Adiprasito Lab

Research focus

ERC Consolidator Grant · 2021

From Hodge theory to combinatorics and geometry

We propose an approach to the Dodziuk-Singer conjecture, a central conjecture in geometric topology, specifically concerning the great challenge that understanding aspherical manifolds can pose, based on newly developed tools from combinatorial commutative algebra and combinatorial Hodge Theory, and discuss several intermediate problems along the way. The main idea is based on a connection to commutative algebra via the partition complex, an interpretation of local cohomology that allows for a translation between data contained in the L2 cohomology of a manifold and Lefschetz properties of toric varieties associated to them. Additionally, we outline connections to other approaches to the…

From the public funding record at EU CORDIS. Describes the funded project, not the reviews below.