AMSI grant recipient profile: Francesco Manicatstri

Born in Pisa, Italy, where I received all my education until starting my PhD in mathematics at the Australian National University. Of course, I have a strong interest in the subject, but to be completely honest the biggest reason why I embarked on this (by now almost decade-long) journey in mathematics is that I just love a good challenge.

(Un)fortunately, there are also other things in my life outside of my research: I enjoy nature and sports, especially martial arts, and I firmly believe that there is a lot of truth to the saying “mens sana in corpore sano”.

I also love art, especially music: I’ve been harassing my neighbours playing metal on my electric guitar since I was 16 and I have no intention of stopping any time soon.

I also love cats, but not dogs.

Give me a quick overview of the type of mathematics you are studying, and/or the aims of your research and its potential applications/outcomes (how you would explain your work and studies to friends who don’t study maths?)

Mathematics and its applications fascinate me, in particular I am drawn to the role of geometry in the modern understanding of theoretical physics, which is what my research project focuses on. In a nutshell, modern physics classifies particles into bosons and fermions, and while the former can be completely understood within the framework of standard differential geometry, the latter require the introduction of some new mathematical objects with an anticommuting property, that is, ab=-ba, that don’t play nicely with standard geometric structures. The new structures that arise from this formalism form the theory of Supergeometry, and that is the primary focus of my research.

How did you get into the mathematical sciences? Was there someone or something that inspired you to this field?

I like to get to the bottom of things. By the very definition of the scientific method, that is not the purpose of science: in science we can ask “how”, but never “why”, and no matter how useful or fascinating the object of study might be, this philosophy has always put me off.

On the other hand, humanities are certainly interesting: as I said I love art, and I appreciate how philosophy in particular puts a lot of emphasis on understanding the “why” of things, but the lack of method and the excessive verbosity make humanities very difficult for me personally to study deeply.

Mathematics is rigorous and concise, so that it’s clear that the goal of the language is to communicate information in the clearest and most efficient way possible, and in some sense it already “starts” from the bottom. So, what made me interested in it is that it takes the best parts of science and the humanities, in that there is method and clarity, but also elegance and beauty, and combines them into one of the greatest achievements of humanity as a species.

Winter School is designed to give students a deeper understanding of their area of research and expose them to others working in different fields/industries. Tell me about your Winter School experience. What was the most valuable part of the program for you?

For me personally it was my first proper conference trip, so I would have appreciated the experience even just for being something new. Fortunately, there was a lot more to it, and networking with my colleagues, sharing ideas about mathematics, experiences about our (very different) university environments and backgrounds was probably the most interesting part of the school.

What was your main take away/s from AMSI Winter School? Something you learnt? A connection you made? Do you have new ideas for your work/research or see it in a new light?

Because the subject of the school was not exactly my field of research, but something adjacent to it, I was not particularly familiar with the content of the courses beforehand, so the experience has definitely inspired me to incorporate the new (at least for me) ideas explored in the courses into the research that I am conducting myself. The two courses about Einstein manifolds in particular were very inspiring, I wonder if a supergeometric formulation of this problem would be relevant for physics.

What surprised you most about Winter School?

Seeing how during the tutorials despite coming from wildly different backgrounds, all of my peers had a surprisingly similar approach to solving the proposed problems.

What is the importance of in-person communication at an event like Winter School?

As I said, the networking was the most interesting part of the whole experience, so attending in person was absolutely vital for it. Also, it was an absolute joy to get to know the professors in person.

You received a grant to attend AMSI Winter School. How important was this in terms of your ability to attend, fully participate in the program and meet others studying in similar fields?

Without the grant I couldn’t have participated, so it was really essential. It allowed me to focus entirely on the tutorials and networking without financial stress.

What advice would you give to someone who is considering applying for Winter School? How would you describe the conference to them?

 Save some time to also enjoy the trip! A lot of my colleagues were so taken by the mathematics that they didn’t have a lot of time to visit the city and the campus, and I think seeing a different work environment and understanding how it affects the research is absolutely a big part of the experience – especially when Brisbane is so nice!

Tell us about a moment that changed a preconceived idea about your field?

Research in mathematics is much, much more messy than I anticipated, and supergeometry in particular is still quite underdeveloped. It is all based on this idea of anticommuting variables, so there are signs popping up all over the place, and these signs are in some sense the whole point of the theory. However, not everyone agrees on where these signs should appear, and that makes reading the literature a nightmare of conflicting (and often inequivalent!) sign conventions.

So this definitely challenged my preconceived notion of how clean mathematics research really is (and especially mathematical physics).

Where do you want the mathematical sciences to take you? Where do you see yourself in five, ten years time?

The most natural direction after a PhD in pure mathematics is to apply for a postdoctoral position, so that is the idea for now – although, honestly, for the moment I am only studying what interests me without worrying about plans so far into the future.

Any other feedback/comments you would like to provide on the travel grant or AMSI Winter School?

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