Hello! I am Morgan Rogers, one of Professor Caramello's PhD students, and at the time of writing I am in my third year.

I primarily study toposes of monoid actions, including categories of actions of topological monoids on sets (viewed as discrete spaces), and related classes of toposes. Ultimately, I'm hopint that this will lead to a "Topological semi-Galois theory", extending the topos-theoretic Topological Galois theory of Caramello.

My second topos-theoretic passion is the zoology of geometric morphisms: just as toposes have rich and varied structure, the variety that exists amongst geometric morphisms is just as rich, and there are many open questions about how different properties relate to one another. These two interests are related, because most of the well-studied properties of geometric morphisms come from studying localic toposes and the associated localic geometric morphisms, and so are very geometric in nature. I'm curious if morphisms of an algebraic nature coming from the study of (topological) monoids will give interesting new classes of geometric morphism.

Outside of topos theory, I have an academic interest in philosophy, especially in understanding philosophical frameworks that enable us to reason about the ethics issues surrounding artificial intelligence. While it's unlikely to feature in this forum, if and when in-person conferences resume, feel free to strike up a conversation with me on this subject.