### Navigation on the Riemann Sphere (TGG lecture)

A formal "dear all" escaped me, and upon being erased a very informal "hey" followed it. As you can see I have erased both and instead decided to let you choose how you want to be greeted.

This Wednesday in the Alan Turing Building, you will all have the glorious opportunity to listen to a lecture by Professor Alexandre Borovik. Yes, the one and only, author of Mathematics Under the Microscope, if your eyes were asking the question!

Please whatever you're doing, drop it and come along to G205 at 1:10pm on 12th March--registration is not required! (You don't have to be a mathematician or a member of my university). The lecture is open to the whole wide world so don't have any reservations whatsoever. You would be mad to miss it. Trust me on this, for Dr. E is feeling really bad about not being able to make it... (he'll deny this obviously, but don't say you heard it from me!)

Being under the weather has meant that all you lucky people out there, haven't felt my annoying presence like normal. Nevertheless, the fact that this is the last Galois Group lecture before Easter, has given me all the motivation I need to find my old "annoying form". I will disclose the abstract in two ticks, but first I have to do all that Demon Headmaster (aka Jack Straw!) hocus pocus, to ensure that people attend. Free refreshments will be available, and if you're lucky your picture might even be taken. Pretty please with a cherry on top, will you attend if you can. I always aim for 50 people and so far I haven't been let down. (Rounding up is a fascinating thing taught at schools!)

Now to the formal details and the abstract (which can also be seen from the poster of the lecture):

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Wednesday 12th March 2008 at 1:10-2pm

Professor Alexandre Borovik - Navigation on the Riemann Sphere

Alan Turing Building - G205

Abstract:

Seafarers of 16th century were skilful in keeping course of constant direction -- with the help of a magnetic compass and astronomic instruments -- but they had no control over distance travelled since they had no control over strength of wind. In effect, they lived in a strange geometry where only angles mattered, but which was lacking the concept of distance. Nowadays this geometry is known under the name of conformal geometry. The best way to understand it is to view the globe as the Riemann sphere invented by Bernhard Riemann (1826 - 1866) as a

geometric model for representation of complex numbers.

The famous geographer and cartographer Gerard Mercator (1512 - 1594) has not left to us any clues as to how he made his world map of 1569; but it was the first map in the history where lines of constant direction on the globe (loxodromes) were represented as straight lines (rhumb lines, in seafaring terminology) on the map. The first systematic theory of Mercator's projections appeared some years later, in Edward Wright's book of 1599. However, Wright's work created more mathematical mysteries than mathematicians of that time could resolve.

In my lecture, I will discuss some elementary and exceptionally beautiful mathematics related to the Mercator projection and Riemann sphere. In particular, I will explain why the Mercator projection is exactly the logarithm function Log(z) in the complex domain.

My lecture is based on ideas of our colleague Dr Hovhannes Khudaverdian.

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Look at all those empty seats--one of them HAS your name written on it. Come along this Wednesday to find out which one!

(I wouldn't click on that picture by the way--it's one of them large 'uns. )

PS: Have I forgotten to mention anything? Please do remind me if I have!

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