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BEGIN:VEVENT
SUMMARY:Maggie Miller (Princeton University)
DTSTART:20200420T130000Z
DTEND:20200420T140000Z
DTSTAMP:20260404T095040Z
UID:ckvk_astrks/1
DESCRIPTION:Title: The effect of link Dehn surgery on the Thurston norm\nby Ma
ggie Miller (Princeton University) as part of Classical knots\, virtual kn
ots\, and algebraic structures related to knots\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/ckvk_astrks/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Colin Adams (Williams College)
DTSTART:20200427T130000Z
DTEND:20200427T140000Z
DTSTAMP:20260404T095040Z
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://stable.researchseminars.org/talk/ckvk_astrks/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Puttipong Pongtanapaisan (University of Iowa)
DTSTART:20200504T130000Z
DTEND:20200504T140000Z
DTSTAMP:20260404T095040Z
UID:ckvk_astrks/3
DESCRIPTION:Title: Knots with critical bridge spheres\nby Puttipong Pongtanapa
isan (University of Iowa) as part of Classical knots\, virtual knots\, and
algebraic structures related to knots\n\n\nAbstract\nDavid Bachman introd
uced the notion of critical surfaces and showed that they satisfy useful p
roperties. In particular\, they behave like incompressible surfaces and s
trongly irreducible surfaces. In this talk\, I will review some techniques
that have been used to study bridge spheres and give examples of nontrivi
al knots with critical bridge spheres. This is joint work with Daniel Rod
man.\n
LOCATION:https://stable.researchseminars.org/talk/ckvk_astrks/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Micah Chrisman (OSU)
DTSTART:20200518T130000Z
DTEND:20200518T140000Z
DTSTAMP:20260404T095040Z
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\, vir
tual knots\, and algebraic structures related to knots\n\n\nAbstract\nMiln
or's $\\bar{\\mu}$-invariants for links in the 3-sphere vanish on any link
concordant to a boundary link. In particular\, they are are trivial for a
ny classical knot. Here we define an analogue of Milnor's concordance inva
riants for knots in thickened surfaces $\\Sigma \\times [0\,1]$\, where $\
\Sigma$ is closed and oriented. These invariants vanish on any knot concor
dant to a homologically trivial knot in $\\Sigma \\times [0\,1]$. We use t
hem to give new examples of non-slice virtual knots having trivial Rasmuss
en invariant\, graded genus\, affine index polynomial\, and generalized Al
exander polynomial. Moreover\, we complete the slice status classification
of the 2564 virtual knots having at most five classical crossings and red
uce to four (of 90235) the number of virtual knots with six classical cros
sings having unknown slice status. Furthermore\, we prove that in contrast
to the classical knot concordance group\, the virtual knot concordance gr
oup is not abelian. As part of the construction of the extended $\\bar{\\m
u}$-invariants\, we also obtain a generalization of the $\\bar{\\mu}$-inva
riants of classical links in $S^3$ to ribbon torus links in $S^4$ and weld
ed links.\n
LOCATION:https://stable.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:20260404T095040Z
UID:ckvk_astrks/5
DESCRIPTION:Title: Rotational Virtual Links\, Parity Polynomials and Quantum Link
Invariants\nby Lou Kauffman (University of Illinois\, Chicago and Novo
sibirsk State University) as part of Classical knots\, virtual knots\, and
algebraic structures related to knots\n\n\nAbstract\nThis talk discusses
virtual knot theory and rotational virtual knot theory. In virtual knot th
eory we introduce a virtual crossing in the diagrams along with over cross
ings and under crossings. Virtual crossings are artifacts of representing
knots in higher genus surfaces as diagrams in the plane.\n \nVirtual diagr
ammatic equivalence is the same as studying knots in thickened surfaces up
to ambient isotopy\, surface homeomorphisms and handle stabilization. At
the diagrammatic level\, virtual knot equivalence is generated by Reidemei
ster moves plus detour moves. In rotational virtual knot theory\, the deto
ur moves are restricted to regular homotopy of plane curves (the self-cros
sings are virtual). Rotational virtual knot theory has the property that a
ll classical quantum link invariants extend to quantum invariants of rotat
ional virtual knots and links. We explain this extension\, and we consider
the question of the power of quantum invariants in this context.\n \nBy c
onsidering first the bracket polynomial and its extension to a parity brac
ket polynomial for virtual knots (Manturov) and its further extension to a
rotational parity bracket polynomial for knots and links (Kaestner and Ka
uffman)\, we give examples of links that are detected via the parity invar
iants that are not detectable by quantum invariants. In the course of the
discussion we explain a functor from the rotational tangle category to the
diagrammatic category of a quantum algebra. We delineate significant weak
nesses in quantum invariants and how these gaps can be fulfilled by taking
parity into account.\n
LOCATION:https://stable.researchseminars.org/talk/ckvk_astrks/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Scott Carter (University of South Alabama)
DTSTART:20200525T140000Z
DTEND:20200525T150000Z
DTSTAMP:20260404T095040Z
UID:ckvk_astrks/6
DESCRIPTION:Title: Diagrammatic Algebra\, Part 1\nby Scott Carter (University
of South Alabama) as part of Classical knots\, virtual knots\, and algebra
ic structures related to knots\n\n\nAbstract\nThis talk is based upon join
t work with Seiichi Kamada.\nAbstract tensor notation for multi-linear map
s uses boxes with in-coming and out-going strings to represent structure c
onstants. I judicious choice of variables for such constants leads to the
diagrammatic representation: boxes are replaced by glyphs. One of the most
simple examples of a multi-category is the diagrammatic representation of
embedded surfaces in 3-space that we all grew up learning. The standard d
rawing of a torus (an oval\, a smile and a moustache) is a representation
based upon drawings of surface singularities. We start from a two object c
ategory with a pair of arrows that relate them. Cups and caps are construc
ted easily. From these\, births\, deaths\, saddles\, forks\, and cusps are
created as triple arrows. At the top level\, there are critical cancelati
ons\, lips\, beak-to-beak\, horizontal cusps\, and swallow-tails. \n\nInte
restingly\, the structure extends inductively to describe many relations
about handles. in higher dimensions.\n
LOCATION:https://stable.researchseminars.org/talk/ckvk_astrks/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Scott Taylor (Colby College)
DTSTART:20200615T140000Z
DTEND:20200615T150000Z
DTSTAMP:20260404T095040Z
UID:ckvk_astrks/7
DESCRIPTION:Title: Lower bounds on the tunnel number of composite spatial graphs.<
/a>\nby Scott Taylor (Colby College) as part of Classical knots\, virtual
knots\, and algebraic structures related to knots\n\n\nAbstract\nThe tunne
l number of a graph embedded in a 3-dimensional manifold is the fewest num
ber of arcs needed so that the union of the graph with the arcs has handle
body exterior. The behavior of tunnel number with respect to connected sum
of knots can vary dramatically\, depending on the knots involved. However
\, a classical theorem of Scharlemann and Schultens says that the tunnel n
