This is the website of the research group on Quantum Geometry led by Prof. Murad Alim at the department of mathematics of the School of Computation, Information and Technology of the Technical University of Munich as well as at mathematics department of Heriot-Watt University and the Maxwell institute for Mathematical Sciences in Edinburgh. We work on quantum geometry, an area where mathematical structures are developed which are adapted to problems of quantization of physical systems and their dualities using methods from complex algebraic geometry, representation theory and number theory. We are particularly interested in studying the interplay of perturbative and non-perturbative structures using resurgence techniques in the context of topological string theory, mirror symmetry and BPS structures of supersymmetric theories. 

Here is a video explaining what quantum geometry is (in German with English subtitles)