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Office 625

Courriel: shenry2 at uottawa dot ca

Research Interests

I am assistant professor at the university of Ottawa (Ontario) since 2019. My work revolve around several aspect of category theory including:

If you would be interested in doing a PhD or a MSc project at the university of Ottawa under my supervision, you can email me.

Here is a very brief presentation of my research areas. A list of publications can be found below. More details can be also be found in one of these research statements:

which also includes (not totally up to date) informations about my current work and projects.

I've started my research with a phd thesis under the supervision of Alain Connes on the relation between topos theory and non-commutative geometry between 2010 and 2014.

Roughly, topos theory and C*-algebra theory are two generalisations of ordinary topology. My goal was to understand if and how they are related. I studied more precisely continuous fields of Hilbert spaces over toposes, i.e. Hilbert spaces defined in the internal logique of a topos. The algebra of endomorphisms of such a field of Hilbert spaces is a C* algebra closely related to the geometry of the topos. The study of the properties of such continuous fields allow to understand several relations between topos theory and operator algebras.
The introduction of my thesis (linked above) contains a more detailled explanation of theses ideas.

In addition of topos theory and C*-algebra theory, this first project lead me to constructive mathematics (in order to handle Hilbert spaces of the internal logic) and Pointfree topology arised naturally in my works as an extremely powerfull to do constructive analysis.

Since 2015, I have been moving to higher category theory, and more precisely on the construction and comparison of models for higher structures. I was initally interested in higher category theory because of the developement of higher topos theory and homotopy type theory. But, because of the importance of constructive mathematics to topos theory and category theory, I was worried by the non-constructivity of the methods of higher category theory. I hence started to work on the developement on new models and methods for higher category theory and higher structures. And this is at the moment my main area of research. I'm especially interested in the Simpson conjecture, of which I proved a special case , as well as more generally the question of obtaining general strictification theorems. I have also worked on Grothendieck homotopy hypothesis on which I obtained partial results.

I am also active on mathoverflow.


University of Ottawa