Gunnar Wilken

Profile

I am a mathematician, working as Science and Technology Associate (STA) at the Okinawa Institute of Science and Technology Graduate University (OIST) in Japan. My central research topic is mathematical logic, in particular proof theory, where I study structures called elementary patterns of resemblance and ordinal notation systems in general. My research interests furthermore cover topics in theoretical computer science, where I worked on term rewriting systems such as Gödel’s T, and logic programming. My past research also touched upon signal processing in the context of electron tomography of proteins, particularly on improvements in 3D reconstruction of biological molecules and related software development. My teaching experience covers various fields of mathematics and computer science (proof and set theory in mathematical logic, introduction to theoretical computer science, as well as discrete mathematics, Fourier transforms and tomography. In 2023 I earned the MIT IDSS certificate on Data Science and Machine Learning. I received my Diplom (comparable to Master’s degree), PhD (Dr. rer. nat.), and Habilitation (Priv.Doz.) in mathematics at the University of Münster in Germany. Please see my CV for detailed lists of publications, invited conference presentations, and teaching. For further questions, contact me via email: wilken@oist.jp.

Selected Publications:

Peer-reviewed Articles

Wilken, G. (2024). Fundamental sequences based on localization.
LNCS Proceedings of the 20th Conference on Computability in Europe (CiE): Twenty Years of Theoretical and Practical Synergies, 324-338.

Wilken, G. (2021). Pure Σ₂-Elementarity beyond the Core.
Annals of Pure and Applied Logic, 172, 1-93.
https://www.sciencedirect.com/science/article/pii/S0168007221000592/

Wilken, G. (2018). Pure Patterns of Order 2.
Annals of Pure and Applied Logic, 169, 54-82.
https://www.sciencedirect.com/science/article/pii/S0168007217301069?via%3Dihub

Weiermann, A., Wilken, G. (2013). Goodstein sequences for prominent ordinals up to the ordinal of Π¹₁-CA₀.
Annals of Pure and Applied Logic, 164, 1493-1506.

Carlson, T.J., Wilken, G. (2012). Normal Forms for Elementary Patterns.
The Journal of Symbolic Logic, 77, 174-194.

Wilken, G., Weiermann, A. (2012). Derivation Lengths Classification of Gödel’s T extending Howard’s Assignment.
Logical Methods in Computer Science, 8, 1-44.

Carlson, T.J., Wilken, G. (2012). Tracking Chains of Σ₂-elementarity.
Annals of Pure and Applied Logic, 163, 23-67.

Wilken, G., Weiermann, A. (2011). Ordinal Arithmetic with Simultaneously defined Theta-Functions.
Mathematical Logic Quarterly, 57, 116-132.

Wilken, G., Weiermann, A. (2009). Complexity of Gödel’s T in lambda-Formulation.
Lecture Notes in Computer Science, 5608, 386-400.

Wilken, G. (2007). Assignment of Ordinals to Patterns of Resemblance.
The Journal of Symbolic Logic, 72, 704-720.

Wilken, G. (2007). Σ₁-elementarity and Skolem Hull Operators.
Annals of Pure and Applied Logic, 145, 162-175.

Wilken, G. (2007). Ordinal Arithmetic based on Skolem Hulling.
Annals of Pure and Applied Logic, 145, 130-161.

Wilken, G. (2006). The Bachmann-Howard Structure in terms of Σ₁-elementarity.
Archive for Mathematical Logic, 45, 807-829.

Peer-reviewed Book Chapters

Wilken, G. (2020). A Glimpse of Σ₃-Elementarity.
Invited, peer-reviewed book chapter in:Kahle, R., Rathjen, M. (eds.), The Legacy of Kurt Schuette, 415-441. Springer Nature Switzerland 2020.
https://link.springer.com/chapter/10.1007/978-3-030-49424-7_21

Wilken, G. (2017). Tracking Chains Revisited.
Invited, peer-reviewed book chapter in: Friedman, S.-D., Raghavan, D., Yang, Y. (eds.), Sets and Computations, 183-220. Lecture Notes Series, Institute for Mathematical Sciences, National University of Singapore 2017.
https://www.worldscientific.com/doi/abs/10.1142/9789813223523_0008

Recent Preprints

Wilken, G. (2024). Fundamental Sequences based on Localization.
(Extended version of the LNCS Proceedings of CiE 2024 in Amsterdam containing complete proofs.)
https://arxiv.org/abs/2410.15953