Semiorthogonal decompositions of derived categories of singular varieties

• Applicant: Dr. Martin Kalck
• Subject Area: Mathematics
• Term: since 2022
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 496500943

In this project, I study fundamental algebraic invariants of singular spaces -- in particular, their derived and singularity categories. My motivation stems from intensely studied classical problems in higher-dimensional geometry and inspiring relations to theoretical physics. In both areas, singular spaces play a key role. This includes non-Gorenstein singularities in relation with the fundamental operations of "flips" in the minimal model program (MMP). Despite this, main streams of current research focus on derived categories of non-singular spaces and singularity categories in the Gorenstein case. My recent work also provides new insights beyond these cases, opening up interesting areas for further research. I would like to explore these areas, using methods from cluster theory, Wemyss's homological minimal model program, quasi-hereditary algebras and the technique of relative singularity categories, which was developed in joint works with my collaborators.

• DFG Programme: Research Grants
• International Connection: Austria