Being a root stack imposes strong conditions on inertia groups. Given a group acting on an algebraic variety I will discuss when these conditions are fulfilled and the resulting quotient turns out to be a root stack. This joint work with Ivan Kobyzev uses some fundamental theorems of algebraic geometry, Abhyankar's lemma, the Chevellary-Shephard-Todd theorem and Luna's etale slice theorem. These results will be introduced.

The study of instantons on the infinite cylinder $\mathbb{R} \times \mathbb{T}^3$ is facilitated by the Nahm transform, a sort of non-linear Fourier transform for connections. Proving that the Nahm transform does what one believes it should do is a task requiring input from geometric analysis and algebraic geometry. This talk focuses on the geometric analysis aspects. This is joint work with Jacques Hurtubise.

Speaker's web page: http://www.math.uwaterloo.ca/~bcharbon/

We will generalize the concept of adjoint functors to the theory of quasicategories.