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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Modularity of Calabi-Yau Varieties - Noriko Yui (Q
ueen's University\, Canada)
DTSTART;TZID=Europe/London:20220720T160000
DTEND;TZID=Europe/London:20220720T170000
UID:TALK175025AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/175025
DESCRIPTION:Let X be a Calabi-Yau variety of dimension d. We w
ill confine ourselves to Calabi-Yauvarieties of sm
all dimensions\, e.g.\, d &le\; 3. Dimension one C
alabi&ndash\;Yaus are elliptic curves\, those of d
imensiontwo are K3 surfaces\, and dimension three
ones are Calabi-Yau threefolds. Geometry and physi
cs are bothvery much in evidence in Calabi-Yau var
ieties over the field of complex numbers.\nToday I
will focus on Calabi-Yau varieties defined over t
he field Q of rational numbers (or number fields)\
,and will discuss the modularity/automorphy of Cal
abi-Yau varieties in the framework of the Langland
sPhilosophy. In the last thirty years or so\, we h
ave witnessed tremendous advances on the modularit
yquestions for Calabi-Yau varieties. iMost of thes
e results rest on the modularity of the two-dimens
ionalGalois representations associated to them.\nI
n the first part of the lecture\, I will present t
hese fascinating modularity results for Calabi&nda
sh\;Yau varietiesover Q of dimension &le\; 3\, as
well as conjectures.\nThen I will discuss the curr
ent research in progess on the rank 4 weight 3 Cal
abi&ndash\;Yau motives over Qand their Siegel modu
larity.
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:
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