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URL:https://uwaterloo.ca/pure-mathematics/events/number-theory-seminar-144
SUMMARY:Number Theory Seminar
CLASS:PUBLIC
DESCRIPTION:ZAHRA JANBAZI\, UNIVERSITY OF TORONTO\n\nExtensions of Birch-Me
 rriman and Related Finiteness Theorems\n\nA classical theorem of Birch and
  Merriman states that\, for fixed n\,\nthe set of integral binary n-ic for
 ms with fixed nonzero discriminant\nbreaks into finitely many GL(2\, Z)-or
 bits. In this talk\, I’ll\npresent several extensions of this finiteness
  result.\n\nIn joint work with Arul Shankar\, we study a representation-th
 eoretic\ngeneralization to ternary n-ic forms and prove analogous finitene
 ss\ntheorems for GL(3\,Z)-orbits with fixed nonzero discriminant. We also\
 nprove a similar result for a 27-dimensional representation associated\nwi
 th a family of K3 surfaces.\n\nIn joint work with Sajadi\, we take a geome
 tric perspective and prove a\nfiniteness theorem for Galois-invariant poin
 t configurations on\narbitrary smooth curves with controlled reduction. Th
 is result unifies\nclassical finiteness theorems of Birch–Merriman\, Sie
 gel\, and\nFaltings.\n\nMC 5479
DTSTAMP:20260408T022811Z
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