A formally verified proof of the prime number theorem

The prime number theorem, established by Hadamard and de la Vall'ee Poussin independently in 1896, asserts that the density of primes in the positive integers is asymptotic to 1 / ln x. Whereas their proofs made serious use of the methods of complex analysis, elementary proofs were provided by Selberg and Erd"os in 1948. We describe a formally verified version of Selberg's proof, obtained using the Isabelle proof assistant.Comment: 23 page

Perspectives for proof unwinding by programming languages techniques

In this chapter, we propose some future directions of work, potentially beneficial to Mathematics and its foundations, based on the recent import of methodology from the theory of programming languages into proof theory. This scientific essay, written for the audience of proof theorists as well as the working mathematician, is not a survey of the field, but rather a personal view of the author who hopes that it may inspire future and fellow researchers

A Theory of Urban Squatting and Land-Tenure Formalization in Developing Countries

This paper offers a new theoretical approach to urban squatting, reflecting the view that squatters and formal residents compete for land within a city. The key implication of this view is that squatters “squeeze” the formal market, raising the price paid by formal residents. The squatter organizer, however, ensures that this squeezing is not too severe, since otherwise the formal price will rise to a level that invites eviction by landowners (defensive expenditures by squatter households also help to forestall eviction). Because eviction is thus absent in equilibrium, the model differs crucially from previous analytical frameworks, where eviction occurs with some probability.