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Research

Model-theoretic algebra or algebraic model theory?

tl;dr I am working at the intersection of algebra and logic. The objects I care about are algebraic in nature (they are fields with some extra special decoration), but the questions I try to understand come from model theory. Often, this boils down to understanding how much of a certain object can be described using purely formal statements, not unlike the \(\epsilon-\delta\) definition of a limit you might have seen in your first Analysis class. If you're not interested in more details, you can skip ahead to Preprints.

The full story At the center of my research stand valued fields, which are fields enriched with a map onto an ordered abelian group with special properties, a valuation. Understanding a valued field \((K,v)\) (possibly with extra structure) has historically been a game of finding the correct invariants for its theory, reducing the possibly complicated valuational structure to something easier to understand and classify. Two natural invariants are the value group \(\Gamma_K\) and the residue field \(k\) of \((K,v)\), which can be combined in the leading terms structure \(\mathrm{RV}\). Ever since the first instance of this philosophy, the celebrated Ax-Kochen/Ershov theorems, a great industry has blossomed which seeks to understand the model theory of valued fields along these lines.
I am specifically interested in two direction:

Preprints The icons connect the preprints to the interests/projects specified above.

Talks The talks are divided into major topic or work they are based on, even though each one might have a slightly different title.

Notes and theses