BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Nha Truong (Hawaii) DTSTART:20230406T210000Z DTEND:20230406T220000Z DTSTAMP:20260423T024737Z UID:UCSD_NTS/94 DESCRIPTION:Title: Slopes of modular forms and geometry of eigencurves\nby Nha Truong ( Hawaii) as part of UCSD number theory seminar\n\nLecture held in APM 6402 and online.\n\nAbstract\nThe slopes of modular forms are the $p$-adic valu ations of the eigenvalues of the Hecke operators $T_p$. The study of slope s plays an important role in understanding the geometry of the eigencurves \, introduced by Coleman and Mazur. \n\nThe study of the slope began in th e 1990s when Gouvea and Mazur computed many numerical data and made severa l interesting conjectures. Later\, Buzzard\, Calegari\, and other people m ade more precise conjectures by studying the space of overconvergent modul ar forms. Recently\, Bergdall and Pollack introduced the ghost conjecture that unifies the previous conjectures in most cases. The ghost conjecture states that the slope can be predicted by an explicitly defined power seri es. We prove the ghost conjecture under a certain mild technical condition . In the pre-talk\, I will explain an example in the quaternionic setting which was used as a testing ground for the proof. \nThis is joint work wit h Ruochuan Liu\, Liang Xiao\, and Bin Zhao.\n\npre-talk at 1:30pm (note un usual time)\n LOCATION:https://researchseminars.org/talk/UCSD_NTS/94/ END:VEVENT END:VCALENDAR