Graduate Programs      Graduate Home Ph D Programs Masters Degree Ph D Program Requirements Course Descriptions Current Courses Admissions Current Graduate Students Graduate Student Seminar SIAM Chapter Seminar Recent Graduates Incoming Students 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, 2017Time: 5:30 pmLocation: Wean Hall 8220Submitted by:  Yangxi OuNote: 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.