xU(1)-equivaria
nt Khovanov homology. This theory was also studied extensively by Taketo S
ano. Ross Akhmechet was able to construct an equivariant annular Khovanov
homology theory using the U(1)xU(1)-equivariant theory\, while the existen
ce of a U(2)-equivariant annular construction is still unclear.\n \nObserv
ing that the U(1)xU(1) complex admits two symmetric algebraic gradings\, t
hose familiar with knot Floer homology over the ring F[U\,V] may naturally
ask if these filtrations allow for algebraic constructions already seen i
n the knot Floer context\, such as Ozsváth-Stipsicz-Szabó's Upsilon. In
this talk\, I will describe the construction and properties of such an inv
ariant. I will also discuss some ideas on how future research might use t
he U(1)xU(1) framework to identify invariants similar to those constructed
from knot Floer homology over F[U\,V]\, and speculate on the topological
information these constructions might illuminate.\n \nThis is based on joi
nt work with Ross Akhmechet.\n
LOCATION:https://researchseminars.org/talk/ckvk_astrks/45/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jose Ceniceros (Hamilton College)
DTSTART:20210907T140000Z
DTEND:20210907T150000Z
DTSTAMP:20260422T213051Z
UID:ckvk_astrks/46
DESCRIPTION:Title: Cocycle Enhancements of Psyquandle Counting Invariants\nby Jose C
eniceros (Hamilton College) as part of Classical knots\, virtual knots\, a
nd algebraic structures related to knots\n\n\nAbstract\nIn this talk we di
scuss pseudoknots and singular knots. Specifically\, we discuss psyquandle
s and their application to oriented pseudoknots and oriented singular knot
s. Additionally\, we bring cocycle enhancement theory to the case of psyqu
andles to define enhancements of the psyquandle counting invariant via pai
rs of a biquandle 2-cocycle and a new function. As an application\, we def
ine a single-variable polynomial invariant of both oriented pseudoknots an
d oriented singular knots.\n
LOCATION:https://researchseminars.org/talk/ckvk_astrks/46/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jason Joseph (Rice University)
DTSTART:20211019T140000Z
DTEND:20211019T150000Z
DTSTAMP:20260422T213051Z
UID:ckvk_astrks/47
DESCRIPTION:Title: Meridional rank and bridge numbers of knotted surfaces and welded kno
ts\nby Jason Joseph (Rice University) as part of Classical knots\, vir
tual knots\, and algebraic structures related to knots\n\n\nAbstract\nThe
meridional rank conjecture (MRC) posits that the meridional rank of a clas
sical knot is equal to its bridge number. In this talk we investigate whet
her or not this is a reasonable conjecture for knotted surfaces and welded
knots. In particular\, we find criteria to establish the equality of thes
e values for several large families. On the flip side\, we examine the beh
avior of meridional rank of knotted spheres under connected sum\, and\, us
ing examples first studied by Kanenobu\, show that any value between the t
heoretical limits can be achieved. This means that either the MRC is false
for knotted spheres\, or that their bridge number fails to be (-1)-additi
ve. This is joint work with Puttipong Pongtanapaisan.\n
LOCATION:https://researchseminars.org/talk/ckvk_astrks/47/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marithania Silvero (Universidad de Sevilla)
DTSTART:20211207T150000Z
DTEND:20211207T160000Z
DTSTAMP:20260422T213051Z
UID:ckvk_astrks/48
DESCRIPTION:Title: Khomotopy type via simplicial complexes and presimplicial sets\nb
y Marithania Silvero (Universidad de Sevilla) as part of Classical knots\,
virtual knots\, and algebraic structures related to knots\n\n\nAbstract\n
At the end of the past century\, Mikhail Khovanov introduced the first hom
ological invariant\, now known as Khovanov homology\, as a categorificatio
n of Jones polynomial. It is a bigraded homology supported in homological
and quantum gradings. Given a link diagram\, we refer to the maximal (resp
. second-to-maximal) quantum grading such that the associated Khovanov com
plex is non-trivial as extreme (resp. almost extreme) grading. \n\nIn thi
s talk we present a new approach to the geometrization of Khovanov homolog
y in terms of simplicial complexes and presimplicial sets\, for the extrem
e and almost-extreme gradings\, respectively. We also study the relations
of these models with Khovanov spectra\, introducec by Robert Lipshitz and
Sucharit Sarkar as a spatial refinement of Khovanov homology.\n
LOCATION:https://researchseminars.org/talk/ckvk_astrks/48/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Joseph Boninger (CUNY)
DTSTART:20220111T150000Z
DTEND:20220111T160000Z
DTSTAMP:20260422T213051Z
UID:ckvk_astrks/49
DESCRIPTION:Title: The Jones Polynomial from a Goeritz Matrix\nby Joseph Boninger (C
UNY) as part of Classical knots\, virtual knots\, and algebraic structures
related to knots\n\n\nAbstract\nThe Jones polynomial holds a central plac
