BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Andrew Linshaw (University of Denver) DTSTART:20220413T200000Z DTEND:20220413T210000Z DTSTAMP:20260414T173525Z UID:BUGeom/36 DESCRIPTION:Title: Global sections of the chiral de Rham complex for Calabi-Yau and hyperkahl er manifolds\nby Andrew Linshaw (University of Denver) as part of Bost on University Geometry/Physics Seminar\n\nLecture held in Zoom meeting ID: 953 4652 9200.\n\nAbstract\nFor any complex manifold M\, the chiral de Rh am complex is a sheaf of vertex algebras on M that was introduced in 1998 by Malikov\, Schechtman\, and Vaintrob. It is N-graded by conformal weight \, and the weight zero piece coincides with the ordinary de Rham sheaf. Wh en M is a Calabi-Yau manifold with holonomy group SU(d)\, it was shown by Ekstrand\, Heluani\, Kallen and Zabzine that the algebra of global section s \\Omega^{ch}(M) contains a certain vertex algebra defined by Odake which is an extension of the N=2 superconformal algebra. When M is a hyperkahle r manifold\, it was shown by Ben-Zvi\, Heluani\, and Szczesny that \\Omega ^{ch}(M) contains the small N=4 superconformal algebra. In this talk\, we will show that in both cases\, these subalgebras are actually the full alg ebras of global sections. In an earlier work\, Bailin Song has shown that the global section algebra can be identified with a certain subalgebra of a free field algebra which is invariant under the action of an infinite-di mensional Lie algebra of Cartan type. The key observation is that this alg ebra can be described using the arc space analogue of Weyl's first and sec ond fundamental theorems of invariant theory for the special linear and sy mplectic groups. \n\n \n\nThis is a joint work with Bailin Song.\n LOCATION:https://researchseminars.org/talk/BUGeom/36/ END:VEVENT END:VCALENDAR