This semester-long program will be focused on the enumerative invariants of moduli spaces of sheaves in low dimensions. The main examples of the moduli spaces we will consider are the moduli spaces of sheaves on surfaces and Calabi-Yau 3-folds, the moduli spaces of vector and Higgs bundles on curves, and quiver varieties.
The program will cover a wide range of aspects of this problem: enumerative geometry, knot theory, singularity theory and arithmetic, aiming to facilitate fruitful interactions between the various approaches.