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Emma Hansen (she/her)

I am a PhD student in the Department of Mathematics at the University of British Columbia, working with Dr. Michael Friedlander. 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 really like math. My current research focusses on optimisation over matrix spaces, with application to quantum key distribution.

Outside of academics I am an avid climber, and enjoy hiking, running, and being outdoors.

Research

My current research focusses 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. My work is 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!