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UID:66f9a21527dac2c41239cc9f2c6159a8
CATEGORIES:Lie Group Quantum Mathematics Seminar
CREATED:20211111T131003
SUMMARY:Moonshine and Elliptic Curves
DESCRIPTION:Abstract: The study of moonshine originated from a series of numerical coin
 cidences connecting finite groups to modular forms. It has since evolved in
 to a rich theory that sheds light on the underlying algebraic structures th
 at these coincidences reflect.\nWe prove the existence of one such structur
 e, a module for Thompson's sporadic simple group, whose graded traces are s
 pecific half-integral weight weakly holomorphic modular forms. We then use 
 this module to study the ranks of certain families of elliptic curves. In p
 articular, this serves as an example of moonshine being used to answer ques
 tions in number theory.\n
X-ALT-DESC;FMTTYPE=text/html:<p style="margin: 0in;">Abstract:&nbsp;The study of moonshine originated fr
 om a series of numerical coincidences connecting finite groups to modular f
 orms. It has since evolved into a rich theory that sheds light on the under
 lying algebraic structures that these coincidences reflect.</p><p style="ma
 rgin: 0in;">We prove the existence of one such structure, a module for Thom
 pson's sporadic simple group, whose graded traces are specific half-integra
 l weight weakly holomorphic modular forms. We then use this module to study
  the ranks of certain families of elliptic curves. In particular, this serv
 es as an example of moonshine being used to answer questions in number theo
 ry.</p>
CONTACT:Maryam Khaqan, Stockholm University
X-EXTRAINFO:Zoom link https://rutgers.zoom.us/j/93921465287\nMeeting ID: 939 2146 5287\
 nPasscode: 196884, the dimension of the weight 2 homogeneous \nsubspace of 
 the moonshine module\n
DTSTAMP:20260901T083255
DTSTART;TZID=America/New_York:20211112T110000
DTEND;TZID=America/New_York:20211112T120000
SEQUENCE:0
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