What is modern geometry?
Professor Michael Wemyss (University of Glasgow)
Friday 4th November, 2016 16:00-17:00 Western Infirmary Lecture Theatre
With its fostering of key analytical skills, with its ability to see structure in the most unlikely of places, and above all its ability to analyse information critically, effectively, and with the power of abstraction, the time has never been better to be a mathematician. Largely hidden from view, mathematics is underpinning and percolating into our everyday lives at an ever increasing rate, since its core is forged from the idea that structure is the key to mathematics, and hence the living world. It is really a structural understanding, not a superficial one, that is one of the great human desires.
Solving equations is what mathematicians are expected to do, but most only do so indirectly. The structures used to obtain the solutions are as important as the solutions themselves, as these can then be analysed in their own right, and transported to solve problems in very different contexts. In solving equations, we are naturally led into an ever deeper understanding. From the first realisation that the solutions form a space, to the initial attempts of understanding its properties, to the very modern tools that optimally extract and encode information, our understanding of the underlying structure is both deepening and evolving. This inaugural lecture will explain the development of this algebraic form of geometry and its applications, from both a historic and mathematical perspective.