My project aims to develop a precise mathematical framework for quantum mechanics on curved spaces. In particular, it aims to construct a rigorous formulation of quantum dynamics on K¨ahler manifolds using tools from modern differential geometry and geometric analysis.

To complete this project, I will use cutting edge tools from pure mathematics, drawing from my experience in differential geometry and work with Fields medalist Professor Sir Donaldson. Precisely, I intend to develop the theory of geometric quantisation to produce a precise analogue of the Sch¨odinger equation, which will allow for precise descriptions of the time evolution of quantum systems.

As quantum computing is becoming an ever more accessible reality, it is now more important than ever to have a robust understanding of the mathematics which underpins it. Beyond clear theoretical applications, there are immediate practical uses. For example, non-linear Gaussian Boson sampling has the potential to streamline many industries, such as drug development and environmental modeling.

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