My presentation at the 30th Brazilian Mathematics Colloquium at the National Institute of Pure and Applied Mathematics (IMPA). If you speak Portuguese, you may want to look at the video of the talk, which fortunately includes mostly the slides, with only a brief appearance of my (not!) beautiful self.
I am specially grateful to my mathematician friends Erick Matsen, Mike Steel and Felipe Figueiredo for insights and proof-reading.
Here are some links I found extremely useful when preparing this talk:
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http://www.math.canterbury.ac.nz/~m.steel/files/presentations/winthrop1_to_4.pdf
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http://www.math.canterbury.ac.nz/~m.steel/files/presentations/winthrop5_to_10.pdf
For more, please look at the list of references of the talk.