Nicolas Kainz, M. Sc.
Institute of Numerical Mathematics, Helmholtzstr. 20, Room 1.06, 89081 Ulm
Tel: (+49) 731 50 23937
E-mail: nicolas.kainz(at)uni-ulm.de
Office Hours: Please make an appointment via e-mail.
Nicolas Kainz, M. Sc.
Short CV
- Oct. 2017 - Sep. 2021: Bachelor of Science, Mathematics, Ulm University
- Oct. 2021 - Mar. 2023: Master of Science, Mathematics, Ulm University
- Since Apr. 2023: PhD student, Institute of Numerical Mathematics, Ulm University
Teaching
- Elements of Topology (Summer term 2022)
- Numerical Methods for Ordinary Differential Equations (Summer term 2023)
- Modeling on Manifolds (Winter term 2023/2024)
- Numerical Methods for Ordinary Differential Equations (Summer term 2024)
- SAPS - Preparation course for the DAV maths entrance exam (Summer term 2024)
- Differential Topology and Mathematical Physics (Winter term 2024/2025)
- SAPS - Preparation course for the DAV maths entrance exam (Winter term 2024/2025)
Research
Research Fields
- Holomorphic and meromorphic Dynamical Systems
- Characterization of Separatrizes in the phase space of Holomorphic Dynamical Systems, especially for complex polynomial flows
- Local-global relations in complex polynomial flows
- Number of Separatrices of complex polynomial flows
- Behaviour of orbits near Infinity for complex polynomial flows
- Newton flows
Publications
Planar Analytic Dynamical Systems and their phase space structure, master thesis, 03/2023, available here: master thesis
Local geometry of Equilibria and a Poincare-Bendixson-type Theorem for Holomorphic Flows, Topology Proc. 65 (2025), pp. 99-116, e-published on November 7, 2024. Preprint: https://doi.org/10.48550/arXiv.2402.07612
Basins of Equilibria and geometry of Global Sectors in Holomorphic Flows, article for the Topology Proceedings journal, 10/2024, preprint: https://doi.org/10.48550/arXiv.2410.04895
University committees
I represent the interests of doctoral students at Ulm University in the following committees. If you have any concerns in this regard, please do not hesitate to contact me.
- Board of Promovierendenkonvent - Vorstand des Promovierendenkonvents (October 2023 - September 2025)
- Faculty Council Mathematics and Economics - Fakultätsrat Mathematik und Wirtschaftswissenschaften (October 2023 - September 2025)
- Student Parliament - Studierendenparlament (October 2023 - September 2025)
- LGFG Scholarship Award Committee - Vergabekommission für LGFG-Stipendien (November 2023 - September 2025)
- Working group for quality assurance funds - Arbeitskreis für Qualitätssicherungsmittel (April 2024 - September 2025)
- Senate - Senat (October 2024 - September 2025)