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BEGIN:VEVENT
SUMMARY:Lou Kauffman
DTSTART:20230715T150000Z
DTEND:20230715T160000Z
DTSTAMP:20260422T225638Z
UID:IntMathCircle/1
DESCRIPTION:Title: Introduction to Combinatorial Knot Theory\nby Lou Kauffman as pa
rt of International math circle\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/IntMathCircle/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Scott Baldridge
DTSTART:20230730T123000Z
DTEND:20230730T140000Z
DTSTAMP:20260422T225638Z
UID:IntMathCircle/2
DESCRIPTION:Title: The strange fascination physicists have had with the 4-Color Theorem
and why their fascination may be justified\nby Scott Baldridge as par
t of International math circle\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/IntMathCircle/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vladlen Timorin
DTSTART:20230806T123000Z
DTEND:20230806T133000Z
DTSTAMP:20260422T225638Z
UID:IntMathCircle/3
DESCRIPTION:Title: (Self-)similarity in mathematics\nby Vladlen Timorin as part of
International math circle\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/IntMathCircle/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Roger Fenn
DTSTART:20230813T153000Z
DTEND:20230813T163000Z
DTSTAMP:20260422T225638Z
UID:IntMathCircle/4
DESCRIPTION:Title: Planar Doodles: properties\, codes and tables\nby Roger Fenn as
part of International math circle\n\n\nAbstract\nThis is joint work with A
ndy Bartholomew which started as an investigation into the possibilities o
f cataloguing doodles on the plane or sphere. As the work progressed more
properties were discovered which led us to divide the doodles by connectiv
ity. The second most connected are called prime and the most connected are
called super prime. The word prime suggests that the doodle is not a sum
and this is necessary by the Kishino effect which also occurs for virtual
knots. The super prime doodles have a hamiltonian circuit by a theorem of
Tutte. Whether this condition extends to other doodles is unknown to us\,
but it does mean that super prime doodles have a simple code using this cy
cle.\n
LOCATION:https://researchseminars.org/talk/IntMathCircle/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Aleksey Glibichuk
DTSTART:20230827T123000Z
DTEND:20230827T133000Z
DTSTAMP:20260422T225638Z
UID:IntMathCircle/5
DESCRIPTION:Title: Point-line incidences and their applications\nby Aleksey Glibich
uk as part of International math circle\n\n\nAbstract\nI'll give a proof o
f the Szemeredi - Trotter theorem which gives optimal up to constants boun
d for number of point - line incidences. I'll also give several interestin
g applications of this theorem\, including application to so-called sum-pr
oduct estimates.\n
LOCATION:https://researchseminars.org/talk/IntMathCircle/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ilya Mednykh
DTSTART:20230903T123000Z
DTEND:20230903T133000Z
DTSTAMP:20260422T225638Z
UID:IntMathCircle/6
DESCRIPTION:Title: Some spectral invariants of circulant graphs\nby Ilya Mednykh as
part of International math circle\n\n\nAbstract\nThe report is devoted to
investigation of some spectral invariants of a family of circulant graphs
. The invariants are: number of spanning trees (or complexity of a graph)\
, number of rooted spanning forests and Kirchhoff index. They all can be e
xpressed through eigenvalues of Laplacian (or Kirchhoff) matrix for a give
n graph.\n
LOCATION:https://researchseminars.org/talk/IntMathCircle/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lou Kauffman (University of Illinois at Chicago)
DTSTART:20230910T130000Z
DTEND:20230910T140000Z
DTSTAMP:20260422T225638Z
