# Joint IAS/PU Number Theory Seminar

## Counting Low Degree Number Fields with Almost Prescribed Successive Minima

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 function field analogues of this problem.

### Date & Time

January 26, 2023 | 4:30pm – 5:30pm

### Location

Simonyi Hall 101 and Remote Access### Speakers

Sameera Vemulapalli

### Affiliation

Princeton University