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Emma Hansen (she/her)

I completed my Master's of Science in Aeronautics and Astronautics from the University of Washington, where my studies focused on control theory and optimisation.

I have four years of experience in the Mathematics PhD program at the University of British Columbia (UBC). My research focussed on applying convex optimisation techniques to problems in quantum key distribution key rate calculations. At the end of the 2024 academic year I made the difficult decision to withdraw from my PhD, to give myself the opportunity to study something that I have always wanted to. In September 2025 I will be re-starting in a Master's program in the UBC Mathematics department, studying differential geometry under Dr. Ailana Fraser.

Outside of academics I am an avid climber, and enjoy hiking, running, and being outdoors. I coach climbing with the youth High Performance Team at the Richmond Olympic Oval.

Research

Previously, my research focussed on optimisation of spectral functionals, these are functions which act on the eigenvalues of a matrix. Many of the methods used to analyse vector problems extend nicely to the matrix case for commuting matrices, but restricting to commuting matrices is not that practical. Extending existing methods to work in the non-commuting matrix case is one of my interests. This work was approached through the lens of studying key rate calculations for quantum key distribution protocols. This is a convex optimisation problem, over the density matrix of a quantum system, and is important in the development of new key distribution protocols.

For a collection of course projects I've done over the years, and a list of publications, see the links at the top!