BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Haowu Wang (IBS-CGP\, Pohang) DTSTART:20220822T070000Z DTEND:20220822T080000Z DTSTAMP:20260409T043346Z UID:kias-string-seminars/90 DESCRIPTION:Title: Finite groups and automorphic products\nby Haowu Wang (I BS-CGP\, Pohang) as part of KIAS Strings Seminar\n\n\nAbstract\nIn 1992 Bo rcherds proved Monstrous Moonshine Conjecture by lifting Mckay--Thomson se ries to twisted denominator identities of the monster Lie algebra. Borcher ds' proof inspires an intriguing relation between vertex algebras\, Borche rds--Kac--Moody algebras and automorphic products. In this talk we introdu ce several new results related to this relation. We classify nice BKM alge bras whose denominators are automorphic products. We prove twists of denom inator identities of the fake monster Lie algebra by the Conway group defi ne automorphic products on orthogonal groups. To prove the results\, we es tablish a new expression of automorphic products in terms of Jacobi forms. Using this representation\, we also show that some infinite products invo lving twisted elliptic genera of K3 surfaces (appearing in Mathieu Moonshi ne) are meromorphic Siegel modular forms on congruence subgroups\, which p roves a conjecture of Miranda Cheng. This talk is based on joint work with Brandon Williams.\n LOCATION:https://researchseminars.org/talk/kias-string-seminars/90/ END:VEVENT END:VCALENDAR