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Alexander Domke

Mira Tartarotti: Relative distality and incidence bounds for valued fields with finite residue field

Thursday, 29.01.2026 11:00 im Raum SR1D

Mathematik und Informatik

The class of so-called distal theories was isolated by Simon as a class of purely unstable NIP theories. Examples include all o-minimal theories and the theory of the p-adics. A rare natural example of an NIP theory that is neither stable nor distal is the theory of algebraically closed valued fields (ACVF), which interprets an o-minimal part (the value group) and a stable part (the residue field). We introduce the notion of relative distality and show that ACVF is distal relative to the residue field. As an application, we strengthen a result of Bays and Martin by proving that valued fields with finite residue field uniformly satisfy incidence bounds in the sense of the Szemerédi?Trotter Theorem. The argument relies on distal incidence bounds due to Chernikov, Galvin, and Starchenko. I will review the relevant model-theoretic and combinatorial background, and explain the main ideas of the proofs as time permits.



Angelegt am 27.01.2026 von Alexander Domke
Geändert am 27.01.2026 von Alexander Domke
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