MATH Seminar
| Title: Counting low degree number fields with almost prescribed successive minima |
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| Seminar: Algebra |
| Speaker: Sameera Vemulapalli of Princeton University |
| Contact: Andrew Kobin, ajkobin@emory.edu |
| Date: 2023-03-28 at 4:00PM |
| Venue: MSC W301 |
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| Abstract: 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 $\mathbb{P}^1$. |
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