umber of a composite knot is at least the number of factors. For theta gra
phs\, trivalent vertex sum is the operation which most closely resembles t
he connected sum of knots.The analogous theorem of Scharlemann and Schulte
ns no longer holds\, however. I will provide a sharp lower bound for the t
unnel number of composite theta graphs\,using recent work on a new knot in
variant which is additive under connected sum and trivalent vertex sum. Th
is is joint work with Maggy Tomova.\n
LOCATION:https://stable.researchseminars.org/talk/ckvk_astrks/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Emanuele Zappala (University of South Florida)
DTSTART:20200622T140000Z
DTEND:20200622T150000Z
DTSTAMP:20260404T095040Z
UID:ckvk_astrks/8
DESCRIPTION:Title: Invariants of framed links from cohomology of ternary self-dist
ributive structures\nby Emanuele Zappala (University of South Florida)
as part of Classical knots\, virtual knots\, and algebraic structures rel
ated to knots\n\n\nAbstract\nn this talk I recall the definitions of shelf
/rack/quandle and their cohomology theory. I also give the construction of
cocycle invariant of links\, due to Carter\, Jelsovsky\, Kamada\, Langfor
d and Saito (Trans. Amer. Math. Soc. 355 (2003)\, 3947-3989). Then\, I int
roduce higher arity self-distributive structures and show that an appropri
ate diagrammatic interpretation of them is suitable to define a ternary ve
rsion of the cocycle invariant for framed link invariants\, via blackboard
framings. I discuss the computation of cohomology of ternary structures\,
as composition of mutually distributive operations\, and a cohomology the
ory of certain ternary quandles called group heaps. Furthermore I mention
a categorical version of self-distributivity\, along with examples from Li
e algebras and Hopf algebras\, and the construction of ribbon categories f
rom ternary operations that provide a quantum interpretation of the (terna
ry) cocycle invariant.\n
LOCATION:https://stable.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:20260404T095040Z
UID:ckvk_astrks/9
DESCRIPTION:Title: What is a braidoid diagram?\nby Neslihan Gugucmcu (\, Izmir
Institute of Technology and Universityof Goettingen) as part of Classical
knots\, virtual knots\, and algebraic structures related to knots\n\n\nAb
stract\nIn this talk we first review the basics of the theory of knotoids
introduced 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 loc
al region complementary to the plane of the diagram. The theory of knotoid
s extends the classical knot theory and brings up some interesting problem
s and features such as the height problem [1\,3] and parity notion and rel
ated invariants such as off writhe and parity bracket polynomial [4]. It w
as a curious problem to determine a "braid like object" corresponding to k
notoid diagrams. The second part of this talk is devoted to the theory of
braidoids\, introduced by the author and Sofia Lambropoulou [2]. We presen
t the notion of a braidoid and analogous theorems to the classical Alexand
er Theorem and the Markov Theorem\, that relate knotoids/multi-knotoids in
the plane to braidoids.\n
LOCATION:https://stable.researchseminars.org/talk/ckvk_astrks/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:J. Scott Carter (niversity of South Alabama)
DTSTART:20200713T140000Z
DTEND:20200713T150000Z
DTSTAMP:20260404T095040Z
UID:ckvk_astrks/10
DESCRIPTION:Title: Diagrammatic algebra\, part 2\nby J. Scott Carter (niversi
ty of South Alabama) as part of Classical knots\, virtual knots\, and alge
braic structures related to knots\n\n\nAbstract\nIn this talk\, I discuss
replacing axioms in a Frobenius algebra with diagrams and constructing gly
phs to represent those diagrams. The ideas are extended to considering iso
topy classes of knots as a 4-category. Then we discuss braids\, braided ma
nifolds\, braid movies\, charts\, chart movies\, curtains\, and curtain mo
vies as methods of braiding simple branched covers in codimension 2. As us
ual\, there are lots of diagrams.\n
LOCATION:https://stable.researchseminars.org/talk/ckvk_astrks/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David Freund (Harvard University)
DTSTART:20200720T140000Z
DTEND:20200720T150000Z
DTSTAMP:20260404T095040Z
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 algebraic structures related to knots\n\n\nAbstract\nFlat virtual link
s are generalizations of curves on surfaces that have come out of Kauffman
's virtual knot theory. In particular\, we consider the curves up to homot
opy and allow the supporting surface to change via the addition or removal
of empty handles. Under this equivalence\, a flat virtual link obtains a
completely combinatorial structure.\n\nAnalogous to the classical problem
of finding the minimal number of intersection points between two curves\,
we can ask for the minimal number of intersection points between component
s of a flat virtual link. By moving between geometric and combinatorial mo
dels\, we develop generalizations of the Andersen-Mattes-Reshetikhin Poiss
on bracket and compute it for infinite families of two-component flat virt
ual links using a generalization of Henrich's singular based matrix for fl
at virtual knots. Throughout the talk\, we emphasize the motivation behind
different constructions.\n
LOCATION:https://stable.researchseminars.org/talk/ckvk_astrks/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rhea Palak Bakshi (George Washington University)
DTSTART:20200727T140000Z
DTEND:20200727T150000Z
DTSTAMP:20260404T095040Z
UID:ckvk_astrks/12
DESCRIPTION:Title: Skein modules and framing changes of links in 3-manifolds\
nby Rhea Palak Bakshi (George Washington University) as part of Classical
knots\, virtual knots\, and algebraic structures related to knots\n\n\nAbs
tract\nWe show that the only way of changing the framing of a link by ambi
ent isotopy in an oriented $3$-manifold is when the manifold admits a prop
erly embedded 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 particula
r\, we relate our results to the presence of torsion in the framing skein
module.\n
LOCATION:https://stable.researchseminars.org/talk/ckvk_astrks/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nic Petit (Boston College)
DTSTART:20200810T140000Z
DTEND:20200810T150000Z
DTSTAMP:20260404T095040Z
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
structures related to knots\n\n\nAbstract\nWe will be going over a recent
generalization of the affine index polynomial to the case of virtual link
s. We will give some background on the invariant\, present the generalizat
ion\, and discuss how different colorings of the link produce different in
variants.\n
LOCATION:https://stable.researchseminars.org/talk/ckvk_astrks/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Homayun Karimi (McMaster University)
DTSTART:20200817T140000Z
DTEND:20200817T150000Z
DTSTAMP:20260404T095040Z
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 kn
ots\, virtual knots\, and algebraic structures related to knots\n\n\nAbstr
act\nWe prove a Kauffman-Murasugi-Thistlethwaite theorem for alternating\n
links in thickened surfaces. It implies that any reduced alternating diagr
am of a link\nin a thickened surface has minimal crossing number\, and any
two reduced alternating\ndiagrams of the same link have the same writhe.
