TBA

How to mathematically describe the structure of D-brane charges in string theory turns out to be a surprisingly rich question. Stacking D-branes has a natural mathematical interpretation as summing vector bundles, but the mathematical analogue of brane-antibrane annihilation requires the sophisticated machinery of topological K-theory. In this talk I will present a physics-motivated introduction to the subject using the language of non-abelian gauge theory. 

We extend the construction of BPHZ renormalised models in regularity structures via the spectral gap inequality to the fractional heat operator. Its Green’s function fails to be smooth across the entire time-zero hyperplane, violating the classical assumption that kernels are smooth away from the origin. The proof requires a delicate balance between the gain in regularity provided by the spectral gap approach and the limited spatial decay of the kernel. 

Joint work with L. Broux and R. Steele.

Your chance to ask Mathematrix DPhil students about the process of applying to PhD programs, including written stages and interviews!

Make mathematical crafts and get to know other Mathematrix members! Materials provided.