Holographic Superconductors in M-Theory
Abstract
On the classification of Brane Tilings
Abstract
Dynamical Logic
Abstract
On the abstract images of profinite groups
Abstract
I will discuss the following
Conjecture B: Finitely generated abstract images of profinite groups are finite.
I will explain how it relates to the width of words and conjugacy classes in finite groups. I will indicate a proof in the special case of 'non-universal' profinite groups and propose several directions for future work.
This conjecture arose in my discussions with various participants of a workshop in Blaubeuren in May 2007 for which I am grateful. (You know who you are!)
On the existence of extreme waves and the Stokes conjecture with vorticity
Abstract
We present some recent results on singular solutions of the problem of travelling gravity water waves on flows with vorticity. We show that, for a certain class of vorticity functions, a sequence of regular waves converges to an extreme wave with stagnation points at its crests. We also show that, for any vorticity function, the profile of an extreme wave must have either a symmetric corner of 120 degrees or a horizontal tangent at any isolated stagnation point. Moreover, the profile necessarily has a symmetric corner of 120 degrees if the vorticity is nonnegative near the free surface.