This result is proved more generally\nfor link diagrams that are adequate\
, and the proof involves a two-variable generalization\nof the Jones polyn
omial for surface links defined by Krushkal. The main result is\nused to e
stablish the first and second Tait conjectures for links in thickened surf
aces\nand for virtual links\n
LOCATION:https://stable.researchseminars.org/talk/ckvk_astrks/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Allison Moore (Virginia Commonwealth University)
DTSTART:20200824T140000Z
DTEND:20200824T150000Z
DTSTAMP:20260404T095040Z
UID:ckvk_astrks/15
DESCRIPTION:Title: Triple linking and Heegaard Floer homology\nby Allison Moo
re (Virginia Commonwealth University) as part of Classical knots\, virtual
knots\, and algebraic structures related to knots\n\n\nAbstract\nWe will
describe several appearances of Milnor’s link invariants in the link Flo
er complex. This will include a formula that expresses the Milnor triple l
inking number in terms of the h-function. We will also show that the tripl
e linking number is involved in a structural property of the d-invariants
of surgery on certain algebraically split links. We will apply the above p
roperties toward new detection results for the Borromean and Whitehead lin
ks. This is joint work with Gorsky\, Lidman and Liu.\n
LOCATION:https://stable.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:20260404T095040Z
UID:ckvk_astrks/16
DESCRIPTION:Title: Using virtual knots to define groups\nby Heather Dye and A
aron Kastner (McKendree U. and North Park U. (resp.)) as part of Classical
knots\, virtual knots\, and algebraic structures related to knots\n\n\nAb
stract\nIn the paper Virtual Alexander Polynomials\, we defined a virtual
knot group that used information about the parity of the classical crossin
gs. This virtual knot group was defined using ad-hoc methods. In the paper
\, Virtual knot groups and almost classical knots\, Boden et al describes
several different knot groups obtained from virtual knots. These knot grou
ps are related and specializations lead to the classical knot group. Here\
, we construct a formal structure for virtual knot groups and examine spec
ializations and extensions of the groups.\n
LOCATION:https://stable.researchseminars.org/talk/ckvk_astrks/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Scott Baldridge (LSU)
DTSTART:20200922T130000Z
DTEND:20200922T140000Z
DTSTAMP:20260404T095040Z
UID:ckvk_astrks/17
DESCRIPTION:Title: Why unoriented Khovanov homology is useful in graph theory
\nby Scott Baldridge (LSU) as part of Classical knots\, virtual knots\, an
d algebraic structures related to knots\n\n\nAbstract\nThe Jones polynomia
l and Khovanov homology of a classical link are oriented link invariants
—they depend upon an initial choice of orientation for the link. In this
talk\, we describe a Jones polynomial and Khovanov homology theory for un
oriented virtual links. We then show how to transfer these unoriented vers
ions over to graph theory to construct the Tait polynomial of a trivalent
graph. This invariant polynomial counts the number of 3-edge colorings of
a graph when evaluated at 1. If this count is nonzero for all bridgeless p
lanar trivalent graphs\, then the famous four color theorem is true. Thus\
, we show how topological ideas can be used to have an impact in graph the
ory. This is joint work with Lou Kauffman and Ben McCarty.\n
LOCATION:https://stable.researchseminars.org/talk/ckvk_astrks/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Matthew Harper (OSU)
DTSTART:20200928T130000Z
DTEND:20200928T140000Z
DTSTAMP:20260404T095040Z
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\, v
irtual knots\, and algebraic structures related to knots\n\n\nAbstract\nMu
rakami and Ohtsuki have shown that the Alexander polynomial is an $R$-matr
ix invariant associated with representations $V(t)$ of unrolled restricted
quantum $\\mathfrak{sl}_2$ at a fourth root of unity. In this context\, t
he highest weight $t\\in\\mathbb{C}^\\times$ of the representation determi
nes the polynomial variable. In this talk\, we discuss an extension of the
ir construction to a link invariant $\\Delta_{\\mathfrak{g}}$\, which take
s values in $n$-variable Laurent polynomials\, where $n$ is the rank of $\
\mathfrak{g}$. We begin with an overview of computing quantum invariants a
nd of the $\\mathfrak{sl}_2$ case. Our focus will then shift to $\\mathfra
k{g}=\\mathfrak{sl}_{3}$. After going through the construction\, we briefl
y sketch the proof of the following theorem: For any knot $K$\, evaluating
$\\Delta_{\\mathfrak{sl}_3}$ at ${t_1=\\pm1}$\, ${t_2=\\pm1}$\, or ${t_2=
\\pm it_1^{-1}}$ recovers the Alexander polynomial of $K$. We also compare
$\\Delta_{\\mathfrak{sl}_3}$ with other invariants by giving specific exa
mples. In particular\, this invariant can detect mutation and is non-trivi
al on Whitehead doubles.\n
LOCATION:https://stable.researchseminars.org/talk/ckvk_astrks/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mustafa Hajij (Santa Clara University)
DTSTART:20201019T140000Z
DTEND:20201019T150000Z
DTSTAMP:20260404T095040Z
UID:ckvk_astrks/19
DESCRIPTION:Title: Topological Deep Learning\nby Mustafa Hajij (Santa Clara U
niversity) as part of Classical knots\, virtual knots\, and algebraic stru
ctures related to knots\n\n\nAbstract\nIn this work\, we introduce topolog
ical deep learning\, a formalism that is aimed at two goals (1) Introducin
g topological language to deep learning for the purpose of utilizing the m
inimal mathematical structures to formalize problems that arise in a gener
ic deep learning problem and (2) augment\, enhance and create novel deep l
earning models utilizing tools available in topology. To this end\, we def
ine and study the classification problem in machine learning in a topologi
cal setting. Using this topological framework\, we show that the classific
ation problem in machine learning is always solvable under very mild condi
tions. Furthermore\, we show that a softmax classification network acts on
an input topological space by a finite sequence of topological moves to a
chieve the classification task. To demonstrate these results\, we provide
example datasets and show how they are acted upon by neural nets from thi
s topological perspective.\n
LOCATION:https://stable.researchseminars.org/talk/ckvk_astrks/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Joshua Edge (Denison University)
DTSTART:20201026T140000Z
DTEND:20201026T150000Z
DTSTAMP:20260404T095040Z
UID:ckvk_astrks/20
DESCRIPTION:Title: Classifying small virtual skein theories\nby Joshua Edge (
Denison University) as part of Classical knots\, virtual knots\, and algeb
raic structures related to knots\n\n\nAbstract\nA skein theory for the vir
tual Jones polynomial can be obtained from its original version with the a
ddition of a virtual crossing that satisfies the virtual Reidemeister move
s as well as a naturality condition. In general\, though\, knot polynomial
s will not have virtual counterparts. In this talk\, we classify all skein
-theoretic virtual knot polynomials with certain smallness conditions. In
particular\, we classify all virtual knot polynomials giving non-trivial i
nvariants strictly smaller than the one given by the Higman-Sims spin mode
l by classifying the planar algebras associated with them. This classifica
tion includes a family of skein theories coming from $\\text{Rep}(O(2))$ w
ith an interesting braiding. This talk is given in memory of Vaughan Jones
.\n
LOCATION:https://stable.researchseminars.org/talk/ckvk_astrks/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Thomas Kindred (University of Nebraska Lincoln)
DTSTART:20201109T150000Z
DTEND:20201109T160000Z
DTSTAMP:20260404T095040Z
UID:ckvk_astrks/21
DESCRIPTION:Title: The geometric content of Tait's conjectures\nby Thomas Kin
dred (University 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 re
mained unproven until the discovery of the Jones polynomial in 1985. Durin
g that time\, Fox asked\, ``What [geometrically] is an alternating knot?"
