Michal Szachniewicz

Bachelor's degree: Mathematics (University of Wroclaw 2019), Master's degree: Mathematics (University of Warsaw 2021).

Status

Postgraduate Student

+44 1865 283875

Contact form

Research groups

Mathematical Logic

Address

Mathematical Institute
University of Oxford
Andrew Wiles Building
Radcliffe Observatory Quarter
Woodstock Road
Oxford
OX2 6GG

Major / recent publications

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

Research interests

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

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)