BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Antonio Cauchi (Universitat Politècnica de Catalunya) DTSTART:20210519T083000Z DTEND:20210519T093000Z DTSTAMP:20260423T022732Z UID:RSVP/1 DESCRIPTION:Title: Alg ebraic cycles for the Siegel sixfold and the exceptional theta lift from G 2\nby Antonio Cauchi (Universitat Politècnica de Catalunya) as part o f Rendez-vous on special values and periods\n\n\nAbstract\nIn this talk\, we will report some progress towards the Beilinson conjectures for Shimura varieties associated to the symplectic group $\\mathrm{GSp}(6)$. \nWe wi ll describe a cohomological formula for the residue at $s=1$ of the degree 8 spin $L$-function. We will then discuss an important family of cuspidal automorphic representations for $\\mathrm{PGSp}(6)$ for which the residue is non-zero and relate this to the existence of an algebraic cycle coming from a Hilbert modular subvariety. This relation partially answers a ques tion of Gross and Savin on motives with Galois group of type $\\mathrm{G}2 $. \nThis is joint work with Francesco Lemma and Joaquin Rodrigues Jacinto .\n LOCATION:https://researchseminars.org/talk/RSVP/1/ END:VEVENT END:VCALENDAR