By 1993\, the Jones polynomial had led to proofs of all of Tait's conjectu
res\, but the geometric content of these new results remained mysterious.\
n\nIn 2017\, 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 charac
terizations\, among other techniques\, to give the first entirely geometri
c proof of Tait's flyping conjecture (first proven in 1993 by Menasco and
Thistlethwaite). I will describe these recent developments and sketch appr
oaches to other parts of Tait's conjectures\, and related facts about tang
les and adequate knots\, which remain unproven by purely geometric means.\
n
LOCATION:https://stable.researchseminars.org/talk/ckvk_astrks/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Cornelia van Cott (University of San Francisco)
DTSTART:20201116T150000Z
DTEND:20201116T160000Z
DTSTAMP:20260404T095040Z
UID:ckvk_astrks/22
DESCRIPTION:Title: Two-bridge knots and their crosscap numbers\nby Cornelia v
an Cott (University of San Francisco) as part of Classical knots\, virtual
knots\, and algebraic structures related to knots\n\n\nAbstract\nBegin wi
th two knots $K$ and $J$. Simon conjectured that if the knot group of $K$
surjects onto that of $J$\, then the genera of the orientable surfaces tha
t the two knots bound are constrained. Specifically\, he conjectured $g(K)
\\geq g(J)$\, where $g(K)$ denotes the genus of $K$. This conjecture has
been proved for alternating knots and can be strengthened to an even stron
ger result in the case of two-bridge knots. In this talk\, we consider the
same sorts of questions\, but in the world of nonorientable surfaces. We
focus on two-bridge knots and find relationships among their crosscap numb
ers. This is joint work with Jim Hoste and Pat Shanahan.\n
LOCATION:https://stable.researchseminars.org/talk/ckvk_astrks/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Samantha Allen (Dartmouth College)
DTSTART:20201012T140000Z
DTEND:20201012T150000Z
DTSTAMP:20260404T095040Z
UID:ckvk_astrks/23
DESCRIPTION:Title: Unknotting with a single twist\nby Samantha Allen (Dartmou
th College) as part of Classical knots\, virtual knots\, and algebraic str
uctures related to knots\n\n\nAbstract\nOhyama showed that any knot can be
unknotted by performing two full twists\, each on a set of parallel stran
ds. We consider the question of whether or not a given knot can be unknott
ed with a single full twist\, and if so\, what are the possible linking nu
mbers associated to such a twist. It is observed that if a knot can be unk
notted with a single twist\, then some surgery on the knot bounds a ration
al homology ball. Using tools such as classical invariants and invariants
arising from Heegaard Floer theory\, we give obstructions for a knot to be
unknotted with a single twist of a given linking number. In this talk\, I
will discuss some of these obstructions\, their implications (especially
for alternating knots)\, many examples\, and some unanswered questions. Th
is talk is based on joint work with Charles Livingston.\n
LOCATION:https://stable.researchseminars.org/talk/ckvk_astrks/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hans Boden (McMaster University)
DTSTART:20201123T130000Z
DTEND:20201123T140000Z
DTSTAMP:20260404T095040Z
UID:ckvk_astrks/24
DESCRIPTION:Title: The Gordon-Litherland pairing for knots and links in thickened
surfaces\nby Hans Boden (McMaster University) as part of Classical kn
ots\, virtual knots\, and algebraic structures related to knots\n\n\nAbstr
act\nWe introduce the Gordon-Litherland pairing for knots and links in thi
ckened surfaces that bound unoriented spanning surfaces. Using the GL pair
ing\, we define signature and determinant invariants for such links. We re
late the invariants to those derived from the Tait graph and Goeritz matri
ces. These invariants depend only on the $S^*$ equivalence class of the sp
anning surface\, and the determinants give a simple criterion to check if
the knot or link is minimal genus. This is joint work with M. Chrisman and
H. Karimi. In further joint work with H. Karimi\, we apply the GL pairing
to give a topological characterization of alternating links in thickened
surfaces\, extending the results of J. Greene and J. Howie.\n
LOCATION:https://stable.researchseminars.org/talk/ckvk_astrks/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Christopher Davis (University of Wisconsin-Eau Claire)
DTSTART:20210208T150000Z
DTEND:20210208T160000Z
DTSTAMP:20260404T095040Z
UID:ckvk_astrks/25
DESCRIPTION:Title: Links in homology spheres are homotopic to slice links - an ap
plication of the relative Whitney trick.\nby Christopher Davis (Univer
sity of Wisconsin-Eau Claire) as part of Classical knots\, virtual knots\,
and algebraic structures related to knots\n\n\nAbstract\nGeneralizing the
notion of sliceness for links in $S^3$\, a link in a homology sphere is c
alled slice if it bounds a disjoint union of locally flat embedded disks i
n a contractible 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 homotopi
c to the unlink. We prove that the same is true for links in homology sph
eres. Our argument passes through a novel geometric construction which we
call the relative Whitney trick. If time permits we will explore an appl
ication of the relative Whitney trick to the existence of Whitney towers.\
n
LOCATION:https://stable.researchseminars.org/talk/ckvk_astrks/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Benjamin Audoux (Aix-Marseille Université)
DTSTART:20210222T150000Z
DTEND:20210222T160000Z
DTSTAMP:20260404T095040Z
UID:ckvk_astrks/26
DESCRIPTION:Title: Cut-diagrams and a Chen--Milnor presentation result for knotte
d surfaces\nby Benjamin Audoux (Aix-Marseille Université) as part of
Classical knots\, virtual knots\, and algebraic structures related to knot
s\n\n\nAbstract\nIn this talk\, I will introduce cut-diagrams\, a combinat
orial data which generalizes welded links to higher dimensions. Using them
\, I will give and discuss then Chen-Milnor presentations for the nilpoten
t and reduced fundamental groups of knotted surfaces. This is joint work i
n progress with J-B. Meilhan and A. Yasuhara.\n
LOCATION:https://stable.researchseminars.org/talk/ckvk_astrks/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Carmen Caprau (California State University-Fresno)
DTSTART:20210301T150000Z
DTEND:20210301T160000Z
DTSTAMP:20260404T095040Z
UID:ckvk_astrks/27
DESCRIPTION:Title: Movie moves for singular link cobordisms in 4-dimensional spac
e\nby Carmen Caprau (California State University-Fresno) as part of Cl
assical knots\, virtual knots\, and algebraic structures related to knots\
n\n\nAbstract\nTwo singular links are cobordant if one can be obtained fro
m the other by singular link isotopy together with a combination of births
or deaths of simple unknotted curves\, and saddle point transformations.
