Jun 15. 2026, 13:50 — 15:00

We review the powerful correspondence between four-dimensional ${\cal N}=1$ supersymmetric quiver gauge theories and the geometry of 3d toric Gorenstein singularities. Central to this correspondence are Brane Tilings—also known as dimer models—which are bipartite graphs drawn on a two-torus that completely specify the field content, superpotential, and gauge interactions of theories living on a stack of N D3-branes probing a toric singularity.

In this talk, we show how to construct these tilings directly from the toric data (toric diagram) of the singularity. The method utilizes an "inverse algorithm" that translates the geometry into the combinatorics of perfect matchings on the dimer model. We further discuss the "forward algorithm," which reconstructs the toric geometry from a given tiling.