Title: The Story of Flat Surfaces

Abstract: Most surfaces are not flat. Nevertheless we usually try to cover them with flat pieces.
Cartographers picture our round Earth in planar maps. Soccer balls used to be made from flat pieces of leather. Tailors cover our (non flat!) bodies with clothes made out of fabric.
In this talk I will tell the story of flat surfaces, from Euler with his beautiful developable surfaces (1770), to Thurston’s pleated surfaces (1980), or the official soccer ball of the World Cup in Brazil (2014).
Following Chebyshev (1878), I will show how to clothe a round ball with no wrinkles (2011).
I will show incredible flat surfaces by Borrelli et al (2012), following theorems of Lebesgue (1898) and Nash (1954). So many questions are still open.

2015-01-20 @5:00 PM

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