e in knot theory\, but its topological meaning is not well understood—it
remains an open problem\, posed by Atiyah\, to give a three-dimensional i
nterpretation of the polynomial. In this talk\, we’ll share an original
construction of the Jones polynomial from a Goeritz matrix\, a combinatori
al object with topological significance. In the process we extend the Kauf
fman bracket to any symmetric\, integer matrix\, with applications to link
s in thickened surfaces. Matroid theory plays a role.\n
LOCATION:https://researchseminars.org/talk/ckvk_astrks/49/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rima Chaterjee (University of Cologne)
DTSTART:20220125T150000Z
DTEND:20220125T160000Z
DTSTAMP:20260422T213051Z
UID:ckvk_astrks/50
DESCRIPTION:Title: Knots in overtwisted contact manifolds\nby Rima Chaterjee (Univer
sity of Cologne) as part of Classical knots\, virtual knots\, and algebrai
c structures related to knots\n\n\nAbstract\nKnots associated to overtwist
ed manifolds are less explored.\nThere are two types of knots in an overtw
isted manifold - loose and\nnon-loose. Non-loose knots are knots with tigh
t complements where as\nloose knots have overtwisted complements. While we
understand loose\nknots\, non-loose knots remain a mystery. The classific
ation and\nstructure problems of these knots vary greatly compared to the
knots\nin tight manifolds. In this talk\, I'll give a brief survey followe
d by \nsome interesting recent work. Especially I'll show how satellite\no
perations on a knot in overtwisted manifold changes the geometric\npropert
y of the knot. I will discuss under what\nconditions cabling operation on
a non-loose knot preserves\nnon-looseness. The ''recent part'' of this tal
k is based on joint work \nwith Etnyre\, Min and Mukherjee.\n
LOCATION:https://researchseminars.org/talk/ckvk_astrks/50/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Fara Renaud (Université Catholique de Louvain)
DTSTART:20220329T140000Z
DTEND:20220329T150000Z
DTSTAMP:20260422T213051Z
UID:ckvk_astrks/51
DESCRIPTION:Title: Higher coverings of racks and quandles\nby Fara Renaud (Universit
é Catholique de Louvain) as part of Classical knots\, virtual knots\, and
algebraic structures related to knots\n\n\nAbstract\nThis talk is based o
n a series of papers called \\textit{Higher coverings of racks and quandle
s}. This project is rooted in M. Eisermann’s work on quandle coverings\,
and the categorical perspective brought to the subject by V. Even\, who c
haracterizes quandle coverings as those surjections which are \\emph{centr
al}\, relatively to trivial quandles. We revisit and extend this work by a
pplying the techniques from higher categorical Galois theory\, in the sens
e of G. Janelidze.\n\nIn these articles we consolidate the understanding o
f rack and quandle coverings' relationship with central extensions of grou
ps on the one hand and topological coverings on the other. We further iden
tify and study a meaningful two-dimensional (and higher-dimensional) centr
ality condition defining our double coverings of racks and quandles (and h
igher coverings of arbitrary dimension). We also introduce a suitable comm
utator which describes the zero\, one and two-dimensional concepts of cent
ralization in this context.\n\nThese results provide new tools to study ra
cks and quandles\, with potential applications to the development of homol
ogy theory and homotopy theory in this context. From the perspective of ca
tegory theory\, they provide a new context of application for higher Galoi
s theory.\n\nIn this talk\, I would like to summarize some of this materia
l\, to share it with an audience which is familiar with knot theory\, and
which is potentially interested in trying out those concepts in their own
field of study.\n
LOCATION:https://researchseminars.org/talk/ckvk_astrks/51/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jagdeep Basi (California State University-Fresno)
DTSTART:20220308T150000Z
DTEND:20220308T160000Z
DTSTAMP:20260422T213051Z
UID:ckvk_astrks/52
DESCRIPTION:Title: Quandle Coloring Quivers of (p\,2)-Torus Knots and Links\nby Jagd
eep Basi (California State University-Fresno) as part of Classical knots\,
virtual knots\, and algebraic structures related to knots\n\n\nAbstract\n
A quandle coloring quiver is a quiver structure\, introduced by Karina Cho
and Sam Nelson\, and defined on the set of quandle colorings of an orient
ed knot or link with respect to a finite quandle. In this talk\, we study
quandle coloring quivers of $(p\, 2)$-torus knots and links with respect t
o dihedral quandles.\n
LOCATION:https://researchseminars.org/talk/ckvk_astrks/52/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kate Petersen (University of Minnesota Duluth)
DTSTART:20220322T140000Z
DTEND:20220322T150000Z
DTSTAMP:20260422T213051Z
UID:ckvk_astrks/53
