By Lotte Hollands
This thesis provides numerous new insights at the interface among arithmetic and theoretical physics, with a vital position for Riemann surfaces. to begin with, the duality among Vafa-Witten idea and WZW types is embedded in string thought. Secondly, this version is generalized to an online of dualities connecting topological string conception and N=2 supersymmetric gauge theories to a configuration of D-branes that intersect over a Riemann floor. This description yields a brand new point of view on topological string conception when it comes to a KP integrable approach in keeping with a quantum curve. Thirdly, this thesis describes a geometrical research of wall-crossing in N=4 string idea. And finally, it deals a singular method of constuct metastable vacua in sort IIB string conception.