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SUMMARY:Matilde Lalín (Université de Montréal)
DTSTART:20260929T180000Z
DTEND:20260929T190000Z
DTSTAMP:20260930T020311Z
UID:AI-CoNT/2
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/AI-CoNT/2/">
 The arithmetic of Boyd’s Mahler measure conjectures: from data analysis 
 to machine learning</a>\nby Matilde Lalín (Université de Montréal) as p
 art of AI\, Combinatorics and Number Theory Seminar\n\n\nAbstract\nThe Mah
 ler measure is an invariant of multivariable rational functions defined by
  averaging\n$\\log |P|$ over the unit torus. Boyd conjectured that\, for\n
 \\[\nx+y+\\frac{1}{x}+\\frac{1}{y}+k\,\n\\]\nits Mahler measure is a ratio
 nal multiple $r_k L'(E_k\,0)$\, where $E_k$ is an associated\nelliptic cur
 ve. We study the arithmetic of the factors $r_k$ using a dataset of the fi
 rst\n250\,000 values of $k$\, combining large-scale statistical analysis w
 ith transformer-based\nexperiments. We observe several striking patterns i
 n their size and $p$-adic behavior\,\nand find that the neural networks re
 cover substantial arithmetic structure from the data\,\nand perhaps a bit 
 more. This is joint work with Alberto Alfarano\, Pablo Bianucci\, and\nBer
 end Ringeling.\n
LOCATION:https://researchseminars.org/talk/AI-CoNT/2/
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