Nicolas Kainz
Short CV
- October 2017 - September 2021: Bachelor of Science in Mathematics, Ulm University
- October 2021 - March 2023: Master of Science in Mathematics, Ulm University
- April 2023 - May 2026: Doctorate in Mathematics and scientific assistant at the 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)
- Differential Geometry and Mathematical Physics (Summer term 2025)
- Elements of Complex Analysis (Summer term 2025)
- SAPS - Preparation course for the DAV maths entrance exam (Summer term 2025)
- Geometric Complex Analysis (Winter term 2025/2026)
- SAPS - Preparation course for the DAV maths entrance exam (Winter term 2025/2026)
Research
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 Proceedings 65, pp. 99-116, 11/2024.
- Geometry of canonical regions and elliptic sectors in holomorphic flows. Topology Proceedings 68, pp. 95-121, 01/2026.
- Separatrix configurations in holomorphic flows. Qualitative Theory of Dynamical Systems 25:61, Springer Nature, 03/2026.
Talks at Conferences and Schools
- Global elliptic sectors in real time holomorphic flows. June 3, 2025, at the Summer School Topics in Complex Dynamics 2025: Connections to geometry and analysis, Barcelona (Spain)
- Elliptic sectors and heteroclinic regions in real time holomorphic flows. August 12, 2025, at the Summer Topology and Its Applications Conference, Mobile (South Alabama, USA)
- Basins, sectors and regions in holomorphic dynamical systems. August 26, 2025, at the Holomorphic Dynamics Conference, Oaxaca (Mexico)
University committees
I represented the interests of doctoral students at Ulm University in the following committees:
- Board of Promovierendenkonvent - Vorstand des Promovierendenkonvents (October 2023 - September 2025)
- Senate - Senat (October 2024 - September 2025)
- Faculty Council Mathematics and Economics - Fakult盲tsrat Mathematik und Wirtschaftswissenschaften (October 2023 - September 2025)
- Student Parliament - Studierendenparlament (October 2023 - September 2025)
- Working group for quality assurance funds - Arbeitskreis f眉r Qualit盲tssicherungsmittel (April 2024 - September 2025)
- Budget Committee of the Senate - Haushaltsausschuss des Senats (October 2024 - September 2025)
- LGFG Scholarship Award Committee - Vergabekommission f眉r LGFG-Stipendien (November 2023 - September 2025)
