BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Lou Kauffman DTSTART:20230715T150000Z DTEND:20230715T160000Z DTSTAMP:20260404T110643Z UID:IntMathCircle/1 DESCRIPTION:Title: Introduction to Combinatorial Knot Theory\nby Lou Kauffma n as part of International math circle\n\nAbstract: TBA\n LOCATION:https://stable.researchseminars.org/talk/IntMathCircle/1/ END:VEVENT BEGIN:VEVENT SUMMARY:Scott Baldridge DTSTART:20230730T123000Z DTEND:20230730T140000Z DTSTAMP:20260404T110643Z 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 part of International math circle\n\nAbstract: TBA\n LOCATION:https://stable.researchseminars.org/talk/IntMathCircle/2/ END:VEVENT BEGIN:VEVENT SUMMARY:Vladlen Timorin DTSTART:20230806T123000Z DTEND:20230806T133000Z DTSTAMP:20260404T110643Z UID:IntMathCircle/3 DESCRIPTION:Title: (Self-)similarity in mathematics\nby Vladlen Timorin as p art of International math circle\n\nAbstract: TBA\n LOCATION:https://stable.researchseminars.org/talk/IntMathCircle/3/ END:VEVENT BEGIN:VEVENT SUMMARY:Roger Fenn DTSTART:20230813T153000Z DTEND:20230813T163000Z DTSTAMP:20260404T110643Z UID:IntMathCircle/4 DESCRIPTION:Title: Planar Doodles: properties\, codes and tables\nby Roger F enn as part of International math circle\n\n\nAbstract\nThis is joint work with Andy Bartholomew which started as an investigation into the possibil ities of cataloguing doodles on the plane or sphere. As the work progresse d more properties were discovered which led us to divide the doodles by co nnectivity. The second most connected are called prime and the most connec ted 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 v irtual knots. The super prime doodles have a hamiltonian circuit by a theo rem of Tutte. Whether this condition extends to other doodles is unknown t o us\, but it does mean that super prime doodles have a simple code using this cycle.\n LOCATION:https://stable.researchseminars.org/talk/IntMathCircle/4/ END:VEVENT BEGIN:VEVENT SUMMARY:Aleksey Glibichuk DTSTART:20230827T123000Z DTEND:20230827T133000Z DTSTAMP:20260404T110643Z UID:IntMathCircle/5 DESCRIPTION:Title: Point-line incidences and their applications\nby Aleksey Glibichuk as part of International math circle\n\n\nAbstract\nI'll give a proof of the Szemeredi - Trotter theorem which gives optimal up to constan ts bound for number of point - line incidences. I'll also give several int eresting applications of this theorem\, including application to so-called sum-product estimates.\n LOCATION:https://stable.researchseminars.org/talk/IntMathCircle/5/ END:VEVENT BEGIN:VEVENT SUMMARY:Ilya Mednykh DTSTART:20230903T123000Z DTEND:20230903T133000Z DTSTAMP:20260404T110643Z UID:IntMathCircle/6 DESCRIPTION:Title: Some spectral invariants of circulant graphs\nby Ilya Med nykh as part of International math circle\n\n\nAbstract\nThe report is dev oted 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 c an be expressed through eigenvalues of Laplacian (or Kirchhoff) matrix for a given graph.\n LOCATION:https://stable.researchseminars.org/talk/IntMathCircle/6/ END:VEVENT BEGIN:VEVENT SUMMARY:Lou Kauffman (University of Illinois at Chicago) DTSTART:20230910T130000Z DTEND:20230910T140000Z DTSTAMP:20260404T110643Z UID:IntMathCircle/7 DESCRIPTION:Title: Introduction to Knot Invariants - Linking Numbers and Colorin g Knot Diagrams\nby Lou Kauffman (University of Illinois at Chicago) a s part of International math circle\n\n\nAbstract\nWe will discuss how to find linking numbers to show that curves can be topologically linked\, and we will show how to color knot and link diagrams to show further properti es of knotting and linking. This talk is related to our previous talk abou t knot diagrams\, but the present talk will be self-contained.\n LOCATION:https://stable.researchseminars.org/talk/IntMathCircle/7/ END:VEVENT BEGIN:VEVENT SUMMARY:Amit Kumar DTSTART:20230917T140000Z DTEND:20230917T150000Z DTSTAMP:20260404T110643Z UID:IntMathCircle/8 DESCRIPTION:Title: Graph coloring via defect TQFT\nby Amit Kumar as part of International math circle\n\n\nAbstract\nOn the most intuitive level\, def ects are subsets of a space-time or a material where something special is going on. They are defective in the sense that the theory that governs the m is different than the theory that governs the rest of the space. A topol ogical defect is a defect that does not depend on metric. The theme of our work is the interpretation of an embedded graph as a defect\, which facil itates the TQFT with defect to capture that number of ways a trivalent gra ph 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 speci al cases.