This is the website of the research group on Quantum Geometry led by Murad Alim at the mathematics department of Heriot-Watt University, at the Maxwell institute for Mathematical Sciences in Edinburgh as well as at the Mathematics Department of the University of Hamburg. 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.