Michal Szachniewicz
Bachelor's degree: Mathematics (University of Wroclaw 2019), Master's degree: Mathematics (University of Warsaw 2021).
Status
Postgraduate Student
Research groups
Address
Mathematical Institute
University of Oxford
Andrew Wiles Building
Radcliffe Observatory Quarter
Woodstock Road
Oxford
OX2 6GG
Major / recent publications
- Continuity of heights in families and complete intersections in toric varieties, with Pablo Destic and Nuno Hultberg, pdf
- Globally valued fields: foundations, with Itaï Ben Yaacov, Pablo Destic, Ehud Hrushovski, arXiv:2409.04570
- Hyperbolicity and model-complete fields, with Jinhe Ye, arxiv:2403.15300
- Existential closedness of $\overline{\mathbb{Q}}$ as a globally valued field via Arakelov geometry, arXiv:2306.06275
- Non-reducedness of the Hilbert schemes of few points, arXiv:2109.11805
Research interests
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.