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SUMMARY:Periods and quasiperiods of modular forms
DTSTART;VALUE=DATE-TIME:20181204T133000Z
DTEND;VALUE=DATE-TIME:20181204T143000Z
DTSTAMP;VALUE=DATE-TIME:20190424T063055Z
UID:indico-event-8813@ictp.it
DESCRIPTION:\n An elliptic curve over the complex numbers has an associate
d period lattice\, generated by two complex numbers ω1 and ω2\, but as w
ell as these two periods there are also two “quasiperiods” η1 and η2
satisfying the Legendre relatin ω1η2 − ω2η1 = 2πi. On the other ha
nd\, modular forms of integral weight have associated “period polynomial
s” whose coefficients are also called periods. In the first part of the
lecture I will review the classical construction of these period polynomia
ls (associated with the names Eichler\, Shimura\, and Manin) and explain t
hat modular forms also have quasiperiods\, although this was apparently no
t noticed until a couple of years ago. In the second part\, which can be s
een as a continuation of Albrecht Klemm’s talk two weeks ago\, we will s
ee that the periods and quasiperiods of certain modular forms appear (conj
ecturally\, and numerically to high precision) in the transition matrices
for the Picard-Fuchs differential equations of certain families of Calabi-
Yau varieties.\n\nhttp://indico.ictp.it/event/8813/
LOCATION:ICTP Leonardo Building - Euler Lecture Hall
URL:http://indico.ictp.it/event/8813/
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