In this talk, I will discuss the construction of 2d (0,2) supersymmetric gauge theories corresponding to the 18 smooth Fano 3-folds and the families of Y^(p,k)(CP1xCP1) and Y^(p,k)(CP2) Sasaki-Einstein 7-manifolds. These 2d (0,2) gauge theories can be considered as the worldvolume theories of D1-branes probing toric Calabi-Yau 4-folds. The talk will illustrate how the map between gauge theory and the corresponding geometry is considerably simplified by a Type IIA brane configuration called brane brick models.

In this talk, I will discuss Type IIA brane configurations consisting of D4-branes suspended between NS5-branes which represent a large class of 2d (0,2) quiver gauge theories. We call these new constructions Brane Brick models. These are T-dual to D1-branes over singular toric Calabi-Yau 4-folds and encode information about the probed Calabi-Yau geometry as well as the corresponding GLSM. If time permits, I will present how Brane Brick models naturally realise in terms of a brane configuration 2d (0,2) Gadde-Gukov-Putrov triality.