I am a postdoctoral fellow in the logic group of the Department of Pure Mathematics of the University of Waterloo. I obtained my Ph.D. in 2019 from the Vienna University of Technology under the supervision of Ekaterina Fokina.
Please see my publications or read the short statement about my research interests below. You can find preprints of most of my publications on arXiv.
My research area is computability theory. I am specifically interested in the computational and descriptive complexity of mathematical objects. In my research I typically aim to answer questions of the following kind.
- Given a mathematical structure (for example a field), how complicated is it to compute an isomorphism between any two isomorphic copies of it?
- Given a mathematical structure for which we can not necessarily compute its basic operations, in which Turing degrees can we find isomorphic copies of it?
- Given a structure, how complicated is its Scott sentence (A sentence in infinitary logic whose models are isomorphic to the given structure)?
- Given a structure with interesting computational properties, can we find a structure with such properties in natural classes of structures?
In my Ph.D. thesis I focused on question 1,2, and 4 if we consider computational properties not up to isomorphism but up to other equivalence relations such as elementary equivalence and bi-embeddability. Because of this I developed an interest in the complexity of equivalence relations both from a descriptive as well as from a computational point of view.