The unification of Mathematics via Topos Theory

Abstract

I will propose a new view of Grothendieck toposes as unifying spaces in
Mathematics being able to serve as 'bridges' for transferring information
between distinct mathematical theories. This approach, first introduced in
my Ph.D. dissertation, has already generated ramifications into different
mathematical fields and points towards a realization of Topos Theory as a
unifying theory of Mathematics.

In the talk, I will explain the fundamental principles that characterize my
view of toposes as unifying spaces, and demonstrate the technical usefulness
of these methodologies by providing applications in several distinct areas
including Algebra, Geometry, Topology, Model Theory and Proof Theory.