##### Department of Mathematics,

University of California San Diego

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### Math 209 - Number Theory Seminar

## Masahiro Nakahara

#### U. Washington

## Uniform potential density for rational points on algebraic groups and elliptic K3 surfaces

##### Abstract:

A variety satisfies potential density if it contains a dense subset of rational points after extending its ground field by a finite degree. A collection of varieties satisfies uniform potential density if that degree can be uniformly bounded. I will discuss this property for connected algebraic groups of a fixed dimension and elliptic K3 surfaces. This is joint work with Kuan-Wen Lai.

### May 5, 2022

### 2:00 PM

Pre-talk at 1:20 PM

APM 6402 and Zoom

See https://www.math.ucsd.edu/~nts/

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