Higher Complex Structures and Flat Connections

In 2018, Vladimir Fock and the author introduced a new geometric structure on surfaces, called higher complex structure, whose moduli space is conjecturally diffeomorphic to Hitchin's component. This would give a new geometric approach to higher Teichm\"uller theory. In this paper, we prove several steps towards this conjecture and give a precise picture what has to be done. We show that higher complex structures can be deformed to flat connections. More precisely we show that the cotangent bundle of the moduli space of higher complex structures can be included into a 1-parameter family of spaces of flat connections.Comment: 31 page

Feynman Rules for QCD in Space-Cone Gauge

We present the Lagrangian and Feynman rules for QCD written in space-cone gauge and after eliminating unphysical degrees of freedom from the gluonic sector. The main goal is to clarify and allow for straightforward application of these Feynman rules. We comment on the connection between BCFW recursion relations and space-cone gauge.Comment: 7 pages, typos corrected, diagrams and clarifying text adde