Seminars in April 2013

  • Imre Bárány; Tensors, colours, octahedra
    Tensors, colours, octahedra
    Imre Bárány
    Alfréd Rényi Mathematical Institute
    Hungarian Academy of Sciences
    and
    University College London
    2013/04/26 Fri 4PM-5PM – ROOM 3433
    Several classical results in convexity, like the theorems of Caratheodory, Helly, and Tverberg, have colourful versions. In this talk I plan to explain how two methods, the octahedral construction and Sarkaria’s tensor trick, can be used to prove further extensions and generalizations of such colourful theorems.
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  • Sang-hyun Kim, Acute Triangulations of the Sphere
    Acute Triangulations of the Sphere
    Sang-hyun Kim
    KAIST
    2013/04/19 Friday 4PM-5PM – ROOM 3433
    We prove that a combinatorial triangulation L of a sphere admits an acute geodesic triangulation if and only if L does not have a separating three- or four-cycle. The backward direction is an easy consequence of the Andreev–Thurston theorem on orthogonal circle packings. For the forward direction, we consider the Davis manifold M from L. The acuteness of L will provide M with a CAT(-1) (hence, hyperbolic) metric. As a non-trivial example, we show the non-existence of an acute realization for an abstract triangulation suggested by Oum; the degrees of the vertices in that triangulation are all larger than four. This approach generalizes to triangulations coming from more general Coxeter groups, and also to planar triangulations. (Joint work with Genevieve Walsh)
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  • Mark Siggers, The structure of near-unanimity graphs
    The structure of near-unanimity graphs
    Mark Siggers
    Department of Mathematics
    College of Natural Sciences
    Kyungpook National University
    2013/04/12 Fri 4PM-5PM – ROOM 3433
    The class of structures that admit near-unanimity functions is of interest in the field of computational complexity as they yield constraint satisfactions problems that are solvable in deterministic log-space. In the literature, there are diverse characterisations near-unanimity structures, but none that make the generation of all such graphs transparent. We present a new description of reflexive graphs and irreflexive symmetric graphs admitting near-unanimity functions. This description brings together many of the known descriptions, and provides a good picture of near unanimity graphs.
    This is joint work with Tomas Feder, Pavol Hell, Benoit Larose, Cindy Loten and Claude Tardif.
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