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Some Topos Theory

2015
This chapter is a rapid introduction to the geometric flavour of topos theory that is used thoughout the book. A Grothendieck topology is a formal calculus of coverings which generalizes the algebra of open covers of a topological space, and can exist in much more generality.
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TOPOS THEORY AND SPACETIME STRUCTURE

International Journal of Geometric Methods in Modern Physics, 2007
According to the recently proposed model of spacetime, various difficulties of quantum field theories and semiclassical quantum gravity on curved 4-Minkowski spacetimes gain new formulations, leading to new solutions. The quantum mechanical effects appear naturally when diffeomorphisms are lifted to 2-morphisms between topoi.
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Class forcing and topos theory

2015
These are notes for a talk delivered at IHES in November 2015, titled "Class forcing and topos theory", video at https://www.youtube.com/watch?v=4AaSySq8 ...
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