Disputation: Lorenzo Ciardo

Doctoral candidate Lorenzo Ciardo at the Department of Mathematics, Faculty of Mathematics and Natural Sciences, is  defending the thesis Spectral graph parameters and connectivity for the degree of Philosophiae Doctor.

Picture of the candidate.

Doctoral candidate Lorenzo Ciardo

The University of Oslo is closed. The PhD defence and trial lecture will therefore be digital and streamed directly using Zoom. The host of the session will moderate the technicalities while the chair of the defence will moderate the disputation.

Ex auditorio questions: the chair of the defence will invite the audience to ask questions ex auditorio at the end of the defence. If you would like to ask a question, click 'Raise hand' and wait to be unmuted.

Trial lecture

8th of December, 10:15, Zoom

"Determinants, permanents and immanants"

  • Join the trial lecture
    The webinar opens for participation just before the trial lecture starts, participants who join early will be put in a waiting room.

Main research findings

Connection is what makes molecules out of atoms, societies out of individuals, knowledge out of data. Complex entities and behaviours arise from their elementary components through the laws of connection. The main purpose of this work is to investigate the mathematics of these laws in the context of graphs - simple mathematical objects modelling discrete structures. In particular, the notions of algebraic connectivity and Kemeny’s constant provide two distinct ways to understand connection for graphs. The former can be derived by comparing the shapes of substructures of a given graph; the latter comes from observing the behaviour of a random walker travelling in the graph. Like a guitar string or a star in the sky, each graph emits information at some specific frequencies, which form the spectrum of the graph. Both the algebraic connectivity and Kemeny’s constant are deeply linked to these frequencies. In this work, spectral methods are used to study the properties of connection and relate it to other graph-theoretical notions. Unexpected phenomena can be brought to the surface through the set of spectral tools. As an example, a paradoxical behaviour, apparently breaking the laws of connection, is shown to concern a surprisingly large class of graphs.

Published Nov. 24, 2020 2:44 PM - Last modified Dec. 2, 2020 2:29 PM