What do social media, the street outside your door, your blood vessels and the number of people who catch the flu have in common?
All involve connecting networks of one kind or another.
Networks and the connections they form define the mathematical research undertaken by Prof Daniel Spielman of Yale University in the US.
He is visiting Dublin to deliver the annual Hamilton Day Lecture organised by the Royal Irish Academy and taking place on Friday evening, October 16th, in the Burke Theatre at Trinity College Dublin.
Networks are all around us and in us, said Prof Spielman, speaking before his lecture. “Everyone connects through them and everyone can understand them,” he said.
Mathematicians and scientists try to understand them because of the real-world advantages that come from learning how to control them, said Prof Spielman, the Henry Ford II professor of computer science, mathematics and applied mathematics, and co-director of the Yale Institute of Network Science.
For instance, he said, we use the road network to drive about, but imagine someone builds a handy shortcut that everyone uses.
The shortcut works but causes traffic jams which will slow rather than speed up traffic. Analysing the network beforehand might have suggested a different shortcut, or several shortcuts.
He gives another example. If traffic on social media becomes too heavy, the routers that move the signals about may begin to drop messages to relieve congestion. Understanding the network and modelling the network components should then help to speed up messages moving across the system.
Viruses can spread from a source across personal networks and it is valuable for those tracking the movement of a disease agent to know how these crisscrossing personal networks operate, he said.
Networks capable of influencing people are also useful, for example encouraging people on Facebook or Twitter to say whether they had voted in an election.
A mathematician studying this would want to learn who is connected and how are they connected in order to predict the impact on voting patterns.
Imagining the connecting points as real things helps Prof Spielman to visualise network connections.
“I act as if they were physical objects, springs or rubber bands for the nodes,” he said.
He and his research team, including seven faculty members and 10 post-doctoral students and graduates, develop tools to help people understand the networks they are studying.
A great advantage is that the mathematics needed - the calculus and linear algebra commonly used in physics - is very well known, he said.
The Hamilton lecture is organised by the RIA and supported by ARUP and The Irish Times.
It is held each year on October 16th to commemorate the day when, in a flash of inspiration, Irish mathematician William Rowan Hamilton invented a new form of algebra, Quaternions, that is still in widespread use today.
The lecture takes place in the Burke Theatre, Trinity College Dublin, on Friday evening at 7.30pm. Although heavily booked, a few places may become available at the door for those without tickets.
Lecture tickets are €5 or €3 for concessions. They are available online at ria.ie