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SUMMARY:Modularity of Calabi-Yau Varieties - Noriko Yui (Queen's Universit
 y\, Canada)
DTSTART:20220720T150000Z
DTEND:20220720T160000Z
UID:TALK175025@talks.cam.ac.uk
DESCRIPTION:Let X be a Calabi-Yau variety of dimension d. We will confine 
 ourselves to Calabi-Yauvarieties of small dimensions\, e.g.\, d &le\; 3. D
 imension one Calabi&ndash\;Yaus are elliptic curves\, those of dimensiontw
 o are K3 surfaces\, and dimension three ones are Calabi-Yau threefolds. Ge
 ometry and physics are bothvery much in evidence in Calabi-Yau varieties o
 ver the field of complex numbers.\nToday I will focus on Calabi-Yau variet
 ies defined over the field Q of rational numbers (or number fields)\,and w
 ill discuss the modularity/automorphy of Calabi-Yau varieties in the frame
 work of the LanglandsPhilosophy. In the last thirty years or so\, we have 
 witnessed tremendous advances on the modularityquestions for Calabi-Yau va
 rieties. iMost of these results rest on the modularity of the two-dimensio
 nalGalois representations associated to them.\nIn the first part of the le
 cture\, I will present these fascinating modularity results for Calabi&nda
 sh\;Yau varietiesover Q of dimension &le\; 3\, as well as conjectures.\nTh
 en I will discuss the current research in progess on the rank 4 weight 3 C
 alabi&ndash\;Yau motives over Qand their Siegel modularity.
LOCATION:Seminar Room 1\, Newton Institute
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