CRM: Centro De Giorgi
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Configuration Spaces: Geometry, Combinatorics and Topology

seminar: WEEKLY SEMINAR: A correlation inequality with applications in algebraic combinatorics

speaker: Anders Bjorner (Royal Institute of Technology (KTH) and Mittag-Leffler Institute, Stockholm)

abstract: The FKG inequality of Fortuin, Kasteleyn and Ginibre (1971) originated as a correlation inequality in statistical mechanics. It has many applications in discrete probability and extremal combinatorics.

In this talk we present a polynomial coefficient-wise inequality that refines the original FKG inequality. This polynomial FKG inequality has applications to f-vectors of joins of simplicial complexes, to Betti numbers of intersection of certain Schubert varieties, and to power series weighted by Young tableaux. The latter case includes a correlation inequality for Plancherel measure on integer partitions, and for its poissonization.

The talk will mostly be quite elementary and no previous familiarity with these topics will be assumed.

Wed 5 May, 16:00 - 17:00, Sala Conferenze Centro De Giorgi
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