UID:IntMathCircle/7
DESCRIPTION:Title: Introduction to Knot Invariants - Linking Numbers and Coloring Knot
Diagrams\nby Lou Kauffman (University of Illinois at Chicago) as part
of International math circle\n\n\nAbstract\nWe will discuss how to find li
nking numbers to show that curves can be topologically linked\, and we wil
l show how to color knot and link diagrams to show further properties of k
notting and linking. This talk is related to our previous talk about knot
diagrams\, but the present talk will be self-contained.\n
LOCATION:https://researchseminars.org/talk/IntMathCircle/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Amit Kumar
DTSTART:20230917T140000Z
DTEND:20230917T150000Z
DTSTAMP:20260422T225638Z
UID:IntMathCircle/8
DESCRIPTION:Title: Graph coloring via defect TQFT\nby Amit Kumar as part of Interna
tional math circle\n\n\nAbstract\nOn the most intuitive level\, defects ar
e subsets of a space-time or a material where something special is going o
n. They are defective in the sense that the theory that governs them is di
fferent than the theory that governs the rest of the space. A topological
defect is a defect that does not depend on metric. The theme of our work i
s the interpretation of an embedded graph as a defect\, which facilitates
the TQFT with defect to capture that number of ways a trivalent graph can
be colored. In the process we construct a surface with defect for a given
group and thus extending the work of Turaev (1999) in certain special case
s.\n
LOCATION:https://researchseminars.org/talk/IntMathCircle/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anna Taranenko
DTSTART:20231001T080000Z
DTEND:20231001T090000Z
DTSTAMP:20260422T225638Z
UID:IntMathCircle/9
DESCRIPTION:Title: Latin squares\, latin hypercubes and their transversal\nby Anna
Taranenko as part of International math circle\n\n\nAbstract\nA latin squa
re of order n is an nxn table filled by n symbols so that each symbol appe
ar in each line exactly once\, and a transversal in a latin square is its
diagonal hitting each symbol exactly ones. Natural multidimensional genera
lizations of latin squares are known as latin hypercubes. In this talk we
overview most important results and open problems on transversals in latin
squares and hypercubes.\n
LOCATION:https://researchseminars.org/talk/IntMathCircle/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mehdi Golafshan (University of Liège\, Belgium)
DTSTART:20231008T123000Z
DTEND:20231008T133000Z
DTSTAMP:20260422T225638Z
UID:IntMathCircle/10
DESCRIPTION:Title: A generalization of the binomial coefficients by words\nby Mehd
i Golafshan (University of Liège\, Belgium) as part of International math
circle\n\n\nAbstract\nA word w being given it is easy to compute the set
of its subwords and their multiplicity\; this computation is obtained by a
simple induction formula. The main problem of interest in this talk\, som
etimes implicitly but more often explicitly\, is the one of the inverse co
rrespondence. Under what conditions is a given set of words S the set of s
ubwords\, or a subset of certain kind of the set of subwords\, of a word w
? Once these conditions are met\, what are the words w that are thus deter
mined? In which cases are they uniquely determined? Some of these conditio
ns on that set S are rather obvious. For instance if u is a subword ofw\,
then any subword of u is a subword of w. Some conditions are more subtle\;
if for instance a and b are two letters of A\, and if ab and ba are subwo
rds of w\, then at least one of the two words aba and bab is also a subwor
d of w. In fact\, we shall consider the subwords with their multiplicity.
