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Introduction

Hello, I'm Andrew and I'm working at Sorbonne Univerité, Paris, with my advisors Mohab Safey El Din and Jérémy Berthomieu as one of the 15 POEMA ESRs. This will be a blog about my research and related topics. The team here has been very welcoming and have helped me to find my place here in a very crowded city and settle me into research life. I have also had the opportunity to take French classes here which I've found to be very useful and enjoyable. Since I started in October I have mainly been reading articles on generalised critical values, which are the tools with which we plan to solve exactly polynomial optimisation problems which cannot be tackled with SDP solvers, and on Gröbner bases, particularly the implementation of fundamental computer algebra algorithms relating Gröbner bases. Besides the reading, we've been looking at a couple main areas to make progress in the area of generalised critical values and we hope to get our first results soon.