What: 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.

How: 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.

Why: 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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