Higher Gauge Theory is a categorical way of thinking about parallel transport of extended objects. Such parallel transport appears naturally within string and M-theory. In particular, the six-dimensional maximally superconformal theory or at least self-dual strings in four dimensions should be captured by Higher Gauge Theory. I will review some of my recent work in this area, including how M2-brane models fit into the picture, how twistor geometry can yield field equations containing the non-abelian tensor multiplet and give explicit higher versions of the BPST instanton and the 't Hooft-Polyakov monopole. If time permits, I will also talk a bit about a higher version of the IKKT matrix model.

I will present an ADHMN-like construction which generates self-dual string solutions to the effective M5-brane worldvolume theory from solutions to the Basu-Harvey equation.

We consider the hermitian matrix model corresponding to scalar field theory on the fuzzy sphere. Using an expansion of the model which is similar to a high-temperature expansion, we are able to reformulate the model in terms of its eigenvalues. Applying subsequently the saddle point method allows us to extract analytically information on the phase diagram of the theory. Eventually, we can also predict qualitatively the effect of proposed modifications of this theory which are necessary for the theory to be a regularized version of scalar field theory on the plane.