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“Rational Points in One-Parameter Families”

Special Seminar

Come join us Monday January 22, 2018 at 12 pm in RM 507, Professor Ari Shnidman (Boston College) will be giving a special lecture about “Rational Points in One-Parameter Families”.


How often does a “random” algebraic plane curve f (x , y) = 0 have a solution with rational coordinates? For one-parameter “twist” families of elliptic curves, Goldfeld conjectured that there is a rational point exactly half of the time. Recent progress towards this conjecture makes use of Selmer groups, and I’ll explain the simple geometric idea underlying their construction. I’ll also describe results for families of curves of higher genus and abelian varieties of higher dimension.

Mathematics Hall, room 507

Monday January 22, 2018 12 pmĀ 

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