Konstantinos Kartas

I am a Humboldt research fellow at the University of Münster. I am interested in the interactions between model theory and arithmetic geometry. 

Previously, I held postdoctoral positions in the arithmetic geometry group at MPIM Bonn and at IMJ-PRG/Sorbonne Université, mentored by F. Loeser. I completed my PhD at the University of Oxford in 2022, under the supervision of E. Hrushovski and J. Koenigsmann. 

PhD Thesis:

Contributions to the model theory of henselian fields (2022)

Research papers:

1. Perfectoid C_i transfer (2025), (submitted) | arXiv

2. On geometrically C_1 fields (2024), (submitted) arXiv

3. Beyond the Fontaine-Wintenberger theorem, with Franziska Jahnke (2025), J. Am. Math. Soc. 38, No. 4, 997-1047| arXiv
   (Upcoming Bourbaki Seminar La théorie des modèles des corps perfectoïdes, d'après Jahnke et Kartas)

4. Decidability via the tilting correspondence (2024), Algebra & Number Theory Vol. 18 No. 2, pp.209-248 | arXiv

5. Valued fields with a total residue map (2024), Journal of Mathematical Logic Vol. 24, No.3 | arXiv

6. Diophantine problems over tamely ramified fields (2023), Journal of Algebra Volume 617, pp. 127-159|arXiv

7. An undecidability result for the asymptotic theory of p-adic fields (2023), Annals of Pure and Applied Logic, Volume 174, Issue 2  |arXiv

8. Diophantine problems over Z^ab modulo prime numbers (2021), (preprint) arXiv

Survey papers/Miscellanea: 

1. Taming perfectoid rings, with Franziska Jahnke, Oberwolfach report

2. Decidability of local fields and their extensions (2021), Proceedings of the PLS '22

3. Stable groups (2018), M.Sc Thesis (under the supervision of E. Hrushovski)

Selected Talks (with slides or recording): 

1. Nonstandard methods in almost mathematics (2025), HCM Bonn (video)

2. Reflections on the work of Thanases Pheidas (2024), Panhellenic Logic Symposium (slides)

3. Beyond the Fontaine-Wintenberger theorem (2023), Luminy CIRM 2023 (video, slides)

4. Decidability via the tilting correspondence (2022), Géométrie et Théorie des Modèles (video , slides)

5. Decidability via the tilting correspondence (2021), Fields Institute (video) 

6. Diophantine problems over infinitely ramified fields (2020), MSRI (video)

PhD supervision: 

1. Jonas van der Schaaf (co-supervision with Franziska Jahnke)