About Me

I am working on the algebraic study of differential equations in characteristic zero as well as in positive characteristic. In particular, I am interested in work regarding the algebraicity of solutions of differential equations, (differential) Galois groups, the Tannakian formalism, hypergeometric functions, and work related to the Grothendieck \(p\)-curvature conjecture. Moreover, I have a strong interest in combinatorics.

I started my PhD studies in October 2022. Before, I also obtained my Bachelor’s and Master’s degree at the University of Vienna; my studies lasted from 2017-2020, and from 2020-2022, respectively.

For an extended CV see here.

Publications and Preprints

Publications

• Fürnsinn, F., Yurkevich, S., Algebraicity of hypergeometric functions with arbitrary parameters. Bull. London Math. Soc., 56: 2824-2846. 2024. DOI: 10.1112/blms.13103
  
• Hula, A., Fürnsinn, F., Schwieger, K., Saleh, P., Neumann, M., Ecker, H., Deriving a joint risk estimate from dynamic data collected at motorcycle rides. Accident Analysis & Prevention, 159. 2021. DOI: 10.1016/j.aap.2021.106297

Preprints

• Fürnsinn, F., Hauser, H., Kawanoue, H., On Abel’s Problem about Logarithmic Integrals in Positive Characteristic, 2024. preprint.
• Fürnsinn F., Hauser, H., Fuchs’ theorem on linear differential equations in arbitrary characteristic, 2023. preprint.

Theses

• Fürnsinn, F., A normal form theorem for regular singular differential operators in positive characteristic. 2022. Master’s thesis submitted at the University of Vienna.
• Fürnsinn, F., The Kakeya Problem. 2020. Bachelor’s thesis submitted at the University of Vienna.

Thanks to Professor Juan Arias de Reyna the article “Algebraicity of hypergeometric functions with arbitrary parameters” is featured in the blog entry “Flowers of the hypergeometric garden“, on the Blog “Uncharted Waters” of IMUS at the University of Sevilla.

Talks

• November 26, 2024, Arbeitsgemeinschaft Diskrete Mathematik, Vienna, “An Unexpected Symmetry on Graphs”.
• November 12, 2024, Séminaire Différentiel, Versailles, “Fuchs’ Theorem, an Exponential Function, and Abel’s Problem in Positive Characteristic”. (Slides).
• May 17, 2024, MATHEXP-Polsys Seminar, Paris-Saclay, “Fuchs’ Theorem, an Exponential Function, and Abel’s Problem in Positive Characteristic”. (Slides).
• March 26, 2024, Functional Equations in LIMoges: FELIM 2024, Limoges, “Algebraicity of Hypergeometric Functions with Arbitrary Parameters”. (Slides).
• February 15, 2024, Workshop Fuchsian Differential Equations in Zero and Positive Characteristic, Lisbon, “Fuchs’ Theorem, an Exponential Function, and Abel’s Problem in Positive Characteristic”.
• January 23, 2024, Arbeitsgemeinschaft Diskrete Mathematik, Vienna, “Algebraicity of Hypergeometric Functions with Arbitrary Parameters”. (Slides).
• November 9, 2023, Séminaire Calcul Formel, Limoges, “Fuchs’ Theorem and an Exponential Function in Positive Characteristic”.
• November 6, 2023, Séminaire de l’équipe combinatoire et interactions, Bordeaux, “Algebraicity of Hypergeometric Functions with Arbitrary Parameters”. (Slides).
• October 18, 2023, Seminar Commutative Algebra & Differential Equations, Vienna, “An Exponential Function in Characteristic p”.
• February 17, 2023, Workshop Periods, Lisbon, “An Exponential Function in Characteristic p”.
• May 13, 2022, Workshop Fuchsian Differential Equations, Lisbon, “The Fuchs-Frobenius Method in Characteristic p”.

Teaching

I was teaching the following courses at the University of Vienna:

• Winter Term 2024/2025: Exercise classes on Introduction to Mathematics
• Summer Term 2022: Tutorials on Discrete Mathematics
• Summer Term 2020 – Winter Term 2021/2022: Tutorials for first and second semester students