Number theory seminar: Tuesday April 25

[Masahiro Nakahara]

Hi everyone,

Our next NT seminar will be Anwesh Ray from Université de Montréal (CRM). Note that this talk will be virtual.

Time: Tuesday, April 25, 11am 

Location: Zoom: 934 8731 7861 Passcode: C401

Title: Diophantine stability for elliptic curves on average

Abstract: Let K be a number field and ℓ≥ 5 be a prime number.  Mazur and Rubin introduced the notion of diophantine stability for a variety X/K at a prime ℓ. Under the hypothesis that all elliptic curves E/ℚ have finite Tate-Shafarevich group, we show that there is a positive density set of elliptic curves E/ℚ of rank 1, such that E/K is diophantine stable at ℓ. This result has implications to Hilbert's tenth problem for number rings. This is joint work with Tom Weston.

See you there!

Masahiro

[Masahiro Nakahara]

Friendly reminder about the seminar happening soon :)