##### Department of Mathematics,

University of California San Diego

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### Math 209: Number Theory Seminar

## Sameera Vemulapalli

#### Princeton

## Counting low degree number fields with almost prescribed successive minima

##### 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 function field analogues of this problem.

[pre-talk at 1:20PM]

### February 23, 2023

### 2:00 PM

APM 6402 and Zoom; see https://www.math.ucsd.edu/~nts

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