A movie description of a singular link cobordism in 4-space is a sequence
of singular link diagrams obtained from a projection of the cobordism into
3-space by taking 2-dimensional cross sections perpendicular to a fixed d
irection. We present a set of movie moves that are sufficient to connect a
ny two movies of isotopic singular link cobordisms.\n
LOCATION:https://stable.researchseminars.org/talk/ckvk_astrks/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Miriam Kuzbary (Georgia Tech)
DTSTART:20210308T150000Z
DTEND:20210308T160000Z
DTSTAMP:20260404T095040Z
UID:ckvk_astrks/28
DESCRIPTION:Title: Pure Braids and Link Concordance\nby Miriam Kuzbary (Georg
ia Tech) as part of Classical knots\, virtual knots\, and algebraic struct
ures related to knots\n\n\nAbstract\nThe knot concordance group can be con
textualized as organizing problems about 3- and 4-dimensional spaces and t
he relationships between them. Every 3-manifold is surgery on some link\,
not necessarily a knot\, and thus it is natural to ask about such a group
for links. In 1988\, Le Dimet constructed the string link concordance grou
ps and in 1998\, Habegger and Lin precisely characterized these groups as
quotients of the link concordance sets using a group action. Notably\, the
knot concordance group is abelian while\, for each n\, the string link co
ncordance group on n strands is non-abelian as it contains the pure braid
group on n strands as a subgroup. In this talk\, I will discuss my result
the quotient of each string link concordance group by its pure braid subgr
oup is still non-abelian.\n
LOCATION:https://stable.researchseminars.org/talk/ckvk_astrks/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jean-Babtiste Meilhan (Université Grenoble Alpes)
DTSTART:20210322T140000Z
DTEND:20210322T150000Z
DTSTAMP:20260404T095040Z
UID:ckvk_astrks/29
DESCRIPTION:Title: Characterization(s) of the Reduced Peripheral System\nby J
ean-Babtiste Meilhan (Université Grenoble Alpes) as part of Classical kno
ts\, virtual knots\, and algebraic structures related to knots\n\n\nAbstra
ct\nThe reduced peripheral system was introduced by Milnor in the 50’s\n
for the study of links up to link-homotopy\, i.e. up to homotopies\nleavin
g distinct components disjoint. This invariant\, however\, fails\nto class
ify links up to link-homotopy for links of 4 or more\ncomponents. The purp
ose of this paper is to show that the topological\ninformation which is de
tected by Milnor’s reduced peripheral system is\nactually 4-dimensional.
We give a topological characterization in\nterms of ribbon solid tori in
4-space up to link-homotopy\, using a\nversion of Artin’s Spun construc
tion. The proof relies heavily on an\nintermediate characterization\, in t
erms of welded links up to\nself-virtualization\, providing hence a purely
topological application\nof the combinatorial theory of welded links.\n
LOCATION:https://stable.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:20260404T095040Z
UID:ckvk_astrks/31
DESCRIPTION:Title: The reductivity of a knot projection\nby Ayaka Shimizu (Na
tional Institute of Technology\, Gunma College\, Japan) as part of Classic
al knots\, virtual knots\, and algebraic structures related to knots\n\n\n
Abstract\nThe reductivity of a knot projection is defined to be the minimu
m number of splices required to make the projection reducible\, where the
splices are applied to a knot projection resulting in another knot project
ion. It has been shown that the reductivity is four or less for any knot p
rojection and shown that there are infinitely many knot projections with r
eductivity 0\, 1\, 2\, and 3. The "reductivity problem" is a problem askin
g the existence of a knot projection whose reductivity is four. In this ta
lk\, we will discuss some strategies for the reductivity problem focusing
on the region of a knot projection.\n
LOCATION:https://stable.researchseminars.org/talk/ckvk_astrks/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michael Klug (UC-Berkeley)
DTSTART:20210315T140000Z
DTEND:20210315T150000Z
DTSTAMP:20260404T095040Z
UID:ckvk_astrks/32
DESCRIPTION:Title: Arf invariants in low dimensions\nby Michael Klug (UC-Berk
eley) as part of Classical knots\, virtual knots\, and algebraic structure
s related to knots\n\n\nAbstract\nI will briefly discuss some work in prog
ress regarding a relationship between several different mod 2 invariants i
n dimensions 2\, 3\, and 4. In particular\, I will relate the Arf invarian
t of a knot\, the Arf invariant of a characteristic surface\, the Rochlin
invariant of a homology sphere\, and the Kirby-Siebenmann invariant of a 4
-manifold.\n
LOCATION:https://stable.researchseminars.org/talk/ckvk_astrks/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ilya Kofman (CUNY)
DTSTART:20201130T150000Z
DTEND:20201130T160000Z
DTSTAMP:20260404T095040Z
UID:ckvk_astrks/33
DESCRIPTION:Title: A volumish theorem for virtual links\nby Ilya Kofman (CUNY
) as part of Classical knots\, virtual knots\, and algebraic structures re
lated to knots\n\n\nAbstract\nDasbach and Lin proved a “volumish theorem
” for alternating links. We prove the analogue for alternating link diag
rams on surfaces\, which provides bounds on the hyperbolic volume of a lin
k in a thickened surface in terms of coefficients of its reduced Jones-Kru
shkal polynomial. Joint work with Abhijit Champanerkar.\n
LOCATION:https://stable.researchseminars.org/talk/ckvk_astrks/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Akira Yasuhara (Waseda University)
DTSTART:20210419T140000Z
DTEND:20210419T150000Z
DTSTAMP:20260404T095040Z
UID:ckvk_astrks/34
DESCRIPTION:Title: Arrow calculus for welded links\nby Akira Yasuhara (Waseda
University) as part of Classical knots\, virtual knots\, and algebraic st
ructures related to knots\n\n\nAbstract\nWe develop a calculus for diagram
s of knotted objects. We define arrow presentations\, which encode the cro
ssing information of a diagram into arrows in a way somewhat similar to Ga
uss diagrams\, and more generally w–tree presentations\, which can be se
en as “higher-order Gauss diagrams”. This arrow calculus is used to de
velop an analogue of Habiro’s clasper theory for welded knotted objects\
, which contain classical link diagrams as a subset. This provides a “re
alization” of Polyak’s algebra of arrow diagrams at the welded level\,
and leads to a characterization of finite- type invariants of welded knot
s and long knots. \nThis is a joint work with Jean-Baptiste Meilhan (Unive
rsity of Grenoble Alpes).\n
LOCATION:https://stable.researchseminars.org/talk/ckvk_astrks/34/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kodai Wada (Kobe University)
DTSTART:20210531T140000Z
DTEND:20210531T150000Z
DTSTAMP:20260404T095040Z
UID:ckvk_astrks/35
DESCRIPTION:Title: Classification of string links up to $2n$-moves and link-homot
opy\nby Kodai Wada (Kobe University) as part of Classical knots\, virt
ual knots\, and algebraic structures related to knots\n\n\nAbstract\nIn th
is talk\, we give a necessary and sufficient condition for two string link
s to be equivalent up to $2n$-moves and link-homotopy in terms of Milnor i
nvariants. This reveals a relation between Milnor invariants and $2n$-move
s. This is a joint work with Haruko Miyazawa and Akira Yasuhara.\n
LOCATION:https://stable.researchseminars.org/talk/ckvk_astrks/35/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Boris Colombari (Aix-Marseille Université)
