For centuries, imaginary numbers were viewed with suspicion. But once mathematicians stopped philosophising and asking "what are complex numbers?" and started asking "what can we do with complex numbers?", the field of complex analysis swelled from absolutely nothing to a huge and rich subject in just thirty years. This Monday, join us at 7:30pm in MS.04 as Dave McCormick takes us on a tour of geometry of the complex plane as you've never known it before:

• When we generalise differentiation and integration to functions of the complex plane, we discover the remarkable theorem that a function which is once differentiable on the complex plane is automatically infinitely differentiable, in complete contrast to the real line.

• There are natural connections between complex-differentiability and planar geometry; in particular, a map from the complex plane to itself is conformal -- meaning it preserves local angles -- if and only if it is complex-differentiable and its derivative never vanishes.

• Unfortunately, when we try and generalise conformality to higher-dimensional Euclidean space, it becomes an over-determined system of equations and degenerates to become rather boring and useless. We thus introduce the natural generalisation of quasiconformal maps, and explore some of their properties.

Don't forget, Monday at 7:30pm for an exciting tour of the geometry of conformal and quasiconformal mappings. After which we go to the pub.