• Matěj Dostál: Towards HSP theorems for algebras over categories

    11.2.2015 14:00 @ Applied Mathematical Logic

    Birkhoff’s HSP theorem is a celebrated result in universal algebra. Its beauty lies in the connection it establishes between a purely syntactic notion of a set of term equations for a given signature, and a purely semantic notion of a full subcategory with nice closure properties in the ambient category of all algebras for the given signature. Given that categories equipped with an algebraic structure are common in category theory, it is genuinely interesting to study whether Birkhoff’s theorem admits a generalisation into this (2-dimesional) case. The slogan for the expected reset would be the same as in the ordinary case: Equationally definable classes of algebras correspond to HSP-closed classes of algebras. Of course, in this more involved setting we are dealing with algebras that have an underlying category instead of an underlying set, and it is not even clear what should be meant by an equation satisfied by an algebra. Recent advances in the theory of 2-dimensional regularity and exactness by John Bourke and Richard Garner show that there are at least three meaningful ways to define the notion of an equation in this setting. We present an HSP-like theorem for the best-behaved case.

  • Zpět k pramenům: Petr Hájek a seminář aplikované logiky

    18.2.2015 14:00 @ Applied Mathematical Logic

    V tomto měsici slavi Petr Hajek 75. narozeniny. Spolu s oslavencem si nad šalkem kavy připomeneme některe historicke okamžiky nejen tohoto seminaře, jejich nosna temata, jmena a tvaře.

  • Diana Piguet: Extremal graph theory and (quasi)-randomness

    25.2.2015 14:00 @ Applied Mathematical Logic

    After a short introduction to graph theory, I will turn my attention to extremal graph theory and explain its focus and its most important tool. As an illustration I will give some results I have obtained in the field. The first result concerns the Loebl-Komlos-Sos conjecture on tree-embedding and involves a novel technique in extremal graph theory I will shortly present. The second reset concerns a tree-packing conjecture of Gyarfas. Its proof uses the probabilistic method and I will explain the main idea of this method.

  • Filip Šroubek: Slepá rekonstrukce obrazu: od rovnic k aplikacím

    26.2.2015 14:00 @ Machine Learning and Modelling