BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//Claremont Center for the Mathematical Sciences - ECPv6.15.17.1//NONSGML v1.0//EN
CALSCALE:GREGORIAN
METHOD:PUBLISH
X-WR-CALNAME:Claremont Center for the Mathematical Sciences
X-ORIGINAL-URL:https://colleges.claremont.edu/ccms
X-WR-CALDESC:Events for Claremont Center for the Mathematical Sciences
REFRESH-INTERVAL;VALUE=DURATION:PT1H
X-Robots-Tag:noindex
X-PUBLISHED-TTL:PT1H
BEGIN:VTIMEZONE
TZID:America/Los_Angeles
BEGIN:DAYLIGHT
TZOFFSETFROM:-0800
TZOFFSETTO:-0700
TZNAME:PDT
DTSTART:20180311T100000
END:DAYLIGHT
BEGIN:STANDARD
TZOFFSETFROM:-0700
TZOFFSETTO:-0800
TZNAME:PST
DTSTART:20181104T090000
END:STANDARD
BEGIN:DAYLIGHT
TZOFFSETFROM:-0800
TZOFFSETTO:-0700
TZNAME:PDT
DTSTART:20190310T100000
END:DAYLIGHT
BEGIN:STANDARD
TZOFFSETFROM:-0700
TZOFFSETTO:-0800
TZNAME:PST
DTSTART:20191103T090000
END:STANDARD
BEGIN:DAYLIGHT
TZOFFSETFROM:-0800
TZOFFSETTO:-0700
TZNAME:PDT
DTSTART:20200308T100000
END:DAYLIGHT
BEGIN:STANDARD
TZOFFSETFROM:-0700
TZOFFSETTO:-0800
TZNAME:PST
DTSTART:20201101T090000
END:STANDARD
END:VTIMEZONE
BEGIN:VEVENT
DTSTART;TZID=America/Los_Angeles:20190226T121500
DTEND;TZID=America/Los_Angeles:20190226T131000
DTSTAMP:20260419T015612
CREATED:20190112T015039Z
LAST-MODIFIED:20190218T190711Z
UID:1047-1551183300-1551186600@colleges.claremont.edu
SUMMARY:When is the product of Siegel eigenforms an eigenform? (Jim Brown\, Occidental College)
DESCRIPTION:Modular forms are ubiquitous in modern number theory.  For instance\, showing that elliptic curves are secretly modular forms was the key to the proof of Fermat’s Last Theorem.  In addition to number theory\, modular forms show up in diverse areas such as coding theory and particle physics.  Roughly speaking\, a modular form is a complex-valued function defined on the complex upper half-plane that satisfies a large number of symmetries.  A modular form has two invariants: weight and level.  If one fixes a weight and level\, the collection of modular forms of that weight and level form a finite-dimensional complex vector space.  One has a collection of operators on these spaces referred to as Hecke operators.  A natural question is if one takes two eigenforms of these operators and multiplies them\, when is the product still an eigenform?  It was shown in independent work by Duke and Ghate that there is a finite list of pairs of eigenforms whose product is again an eigenform.  In this talk we will report on the case when one replaces modular forms with the more general case of Siegel modular forms.  This is work that was partially conducted during an REU in summer 2018.  No prior familiarity with modular forms is assumed.
URL:https://colleges.claremont.edu/ccms/event/antc-talk-jim-brown-occidental-college/
LOCATION:Millikan 2099\, Pomona College\, 610 N. College Ave.\, Claremont\, CA\, 91711\, United States
CATEGORIES:Algebra / Number Theory / Combinatorics Seminar
END:VEVENT
END:VCALENDAR