## About Me

I am a PhD student at the University of Vienna at the Faculty of Mathematics. My supervisor is Herwig Hauser. 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.

I co-organize the Seminar Commutative Algebra & Differential Equations (CADE) taking place every Thursday from 11.00-12.30 at the Faculty of Mathematics at the University of Vienna.

## Curriculum Vitae

October 2022 – | PhD studies at the University of Vienna |

October 2021 – | Research assistant at the University of Vienna |

October 2020 – October 2022 | Master’s degree in mathematics at the University of Vienna |

March 2020 – August 2022 | Tutor at the University of Vienna |

October 2017 – August 2020 | Bachelor’s degree in mathematics at the University of Vienna |

June 2016 | High school graduation |

## Publications and Preprints

### Publications

- 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.

### Preprints

- Fürnsinn, F., Hauser, H., Kawanoue, H., On Abel’s Problem about Logarithmic Integrals in Positive Characteristic, 2024. preprint.
- Fürnsinn, F., Yurkevich, S., Algebraicity of hypergeometric functions with arbitrary parameters, 2023. preprint. To appear in the Bulletin of the London Mathematical Society.
- Thanks to Professor Juan Arias de Reyna the article is featured in the blog entry “Flowers of the hypergeometric garden“, on the Blog “Uncharted Waters” of IMUS at the University of Sevilla.

- 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.

## Talks

- May 17, 2024, MATHEXP-Polsys Seminar, Paris, “Fuchs’ Theorem, an Exponential Function, and Abel’s Problem in Positive Characteristic”.
- 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”.