Tuesday 19 February 2019 |

Events for day: Thursday 28 February 2019 |

Combinatorial Commutative Algebra Weekly SeminarOn the Polymatroidal Property of Monomial Ideals with a View towards Orderings of Minimal Generators MATHEMATICS We prove that a monomial ideal $I$ generated in a single degree, is polymatroidal if and only if it has linear quotients with respect to the lexicographical ordering of the minimal generators induced by every ordering of variables. We also conjecture that the polymatroidal ideals can be characterized with linear quotients property with respect to the reverse lexicographical ordering of the minimal generators induced by every ordering of variables. We prove our conjecture in many special cases. ... 14:00 - 16:00 Mathtematical Logic Weekly SeminarThe (almost) Pointless Geometries School MATHEMATICS Many philosophical schools of mathematics reject the notion of infinity, and restrict attention to finite structures and objects. At first sight it would seem that they could not deal at all with classical geometry, since its usual entities (segments, lines, circles) all consist of infinitely many points. To bypass the problem, modern mathematics has developed a number of finite versions of Euclidean and non Euclidean geometries, which raise many subtle and difficult problems, the solutions of some of which have even led to a couple of Fields medals. ... 9:30 - 10:30 Combinatorial Commutative Algebra Weekly SeminarOn the Polymatroidal Property of Monomial Ideals with a View towards Orderings of Minimal Generators School MATHEMATICS We prove that a monomial ideal $I$ generated in a single degree, is polymatroidal if and only if it has linear quotients with respect to the lexicographical ordering of the minimal generators induced by every ordering of variables. We also conjecture that the polymatroidal ideals can be characterized with linear quotients property with respect to the reverse lexicographical ordering of the minimal generators induced by every ordering of variables. We prove our conjecture in many special cases. ... |