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SUMMARY:Calabi-Yau periods\, Modularity and Arithmetic Geometry\; Workshop
  Wrap-Up: New Results\,Challenges and Possibilities - Yang-Hui He (London 
 Institute for Mathematical Sciences)\, Albrecht Klemm (Physikalisches Inst
 itut Bonn University)
DTSTART:20231006T133000Z
DTEND:20231006T143000Z
UID:TALK200875@talks.cam.ac.uk
DESCRIPTION:Albrecht Klemm:\n&nbsp\;\nUsing Mirror symmetry and Dworks p-a
 dic deformation of the&nbsp\;\nGauss Manin connection we construct&nbsp\;&
 nbsp\;the Hasse Weil\nZeta function&nbsp\;&nbsp\;$\\zeta(X/\\mathbb{Q}\,s)
 $ for hypergeometric&nbsp\;\nfamilies of Calabi-Yau threefolds $X$. We&nbs
 p\;&nbsp\;then explore the&nbsp\;\nconsequences of its modularity in speci
 al fibres over algebraic&nbsp\;\nextensions of $\\mathbb{Q}$ on enumerativ
 e&nbsp\;geometry as well&nbsp\;\nas the physics of string compactification
  on $X$.\nYang-Hui He:\nWe present a number of recent experiments on how v
 arious standard machine-learning algorithms can help with pattern detectio
 n across disciplines ranging from algebraic geometry\, to representation t
 heory\, to combinatorics\, and to number theory.We speculate on whether th
 ere is an inherent hierarchy of "difficulty" in mathematics reflected by d
 ata. At the heart of the programme is the question how does AI help with m
 athematical discovery.
LOCATION:Seminar Room 1\, Newton Institute
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