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
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.
Preferred address