BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//University of California\, Berkeley//UCB Events Calendar//EN
CALSCALE:GREGORIAN
METHOD:PUBLISH
BEGIN:VTIMEZONE
TZID:America/Los_Angeles
BEGIN:STANDARD
TZOFFSETFROM:-0700
TZOFFSETTO:-0800
DTSTART:19701029T020000
RRULE:FREQ=YEARLY;BYMONTH=11;BYDAY=1SU
END:STANDARD
BEGIN:DAYLIGHT
DTSTART:19700402T020000
TZOFFSETFROM:-0800
TZOFFSETTO:-0700
RRULE:FREQ=YEARLY;BYMONTH=3;BYDAY=2SU
END:DAYLIGHT
END:VTIMEZONE
BEGIN:VEVENT
DTSTAMP:20180129T160341Z
DTSTART;TZID=America/Los_Angeles:20180205T151000
DTEND;TZID=America/Los_Angeles:20180205T170000
TRANSP:OPAQUE
SUMMARY:Arithmetic Geometry and Number Theory RTG Seminar: Automorphy of mod 3 representations over CM fields
UID:115141-ucb-events-calendar@berkeley.edu
ORGANIZER;CN="UC Berkeley Calendar Network":
LOCATION:748 Evans Hall
DESCRIPTION:Patrick Allen\, UIUC\n\nWiles's proof of the modularity of semistable elliptic curves over the rationals uses\, as a starting point\, the Langlands-Tunnell theorem\, which implies that the mod 3 Galois representation attached to an elliptic curve over the rationals arises from a modular form of weight one. In order to feed this into modularity lifting theorems\, one needs to use congruences between modular forms of weight one and modular forms of higher weight. Similar congruences are not known over CM fields\, and Wiles's strategy runs into problems right from the start. We circumvent this congruence problem and show that mod 3 representations over CM field arise from the "correct" automorphic forms. Our argument relies on a 2-adic automorphy lifting theorem over CM fields together with a "2-3 switch" that gives a criterion for when a given mod 6 representation arises from an elliptic curve. This is joint work in progress with Chandrashekhar Khare and Jack Thorne.\n\nSeminar Format: The seminar consists of two 50-minute talks\, a pre-talk (3:10-4:00) and an advanced talk (4:10-5:00)\, with a 10-minute break (4:00-4:10) between them. The advanced talk is a regular formal presentation about recent research results to general audiences in arithmetic geometry and number theory\; the pre-talk (3:10-4:00) is to introduce some prerequisites or background for the advanced talk to audiences consisting of graduate students.
URL:http://events.berkeley.edu/index.php/calendar/sn/pubaff.html?event_ID=115141&view=preview
SEQUENCE:0
CLASS:PUBLIC
CREATED:20180129T160341Z
LAST-MODIFIED:20180129T160341Z
X-MICROSOFT-CDO-BUSYSTATUS:BUSY
X-MICROSOFT-CDO-INSTTYPE:0
X-MICROSOFT-CDO-IMPORTANCE:1
X-MICROSOFT-CDO-OWNERAPPTID:-1
END:VEVENT
END:VCALENDAR