The main theme of this Summer School is enumerative geometry, with particular emphasis on connections with mathematical physics and representation theory. As its core, enumerative geometry is about counting geometric objects. The subject has a history of more than 2 000 years and has enjoyed many wonderful breakthroughs in the golden years of classical algebraic geometry, but we will be interested in more recent developments.

This Summer School will focus on the following main subjects:
- counting curves and sheaves (Gromov-Witten theory, Donaldson-Thomas and related theories)
- gauge theory enumerative geometry (3d gauge theories and Coulomb branches, 4d gauge theories, and Vafa-Witten invariants, etc)
- applications of enumerative geometry to categorification and low-dimensional topology
- Hall algebras and their refined versions (cohomological, K-theoretic, derived categories)