# Michal Szachniewicz

University of Oxford

Andrew Wiles Building

Radcliffe Observatory Quarter

Woodstock Road

Oxford

OX2 6GG

Non-reducedness of the Hilbert schemes of few points (2021) arXiv e-prints: 2109.11805

Existential closedness of $\overline{\mathbb{Q}}$ as a globally valued field via Arakelov geometry (2023) arXiv e-prints: 2306.06275

I work with model theory of some algebraic structures and I am interested in connections between those two areas.

Currently I am working under supervision of Ehud Hrushovski and I am studying Globally Valued Fields (GVFs). I am working on analouges of theorems known for $\overline{k(t)}[1]$ (the geometric case) in the $\overline{\mathbb{Q}}[1]$ (arithmetic case). Since in the geometric case intersection theory and cones of curves are used, in the arithmetic case tools like Arakelov geometry, Berkovich spaces and heights are relevant.

Teaching:

First year (2021-2022):

- TA of two sets of C1.1 Model Theory (MT 2021)
- TA of C2.6 Introduction to Schemes (HT 2022)

Second year (2022-2023):

- TA of B3.3 Algebraic Curves (HT 2023)