This lecture series is an introduction to certain recent developments in applications of supersymmetric field theories in one and two dimensions.

The first half covers basic notions such as supersymmetric quantum mechanics, 2d N=(2,2) supersymmetric sigma models, topological twists and branes.

The second half is intended for advanced topics. The main focus will be Omega-deformation of B-twisted theories and its application to higher-dimensional theories.  One of the goals will be to explain the relation of Costello’s 4d Chern-Simons theory and the Nekrasov-Shatashvili correspondence.