We’re so happy you’re here! What made you apply for this opportunity at Fields?

The initial four years of my PhD introduced me to the captivating world of mathematical research. I cherished every moment of my graduate studies at SISSA and ICTP in Trieste, Italy. Following my PhD, I sought to further cultivate and refine my research prowess through postdoctoral opportunities. During a casual conversation, the Fields-AIMS-Perimeter postdoctoral fellowship emerged as an enticing prospect. One summer, a colleague from the Perimeter Institute visited Italy, and we discovered a shared connection who had previously held the prestigious Fields-AIMS-Perimeter postdoctoral position. Intrigued, I engaged in dialogue with him about his experiences, and he wholeheartedly recommended that I apply. This opportunity not only offered a chance to enhance my skills but also presented the prospect of becoming the first female postdoctoral fellow, promising invaluable learning opportunities.

What is your specific research area?

I'm interested in the area of noncommutative algebras and have been studying  the classification of quantum automorphisms of some singular plane curves. The main object I study are Hopf algebras; they can be thought of as  generalized groups since in the noncommutative (quantum) setting, they behave like groups and we refer to them as quantum groups. What I’ve done in the past is to investigate their (co)actions on domains and function fields which together with some conditions yields a quantum homogeneous space structure on these spaces.  A quantum homogeneous space is a right coideal subalgebra of a Hopf algebra such that the Hopf algebra is faithfully flat as a right module over it. The notion of quantum homogeneous space is a generalization of the classical notion of homogeneous space. This generalization is particularly useful among others  for investigating quantum symmetries – given by Hopf algebra (co)actions –  of spaces that have few or no classical symmetries.  

Was this similar to your Ph.D research?

The broad objective of my Ph.D research was to investigate the conjecture: All plane curves are quantum homogeneous spaces. However we were unable to conclusively establish this in a general context. Instead we demand that like the classical symmetries, the (co)action of the quantum group  extends from the coordinate rings  of these affine curves  to their  fields of rational functions. One of the examples I studied is the cusp; it is a singular plane curve having just two classical symmetries – reflection and the trivial symmetry. Collaborating with my Ph.D advisor, Prof Ulrich Kråhmer, we obtained new (quantum) symmetries for the cusp and  constructed new Hopf algebras for which the cusp admits a new quantum homogeneous space structure different from what has been previously understood. We also showed that like in the classical setting these quantum symmetries can be extended to the field of rational functions of the cusp.

What do you love about this type of math?

I have always loved algebra and the fact that algebra has links beyond mathematics, like in physics. Recently, I’ve been intrigued with Hopf algebras in the algebraic  combinatorics setting – combinatorial Hopf algebras; these are graded connected Hopf algebras. I like the interactions Hopf algebras have with other areas of mathematics.

Favorite part of being in Toronto?

I like the fall season here with the vibrant colours of the leaves and the trees. This being the biggest city I have lived in, the diversity also drew me in. I don't feel out of place. My dad asked me once what was different about the city. I said, it is home to all walks of life. Everyone comes together, accepted and included, and I have never felt like a foreigner. Anything you want to learn about anywhere in the world, anything you want to experience. There's a restaurant or there's a shop, or there's a community. 

What are your ambitions for the coming year?

I'm eager to advance the research I've initiated and am still exploring potential avenues to pursue. Maintaining my collaboration with Professor Nantel Bergeron is a priority, as I believe it holds promising prospects. Additionally, I'm excited about the opportunity to visit one of the AIMS centers in Ghana. My aim is to leverage my mathematical background and passion to contribute positively to the AIMS community, particularly by inspiring students and fostering enthusiasm for the subject. Moreover, I'm considering how I can contribute to the Fields Undergraduate Summer Research Program during my visit. Bryan, the Manager of Scientific Programs, mentioned that Fields is actively seeking more student candidates from Africa, and I see this as an opportunity to help spread awareness and encourage participation among interested students.

Related: Sarobidy Razafimahatratra is our 2024 Fields-AIMS-Perimeter Postdoctoral Fellow

The Fields-AIMS-Perimeter Postdoctoral Fellowship is a unique one-year position intended for new and recent PhDs who are African nationals working in the areas of mathematical sciences or fundamental theoretical physics. The goal of this initiative is to support the careers of young researchers who have a commitment to advance science in Africa.