Abstract: 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/