BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Charles Young (University of Hertfordshire\, UK) DTSTART:20250512T150000Z DTEND:20250512T160000Z DTSTAMP:20260423T021147Z UID:ENAAS/124 DESCRIPTION:Title: Higher current algebras and chiral algebras\nby Charles Young (Univers ity of Hertfordshire\, UK) as part of European Non-Associative Algebra Sem inar\n\n\nAbstract\nVertex algebras capture physicists' notion of OPEs in chiral CFTs\, in complex dimension one. For various motivations\, one woul d like to have analogs of vertex algebras in higher dimensions. Chiral alg ebras\, in the sense of Beilinson-Drinfeld and Francis-Gaitsgory\, provide a promising framework here\, because they re-express the vertex algebra a xioms (which are rather sui generis\, and therefore hard to generalize) as something more recognizable (a chiral algebra is a Lie algebra\, of a sor t).\n\nI will review this\, and then go on to introduce a certain concrete model of the unit chiral algebra in higher complex dimensions. We shall s ee that in going to higher dimensions\, one naturally moves from Lie algeb ras to their homotopy analogs\, L-infinity algebras\, and from chiral alge bras to homotopy chiral algebras in a sense recently introduced by Malikov -Schechtman. The main tool in the talk will be a new model -- the polysimp licial model -- of derived sections of the sheaf of functions on higher co nfiguration spaces. The hope is that this model will prove well-adapted to doing concrete calculations.\n\nThis is joint work in preparation with Zh engping Gui and Laura Felder.\n LOCATION:https://researchseminars.org/talk/ENAAS/124/ END:VEVENT END:VCALENDAR