Six short lectures on the connection between two ubiquitous objects in Mathematics.
Time and place: – ,
NHA 1120
Juliana Novozhilova, Cosmic Tapestry I, 2015.
Matrices (rectangular arrays of symbols), and graphs (sets of points and links connecting pairs of points) are two of the basic objects in Mathematics. They both appear in the most diverse settings, from Representation Theory to Machine Learning and Quantum Theory.
This seminar aims at exploring the deep connection between matrices and graphs, and at showing how this connection is the source of mathematical results of singular beauty.
Overview
(February 14, 14:15 - 15:00, NHA 1120): A short chronicle of matrices and graphs, and an intro on the adjacency matrix of a graph.
(February 21, 10:15 - 11:00, NHA 1120): In every party there is a politician. The distance matrix of a graph is closely related to its adjacency matrix (but only in tropical environments).
(February 28, 10:15 - 11:00, NHA 1120): Using graphs to compute the determinant of a matrix.
(March 06, 10:15 - 11:00, NHA 1120): Counting trees and drawing graphs with the Laplacian matrix.
(June 10, 11:15 - 12:00, ZOOM): Perron-Frobenius theory for nonnegative matrices. Walking on a graph. Lecture recorded.
(June 17, 11:15 - 12:00, ZOOM): Kemeny's constant for Markov chains: using electricity to show that almost all planar graphs are paradoxical.
