BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Angus McAndrew (BU) DTSTART:20201009T140000Z DTEND:20201009T143000Z DTSTAMP:20260423T004549Z UID:BUcomm/1 DESCRIPTION:Title: H ow to prove the Hodge conjecture\nby Angus McAndrew (BU) as part of BU Community Seminar\n\n\nAbstract\nFor a complex manifold or algebraic vari ety\, there are many different invariants one can study. One of the premie r options are certain vector spaces called the cohomology of the space. Th ere are many different approaches to cohomology\, specialised to different context/purposes: singular\, etale\, de Rham\, crystalline\, flat\, etc.\ n\nThere are often ways to take subspaces (called "cycles"\, in reference to classical homology) and map them into the cohomology groups. In the com plex case the ability to integrate over a subspace gives a pairing between the cycles and de Rham cohomology. The Hodge Conjecture states that cohom ology classes of a certain kind always arise from cycles. This is closely related to the Tate conjecture\, which makes a similar claim for etale coh omology\, and more generally to the (conjectural) theory of motives.\n\nIn this talk we'll introduce the above ideas in more detail\, show how to in terpret it in the case of a product of complex elliptic curves\, and in fa ct prove it by explicit computation. This case is actually more generally covered theoretically by the Lefschetz (1\,1) theorem\, which time permitt ing we may also discuss.\n LOCATION:https://researchseminars.org/talk/BUcomm/1/ END:VEVENT END:VCALENDAR