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MMP and Mirrors via Maximal Modification Algebras

Objective

Geometrically, this proposal is concerned primarily with Calabi--Yau threefolds, their (local) classification, their homological properties, various associated structures such as stability conditions and Frobenius manifolds, and the resulting predictions across mirror symmetry. Our approach to these problems is through noncommutative algebra, and necessarily so. We will use techniques from contraction algebras and noncommutative resolutions to classify, using both theoretical and constructive methods, and in the process verify an amended version of a string theory prediction. We will use this to push forward curve-counting and derived category consequences and obstructions, and will work towards building a full database of 3-fold flops. On a parallel track, we will treat fundamental problems in noncommutative resolutions and their variants, and approach some of the founding conjectures in the area. We will tackle problems such as existence of MMAs through to more specific problems such as faithful actions and K(pi,1) through stability manifolds and tilting theory on preprojective algebras. We will furthermore merge all this into an emerging theory of Frobenius manifolds, SKMS, and schobers, and through this expand on recent work constructing mirrors to various flopping contractions.

Field of science

  • /natural sciences/physical sciences/theoretical physics/string theory
  • /natural sciences/mathematics/pure mathematics/algebra

Call for proposal

ERC-2020-COG
See other projects for this call

Funding Scheme

ERC-COG - Consolidator Grant

Host institution

UNIVERSITY OF GLASGOW
Address
University Avenue
G12 8QQ Glasgow
United Kingdom
Activity type
Higher or Secondary Education Establishments
EU contribution
€ 1 889 131

Beneficiaries (1)

UNIVERSITY OF GLASGOW
United Kingdom
EU contribution
€ 1 889 131
Address
University Avenue
G12 8QQ Glasgow
Activity type
Higher or Secondary Education Establishments