The discriminant is a natural invariant of number fields - finite field extensions of Q. Given a positive integer n, how many different field extensions of Q are there of degree n and Discriminant at most X? We only know the answer for n<=5 due to works of Davenport-Heilbronn and Bhargava. However, Bhargava conjectured an answer for all n, and we present some theoretical evidence for this conjecture joint with Arul Shankar. We also review more general conjectures by Malle (with a correction by Turkelli ) regarding number fields with prescribed Galois groups.
Before the talk, at 3:10pm, there will be tea and cookies in Wean 6220.
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