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SUMMARY:Scott Ahlgren (UIUC)
DTSTART:20211028T130000Z
DTEND:20211028T140000Z
DTSTAMP:20260423T024749Z
UID:UCDANT/20
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/UCDANT/20/">
 Congruences for the partition function</a>\nby Scott Ahlgren (UIUC) as par
 t of Dublin Algebra and Number Theory Seminar\n\n\nAbstract\nThe partition
  function p(n) counts the number of ways to break a natural number n into 
 parts. The arithmetic properties of this function have been the topic of i
 ntensive study for many years. Much of the interest (and the difficulty)  
 in this problem arises from the fact that values of the partition function
  are given by the coefficients of a weakly holomorphic modular form of hal
 f-integral weight.  I’ll describe some recent work with Olivia Beckwith 
 and Martin Raum\, and with Patrick Allen and Shiang Tang which goes a long
  way towards explaining exactly when congruences for the partition functio
 n can occur.  The main tools are techniques from the theory of modular for
 ms\, Galois representations\, and analytic number theory.\n
LOCATION:https://researchseminars.org/talk/UCDANT/20/
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