\n LOCATION:https://stable.researchseminars.org/talk/IntMathCircle/8/ END:VEVENT BEGIN:VEVENT SUMMARY:Anna Taranenko DTSTART:20231001T080000Z DTEND:20231001T090000Z DTSTAMP:20260404T110643Z UID:IntMathCircle/9 DESCRIPTION:Title: Latin squares\, latin hypercubes and their transversal\nb y Anna Taranenko as part of International math circle\n\n\nAbstract\nA lat in square of order n is an nxn table filled by n symbols so that each symb ol appear in each line exactly once\, and a transversal in a latin square is its diagonal hitting each symbol exactly ones. Natural multidimensional generalizations of latin squares are known as latin hypercubes. In this t alk we overview most important results and open problems on transversals i n latin squares and hypercubes.\n LOCATION:https://stable.researchseminars.org/talk/IntMathCircle/9/ END:VEVENT BEGIN:VEVENT SUMMARY:Mehdi Golafshan (University of Liège\, Belgium) DTSTART:20231008T123000Z DTEND:20231008T133000Z DTSTAMP:20260404T110643Z UID:IntMathCircle/10 DESCRIPTION:Title: A generalization of the binomial coefficients by words\n by Mehdi Golafshan (University of Liège\, Belgium) as part of Internation al math circle\n\n\nAbstract\nA word w being given it is easy to compute t he set of its subwords and their multiplicity\; this computation is obtain ed by a simple induction formula. The main problem of interest in this tal k\, sometimes implicitly but more often explicitly\, is the one of the inv erse correspondence. Under what conditions is a given set of words S the s et of subwords\, 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 thu s determined? In which cases are they uniquely determined? Some of these c onditions 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 s ubtle\; if for instance a and b are two letters of A\, and if ab and ba ar e subwords of w\, then at least one of the two words aba and bab is also a subword of w. In fact\, we shall consider the subwords with their multipl icity. It is possible to give a complete set of equations that express tho se relations.\n LOCATION:https://stable.researchseminars.org/talk/IntMathCircle/10/ END:VEVENT BEGIN:VEVENT SUMMARY:Vassily O. Manturov DTSTART:20231022T123000Z DTEND:20231022T133000Z DTSTAMP:20260404T110643Z UID:IntMathCircle/11 DESCRIPTION:Title: The photography method\nby Vassily O. Manturov as part o f International math circle\n\n\nAbstract\nWe formulate a general method a llowing one to\n1) solve various equations\n2) construct invariants of top ological objects\nby using some very general notion of data and data trans mission law.\n \nBy data we mean\, say\, objects of geometric origin (len gths\, areas\, etc.)\,\nby data transmission law we mean some equations re writing the data given in\none system of coordinates in terms of some othe r system of coordinates\n(one key example is the Ptolemy equation).\n \nS uch considerations allow one to solve various equations ``for free''.\nWe shall concentrate on obtaining invariants of braids 3-manifolds and 4-mani folds\,\nsolutions to the pentagon equaitons and representations of groups G_{n}^{3}.\n \nThis photography method ties together many branches in ma thematics\; in particular\,\nour data transmission law is naturally relate d to see mutations in cluster algebras.\n \nMany known invariants (or the ir modifications) like Turaev-Viro(-like) invariants\,\nDijkgraaf-Witten-l ike invariants etc. turn out to be partial cases of the photography\nmetho d (and its slight generalisation).\n \nThis is a joint work with L.H.Kauf fman\, I.M.Nikonov\, S.Kim\, and Z.Wan.\n \nhttps://arxiv.org/abs/2305.06 316\n \nhttps://arxiv.org/pdf/2305.11945.pdf\n \nhttps://arxiv.org/abs/2 306.07079\n \nhttps://arxiv.org/abs/2307.03437\n \nhttps://arxiv.org/abs /2309.01735\n LOCATION:https://stable.researchseminars.org/talk/IntMathCircle/11/ END:VEVENT BEGIN:VEVENT SUMMARY:Louis H Kauffman DTSTART:20231029T130000Z DTEND:20231029T140000Z DTSTAMP:20260404T110643Z UID:IntMathCircle/12 DESCRIPTION:Title: Untying Knots via Self-Repulsion Fields\nby Louis H Kauf fman as part of International math circle\n\n\nAbstract\nCoating a knot wi th electrical charge could create a topological entity that would try to r epel itself and find an energy-minimal position in space.\nComputer modeli ng allows experiments with this idea\, and we can try to see if such self- repelling fields will help unknot knots that are not knotted.\nThis talk w ill have demonstrations that such methods of unknotting sometimes work and sometimes do not work. We give systematic classes of examples by using \n rational knots and tangles that give such models great difficulties in unk notting. The talk will have a self-contained exposition of the Conway theo ry of rational tangles and their fractions. This is a very beautiful inter face between the properties of tangles and the properties of continued fra ctions. We will even locate the “Eternal Golden Braid”\nso long-sought since the time of Hofstadter. (I refer to the book by Douglas Hofstadter “Goedel\, Escher\, Bach - An Eternal Golden Braid”.)