Emmanuel Travassaros
Minimal Spectrahedral Representations for Facial Dimension Realisations
This project aims to explore the geometric and algebraic structure of affine slices of the cone of positive semidefinite matrices, known as spectrahedra. The research primarily aims to minimise the size of spectrahedral representations that realise prescribed facial dimension signatures. The project seeks to tighten established upper and lower bounds on spectrahedral representations of convex sets with given facial dimension signatures, particularly in specific cases where the facial dimension signature arises from certain families of finite integer sequences. In addition, the project will investigate characteristics of affine subspaces that produce spectrahedra with specific facial dimension signatures.
Emmanuel Travassaros
The University of New South Wales
Emmanuel Travassaros is pursuing a Bachelor of Actuarial Studies and Advanced Mathematics (Honours) at the University of New South Wales. Through the UNSW Talented Students Program, Emmanuel was introduced to convex optimisation. This field sparked his fascination with semi-definite programming and its diverse applications in control theory, financial modelling, and approximations of NP-hard problems. Emmanuel has greatly enjoyed engaging with advanced mathematical ideas, presenting in a postgraduate reading group on convexity, and collaborating with academics in the discipline. He looks forward to undertaking an honours year, with the intention of pursuing postgraduate research in mathematics. Outside of his studies, Emmanuel enjoys British comedy, international cuisines and spending quality time with his dog.