It is possible to give a complete set of equations that express those rela
tions.\n
LOCATION:https://researchseminars.org/talk/IntMathCircle/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vassily O. Manturov
DTSTART:20231022T123000Z
DTEND:20231022T133000Z
DTSTAMP:20260422T225638Z
UID:IntMathCircle/11
DESCRIPTION:Title: The photography method\nby Vassily O. Manturov as part of Inter
national math circle\n\n\nAbstract\nWe formulate a general method allowing
one to\n1) solve various equations\n2) construct invariants of topologica
l objects\nby using some very general notion of data and data transmission
law.\n \nBy data we mean\, say\, objects of geometric origin (lengths\,
areas\, etc.)\,\nby data transmission law we mean some equations rewriting
the data given in\none system of coordinates in terms of some other syste
m of coordinates\n(one key example is the Ptolemy equation).\n \nSuch con
siderations allow one to solve various equations ``for free''.\nWe shall c
oncentrate on obtaining invariants of braids 3-manifolds and 4-manifolds\,
\nsolutions to the pentagon equaitons and representations of groups G_{n}^
{3}.\n \nThis photography method ties together many branches in mathemati
cs\; in particular\,\nour data transmission law is naturally related to se
e mutations in cluster algebras.\n \nMany known invariants (or their modi
fications) like Turaev-Viro(-like) invariants\,\nDijkgraaf-Witten-like inv
ariants etc. turn out to be partial cases of the photography\nmethod (and
its slight generalisation).\n \nThis is a joint work with L.H.Kauffman\,
I.M.Nikonov\, S.Kim\, and Z.Wan.\n \nhttps://arxiv.org/abs/2305.06316\n
\nhttps://arxiv.org/pdf/2305.11945.pdf\n \nhttps://arxiv.org/abs/2306.070
79\n \nhttps://arxiv.org/abs/2307.03437\n \nhttps://arxiv.org/abs/2309.0
1735\n
LOCATION:https://researchseminars.org/talk/IntMathCircle/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Louis H Kauffman
DTSTART:20231029T130000Z
DTEND:20231029T140000Z
DTSTAMP:20260422T225638Z
UID:IntMathCircle/12
DESCRIPTION:Title: Untying Knots via Self-Repulsion Fields\nby Louis H Kauffman as
part of International math circle\n\n\nAbstract\nCoating a knot with elec
trical charge could create a topological entity that would try to repel it
self and find an energy-minimal position in space.\nComputer modeling allo
ws experiments with this idea\, and we can try to see if such self-repelli
ng fields will help unknot knots that are not knotted.\nThis talk will hav
e demonstrations that such methods of unknotting sometimes work and someti
mes do not work. We give systematic classes of examples by using \nrationa
l knots and tangles that give such models great difficulties in unknotting
. The talk will have a self-contained exposition of the Conway theory of r
ational tangles and their fractions. This is a very beautiful interface be
tween the properties of tangles and the properties of continued fractions.
We will even locate the “Eternal Golden Braid”\nso long-sought since
the time of Hofstadter. (I refer to the book by Douglas Hofstadter “Goe
del\, Escher\, Bach - An Eternal Golden Braid”.)\n
LOCATION:https://researchseminars.org/talk/IntMathCircle/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Louis H Kauffman (University of Illinois at Chicago)
DTSTART:20231119T140000Z
DTEND:20231119T150000Z
DTSTAMP:20260422T225638Z
UID:IntMathCircle/13
DESCRIPTION:Title: Introduction to Knotoids\nby Louis H Kauffman (University of Il
linois at Chicago) as part of International math circle\n\n\nAbstract\nA k
notoid is an equivalence class of knotoid diagrams under Reidemeister move
s. A knotoid diagram is a tangle diagram with two ends. The ends do not ha
ve to be in the same region.\nReidemeister moves are not allowed to pass a
rcs across endpoints. Knotoids were defined by Vladimir Turaev. \nThis tal
k will explain how the theory of knotoids (and more general linkoids and m
ultiknotoids) works\, how we use virtual knot theory to study knotoids\, h
ow knotoids can be interpreted geometrically in terms of embedded graphs a
nd some of their applications. The work we discuss is joint work with Nesl
ihan Gugumcu\, Sofia Lambropoulou\, Eleni Panagiotou and Kasturi Barkataki
.\n
LOCATION:https://researchseminars.org/talk/IntMathCircle/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hayk Sedrakyan