DTSTART:20210607T140000Z
DTEND:20210607T150000Z
DTSTAMP:20260404T095040Z
UID:ckvk_astrks/36
DESCRIPTION:Title: Classification of welded links and welded string links up to $
w_q$-concordance\nby Boris Colombari (Aix-Marseille Université) as pa
rt of Classical knots\, virtual knots\, and algebraic structures related t
o 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 welded analogue of the $C_k$-concordance on classical links coming from
the clasper calculus introduced by K. Habiro. In this talk I will present
a classification of welded string links (resp. welded links) up to $w_q$-c
oncordance by their Milnor invariants (resp. by their q-nilpotent peripher
al system). I will compare these results to the classification of classica
l links up to $C_k$-concordance obtained by J. Conant\, R. Schneiderman an
d P. Teichner before introducing the relevant invariants on welded objects
. I will give elements of the proof of my results using a version of arrow
calculus adapted to the representation of welded objects by Gauss diagram
s.\n
LOCATION:https://stable.researchseminars.org/talk/ckvk_astrks/36/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sam Nelson (Claremont McKenna University)
DTSTART:20210517T140000Z
DTEND:20210517T150000Z
DTSTAMP:20260404T095040Z
UID:ckvk_astrks/37
DESCRIPTION:Title: Region coloring invariants for knots\nby Sam Nelson (Clare
mont McKenna University) as part of Classical knots\, virtual knots\, and
algebraic structures related to knots\n\n\nAbstract\nIn this talk we will
survey some region-coloring structures for knots (Niebrzydowski tribracket
s\, virtual tribrackets\, multitribrackets and psybrackets) and related st
ructures and see applications to counting invariants and enhancement as we
ll as some applications to music.\n
LOCATION:https://stable.researchseminars.org/talk/ckvk_astrks/37/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Zhiyun Cheng (Beijing Normal University)
DTSTART:20210726T140000Z
DTEND:20210726T150000Z
DTSTAMP:20260404T095040Z
UID:ckvk_astrks/39
DESCRIPTION:Title: Chord index type invariants of virtual knots\nby Zhiyun Ch
eng (Beijing Normal University) as part of Classical knots\, virtual knots
\, and algebraic structures related to knots\n\n\nAbstract\nAs an extensio
n of classical knot theory\, virtual knot theory studies the embeddings of
one sphere in thickened surfaces up to stable equivalence. Roughly speaki
ng\, there are two kinds of virtual knot invariants\, the first kind comes
from knot invariants of classical knots but the second kind usually vanis
hes on classical knots. Most of the second kind of virtual knot invariants
are defined by using the chord parity or chord index. In this talk\, I wi
ll report some recent progress on virtual knot invariants derived from var
ious chord indices.\n
LOCATION:https://stable.researchseminars.org/talk/ckvk_astrks/39/
END:VEVENT
BEGIN:VEVENT
SUMMARY:William Rushworth (McMaster University)
DTSTART:20210705T140000Z
DTEND:20210705T150000Z
DTSTAMP:20260404T095040Z
UID:ckvk_astrks/41
DESCRIPTION:Title: Minimal crossing number implies minimal supporting genus\n
by William Rushworth (McMaster University) as part of Classical knots\, vi
rtual knots\, and algebraic structures related to knots\n\n\nAbstract\nWe
prove that a minimal crossing virtual link diagram is a minimal genus diag
ram. That is\, the genus of its Carter surface realizes the supporting gen
us of the virtual link represented by the diagram. The result is obtained
by introducing a new parity theory for virtual links. This answers a basic
question in virtual knot theory\, and recovers the corresponding result o
f Manturov in the case of virtual knots. Joint work with Hans Boden.\n
LOCATION:https://stable.researchseminars.org/talk/ckvk_astrks/41/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Zsuzsanna Dancso (The University of Sydney)
DTSTART:20210921T140000Z
DTEND:20210921T150000Z
DTSTAMP:20260404T095040Z
UID:ckvk_astrks/42
DESCRIPTION:Title: Welded Tangles and the Kashiwara-Vergne Groups\nby Zsuzsan
na Dancso (The University of Sydney) as part of Classical knots\, virtual
knots\, and algebraic structures related to knots\n\n\nAbstract\nIn this t
alk I will explain a general method of "translating" between a certain typ
e of problem in topology\, and solving equations in graded spaces in (quan
tum) algebra. I'll talk through several applications of this method from t
he 90's to today: Drinfel'd associators and parenthesised braids\, Grothen
dieck-Teichmuller groups\, welded tangles and the Alekseev-Enriquez-Toross
ian formulation of the Kashiwara-Vergne equations\, and most recently\, a
topological description of the Kashiwara-Vergne groups. The "recent" porti
on of the talk is based on joint work with Iva Halacheva and Marcy Roberts
on (arXiv: 2106.02373)\, and joint work with Dror Bar-Natan (arXiv: 1405.1
955).\n
LOCATION:https://stable.researchseminars.org/talk/ckvk_astrks/42/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eva Horvat (University of Ljubljana)
DTSTART:20211005T140000Z
DTEND:20211005T150000Z
DTSTAMP:20260404T095040Z
UID:ckvk_astrks/43
DESCRIPTION:Title: Flattening knotted surfaces\nby Eva Horvat (University of
Ljubljana) as part of Classical knots\, virtual knots\, and algebraic stru
ctures 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 po
ints coincides with a hyperbolic diagram of $\\mathcal{K}$. We apply such
projections\, called flattenings\, to define three invariants of embedded
surfaces: the width\, the trunk and the partition number. These invariants
are studied for some families of embedded surfaces.\n
LOCATION:https://stable.researchseminars.org/talk/ckvk_astrks/43/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ben McCarty (University of Memphis)
DTSTART:20211102T140000Z
DTEND:20211102T150000Z
DTSTAMP:20260404T095040Z
UID:ckvk_astrks/44
DESCRIPTION:Title: Khovanov homology for virtual links\nby Ben McCarty (Unive
rsity of Memphis) as part of Classical knots\, virtual knots\, and algebra
ic structures related to knots\n\n\nAbstract\nShortly after Khovanov homol
ogy for classical knots and links was developed in the late 90s\, Bar-Nata
n produced a Mathematica program for computing it from a planar diagram. Y
et when Manturov defined Khovanov homology for virtual links in 2007\, a p
rogram for computing it did not appear until Tubbenhauer's 2012 paper. Eve
n then\, the theoretical framework used was quite different from the one M
anturov described. In this talk\, we describe a theoretical framework for
computing the Khovanov homology of a virtual link\, synthesized from work
by Manturov\, Dye-Kaestner-Kauffman and others. We also show how to use th
is framework to create a program for computing the Khovanov homology of a
virtual link\, which is directly based upon Bar-Natan's original program f
or classical links. This program is joint work with Scott Baldridge\, Hea
ther Dye\, Aaron Kaestner\, and Lou Kauffman.\n
LOCATION:https://stable.researchseminars.org/talk/ckvk_astrks/44/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Melissa Zhang (University of Georgia)
DTSTART:20211117T150000Z
DTEND:20211117T160000Z
DTSTAMP:20260404T095040Z
UID:ckvk_astrks/45
DESCRIPTION:Title: Constructions toward topological applications of U(1) x U(1) e
quivariant Khovanov homology\nby Melissa Zhang (University of Georgia)
