My research

During my Phd: my PhD thesis focused on applications of cluster algebras to representation theory. I developed geometric and cluster-theoretic techniques to study the branching problem for algebraic groups: how do irreducible representations of an algebraic group decompose under the restricted action of a given subgroup. During this period, I also collaborated (independently from my PhD thesis) with Nicolas Ressayre on problems in classical geometric representation theory, such as the Belkale-Kumar deformed cohomology of flag varieties.

Postdoctoral: During my postdoctoral period, I have continued working on cluster algebras and their applications to representation theory, while developing new interests in quantum groups and algebraic geometry. 

With Bernard Leclerc, we gave a geometric interpretation of certain Grothendieck rings of representations of quantum affine algebras, their Borel subalgebras, and their shifted versions via new geometric objects called schemes of bands, leading to a new description of the q-character homomorphism conjectured by Frenkel and Reshetikhin.

I have also investigated cluster structures on Cox rings of algebraic varieties, with applications to flag varieties and cluster varieties. Moreover, with Joshua Enwright, Joaquin Moraga, and Hunter Spink, we introduced mutation semigroup algebras (a concept that generalises both cluster and semigroup algebras) and gave several applications to the study of cluster-type and Fano varieties and their Cox rings.

My favourite obsessions 

When I'm not doing maths, I'm probably climbing, skiing or doing random activities in the mountains. In the worst case scenario, I'm unsuccessfully trying to learn to play the guitar, at the expence of my neighborhoods.