DESCRIPTION:Title: PSL(2\,C) representations of knot groups\nby Kate Petersen (Unive
rsity of Minnesota Duluth) as part of Classical knots\, virtual knots\, an
d algebraic structures related to knots\n\n\nAbstract\nI will discuss a me
thod of producing defining equations for representation varieties of the c
anonical component of a knot group into PSL2(C). This method uses only a k
not diagram satisfying a mild restriction and is based upon the underlying
geometry of the knot complement. In particular\, it does not involve any
polyhedral decomposition or triangulation of the link complement. This re
sults in a simple algorithm that can often be performed by hand\, and in m
any cases\, for an infinite family of knots at once. This is joint work wi
th Anastasiia Tsvietkova.\n
LOCATION:https://researchseminars.org/talk/ckvk_astrks/53/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Oscar Ocampo (Universidade Federal da Bahia)
DTSTART:20220405T140000Z
DTEND:20220405T150000Z
DTSTAMP:20260422T213051Z
UID:ckvk_astrks/54
DESCRIPTION:Title: Virtual braid groups\, virtual twin groups and crystallographic group
s\nby Oscar Ocampo (Universidade Federal da Bahia) as part of Classica
l knots\, virtual knots\, and algebraic structures related to knots\n\n\nA
bstract\nLet $n\\ge 2$. Let $VB_n$ (resp. $VP_n$) be the virtual braid gro
up (resp. the pure virtual braid group)\, and let $VT_n$ (resp. $PVT_n$) b
e the virtual twin group (resp. the pure virtual twin group). Let $\\Pi$ b
e one of the following quotients: $VB_n/\\Gamma_2(VP_n)$ or $VT_n/\\Gamma_
2(PVT_n)$ where $\\Gamma_2(H)$ is the commutator subgroup of $H$.\n\nIn th
is talk\, we show that $\\Pi$ is a crystallographic group and then and the
n we explore some of its properties\, such as: characterization of finite
order elements and its conjugacy classes\, and also the realization of som
e Bieberbach groups and infinite virtually cyclic groups. Finally\, we als
o consider other braid-like groups (welded\, unrestricted\, flat virtual\,
flat welded and Gauss virtual braid group) module the respective commutat
or subgroup in each case.\n\nJoint work with Paulo Cesar Cerqueira dos San
tos Júnior (arXiv: 2110.02392)\n
LOCATION:https://researchseminars.org/talk/ckvk_astrks/54/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mehander Singh (IISER)
DTSTART:20220510T140000Z
DTEND:20220510T150000Z
DTSTAMP:20260422T213051Z
UID:ckvk_astrks/55
DESCRIPTION:Title: Planar knots and related groups\nby Mehander Singh (IISER) as par
t of Classical knots\, virtual knots\, and algebraic structures related to
knots\n\n\nAbstract\nStudy of stable isotopy classes of a finite collecti
on of immersed circles without triple or higher intersections on closed or
iented surfaces can be thought of as a planar analogue of virtual knot the
ory where the sphere case corresponds to the classical knot theory. It is
intriguing to know which class of groups serves the purpose that Artin bra
id groups serve in classical knot theory. Khovanov proved that twin groups
\, a class of right angled Coxeter groups with only far commutativity rela
tions\, serves the purpose for the sphere case. In a recent work we showed
that an appropriate class of groups called virtual twin groups fits into
a virtual analogue of the planar knot theory. The talk will give an overvi
ew of some recent topological and group theoretic developments along these
lines.\n
LOCATION:https://researchseminars.org/talk/ckvk_astrks/55/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jessica Purcell (Monash University)
DTSTART:20220315T140000Z
DTEND:20220315T150000Z
DTSTAMP:20260422T213051Z
UID:ckvk_astrks/56
DESCRIPTION:Title: Geometry of alternating links on surfaces\nby Jessica Purcell (Mo
nash University) as part of Classical knots\, virtual knots\, and algebrai
c structures related to knots\n\n\nAbstract\nIt is typically hard to relat
e the geometry of a knot complement to a diagram of the knot\, but over ma
ny years mathematicians have been able to relate geometric properties of c
lassical alternating knots to their diagrams. Recently\, we have modified
these techniques to investigate geometry of a much wider class of knots\,
namely alternating knots with diagrams on general surfaces embedded in gen
eral 3-manifolds. This has resulted in lower bounds on volumes\, informati
on on the geometry of checkerboard surfaces\, restrictions on exceptional
Dehn fillings\, and other geometric properties. However\, we were unable t
o extend upper volume bounds broadly. In fact\, recently we showed an uppe
r bound must depend on the 3-manifold in which the knot is embedded: We fi
nd upper bounds for virtual knots\, but not for other families. We will di
scuss this work\, and some remaining open questions. This is joint in part
with Josh Howie and in part with Effie Kalfagianni.\n
LOCATION:https://researchseminars.org/talk/ckvk_astrks/56/
END:VEVENT
END:VCALENDAR