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SUMMARY:Fatemehzahra Janbazi (University of Toronto)
DTSTART:20250410T190000Z
DTEND:20250410T200000Z
DTSTAMP:20260423T005808Z
UID:ANTS/15
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/ANTS/15/">Ex
 tensions of Birch-Merriman and Related Finiteness Theorems</a>\nby Fatemeh
 zahra Janbazi (University of Toronto) as part of Calgary Algebra and Numbe
 r Theory Seminar\n\nLecture held in MS 337.\n\nAbstract\nA classical theor
 em of Birch and Merriman states that\, for fixed $n$\, the set of integral
  binary $n$-ic forms with fixed nonzero discriminant breaks into finitely 
 many $\\mathrm{GL}_2(\\mathbb{Z})$-orbits. In this talk\, I’ll present s
 everal extensions of this finiteness result. \n\nIn joint work with Arul S
 hankar\, we study a representation-theoretic generalization to ternary $n$
 -ic forms and prove analogous finiteness theorems for $\\mathrm{GL}_3(\\ma
 thbb{Z})$-orbits with fixed nonzero discriminant. We also prove a similar 
 result for a 27-dimensional representation associated with a family of K3 
 surfaces. \n\nIn joint work with Sajadi\, we take a geometric perspective 
 and prove a finiteness theorem for Galois-invariant point configurations o
 n arbitrary smooth curves with controlled reduction. This result unifies c
 lassical finiteness theorems of Birch–Merriman\, Siegel\, and Faltings.\
 n
LOCATION:https://researchseminars.org/talk/ANTS/15/
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