Apr 22
Math Across the Cannon: Jordan Ellenberg
Speaker: Jordan Ellenberg, University of Wisconsin-Madison
Title: Smyth’s conjecture and a non-deterministic Hasse principle
Abstract: The matrix
3 -3 4 -4 5 -5 0 0
4 -4 -3 3 0 0 5 -5
-5 5 0 0 -3 3 -4 4
has an interesting property. Can you see what it is?
I will explain how to prove a conjecture of Smyth from 1986 about linear relations between Galois conjugates, and explain what this has to do with linear combinations of permutation matrices, Brianchon's theorem on ellipses inscribed in hexagons, weightings on the edges of directed hypergraphs, and the study of Diophantine equations where the equation is to be solved with probability distributions instead of with numbers. This is joint work with Will Hardt.
Note from the organizers: Will Hardt is a 2018 Carleton alum. He was a student of Jordan Ellenberg at the University of Wisconsin-Madison, and graduated with a PhD in mathematics in 2023.
This event is sponsored by The St. Olaf Department of Mathematics, Statistics, and Computer Science; The Carleton Department of Mathematics and Statistics; the TCL Colloquium Fund; and the Michael Morrill Fund.