I am a postdoctoral fellow with 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.
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My newest preprint Degree spectra of analytic complete equivalence relation...
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About my Research
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.
About my Teaching
If you want to know about my teaching experience or access course notes please look at Teaching & Notes.