Objective 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 tocommutative 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 Dodziuk-Singer conjecture as well as special cases, such as the Hopf and Charney-Davis conjectures, and propose ideas to connect the different aspects of the viewpoints into one.Finally, we discuss problems related to the methods proposed, in particular focussing on unrealised and unexploited relations between combinatorics, Hodge theory and geometry. We discuss in particular deformations of polyhedra and metrics, as well as expansion and connectivity. Fields of science natural sciencesmathematicspure mathematicsalgebracommutative algebranatural sciencesmathematicspure mathematicstopologynatural sciencesmathematicspure mathematicsgeometrynatural sciencesmathematicspure mathematicsdiscrete mathematicscombinatorics Programme(s) HORIZON.1.1 - European Research Council (ERC) Main Programme Topic(s) ERC-2021-COG - ERC CONSOLIDATOR GRANTS Call for proposal ERC-2021-COG See other projects for this call Funding Scheme HORIZON-AG - HORIZON Action Grant Budget-Based Host institution THE HEBREW UNIVERSITY OF JERUSALEM Net EU contribution € 1 456 197,00 Address EDMOND J SAFRA CAMPUS GIVAT RAM 91904 Jerusalem Israel See on map Activity type Higher or Secondary Education Establishments Links Contact the organisation Opens in new window Website Opens in new window Participation in EU R&I programmes Opens in new window HORIZON collaboration network Opens in new window Total cost € 1 456 197,00 Beneficiaries (2) Sort alphabetically Sort by Net EU contribution Expand all Collapse all THE HEBREW UNIVERSITY OF JERUSALEM Israel Net EU contribution € 1 456 197,00 Address EDMOND J SAFRA CAMPUS GIVAT RAM 91904 Jerusalem See on map Activity type Higher or Secondary Education Establishments Links Contact the organisation Opens in new window Website Opens in new window Participation in EU R&I programmes Opens in new window HORIZON collaboration network Opens in new window Total cost € 1 456 197,00 KOBENHAVNS UNIVERSITET Denmark Net EU contribution € 491 928,00 Address NORREGADE 10 1165 Kobenhavn See on map Region Danmark Hovedstaden Byen København Activity type Higher or Secondary Education Establishments Links Contact the organisation Opens in new window Website Opens in new window Participation in EU R&I programmes Opens in new window HORIZON collaboration network Opens in new window Total cost € 491 928,00
