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Audiovisual Mathematics Library

Audiovisual Mathematics Library

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Variational and non-Archimedean aspects of the Yau-Tian-Donaldson conjecture - Boucksom, Sébastien (Author of the conference) | CIRM H

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I will discuss some recent developments in the direction of the Yau-Tian-Donaldson conjecture, which relates the existence of constant scalar curvature Kähler metrics to the algebro-geometric notion of $K$-stability. The emphasis will be put on the use of pluripotential theory and the interpretation of $K$-stability in terms of non-Archimedean geometry.

32Q20 ; 32Q26 ; 32Q25 ; 32P05 ; 53C55

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CY-motives and differential equations - Van Straten, Duco (Author of the conference) | CIRM H

Multi angle

The intimate relation between the arithmetic properties of varieties varying in families and the properties of the associated Picard-Fuchs differential is subject with a long and rich history that can be traced back to Deuring, Igusa, Dwork, Honda, Katz from which the notion of crystals emerged. A particular nice situation arises from families of Calabi-Yau motives, which can arise via various constructions, most notably via Mirror-Symmetry. In the two talks I will try to give a rough overview of this field, and illustrate it with specific examples. In particular, I will indicate how Calabi-Yau operators can be used to realise certain rank 4 motives attached Siegel paramodular forms by specific Calabi-Yau threefolds.[-]
The intimate relation between the arithmetic properties of varieties varying in families and the properties of the associated Picard-Fuchs differential is subject with a long and rich history that can be traced back to Deuring, Igusa, Dwork, Honda, Katz from which the notion of crystals emerged. A particular nice situation arises from families of Calabi-Yau motives, which can arise via various constructions, most notably via Mirror-Symmetry. In ...[+]

32Q25 ; 14J33

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