Former Research Area E: ‘Moduli spaces of geometric structures and deformation theory’
The research of Research Area E is continued in Research Area DE as of 10/2012.
Moduli spaces of varieties, sheaves, representations, etc., form themselves varieties or stacks, rigid analytic varieties, Berkovich spaces, depending on the situation. Their study requires various techniques, including modern combinatorial methods and homological algebra like cluster algebras and triangulated categories. Currently, one of the important trends in this broad area is the study of numerical and motivic invariants using moduli spaces, vast generalizations of Donaldson and Gromov-Witten invariants. The numerical information is often encoded by modular forms and the combinatorics is described in terms of wall crossing formulas and cluster algebras. Studied topics are:
- Moduli spaces of bundles and Hitchin fibration,
- Stability conditions and periods,
- Cluster algebras,
- Hyperkähler manifolds,
- Eisenstein series,
- Motivic homotopy theory.