Research group

Mr Zixuan Zhu (PhD student)

TEACHING

---

Responsible for the M.Sc. Mathematics program

---

Module Representative for Mathematical Logic

---

Office hours

during term: Thu, 9:30-10:30 and by appointment

outside term: By appointment

---

Teaching in the summer term 2026

Lecture course Model Theory of Valued Fields (Learnweb page)

Seminar Model Theory of PAC Fields (Learnweb page) 

Research Seminar Model Theroy, Geometry and Group Theory (organised together with Dr. Brück and Prof. Tent, Homepage)

---

Teaching in the winter term 2025/26

Lecture course Introduction to Model Theory (Learnweb page)

Seminar Model Theory of Differential Fields (Learnweb page)

Research Seminar Model Theroy, Geometry and Group Theory (organised together with Dr. Brück, Prof. Jahnke and Prof. Tent, Homepage)

---

Teaching in the summer term 2025

Lecture course Logic 1 (in German, Learnweb page)

Seminar Models of Peano Arithmetic (organised together with Prof. Schindler, Learnweb page) 

Research Seminar Model Theroy, Geometry and Group Theory (organised together with Prof. Jahnke, Prof. Kwiatkowska and Prof. Tent, Homepage)

---

Teaching in the winter term 2024/25

Lecture course Logical Foundations (in German, Learnweb page)

Lecture course Logic 4 - Model Theory of Pseudofinite Fields (Learnweb page)

Seminar Model Theory of the Witt-Frobenius (organised together with Mr Ramello,  Learnweb page)

Research Seminar Model Theroy, Geometry and Group Theory (organised together with Dr. Brück, Prof. Kwiatkowska and Prof. Tent, Homepage)

---

Teaching in the summer term 2024

Lecture course Logic 1 (in German, Learnweb page)

Seminar Model Theory and Combinatorics (organised together with Dr. Sullivan,  Learnweb page)

Research Seminar Model Theroy, Geometry and Group Theory (organised together with Dr. Brück, Prof. Kwiatkowska and Prof. Tent, Homepage)

---

Teaching in the winter term 2023/24

Lecture course Computability (in German, Learnweb page)

Seminar in Model Theory: Continuous Logic and Applications (organised together with Dr. Zou,  Learnweb page)

Research Seminar Model Theory, Geometry and Group Theory (organised together with Prof. Kwiatkowska and Prof. Tent, homepage)

---

Teaching in the summer term 2023

Lecture course Model Theory of Valued Fields (Learnweb page)

Seminar in condensed form (in Landhaus Rothenberge) Model Theory Meets Algebraic Geometry (organised together with Dr. Bays and JProf. Jahnke, Learnweb page)

Research Seminar Model Theroy, Geometry and Group Theory (organised together with Dr. Bays, JProf. Jahnke and JProf. Kwiatkowska,  Homepage)

---

Sabbatical during the winter term 2022/23

---

Teaching in the summer term 2022

Lecture course Logic 3 - NIP Theories (Learnweb page)

Seminar in condensed form (in Landhaus Rothenberge) Model Theory of Fields (organised together with JProf. Jahnke, Learnweb page)

Research Seminar Model Theroy, Geometry and Group Theory (organised together with JProf. Jahnke, JProf. Kwiatkowska and Prof. Tent, homepage)

---

Teaching in the winter term 2021/22

Lecture course Logic 2 - Introduction to Model Theory (in German, Learnweb page)

Seminar Model Theory - Introduction to Stability Theory (Learnweb page)

Research Seminar Model Theroy, Geometry and Group Theory (organised together with Prof. Kwiatkowska and Prof. Tent, homepage)

---

Teaching in the summer term 2021

Lecture course Logic 1 (in German, Learnweb page)

Seminar Model Theory of Pseudofinite Structures (organised together with Dr. Bays and Prof. Tent, Learnweb page)

Research Seminar Model Theory, Geometry and Group Theory (organised together with Prof. Jahnke, Prof. Kwiatkowska and Prof. Tent, homepage)

---

Teaching in the winter term 2020/21

Lecture course Computability (in German, Learnweb page)

Seminar O-Minimality and the André-Oort Conjecture (organised together with Prof. Hartl,  Learnweb page)

Research Seminar Model Theory, Geometry and Group Theory (organised together with Prof. Tent, homepage)

Research

---

Editorial responsibility

Editor-in-chief of the journal Model Theory.

---

Publications

Ph.D. Thesis

Fusion libre et autres constructions génériques (pdf)
(Université Paris 7, 2006).

Habilitation

Contributions à la théorie des modèles des corps (pdf)
(Université Paris Diderot Paris 7, 2013).

---

Textbook

• Martin Hils and François Loeser, A first Journey through Logic, Volume 89 of the series 'Student Mathematical Library', American Mathematical Society, Providence, RI, September 2019, 185 pp.