as part of Classical knots\, virtual knots\, and algebraic structures rel
ated to knots\n\n\nAbstract\nIn 2018\, Khovanov and Robert introduced a ve
rsion of Khovanov homology over a larger ground ring\, termed U(1)xU(1)-eq
uivariant Khovanov homology. This theory was also studied extensively by T
aketo Sano. Ross Akhmechet was able to construct an equivariant annular Kh
ovanov homology theory using the U(1)xU(1)-equivariant theory\, while the
existence of a U(2)-equivariant annular construction is still unclear.\n \
nObserving that the U(1)xU(1) complex admits two symmetric algebraic gradi
ngs\, those familiar with knot Floer homology over the ring F[U\,V] may na
turally ask if these filtrations allow for algebraic constructions already
seen in the knot Floer context\, such as Ozsváth-Stipsicz-Szabó's Upsil
on. In this talk\, I will describe the construction and properties of such
an invariant. I will also discuss some ideas on how future research migh
t use the U(1)xU(1) framework to identify invariants similar to those cons
tructed from knot Floer homology over F[U\,V]\, and speculate on the topol
ogical information these constructions might illuminate.\n \nThis is based
on joint work with Ross Akhmechet.\n
LOCATION:https://stable.researchseminars.org/talk/ckvk_astrks/45/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jose Ceniceros (Hamilton College)
DTSTART:20210907T140000Z
DTEND:20210907T150000Z
DTSTAMP:20260404T095040Z
UID:ckvk_astrks/46
DESCRIPTION:Title: Cocycle Enhancements of Psyquandle Counting Invariants\nby
Jose Ceniceros (Hamilton College) as part of Classical knots\, virtual kn
ots\, and algebraic structures related to knots\n\n\nAbstract\nIn this tal
k we discuss pseudoknots and singular knots. Specifically\, we discuss psy
quandles and their application to oriented pseudoknots and oriented singul
ar knots. Additionally\, we bring cocycle enhancement theory to the case o
f psyquandles to define enhancements of the psyquandle counting invariant
via pairs of a biquandle 2-cocycle and a new function. As an application\,
we define a single-variable polynomial invariant of both oriented pseudok
nots and oriented singular knots.\n
LOCATION:https://stable.researchseminars.org/talk/ckvk_astrks/46/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jason Joseph (Rice University)
DTSTART:20211019T140000Z
DTEND:20211019T150000Z
DTSTAMP:20260404T095040Z
UID:ckvk_astrks/47
DESCRIPTION:Title: Meridional rank and bridge numbers of knotted surfaces and wel
ded knots\nby Jason Joseph (Rice University) as part of Classical knot
s\, virtual knots\, and algebraic structures related to knots\n\n\nAbstrac
t\nThe meridional rank conjecture (MRC) posits that the meridional rank of
a classical knot is equal to its bridge number. In this talk we investiga
te whether or not this is a reasonable conjecture for knotted surfaces and
welded knots. In particular\, we find criteria to establish the equality
of these values for several large families. On the flip side\, we examine
the behavior of meridional rank of knotted spheres under connected sum\, a
nd\, using examples first studied by Kanenobu\, show that any value betwee
n the theoretical limits can be achieved. This means that either the MRC i
s false for knotted spheres\, or that their bridge number fails to be (-1)
-additive. This is joint work with Puttipong Pongtanapaisan.\n
LOCATION:https://stable.researchseminars.org/talk/ckvk_astrks/47/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marithania Silvero (Universidad de Sevilla)
DTSTART:20211207T150000Z
DTEND:20211207T160000Z
DTSTAMP:20260404T095040Z
UID:ckvk_astrks/48
DESCRIPTION:Title: Khomotopy type via simplicial complexes and presimplicial sets
\nby Marithania Silvero (Universidad de Sevilla) as part of Classical
knots\, virtual knots\, and algebraic structures related to knots\n\n\nAbs
tract\nAt the end of the past century\, Mikhail Khovanov introduced the fi
rst homological invariant\, now known as Khovanov homology\, as a categori
fication of Jones polynomial. It is a bigraded homology supported in homol
ogical and quantum gradings. Given a link diagram\, we refer to the maxima
l (resp. second-to-maximal) quantum grading such that the associated Khova
nov complex is non-trivial as extreme (resp. almost extreme) grading. \n\
nIn this talk we present a new approach to the geometrization of Khovanov
homology in terms of simplicial complexes and presimplicial sets\, for the
extreme and almost-extreme gradings\, respectively. We also study the rel
ations of these models with Khovanov spectra\, introducec by Robert Lipshi
tz and Sucharit Sarkar as a spatial refinement of Khovanov homology.\n
LOCATION:https://stable.researchseminars.org/talk/ckvk_astrks/48/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Joseph Boninger (CUNY)
DTSTART:20220111T150000Z
DTEND:20220111T160000Z
DTSTAMP:20260404T095040Z
UID:ckvk_astrks/49
DESCRIPTION:Title: The Jones Polynomial from a Goeritz Matrix\nby Joseph Boni
nger (CUNY) as part of Classical knots\, virtual knots\, and algebraic str
uctures related to knots\n\n\nAbstract\nThe Jones polynomial holds a centr
al place in knot theory\, but its topological meaning is not well understo
od—it remains an open problem\, posed by Atiyah\, to give a three-dimens
ional interpretation of the polynomial. In this talk\, we’ll share an or
iginal construction of the Jones polynomial from a Goeritz matrix\, a comb
inatorial object with topological significance. In the process we extend t
he Kauffman bracket to any symmetric\, integer matrix\, with applications
to links in thickened surfaces. Matroid theory plays a role.\n
LOCATION:https://stable.researchseminars.org/talk/ckvk_astrks/49/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rima Chaterjee (University of Cologne)
DTSTART:20220125T150000Z
DTEND:20220125T160000Z
DTSTAMP:20260404T095040Z
UID:ckvk_astrks/50
DESCRIPTION:Title: Knots in overtwisted contact manifolds\nby Rima Chaterjee
(University of Cologne) as part of Classical knots\, virtual knots\, and a
lgebraic structures related to knots\n\n\nAbstract\nKnots associated to ov
ertwisted manifolds are less explored.\nThere are two types of knots in an
overtwisted manifold - loose and\nnon-loose. Non-loose knots are knots wi
th tight complements where as\nloose knots have overtwisted complements. W
hile we understand loose\nknots\, non-loose knots remain a mystery. The cl
assification and\nstructure problems of these knots vary greatly compared
to the knots\nin tight manifolds. In this talk\, I'll give a brief survey
followed by \nsome interesting recent work. Especially I'll show how satel
lite\noperations on a knot in overtwisted manifold changes the geometric\n
property of the knot. I will discuss under what\nconditions cabling operat
ion on a non-loose knot preserves\nnon-looseness. The ''recent part'' of t
his talk is based on joint work \nwith Etnyre\, Min and Mukherjee.\n
LOCATION:https://stable.researchseminars.org/talk/ckvk_astrks/50/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Fara Renaud (Université Catholique de Louvain)
DTSTART:20220329T140000Z
DTEND:20220329T150000Z
DTSTAMP:20260404T095040Z
UID:ckvk_astrks/51
DESCRIPTION:Title: Higher coverings of racks and quandles\nby Fara Renaud (Un
iversité Catholique de Louvain) as part of Classical knots\, virtual knot
