Antony Maciocia
Ruxandra Icleanu has written the following article as part of our series of Academic Interviews; featuring Antony Maciocia!
Professor Antony Maciocia is both an Academic within the School of Mathematics and the Dean of postgraduate research in the College of Science and Engineering. His area of study is algebraic geometry, with a focus on moduli spaces.
How it all began
As it happens with many professional mathematicians, Antony’s interest for science started to develop at an early age. His own readings were a central part of it, and as he recalls laughing, “often at the expense of schoolwork, unfortunately”. In particular, he was drawn to mathematical logic along with various geometrical aspects of mathematical physics, but he kept a broad interest in science until much later.
He fondly remembers one time when his 12-year old self was taken by complete surprise. As the teachers were aware of his interest in maths, they told him about a competition in which students had to write an essay about a mathematical topic of their choice. Following his teacher’s suggestion, he decided to write about π; he was supposed to draw polygons with increasing number of sides and discover what the total lengths of the sides tends to. But what the teacher didn’t know was that he had taught himself calculus and trigonometry. Naturally, he asked himself: “Why bother when you can just do the calculation?” He drew a few polygons, “just to show that [he] could”, and then went on with the proof. When the teacher asked about errors in his calculations, he was more than surprised: “How can there be errors? Maths doesn’t have errors”. To prove his point, he designed a complicated scheme for computing the errors in a formula. He points out that skipping ahead may not always work out very well for you, especially considering the hierarchical nature of Maths, but having the motivation and keen interest to investigate new ideas is always important.
Yet, he admits “If you asked me as a teenager: ‘What are you going to be?’, I wouldn’t have said a mathematician”. It was only at the age of 17 when he decided that maths was “the subject”. Considering the possibility of a career in physics, and even medicine, he decided that maths underpinned all of them, so that’s what he should study.
University life
Antony did his undergraduate degree at the University of Cambridge, followed by a Certificate of Advanced Study in Mathematics (a postgraduate qualification which is now known as an MMaths degree). As had happened at school, a similar dilemma arose: “I was too interested in the things I was interested in, and less interested in the things I was being taught”.
Fortunately, the university offered a lot of freedom regarding the choice of courses, so he was soon able to intertwine his interests with what he was being taught, typically choosing pure subjects.
At that time, Cambridge was home to some of the world’s most proficient mathematicians and physicists. He was taught cosmology by Herman Bondi whose lectures he describes as “absolutely superb”. Stephen Hawking was writing what is now one his most well-known books, ‘A brief history of time’ and he was giving it as a lecture course; Antony was one of the few lucky students who were able to hear it as it was being developed.
Research
Antony completed his fourth-year dissertation on Lorentzian manifolds. Reading extensively around this topic, he discovered the work of Simon Donaldson, who at the time, had indirectly proved something amazing. “If we consider multidimensional calculus, we can ask ourselves a slightly odd question: ‘Are there different “calculuses” we can do?’ (i.e. differentiable structures). It turns out that, for real numbers, calculus is unique – that is, R has a single differentiable structure. And this is also the case for R2, R3, R5, R6 and all the other dimensions. Simon Donaldson was the one who proved that R4 is unique in that sense – it has infinitely many ways of doing calculus”, Antony explained. That is why he decided to write to him and ask if he would like a PhD student, even though Simon himself had finished his PhD not long before. This is how Antony became the first PhD student to be taken on by Simon, going to Oxford to study mathematical gauge theory, which examines the space of solutions of certain differential equations. From gauge theory, he moved to vector bundles and then moduli of sheaves; becoming especially interested in the Fourier- Mukai transform of these objects.
He also recalls working alongside one of his PhD students, Tom Bridgeland. While mentored by Antony during his Postdoc, Tom discovered what are now known as “Bridgeland’s stability conditions”, which provide a way of studying a range of new types of moduli spaces.
Beside Maths
But Antony’s interests are not limited to research and teaching. For a while now, he has been working on a grade point average scheme for UK, which wouldn’t use the degree classifications that we currently have.
He is excited about the current activity of the doctoral college. The university is home to almost 6000 PhD students who are not getting as much attention as the undergraduate or master students, but the doctoral college aims to address this problem. Antony is currently in the processes of creating new policies which improve the lives of university’s PhD students.
He also enjoys designing new courses or adjusting existing ones. He created distance-learning modules based on the first-year courses for a niche audience of students who want to become maths teachers.
Students & Teaching
Antony believes in a good balance between work and play, thinking that maths students especially have the tendency to overwork themselves. More than that, he believes that following what makes you happiest will yield the best results, whether that is maths or not.