BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Haowu Wang (IBS CGP\, Pohang) DTSTART:20211116T070000Z DTEND:20211116T080000Z DTSTAMP:20260409T030059Z UID:kias-string-seminars/60 DESCRIPTION:Title: Recent results on Jacobi forms of lattice index\nby Haow u Wang (IBS CGP\, Pohang) as part of KIAS Strings Seminar\n\n\nAbstract\nI n 1985 Eichler and Zagier introduced the theory of Jacobi forms. Such form s are holomorphic functions which are modular under SL(2\,Z) in the first variable and quasi-periodic in the second variable. Later\, the Jacobi for m of lattice index was defined by replacing the second variable with many variables associated with a positive-definite lattice. Jacobi forms are an elegant intermediate between different types of modular forms and have ma ny applications in mathematics and physics. In this talk\, I will give a b rief introduction to this theory and present some recent results. (1) In 1992 Wirthmüller proved that for any irreducible root system not of type E_8 the algebra of weak Jacobi forms invariant under the Weyl group is a p olynomial algebra. I will define the Jacobian of Jacobi forms and present an automorphic proof of Wirthmüller's theorem. (2) Weyl invariant weak Ja cobi forms for the exceptional root system E_8 appear in E-string theory. I will prove several conjectures proposed by some physicists. This gives a clear picture of the (non-free) algebra of such Jacobi forms. (3) I will talk about the algebra of weak Jacobi forms for lattices of rank 2. Thi s talk is based on joint works with Brandon Williams and with Kaiwen Sun.\ n LOCATION:https://researchseminars.org/talk/kias-string-seminars/60/ END:VEVENT END:VCALENDAR