At a meeting of the Algebraic Geometry, Number Theory, and Computation Simons
Collaboration, I gave a short talk surveying the results and ideas of
*Improved bounds on number fields of small
degree*, joint work with Anderson, Gafni,
Hughes, Lemke Oliver, Thorne, Wang, and Zhang.

In many ways this is a follow-up to an earlier talk I gave to the Simons
Collaboration
about work towards a quantitative form of Hilbert's irreducibility theorem.
Both of these results grew out of an AIM workshop.

The slides for this talk are available here.

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