\n LOCATION:https://stable.researchseminars.org/talk/IntMathCircle/12/ END:VEVENT BEGIN:VEVENT SUMMARY:Louis H Kauffman (University of Illinois at Chicago) DTSTART:20231119T140000Z DTEND:20231119T150000Z DTSTAMP:20260404T110643Z UID:IntMathCircle/13 DESCRIPTION:Title: Introduction to Knotoids\nby Louis H Kauffman (Universit y of Illinois at Chicago) as part of International math circle\n\n\nAbstra ct\nA knotoid is an equivalence class of knotoid diagrams under Reidemeist er moves. A knotoid diagram is a tangle diagram with two ends. The ends do not have to be in the same region.\nReidemeister moves are not allowed to pass arcs across endpoints. Knotoids were defined by Vladimir Turaev. \nT his talk will explain how the theory of knotoids (and more general linkoid s and multiknotoids) works\, how we use virtual knot theory to study knoto ids\, how knotoids can be interpreted geometrically in terms of embedded g raphs and some of their applications. The work we discuss is joint work wi th Neslihan Gugumcu\, Sofia Lambropoulou\, Eleni Panagiotou and Kasturi Ba rkataki.\n LOCATION:https://stable.researchseminars.org/talk/IntMathCircle/13/ END:VEVENT BEGIN:VEVENT SUMMARY:Hayk Sedrakyan DTSTART:20231126T123000Z DTEND:20231126T133000Z DTSTAMP:20260404T110643Z UID:IntMathCircle/14 DESCRIPTION:Title: Interconnected-distance formulas and their applications\ nby Hayk Sedrakyan as part of International math circle\n\n\nAbstract\nWe provide novel interconnected-distance formulas and discuss their applicati ons. This topic remains widely open\, as no such interconnected-distance f ormulas exist when we increase the number of points\, or if we consider th e points in three-dimensional space.\n LOCATION:https://stable.researchseminars.org/talk/IntMathCircle/14/ END:VEVENT BEGIN:VEVENT SUMMARY:Louis H Kauffman DTSTART:20231203T140000Z DTEND:20231203T150000Z DTSTAMP:20260404T110643Z UID:IntMathCircle/15 DESCRIPTION:Title: Introduction to Quantum Link Invariants\nby Louis H Kauf fman as part of International math circle\n\n\nAbstract\nThis will be an e lementary introduction to quantum link invariants\, based on generalized R eidemeister moves for link diagrams in Morse form.\nWe emphasize how to co nvert such a diagram to an abstract tensor diagram in the sense of Penrose so that the contraction of this tensor is an invariant of regular isotopy .\nWe will discuss how this approach to quantum link invariants is related to categorical formulations and to the finding of solutions to the Yang-B axter equation\, and if time permits\nwith the structure of Hopf algebras. \n LOCATION:https://stable.researchseminars.org/talk/IntMathCircle/15/ END:VEVENT BEGIN:VEVENT SUMMARY:Maximilian Wolfensberger DTSTART:20231210T143000Z DTEND:20231210T153000Z DTSTAMP:20260404T110643Z UID:IntMathCircle/16 DESCRIPTION:Title: Alternative to Heron's and Bretschenider's Formula\nby M aximilian Wolfensberger as part of International math circle\n\n\nAbstract \nWe provide a novel form of Heron's formula and a novel form of Bretschne ider's formula. We provide several applications illustrating what is the a dvantage 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 o f any pentagon (or any other polygon) using its side lengths and the lengt hs of some of its diagonals.\n LOCATION:https://stable.researchseminars.org/talk/IntMathCircle/16/ END:VEVENT BEGIN:VEVENT SUMMARY:V. A. Stukopin DTSTART:20231217T143000Z DTEND:20231217T153000Z DTSTAMP:20260404T110643Z UID:IntMathCircle/17 DESCRIPTION:Title: Quantum (super)algebras: foundations and applications\nb y 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\nalg ebras (quantum groups). The quantum group is a Hopf algebra\, appearing as a quantization or flat deformation of a Lie bialgebra. I will also talk a bout a graded version of this theory\, the theory of quantum supergroups\, as well as an important class of quantum groups\, namely\, triangular (qu asitriangular\, braided) quantum groups\, associated with the quantum Yang -Baxter equation. We will also talk about the classical version of the the ory of quantum algebras\,\nnamely the theory of Lie bialgebras. If there i s time\, I might talk about the representation theory of these objects\, a s well as the categorical version of this theory. I will try to explain al l the necessary concepts during the report\, but it is advisable to know w hat a Lie group and Lie algebra are.\n1\n LOCATION:https://stable.researchseminars.org/talk/IntMathCircle/17/ END:VEVENT BEGIN:VEVENT SUMMARY:Louis H Kauffman DTSTART:20240204T140000Z DTEND:20240204T150000Z DTSTAMP:20260404T110643Z UID:IntMathCircle/18 DESCRIPTION:Title: State Sum Invariants of Knotoids and Linkoids\nby Louis H Kauffman as part of International math circle\n\n\nAbstract\nThis will b e an informal talk about how one can generalize state sum invariants for c lassical knots that model the Alexander Conway polynomial and the Jones po lynomial to two variable state sum invariants for knotoids and linkoids th at are chirality sensitive. This will be a self-contained talk with many e xamples.\n LOCATION:https://stable.researchseminars.org/talk/IntMathCircle/18/ END:VEVENT END:VCALENDAR