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UID:cbc23dd775f13763dcbcee09a8680953
CATEGORIES:Colloquia
CREATED:20221205T133012
SUMMARY:Exceptional theta functions
LOCATION:Zoom
DESCRIPTION:Abstract: Classical theta functions are certain holomorphic functions (of o
 ne or several complex variables) that possess an infinite group of discrete
  symmetries.  They are a key building block of modern number theory: they c
 an be used to prove that the Riemann zeta function satisfies a functional e
 quation (more generally, are very useful in understanding certain L-functio
 ns) and are the first concrete examples of modular forms (more generally, a
 re useful for proving instances of Langlands functoriality).  One way to th
 ink about theta functions is that they are associated to the following pair
  of data: a lattice L in a positive definite quadratic space V, and a vecto
 r in a finite dimensional representation of SO(V).  I will discuss "excepti
 onal" theta functions, which are associated with similar data, where the gr
 oup SO(V) gets replaced by certain compact exceptional groups.  I will also
  discuss some applications.\n
X-ALT-DESC;FMTTYPE=text/html:<p>Abstract: Classical theta functions are certain holomorphic functions (o
 f one or several complex&nbsp;variables) that possess an infinite group of 
 discrete symmetries.&nbsp; They are a key building block of modern number t
 heory: they can be used to prove that the Riemann zeta function satisfies a
  functional equation (more generally, are very useful in understanding cert
 ain L-functions) and are the first concrete examples of modular forms (more
  generally, are useful for proving instances of Langlands functoriality).&n
 bsp; One way to think about theta functions is that they are associated to 
 the following pair of data: a lattice L in a positive definite quadratic sp
 ace V, and a vector in a finite dimensional representation of SO(V).&nbsp; 
 I will discuss "exceptional" theta functions, which are associated with sim
 ilar data, where the group SO(V) gets replaced by certain compact exception
 al groups.&nbsp; I will also discuss some applications.</p>
CONTACT:Aaron Pollack (UCSD)
DTSTAMP:20260827T051643
DTSTART;TZID=America/New_York:20221207T120000
DTEND;TZID=America/New_York:20221207T130000
SEQUENCE:0
TRANSP:OPAQUE
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