{"id":85,"date":"2019-06-12T17:10:23","date_gmt":"2019-06-12T17:10:23","guid":{"rendered":"http:\/\/gqlt.rmc.math.tsu.ru\/?page_id=85"},"modified":"2020-09-08T15:40:02","modified_gmt":"2020-09-08T15:40:02","slug":"program-2019","status":"publish","type":"page","link":"http:\/\/gqlt.rmc.math.tsu.ru\/?page_id=85","title":{"rendered":"Program 2019"},"content":{"rendered":"\n

June 25 (MAIN BUILDING TSU, ROOM 229)<\/p>\n\n\n\n

09:30 \u2013 10:00 Registration<\/p>\n\n\n\n

10:00 \u2013 10:50 Louis KAUFFMAN (Chicago, USA \/ Novosibirsk, Russia)\u00a0 Majorana Fermions, Braiding and the Dirac Equation <\/div>
Abstract: This talk will discuss how the Dirac equation arises from Clifford algebraic considerations and how examining the action of the Dirac operator on a plane wave gives rise to an algebraic reformulation of the Dirac equation (equivalent to the original) that has solutions in terms of nilpotent elements of the Clifford algebra. These nilpotent elements can be regarded as annihi- lation operators for a fermion. We point out how the nilpotents decompose into Majorana operators and discuss how this point of view is related to the braiding of Majorana Fermions and to the original work of Majorana on the Dirac equation. We also discuss how this work is related to the work of Peter Rowlands and how it is related to the author\u2019s program for elucidating discrete physics in terms of non-commutative algebra. <\/div><\/div>\n\n\n\n

Tea\/Coffee (20 min) <\/p>\n\n\n\n

11:10 \u2013 12:00 Sergey MATVEEV (Chelyabinsk, Russia) A new approach to the famous Newman\u2019s Diamond Lemma <\/div>
Abstract: A new approach to the famous Newman\u2019s Diamond Lemma is developed. This approach promises an essential progress in the theory of prime decompositions of geometric objects.<\/div><\/div>\n\n\n\n
12:10 \u2013 13:00 Aleksandr MEDNYKH (Novosibirsk, Russia) Enumeration of spanning trees, spanning forests and Kirchhoff index for circulant graphs<\/div>
Abstract: In this presentation we investigate the infinite family of circulant graphs Cn<\/sub>(s1<\/sub>,s2<\/sub>, … ,sk<\/sub>). We present an explicit formula for the number of spanning trees, rooted spanning forests and the Kirchhoff index. Then we investigate arithmetical and asymptotic properties of the obtained numbers. All formulas are given in terms of the Chebyshev polynomials. We start with some basic definitions.<\/div><\/div>\n\n\n\n

13:00 \u2013 15:00 Lunch <\/p>\n\n\n\n

15:00 \u2013 15:30 Manpreet SINGH (Mohali, India) Residual finiteness of quandles <\/div>
Abstract: Residual finiteness is known to be an important property of groups appearing in combinatorial group theory and low dimensional topology. We investigate residual finiteness of quandles and present some recent observations about residual finiteness of free quandles and linkquandles.<\/div><\/div>\n\n\n\n
15:40 \u2013 16:10 Tatyana KOZLOVSKAYA (Tomsk, Russia) Cyclically presented Sieradski groups with even number of generators and three dimensional manifolds<\/div>
Abstract: We consider the generalised Sieradski group S<\/em>(2n<\/em>,7,2), n<\/em>\u22651. We prove that n-cyclic presentations of their groups are geometric, i.e., correspond to the spines of closed connected orientable 3-manifolds. These manifolds M<\/em>(2n<\/em>,7,2) are the n<\/em>-fold cyclic coverings of the lens space L<\/em>(7,1).<\/div><\/div>\n\n\n\n
16:20 \u2013 16:50 Nikolay ABROSIMOV (Novosibirsk \/ Tomsk, Russia) Volume of a compact hyperbolic tetrahedron in terms of its edge matrix<\/div>
Abstract: A compact hyperbolic tetrahedron T is a convex hull of four points in the hyperbolic space. It is well known that T is uniquely defined up to isometry either by the set of its dihedral angles or the set of its edge lengths. A Gram matrix G(T) of tetrahedron T consists of cosines of its dihedral angles, while an edge matrix E(T) is formed by hyperbolic cosines of its edge lengths. In 1907 Italian mathematician G. Sforza found a formula for the volume of a compact hyperbolic tetrahedron T in terms of its Gram matrix cofactors. The new proof of the Sforza\u2019s formula was recently given by A. Mednykh and N. Abrosimov (2014). At the same time, the Sforza’s formula has some drawback associated with the need to choose the analytical branch of a multivalued function under the integral. In the present work, we obtain an exact formula for the volume of T in terms of its edge matrix cofactors. Our formula is devoid of the above disadvantage since under the integral there is an unambiguous function. Also, this is a first known formula for the volume of a compact hyperbolic tetrahedron of general type in terms of its edge lengths.<\/div><\/div>\n\n\n\n\n\n\n\n

