Over the last few years, there have been interesting developments in the calculation of new protected quantities for supersymmetric field theories in various dimensions. The mathematical implications of such results are still rather unexplored.

One example is the sphere partition function for two-dimensional gauge theories describing Calabi-Yau sigma models in the IR, computed using UV field theory methods, which may lead to important advances in mirror symmetry. Another is the supersymmetric index of certain three-dimensional gauge theories compactified on a two-sphere, which point to the existence of new homological knot invariants.

The goal of the proposed workshop is to bring together leading mathematicians and mathematical physicists interested in the connections between quantum field theory and frontier areas of mathematics, in order to encourage a fruitful exchange of ideas.