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SUMMARY:Louis Gaudet (UMass Amherst)
DTSTART:20251007T200000Z
DTEND:20251007T210000Z
DTSTAMP:20260824T073457Z
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 Pioneer Valley Numbe
 r Theory Seminar\n\nLecture held in Seeley Mudd 207 @Amherst College.\n\nA
 bstract\nMany interesting problems in arithmetic statistics involve counti
 ng number fields (ordered by their discriminants\, say) with certain prope
 rties. In joint work with Siman Wong (UMass Amherst)\, we establish asympt
 otic formulae for the number of biquadratic extensions of $\\mathbb{Q}$ th
 at admit a degree-2 extension with Galois group $G$\, where $G$ is either 
 the quaternion group or the dihedral group (of order 8). We will discuss t
 hese results and how they are proved\, and we will discuss their significa
 nce with regard to a theorem of Tate on lifts of projective Galois represe
 ntations.\n
LOCATION:https://researchseminars.org/talk/FCNTS/8/
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