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Mirror symmetry and the classification of Fano varieties

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Mohammad Akhtar (Imperial College London)

  • Emmy Noether Kolloquium
When Apr 26, 2016
from 01:00 pm to 01:50 pm
Where Mainz, 05-432 (Hilbertraum)
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The classification of Fano varieties is an important long-standing problem in algebraic geometry. A new approach to this problem via mirror symmetry was recently proposed by Coates-Corti-Galkin-Golyshev-Kasprzyk. Their philosophy was that Fano varieties can be classified by studying their Laurent polynomial mirrors. This talk will survey the results of a collaborative effort to apply this philosophy to the classification of Fano orbifold surfaces. We will describe a conjectural picture which suggests that classifying suitable deformation classes of certain Fano orbifold surfaces is equivalent to classifying Fano lattice polygons up to an appropriate notion of equivalence. Central to this framework is the notion of mirror duality (between a Fano orbifold surface and a Laurent polynomial) and the closely related operations of algebraic and combinatorial mutations. We will also discuss how combinatorial mutations allow us to find mirror dual Laurent polynomials in practice and will give experimental evidence supporting our conjectures.

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