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Counting low degree number fields with almost prescribed successive minima

Algebraic Geometry

Speaker: Sameera Vemulapalli, Stanford
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Location: 2112 MSB
Start time: Wed, Dec 6 2023, 3:10PM

The successive minima of an order in a degree n number field are n real numbers encoding information about the Euclidean structure of the order. How many orders in degree n number fields are there with almost prescribed successive minima, fixed Galois group, and bounded discriminant? In this talk, I will address this question for n = 3,4,5. The answers, appropriately interpreted, turn out to be piecewise linear functions on certain convex bodies. If time permits, I will also discuss a geometric analogue of this problem: scrollar invariants of covers of $\mathbb P^1$.