My area of expertise is noncommutative geometry, a generalisation of classical geometry that provides new mathematical tools for both mathematical problems and physical models by allowing for geometric spaces and physical spacetimes whose coordinates no longer commute, viz, a×b need not equal b×a. In mathematical physics, it permits mathematically rigorous semi-classical modelling of quantum physics by classical physics on noncommutative spaces, whose underlying geometry encodes quantum corrections.
My research applies recent advances in unbounded KK-theory and quantum Riemannian geometry towards the theoretical synthesis and completion of existing partial frameworks for Yang–Mills gauge theory on noncommutative spaces. It is supported by an nserc Discovery Grant and a Harrison McCain Foundation Young Scholar Award.
Previously, from 2013 to 2016, I was a postdoctoral visiting assistant professor in the Department of Mathematics at Texas A&M University, College Station, where my mentor was Guoliang Yu. I obtained my PhD in mathematics from the California Institute of Technology in 2013; my thesis advisor was Matilde Marcolli.
Further details can be found in my curriculum vitæ.