June 26 (MAIN BUILDING TSU, ROOM 209)<\/p>\n\n\n\n

10:00 \u2013 10:50 Mahender SINGH (Mohali, India) Twin and pure twin groups<\/div>
Abstract: Twin groups are right angled Coxeter groups that can be thought of as planar analogues of braid groups. Pure twin groups can be defined similar to pure braid groups. We present some recent algebraic and topological observations about these groups.<\/div><\/div>\n\n\n\n

Tea\/Coffee (20 min)<\/p>\n\n\n\n

11:10 \u2013 12:00 Valeriy BARDAKOV (Novosibirsk, Russia) Operation cabling on braids<\/div>
Abstract: In my talk I will introduce operation cabling on braids. This operation gives a possibility to define a new generating sets of the pure braid groups (classical and virtual). Also one can defines simplicial structures on these groups. In the case of classical pure braid groups F. Cohen and J. Wu proved that the simplicial group $AP_*$ contains Milnor\u2019s simplicial sphere $F[S^1]$ that gives, in particular, interpretation generators homotopy groups of 2-sphere in terms of the pure braids.<\/div><\/div>\n\n\n\n
12:10 \u2013 13:00 Madeti PRABHAKAR (Ropar, India) Unknotting operations and gordian complex of knots<\/div>
Abstract: Gordian complex of knots were introduced by Hirasawa and Uchida. Later this concept was extended to virtual knots. In both cases, Gordian complex was defined using classical unknotting operations. In this talk, we will discuss various outcomes if we consider different unknotting operations in defining the Gordian distance of knots\/virtual knots. <\/div><\/div>\n\n\n\n

13:00 \u2013 15:00 Lunch <\/p>\n\n\n\n

15:00 \u2013 15:30 Maksim IVANOV (Novosibirsk, Russia) F-polynomials and connected sums of virtual knots<\/div>
Abstract: In this talk we discuss behavior of F-polynomials under connected sums o virtual knots. We show how to construct an infinite family of different connected sums of the same pair of oriented virtual knots, when one of them has \\nabla J_n \\neq 0.<\/div><\/div>\n\n\n\n
15:40 \u2013 16:10 Andrey EGOROV (Novosibirsk, Russia) Volumes of right-angled hyperbolic polyhedra.<\/div>
Abstract: In three-dimensional hyperbolic space, we consider two types of right-angled polyhedra: compact — all vertices are finite, ideal — with all vertices on the absolute. In this talk, we will discuss boundaries of the volume of these polyhedra in terms of the number of vertices and the sizes of the faces, hypotheses about polyhedra with maximum and minimum volume, correlations between the hyperbolic volume of combinatorial invariants of polyhedra.<\/div><\/div>\n\n\n\n
16:20 \u2013 16:50 Yuong Huu BAO (Novosibirsk, Russia) On the edge matrix of a compact hyperbolic tetrahedron<\/div>
Abstract: We consider a compact hyperbolic tetrahedron T<\/em> of general type. It is well known that T<\/em> is uniquely defined up to isometry either by the set of its dihedral angles or the set of its edge lengths. A Gram matrix G<\/em>(T<\/em>) of tetrahedron T<\/em> consists of cosines of its dihedral angles, while an edge matrix E<\/em>(T<\/em>) is formed by hyperbolic cosines of its edge lengths. There are some relations known for a Gram matrix of a hyperbolic tetrahedron T<\/em>. Also, A. Mednykh and M. Pashkevich (2006) found a formula expressing edge lengths of T<\/em> in terms of its Gram matrix cofactors. In the present work, we obtain analogous relations but in terms of edge matrix of a compact hyperbolic tetrahedron T<\/em>. <\/div><\/div>\n\n\n\n\n\n\n\n

June 27 (MAIN BUILDING TSU, ROOM 209)<\/p>\n\n\n\n

10:00 \u2013 10:50 Krishnendu GONGOPADHYAY (Mohali, India) Commutators of some generalized braid groups<\/div>
Abstract: In this talk, we shall discuss some generalized braid groups, and shall look into the structure of their commutator subgroups.<\/div><\/div>\n\n\n\n

Tea\/Coffee (20 min)<\/p>\n\n\n\n

11:10 \u2013 12:00 Mikhail NESHCHADIM (Novosibirsk, Russia) Skew braces: known and new results<\/div>
Abstract: Skew brace is the algebraic system with two group operations that are connected by the brace axiom. Skew braces have connections with 1) Yang-Baxter equations, 2) Zappa-Szep product, 3) rings and near rings, 4) Hopf-Galois extensions, 5) groups with exact factorizations, 6) triply factorized groups, 7) biquandles and virtual knot theoryand etc. In the talk we formulate some known and new results aboutleft skew braces.<\/div><\/div>\n\n\n\n

13:00 \u2013 14:00 Excursion (Siberian Botanical Garden)<\/p>\n\n\n\n

17:00 Dinner <\/p>\n\n\n\n\n\n\n\n

June 28 (2nd TSU Study Building, ROOM 304)<\/p>\n\n\n\n

10:00 \u2013 15:00 Excursion (Village Park Okolitsa)<\/p>\n\n\n\n

15:00 \u2013 17:00 PROBLEM SESSION<\/p>\n","protected":false},"excerpt":{"rendered":"

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