Calabi-Yau periods, Modularity and Arithmetic Geometry; Workshop Wrap-Up: New Results,Challenges and Possibilities

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• Yang-Hui He (London Institute for Mathematical Sciences), Albrecht Klemm (Physikalisches Institut Bonn University)
• Friday 06 October 2023, 14:30-15:30
• Seminar Room 1, Newton Institute.

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BLHW01 - Number theory, machine learning and quantum black holes

Albrecht Klemm:   Using Mirror symmetry and Dworks p-adic deformation of the  Gauss Manin connection we construct  the Hasse Weil Zeta function  $\zeta(X/\mathbb{Q},s)$ for hypergeometric  families of Calabi-Yau threefolds $X$. We  then explore the  consequences of its modularity in special fibres over algebraic  extensions of $\mathbb{Q}$ on enumerative geometry as well  as the physics of string compactification on $X$. Yang-Hui He: We present a number of recent experiments on how various standard machine-learning algorithms can help with pattern detection across disciplines ranging from algebraic geometry, to representation theory, to combinatorics, and to number theory.We speculate on whether there is an inherent hierarchy of “difficulty” in mathematics reflected by data. At the heart of the programme is the question how does AI help with mathematical discovery.

This talk is part of the Isaac Newton Institute Seminar Series series.

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