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Graduate Seminar

Clive Newstead
Carnegie Mellon University
Title: Seven trees in one: a very explicit tale

Abstract: Inspired by a remark made by Bill Lawvere in his 1991 paper "Some thoughts on the future of category theory", Andreas Blass proved in 1994 that "There is a very explicit bijection between the set of all seven-tuples of trees and the set of all trees." A nonsense proof can be given by pretending that the set $T$ of all trees is a complex number, and then manipulating the equation $T = 1 + T^2$. The nonsense proof is justified by Andreas Blass (1994) and is extended by Marcelo Fiore and Tom Leinster (2002) to a more general class of categories. In this talk, I will make the very explicit bijection very explicit, I will make the notion of "very explicit" very explicit, and I will make the connection with complex numbers very explicit. If time permits, I will make the connection to category theory very explicit, too. This talk is suitable for all age groups.

Date: Tuesday, September 19, 2017
Time: 5:30 pm
Location: Wean Hall 8220
Submitted by:  Yangxi Ou
Note: Video on Youtube: https://youtu.be/LA1RwbmAQhA. However, it was recorded by a webcam on a laptop, without the soundtrack, due to a silly technical carelessness.