Masahiro Nakahara (UW)

PDL C-38

**Preseminar 2-2:30**

**Title**: Potential density of rational points

**Abstract**:A variety over the rational numbers Q may not have any rational points (points with coordinates in Q). However, sometimes we can extend the ground field by a finite extension to gain lots of rational points (Zariski dense many). If this is possible, then the variety is said to satisfy potential density. We explore this concept through examples with particular focus on curves.

**Seminar 2:30-3:30**

**Title**:Uniform potential density for rational points on algebraic groups and elliptic K3 surfaces

**Abstract**:A collection of varieties satisfies uniform potential density if each of them contains a dense subset of rational points after extending its ground field by a bounded degree. I will discuss this property for connected algebraic groups of a fixed dimension over fields of characteristic zero as well as elliptic K3 surfaces over number fields. This is joint work with Kuan-Wen Lai.

The talk will also be available via Zoom: https://washington.zoom.us/j/689897930

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