BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Wonjae Suh (Harvard College) DTSTART:20260917T200000Z DTEND:20260917T213000Z DTSTAMP:20261023T105402Z UID:STAGE/161 DESCRIPTION:Title: Complex multiplication\nby Wonjae Suh (Harvard College) as part of STA GE\n\nLecture held in Room 2-132 in the MIT Simons Building.\n\nAbstract\n Previously\, we showed that every finite abelian extension of $\\mathbb{Q} $ is contained in a cyclotomic extension. Motivated by this theorem\, we b egin this talk with the ideal-theoretic formulation of global class field theory for $K$ an arbitrary number field. One can then ask if the story fo r $K = \\mathbb{Q}$ can be replicated in other settings. We will see that this answer is in the affirmative for $K$ a quadratic imaginary field\; th is is realized beautifully in an analogy between cyclotomic theory and the theory of elliptic curves. Along the way\, we will develop some powerful tools that will allow us to traverse between the realms of algebraic geome try and transcendental complex analysis.\n LOCATION:https://researchseminars.org/talk/STAGE/161/ END:VEVENT END:VCALENDAR