Hello, I'm Alexander. I am interested in mathematics and AI alignment. I work in Samson Abramsky's group at UCL. Outside of graduate school, I serve as Chief Bard at Timaeus.
Hello, I'm Alexander. I am interested in mathematics and AI alignment. I work in Samson Abramsky's group at UCL. Outside of graduate school, I serve as Chief Bard at Timaeus.
email: alexander@timaeus.co
Twitter: @FellowHominid
See here for idle thoughts. More writing can be found at my LessWrong account - see new shortform and old shortform. Perhaps you are interested in my mistakes instead.
A proof of Gödel's incompleteness theorems after A. Joyal is given. The proof uses internal category theory in an arithmetic universe, a predicative generalisation of topoi. A proof of Löb's Theorem using similar techniques is discussed.
We give an introduction to mono-Anabelian geometry, the study of what features of a scheme may be recovered from its etale fundamental group. We treat the case of the reconstruction of the base field of a curve of strictly Belyi type from its fundamental group.