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DTSTAMP:20261001T153257Z
UID:1794398400@ist.ac.at
DTSTART:20261111T130000
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DESCRIPTION:Speaker: Katy Woo\nhosted by Vivian Kuperberg\nAbstract: There 
 is a long-standing history of using prime counting results to prove new th
 eorems about arithmetic objects\; Dirichlet’s theorem on primes in arith
 metic progressions was a key input in Hasse’s original proof of the loca
 l-to-global principle for quadratic forms over Q. In Corollary X.6.2.1 of 
 Silverman’s “The Arithmetic of Elliptic Curves”\, any elliptic curve
  of the form y^2 = x^3 + px for p a prime number congruent to 7 mod 16 is 
 shown to have rank zero\; Dirichlet’s theorem can be applied to show tha
 t there are infinitely many such elliptic curves. The breakthrough work of
  Green\, Tao\, and Ziegler on simultaneously prime values of linear system
 s was applied both to study Brauer-Manin obstructions to local-to-global p
 rinciples for certain conic bundles and to construct families of elliptic 
 curves with rank 1.In this talk\, we will build on the seminal work of Gre
 en and Sawhney to prove new instances of the multivariate Bateman-Horn con
 jecture\; the key input will be methods from additive combinatorics. We wi
 ll then discuss how to use these new prime counting results to study the B
 rauer-Manin obstruction to local-to-global principles for an expanded clas
 s of conic bundles and construct quadratic twist families of elliptic curv
 es with rank 2.This talk is based on joint work with Niven Achenjang.
LOCATION:Mondi 2\, Central Building\, ISTA
ORGANIZER:
SUMMARY:Katy Woo: Arithmetic consequences of additive combinatorics
URL:https://talks-calendar.ista.ac.at/events/6675
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