PIMS/Shell Lunchbox Lecture: Numerics with error bars

Mathematical analysts are typically a careful sort. We sweat over the tiniest details to ensure proofs are rock-solid. The advent of fast and easy to use computers revolutionized science, engineering and some areas of mathematics. Oddly though, most analysts throw rigour to the wind when using a computer. In this talk I will describe some recent developments combining mathematical analysis, numerical analysis and computer science that aims to bring pencil and paper rigour to computational analysis.

I will present some simple problems where classical methods fail and explain the ideas behind rigourous computing. This is an evolving area hoping to put error bars on your computations and (some) analysts out of work.

This talk is intended for a general scientific audience.