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SUMMARY:Jan Vonk (Institute for Advanced Study)
DTSTART:20200505T203000Z
DTEND:20200505T213000Z
DTSTAMP:20260423T124942Z
UID:MITNT/4
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/MITNT/4/">Si
 ngular moduli for real quadratic fields</a>\nby Jan Vonk (Institute for Ad
 vanced Study) as part of MIT number theory seminar\n\n\nAbstract\nIn the e
 arly 20th century\, Hecke studied the diagonal restrictions of Eisenstein 
 series over real quadratic fields. An infamous sign error caused him to mi
 ss an important feature\, which later lead to highly influential developme
 nts in the theory of complex multiplication (CM) initiated by Gross and Za
 gier in their famous work on Heegner points on elliptic curves. In this ta
 lk\, we will explore what happens when we replace the imaginary quadratic 
 fields in CM theory with real quadratic fields\, and propose a framework f
 or a tentative 'RM theory'\, based on the notion of rigid meromorphic cocy
 cles\, introduced in joint work with Henri Darmon. I will discuss several 
 of their arithmetic properties\, and their apparent relevance in the study
  of explicit class field theory of real quadratic fields\, the constructio
 n of rational points on elliptic curves\, and the theory of Borcherds lift
 s. This concerns various joint works\, with Henri Darmon\, Alice Pozzi\, a
 nd Yingkun Li.\n
LOCATION:https://researchseminars.org/talk/MITNT/4/
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