DTSTART:20231126T123000Z
DTEND:20231126T133000Z
DTSTAMP:20260422T225638Z
UID:IntMathCircle/14
DESCRIPTION:Title: Interconnected-distance formulas and their applications\nby Hay
k Sedrakyan as part of International math circle\n\n\nAbstract\nWe provide
novel interconnected-distance formulas and discuss their applications. Th
is topic remains widely open\, as no such interconnected-distance formulas
exist when we increase the number of points\, or if we consider the point
s in three-dimensional space.\n
LOCATION:https://researchseminars.org/talk/IntMathCircle/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Louis H Kauffman
DTSTART:20231203T140000Z
DTEND:20231203T150000Z
DTSTAMP:20260422T225638Z
UID:IntMathCircle/15
DESCRIPTION:Title: Introduction to Quantum Link Invariants\nby Louis H Kauffman as
part of International math circle\n\n\nAbstract\nThis will be an elementa
ry introduction to quantum link invariants\, based on generalized Reidemei
ster moves for link diagrams in Morse form.\nWe emphasize how to convert s
uch a diagram to an abstract tensor diagram in the sense of Penrose so tha
t the contraction of this tensor is an invariant of regular isotopy.\nWe w
ill discuss how this approach to quantum link invariants is related to cat
egorical formulations and to the finding of solutions to the Yang-Baxter e
quation\, and if time permits\nwith the structure of Hopf algebras.\n
LOCATION:https://researchseminars.org/talk/IntMathCircle/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Maximilian Wolfensberger
DTSTART:20231210T143000Z
DTEND:20231210T153000Z
DTSTAMP:20260422T225638Z
UID:IntMathCircle/16
DESCRIPTION:Title: Alternative to Heron's and Bretschenider's Formula\nby Maximili
an Wolfensberger as part of International math circle\n\n\nAbstract\nWe pr
ovide a novel form of Heron's formula and a novel form of Bretschneider's
formula. We provide several applications illustrating what is the advantag
e of these novel forms over the standard forms. Moreover\, written in this
form we see an obvious link between the area formulas of different shapes
and this allows us to state a conjecture for expressing the area of any p
entagon (or any other polygon) using its side lengths and the lengths of s
ome of its diagonals.\n
LOCATION:https://researchseminars.org/talk/IntMathCircle/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:V. A. Stukopin
DTSTART:20231217T143000Z
DTEND:20231217T153000Z
DTSTAMP:20260422T225638Z
UID:IntMathCircle/17
DESCRIPTION:Title: Quantum (super)algebras: foundations and applications\nby V. A.
Stukopin as part of International math circle\n\n\nAbstract\nI’m going
to talk about the basic constructions of the theory of quantum\nalgebras (
quantum groups). The quantum group is a Hopf algebra\, appearing as a quan
tization or flat deformation of a Lie bialgebra. I will also talk about a
graded version of this theory\, the theory of quantum supergroups\, as wel
l as an important class of quantum groups\, namely\, triangular (quasitria
ngular\, braided) quantum groups\, associated with the quantum Yang-Baxter
equation. We will also talk about the classical version of the theory of
quantum algebras\,\nnamely the theory of Lie bialgebras. If there is time\
, I might talk about the representation theory of these objects\, as well
as the categorical version of this theory. I will try to explain all the n
ecessary concepts during the report\, but it is advisable to know what a L
ie group and Lie algebra are.\n1\n
LOCATION:https://researchseminars.org/talk/IntMathCircle/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Louis H Kauffman
DTSTART:20240204T140000Z
DTEND:20240204T150000Z
DTSTAMP:20260422T225638Z
UID:IntMathCircle/18
DESCRIPTION:Title: State Sum Invariants of Knotoids and Linkoids\nby Louis H Kauff
man as part of International math circle\n\n\nAbstract\nThis will be an in
formal talk about how one can generalize state sum invariants for classica
l knots that model the Alexander Conway polynomial and the Jones polynomia
l to two variable state sum invariants for knotoids and linkoids that are
chirality sensitive. This will be a self-contained talk with many examples
.\n
LOCATION:https://researchseminars.org/talk/IntMathCircle/18/
END:VEVENT
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