From Math, to Physics and back again. Meet our PIMS CNRS PDF at UAlberta, Raphaël Belliard.
Ruth A. Situma — PIMS Program and Communications Manager
Raphaël Belliard is presently in Edmonton for his second PDF. A native of Paris, he moved to the University of Alberta in the fall of 2021 to begin his PIMS CNRS PDF. “Moving to Canada was quite nice, for once in my life it only took me a couple of weeks to find a house to live in!” he says. Raphaël adapted quite easily to working from home, but after a year and a half, he says he was happiest when he could finally meet his students — this was about halfway through winter! In Edmonton, he has found communities that are part of his cultural heritage — easing his landing in Alberta. We connected with Raphaël on his research and well-being, as he continues his research in Canada.
Tell us about your academic journey: What field are you in and how did you get connected to your current PDF supervisor Vincent Bouchard at the University of Alberta?
My journey in academia started in Paris where I grew up and pursued my studies. I loved mathematics from a very young age and that love never left me despite choosing physics whenever I had a chance. My Master’s thesis was on the asymptotic spectral analysis of random hermitian matrices and although I didn’t know it by then, this would shape my career. It was conducted under the supervision of my guru Bertrand Eynard at the CEA of Saclay, the historical French research centre for nuclear physics. The large size asymptotics of random matrix models were used quite early as toy models for the spectroscopy of heavy atoms, and the combinatorics of graphs computing the corresponding expansions turned these models into baby versions of the quantum field theory describing the strong force binding nuclei. Eynard and many others related the underlying algebraic structures to enumerative geometry problems.
My doctorate, under the same supervisor, consisted in taking those asymptotic methods beyond perturbation theory, generalising symmetry constraints of random matrix integrals to that of two-dimensional conformal field theories (a geometric take on the representation theory of certain infinite dimensional algebras). In that story, families of differential systems with Lie algebra symmetry defined over Riemann surfaces are central and the ramifications of their study led me to investigate a number of topics ranging from the quantisation of integrable systems to combinatorics of graphs with intersection theoretic interpretations through infinite dimensional representation theory and asymptotic analysis.
On my way, I have had the privilege to participate in international conferences where I met many friends and collaborators, including Vincent Bouchard, my current supervisor at the University of Alberta. His transverse expertise in a wide variety of mathematical topics — as well as that of other members of the lab — is allowing me to push the boundaries of my research even further by considering for instance the summability properties of the aforementioned asymptotic expansions and the elliptic (or quantum) deformations of their underlying algebras of symmetry. I do not however limit myself to that, my main interest lies in using these methods back where they belong, namely the non-perturbative study of quantum properties of nuclear interactions, albeit this time built on its Penrose-Ward twistor-space formulation. The page here https://scholar.google.fr/citations?view_op=list_works&hl=en&user=6sYgcrEAAAAJ contains bits and pieces of my contribution to the mentioned topics.
Were you teaching this semester? What was the experience like?
This winter semester I had the opportunity to teach yet again a calculus course for physical scientists. It wasn’t the first time I taught on this topic (among favourites for a mathematical physicist like myself) but it was the first time with such a large audience. The experience was great, especially after returning in-person, although the pandemic had visibly taken a toll on the students’ well-being. I felt glad to be able to participate in guiding them through that as well.
What do you do to balance your research and life? What does a typical Sunday look like for you and what has been your best discovery since arriving at UA??
Balancing my research from the rest of my activities has always been somewhat of a challenge but I have reached a sort of stable oscillatory behaviour involving science, music (I play several instruments and compose electronically), and cooking (a mash-up of my French and Ethiopian roots). On a typical Sunday, if I am not outdoors enjoying the sun, you can probably find me comfortably installed on my couch, singing some jazz songs with my guitar while the stew is simmering in the kitchen.
In terms of intensity, my best discovery since I arrived in Edmonton has to be the west Canadian Winter! In general, though, it is probably the diversity of cultures present in the city, in and out of the University. In particular, the Ethiopian diaspora that I discovered by accident instantly made me feel at home back when I didn’t really know anyone here yet. A special mention of course goes to the northern lights I saw after only a couple of weeks in town and the glorious nature one has access to with very little effort.
Raphaël Belliard obtained his Ph.D. at the CEA of Saclay, the French historical nuclear physics research center. Under the supervision of Dr. Bertrand Eynard, he studied geometric features of solvable symmetry constraints in two-dimensional quantum field theory using methods directly inspired by statistical models of heavy atom spectroscopy. They involved mathematics ranging from combinatorics to intersection theory and representations of infinite dimensional algebras. In particular extensions of the Virasoro algebra, relevant for conformal field theories that he studied at DESY Hamburg under the supervision of Dr. Joerg Teschner. He is currently a PIMS PDF at the University of Alberta, Edmonton, where he works with Dr. Vincent Bouchard and others on algebraic and geometric structures.
Raphael will be speaking at the PIMS Emergent Research Seminar Series, on May 18, 2022, at 9:30 AM Pacific. Details on his talk, Exact results in quantum field theory from differential systems, can be found here.
