Application of supersymmetric vertex algebras to the investigation of supermoduli spaces

• Applicant: Dr. Christoph Sachse
• Subject Area: Mathematics
• Term: from 2008 to 2010
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 73745670

The subject of the proposed project is the application of supersymmetric vertex algebras to the investigation of the structure of supergeometric moduli spaces. In particular we want to study moduli spaces of superconformal structures, i.e., of complex supercurves and super Riemann surfaces (SRS), and moduli spaces of G-bundles on supercurves, where G is a supergroup. Methods applying vertex algebras to the characaterization of moduli spaces of complex structures and G-bundles on curves have proved extremely fruitful in the purely bosonic case. For this reason we expect the results of these investigations to be of great use to a variety of further applications, e.g., the Geometric Langlands Program or the approaches using supergeometric methods for the study of elliptic objects and elliptic cohomology. I expect to gain invaluable new insights for the proposed questions from collaboration with the group of D. Freed at the University of Texas, Austin, where I would have the chance to work with leading experts in the fields of vertex algebras and supergeometry.

• DFG Programme: Research Fellowships
• International Connection: USA
• Host: Professor Dr. Dan Freed