Graz University of Technology offers two PhD positions in the Institute of Geometry. The research area is computational geometry and topology. Possible topics include topological data analysis, connections of discrete geometry and topology, design and analysis of algorithms in computational topology. We offer a 4-year university assistant position (30 h/week) with a net salary of approximately 29,000 EUR per year. The earliest starting date for both positions is Feb We are looking for outstanding students with a master's degree in Mathematics/Computer Science or a closely related field. Knowledge in at least one of the fields computational geometry or computational topology is a plus. Basic knowledge in algebraic topology, theoretical computer science, and programming skills, in particular in C++ or python, are also desirable. The position includes teaching duties as teaching assistant, both for students of mathematics and others. The ability to teach in English is required. Being able to teach in German is an advantage.