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SUMMARY:Louis Gaudet (UMass Amherst)
DTSTART:20251007T200000Z
DTEND:20251007T210000Z
DTSTAMP:20260422T173622Z
UID:FCNTS/8
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/FCNTS/8/">Co
 unting biquadratic number fields that admit quaternionic or dihedral exten
 sions</a>\nby Louis Gaudet (UMass Amherst) as part of Five College Number 
 Theory Seminar\n\nLecture held in Seeley Mudd 207 @Amherst College.\n\nAbs
 tract\nMany interesting problems in arithmetic statistics involve counting
  number fields (ordered by their discriminants\, say) with certain propert
 ies. In joint work with Siman Wong (UMass Amherst)\, we establish asymptot
 ic formulae for the number of biquadratic extensions of $\\mathbb{Q}$ that
  admit a degree-2 extension with Galois group $G$\, where $G$ is either th
 e quaternion group or the dihedral group (of order 8). We will discuss the
 se results and how they are proved\, and we will discuss their significanc
 e with regard to a theorem of Tate on lifts of projective Galois represent
 ations.\n
LOCATION:https://researchseminars.org/talk/FCNTS/8/
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