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SUMMARY:j-invariant and Borcherds Phi-function - Shu Kawaguchi (Doshisha U
 niversity)
DTSTART:20191015T133000Z
DTEND:20191015T143000Z
UID:TALK130027@talks.cam.ac.uk
CONTACT:Jack Thorne
DESCRIPTION:The j-invariant is the SL_2(Z)-invariant holomorphic function 
 on the \ncomplex upper half-plane\, which is fundamental in many branches 
 of \nmathematics. Besides the j-invariant itself\, the difference of \nj-i
 nvariants have beautiful properties such as Gross--Zagier's result on \nsi
 ngular moduli and the denominator formula for the monster Lie algebra. \nI
 n this talk\, we explain that the difference of j-invariants is closely \n
 related to the Borcherds Phi-function\, an automorphic form on the period 
 \ndomain for Enriques surfaces characterizing the discriminant divisor. \n
 This is joint work with Shigeru Mukai and Ken-Ichi Yoshikawa\, and we use 
 \nan algebraic expression of the Borcherds Phi-function obtained in our \n
 previous paper.
LOCATION:MR13
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