Maths prodigy comes home to establish $5 million world-class maths centre

A sample quote:

I’m standing with Williamson in his office at the University of Sydney, on the seventh floor of the Carslaw Building, looking down at the campus’s historic sandstone quadrangle. The Carslaw is renowned by staff and students as being the university’s ugliest building, an antipodean approximation of a KGB regional headquarters. “The standard joke is that the best thing about working in Carslaw is that you don’t have to look at it,” Williamson says. His office is similarly unappealing – essentially a concrete bunker with bad carpet – and yet it has everything a mathematician might need; a whiteboard, marker pens, a computer, and most important of all, a couch. “When I moved in here, I told them ‘I need a big couch!’ ” he says. “As opposed to things like medicine and science, which require specialised equipment – microscopes, X-rays – mathematicians can do most of their work with a pencil and paper. Really, you spend most of your time sitting around talking.”

Fortunately, Williamson is a good talker – jaunty and light, his sentences tripping along before ending with an upward inflection, like a little trampoline kick-out off the final syllable. He’s a little goofy. He smiles a lot; his eyes go wide. You get the sense that inside his head is a banging dinner party where all these brilliant ideas are elbowing one another to get out and roam around. Turning on his computer, he talks me through a slide display about representation theory – his area of expertise – and how it can, via spectral analysis of fundamental frequencies, explain why a whistle sounds different to a violin, and why, consequently, you’d rather listen to a concerto played by violins than a concerto played by whistles. An intriguing-looking textbook lies open on his desk, the pages crammed with cryptic glyphs and a photo of a Mayan pyramid. There’s also a stack of shiny new books. “Our latest publication,” he says, handing me one. I turn it over and read the back cover. “In this book,” it says, “we conjecture that translation functors give an action of the (diagrammatic) Hecke category of the affine Weyl group on the principal block.”

I want to ask: what is a “functor”? Who is Hecke? And why is the word diagrammatic in brackets? But instead, I ask: “Where can we get a sandwich around here?”

The book is on the arXiv, and published in Astérisque.

**Added 23 August:** Another interesting profile/interview, in the Campus Morning Mail.