s\, and algebraic structures related to knots\n\n\nAbstract\nThis talk is
based on a series of papers called \\textit{Higher coverings of racks and
quandles}. This project is rooted in M. Eisermann’s work on quandle cove
rings\, and the categorical perspective brought to the subject by V. Even\
, who characterizes quandle coverings as those surjections which are \\emp
h{central}\, relatively to trivial quandles. We revisit and extend this wo
rk by applying the techniques from higher categorical Galois theory\, in t
he sense of G. Janelidze.\n\nIn these articles we consolidate the understa
nding of rack and quandle coverings' relationship with central extensions
of groups on the one hand and topological coverings on the other. We furth
er identify and study a meaningful two-dimensional (and higher-dimensional
) centrality condition defining our double coverings of racks and quandles
(and higher coverings of arbitrary dimension). We also introduce a suitab
le commutator which describes the zero\, one and two-dimensional concepts
of centralization in this context.\n\nThese results provide new tools to s
tudy racks and quandles\, with potential applications to the development o
f homology theory and homotopy theory in this context. From the perspectiv
e of category theory\, they provide a new context of application for highe
r Galois theory.\n\nIn this talk\, I would like to summarize some of this
material\, to share it with an audience which is familiar with knot theory
\, and which is potentially interested in trying out those concepts in the
ir own field of study.\n
LOCATION:https://stable.researchseminars.org/talk/ckvk_astrks/51/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jagdeep Basi (California State University-Fresno)
DTSTART:20220308T150000Z
DTEND:20220308T160000Z
DTSTAMP:20260404T095040Z
UID:ckvk_astrks/52
DESCRIPTION:Title: Quandle Coloring Quivers of (p\,2)-Torus Knots and Links\n
by Jagdeep Basi (California State University-Fresno) as part of Classical
knots\, virtual knots\, and algebraic structures related to knots\n\n\nAbs
tract\nA quandle coloring quiver is a quiver structure\, introduced by Kar
ina Cho and Sam Nelson\, and defined on the set of quandle colorings of an
oriented 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 re
spect to dihedral quandles.\n
LOCATION:https://stable.researchseminars.org/talk/ckvk_astrks/52/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kate Petersen (University of Minnesota Duluth)
DTSTART:20220322T140000Z
DTEND:20220322T150000Z
DTSTAMP:20260404T095040Z
UID:ckvk_astrks/53
DESCRIPTION:Title: PSL(2\,C) representations of knot groups\nby Kate Petersen
(University of Minnesota Duluth) as part of Classical knots\, virtual kno
ts\, and algebraic structures related to knots\n\n\nAbstract\nI will discu
ss a method of producing defining equations for representation varieties o
f the canonical component of a knot group into PSL2(C). This method uses o
nly a knot diagram satisfying a mild restriction and is based upon the und
erlying geometry of the knot complement. In particular\, it does not invo
lve any polyhedral decomposition or triangulation of the link complement.
This results in a simple algorithm that can often be performed by hand\, a
nd in many cases\, for an infinite family of knots at once. This is joint
work with Anastasiia Tsvietkova.\n
LOCATION:https://stable.researchseminars.org/talk/ckvk_astrks/53/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Oscar Ocampo (Universidade Federal da Bahia)
DTSTART:20220405T140000Z
DTEND:20220405T150000Z
DTSTAMP:20260404T095040Z
UID:ckvk_astrks/54
DESCRIPTION:Title: Virtual braid groups\, virtual twin groups and crystallographi
c groups\nby Oscar Ocampo (Universidade Federal da Bahia) as part of C
lassical knots\, virtual knots\, and algebraic structures related to knots
\n\n\nAbstract\nLet $n\\ge 2$. Let $VB_n$ (resp. $VP_n$) be the virtual br
aid group (resp. the pure virtual braid group)\, and let $VT_n$ (resp. $PV
T_n$) be the virtual twin group (resp. the pure virtual twin group). Let $
\\Pi$ be 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 this talk\, we show that $\\Pi$ is a crystallographic group and then
and then we explore some of its properties\, such as: characterization of
finite order elements and its conjugacy classes\, and also the realization
of some Bieberbach groups and infinite virtually cyclic groups. Finally\,
we also consider other braid-like groups (welded\, unrestricted\, flat vi
rtual\, flat welded and Gauss virtual braid group) module the respective c
ommutator subgroup in each case.\n\nJoint work with Paulo Cesar Cerqueira
dos Santos Júnior (arXiv: 2110.02392)\n
LOCATION:https://stable.researchseminars.org/talk/ckvk_astrks/54/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mehander Singh (IISER)
DTSTART:20220510T140000Z
DTEND:20220510T150000Z
DTSTAMP:20260404T095040Z
UID:ckvk_astrks/55
DESCRIPTION:Title: Planar knots and related groups\nby Mehander Singh (IISER)
as part of Classical knots\, virtual knots\, and algebraic structures rel
ated to knots\n\n\nAbstract\nStudy of stable isotopy classes of a finite c
ollection of immersed circles without triple or higher intersections on cl
osed oriented surfaces can be thought of as a planar analogue of virtual k
not theory where the sphere case corresponds to the classical knot theory.
It is intriguing to know which class of groups serves the purpose that Ar
tin braid groups serve in classical knot theory. Khovanov proved that twin
groups\, a class of right angled Coxeter groups with only far commutativi
ty relations\, serves the purpose for the sphere case. In a recent work we
showed that an appropriate class of groups called virtual twin groups fit
s into a virtual analogue of the planar knot theory. The talk will give an
overview of some recent topological and group theoretic developments alon
g these lines.\n
LOCATION:https://stable.researchseminars.org/talk/ckvk_astrks/55/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jessica Purcell (Monash University)
DTSTART:20220315T140000Z
DTEND:20220315T150000Z
DTSTAMP:20260404T095040Z
UID:ckvk_astrks/56
DESCRIPTION:Title: Geometry of alternating links on surfaces\nby Jessica Purc
ell (Monash University) as part of Classical knots\, virtual knots\, and a
lgebraic structures related to knots\n\n\nAbstract\nIt is typically hard t
o relate the geometry of a knot complement to a diagram of the knot\, but
over many years mathematicians have been able to relate geometric properti
es of classical alternating knots to their diagrams. Recently\, we have mo
dified these techniques to investigate geometry of a much wider class of k
nots\, namely alternating knots with diagrams on general surfaces embedded
in general 3-manifolds. This has resulted in lower bounds on volumes\, in
formation on the geometry of checkerboard surfaces\, restrictions on excep
tional Dehn fillings\, and other geometric properties. However\, we were u
nable to extend upper volume bounds broadly. In fact\, recently we showed
an upper bound must depend on the 3-manifold in which the knot is embedded
: We find upper bounds for virtual knots\, but not for other families. We
will discuss this work\, and some remaining open questions. This is joint
in part with Josh Howie and in part with Effie Kalfagianni.\n
LOCATION:https://stable.researchseminars.org/talk/ckvk_astrks/56/
END:VEVENT
END:VCALENDAR