Published articles

1. Assaf Hasson and Martin Hils, Fusion over Sublanguages (pdf)
   (J. Symbolic Logic 71(2) (2006), 361-398).
2. Martin Hils, Semifree Actions of Free Groups (pdf)
   (Arch. Math. Logic 46(2) (2007), 93-105).
3. Martin Hils, La fusion libre: le cas simple (pdf)
   (J. Inst. Math. Jussieu 7(4) (2008), 825-868).
4. Andreas Baudisch, Martin Hils, Amador Martin-Pizarro, and Frank O. Wagner, Die böse Farbe (pdf, English translation pdf)
   (J. Inst. Math. Jussieu 8(3) (2009), 415-443).
5. Manuel Bodirsky, Martin Hils, and Barnaby Martin, On the Scope of the Universal-Algebraic Approach to Constraint Satisfaction
   (Proc. of LICS 2010, 25th Annual IEEE Symposium on Logic in Computer Science (2010), 90-99).
   (long version: Log. Meth. Comput. Sci. 8(3:13) (2012), arXiv pdf).
6. Martin Hils, Generic Automorphisms and Green Fields (pdf)
   (J. Lond. Math. Soc. 85(3) (2012), 223-244).
7. Manuel Bodirsky and Martin Hils, Tractable Set Constraints (pdf)
   (J. Artif. Intell. Res. 4 (2012), 731-759).
   (An extended abstract of this article, in collaboration with Manuel Bodirsky and Alex Krimkevich, was published in IJCAI'11, Barcelona.)
8. Martin Bays, Misha Gavrilovich, and Martin Hils, Some Definability Results in Abstract Kummer Theory (pdf)
   (Int. Math. Res. Notices 2014(14) (2014), 3975-4000).
9. Artem Chernikov and Martin Hils, Valued Difference Fields and NTP2 (pdf)
   (Israel J. Math 2014 204(1) (2014), 299-327).
10. Juan Diego Caycedo and Martin Hils, Bad Fields with Torsion (pdf).
    (J. Symbolic Logic 80(1) (2015), 221-233).
11. Martin Bays, Martin Hils, and Rahim Moosa, Model Theory of Compact Complex Manifolds with an Automorphism (pdf)
    (Trans. Amer. Math. Soc. 369(6) (2017), 4485-4516).
    Correction to the statement of the abelian group configuration theorem (Theorem C.2).
12. Martin Hils, Moshe Kamensky and Silvain Rideau, Imaginaries in Separably Closed Valued Fields (pdf)
    (Proc. Lond. Math. Soc. 116(6) (2018), 1457-1488).
13.  Martin Hils and Rosario Mennuni, Some definable types that cannot be amalgamated (pdf) (MLQ Math. Log. Q. 69(1) (2023), 46-49).

14. Martin Hils and Rosario Mennuni, The domination monoid in henselian valued fields (pdf) (Pacific J. Math. 328(2) (2024), 287-323).

15. Martin Hils and Silvain Rideau-Kikuchi, Un principe d'Ax-Kochen-Ershov imaginaire (pdf)
    (J. Eur. Math. Soc. 28 (2026), 1009-1080).

16. Pablo Cubides Kovacsics, Martin Hils and Jinhe Ye, Beautiful pairs (pdf)
    (J. Reine Angew. Math., Ahead of Print (2026) DOI 10.1515/crelle-2026-0014).

17. Martin Hils and Stefan Marian Ludwig, An Approximate AKE Principle for Metric Valued Fields
    (J. Symbolic Logic. Published online 2026:1-23. doi:10.1017/jsl.2026.10206).

 

Preprints

• Martin Hils, Ehud Hrushovski, and Pierre Simon, Definable Equivariant Retractions in Non-Archimedean Geometry (arXiv:2101.02619v1 [math.LO] pdf (2021), 29 pages).
• Martin Hils, Martina Liccardo, and Pierre Touchard, Stably Embedded Pairs of Ordered Abelian Groups (arXiv:2308.09989v1 [math.LO] pdf (2023), 33 pages).
• Martin Hils, Ehud Hrushovski, Jinhe Ye and Tingxiang Zou, Lang-Weil Type Estimates in Finite Difference Fields (arXiv:2406.00880v1 [math.NT] pdf (2024), 36 pages).
• Juan Pablo Acosta López and Martin Hils, One-dimensional Commutative Groups Definable in Algebraically Closed Valued Fields and in Pseudo-local Fields pdf (arxiv:2112.00430v2 [math.LO] (2025), 36 pages).

Chapter in a textbook

• Martin Hils, Model Theory of Valued Fields (pdf)
  (Chapter in the textbook Lectures in Model Theory,  Franziska Jahnke, Daniel Palacin and Katrin Tent (editors), published in the series Münster Lectures in Mathematics of the European Mathematical Society, ISBN 978-3-03719-184-2, April 2018, 151-180).

 

 

---

Some talks and tutorials

• Imaginaries in Model Theory (slides)
  (Talk at the conference Philosophy and Model Theory, Université Paris Ouest & ENS, June 2010)
• Introduction to Model Theory (slides)
  (Tutorial at the Second International Conference and Workshop on Valuation Theory, Segovia / El Escorial, July 2011)
• Tameness in non-archimedean geometry through model theory (after Hrushovski-Loeser) (slides)
  (Tutorial at the conference Model Theory 2013, Ravello, June 2013)
• A Model Theoretic Approach to Berkovich Spaces (video)
  (Tutorial at the Introductory Workshop: Model Theory, Arithmetic Geometry and Number Theory, MSRI, Berkeley, February 2014)
• Model Theory of Compact Complex Manifolds with an Automorphism (video)
  (Talk at the Workshop on Interactions between Model Theory and Arithmetic Dynamics, Fields Institute, Toronto, July 2016)
• Definable equivariant retractions onto skeleta in non-Archimedean geometry (video)
  (Talk at the conference Model Theory and Applications, IHP, Paris, March 2018)
• Imaginaries in Separably Closed Valued Fields (video)
  (Talk in the Kolchin Seminar in Differential Algebra, CUNY, New York, March 2019)
• Spaces of definable types and beautiful pairs in unstable theories (video)
  (Talk in the Model Theory Seminar, MSRI, Berkeley, December 2020)
• Beautiful pairs of unstable theories and spaces of definable types  (video)
  (Talk at the Workshop on Trends in Pure and Applied Model Theory, Fields Institute, Toronto, July 2021)
• Lang-Weil type bounds in finite difference fields (video)
  (Talk at the Thematic Meeting Model Theory of Valued Fields, CIRM, Marseille, May/June 2023)