Gauge Theories, Tessellations & Riemann Surfaces

Understand

We study and classify regular and semi-regular tessellations of Riemann surfaces of various genera and investigate their corresponding supersymmetric gauge theories.

• These tessellations are generalizations of brane tilings, or bipartite graphs on the torus as well as the Platonic and Archimedean solids on the sphere.
• On higher genus they give rise to intricate patterns.
• Special attention will be paid to the master space and the moduli space of vacua of the gauge theory and to how their geometry is determined by the tessellations.