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Date: Thursday 13th October 2011Speaker: Victor Przyjalkowski (Moscow, Vienna).Title: Laurent Polynomials in Mirror SymmetryAbstract: We discuss quantitative properties of Mirror Symmetry correspondencefor Fano varieties. Laurent polynomials naturally appear in this picture.They describe (the essential part of) dual Landau--Ginzburg models for Fanos.They are related to toric degenerations of the initial Fano varieties.Their relative compactifications are candidates for Landau--Ginzburgmodels from the Homological Mirror Symmetry point of view.We consider our main example --- Fano threefolds.We discuss why Landau--Ginzburg model (for given Fano variety)represented by Laurent polynomial is unique and why it is not unique.Web: http://www.maths.ed.ac.uk/cheltsov/seminar/