Joshua Ruiter

Joshua studies algebraic groups, which are kind of like houseboats. A houseboat is both a house and a boat, so building one involves solving engineering problems common to houses (plumbing) and problems common to boats (floating). Additional complications emerge from the interplay of the two structures - for instance, the presence of water may require more safeguards in the electrical system.

An algebraic group is a mathematical object with two structures: it is both an algebraic variety and a group. Studying them involves both algebraic geometry and group theory. Group homomorphisms are the main tool for describing relationships between different groups. Usually when looking at algebraic groups, a mathematician would use algebraic group homomorphisms, group homomorphisms which are also compatible with the algebraic structure.

But wait! In the 1970's some mathematicians discovered that sometimes the "algebraic" assumption is superfluous. They proved that, in some circumstances, an ordinary group homomorphism between two algebraic groups has to be basically algebraic. But they thought it should happen more than just in that situation, so they made a conjecture. Joshua's research is about making progress towards that conjecture and understanding when "algebraic" is a superfluous assumption.

In his free time, Joshua enjoys playing board games, listening to podcasts, and reading science fiction. His recent favorite games are Spirit Island, Dominion, and chess.