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STABREP SIGNED

Geometric Models for Calabi-Yau Algebras and Homological Mirror Symmetry

Total Cost €

EC-Contrib. €

Partnership

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STABREP project word cloud

Explore the words cloud of the STABREP project. It provides you a very rough idea of what is the project "STABREP" about.

combinatorics theories consisting geometric duality phenomenon diagrams connections superstring mirror kontsevich conjecture setting combinatorial coherent symplectic homological theory origin 2000s canonical yau model categories cluster geometry ideas co opening formulated sheaves manifold x encoding wild linked bases stability multiserial dimer complete first homology framework surfaces dual calabi introduction famous symmetry intrinsically fukaya algebras special representation riemann appear models category natural generalize scattering

Project "STABREP" data sheet

The following table provides information about the project.

Coordinator	UNIVERSITY OF LEICESTER Organization address address: UNIVERSITY ROAD city: LEICESTER postcode: LE1 7RH website: www.le.ac.uk contact info title: n.a. name: n.a. surname: n.a. function: n.a. email: n.a. telephone: n.a. fax: n.a.
Coordinator Country	United Kingdom [UK]
Total cost	212˙933 €
EC max contribution	212˙933 € (100%)
Programme	1. H2020-EU.1.3.2. (Nurturing excellence by means of cross-border and cross-sector mobility)
Code Call	H2020-MSCA-IF-2018
Funding Scheme	MSCA-IF-EF-ST
Starting year	2020
Duration (year-month-day)	from 2020-09-01 to 2022-08-31

Partnership

Take a look of project's partnership.

#	participants	country	role	EC contrib. [€]
1	UNIVERSITY OF LEICESTER UNIVERSITY OF LEICESTER Organization address address: UNIVERSITY ROAD city: LEICESTER postcode: LE1 7RH website: www.le.ac.uk contact info title: n.a. name: n.a. surname: n.a. function: n.a. email: n.a. telephone: n.a. fax: n.a.	UK (LEICESTER)	coordinator	212˙933.00

Map

Project objective

In this project, I will establish new connections between cluster algebras, mirror symmetry and representation theory through the introduction of geometric models.

Mirror symmetry is a natural phenomenon, first observed in superstring theory, consisting of two main approaches: the A-model, focused on the symplectic side of a Calabi-Yau manifold X, and the B-model, focused on the complex side of the manifold. Mirror symmetry is a duality between the two models. Based on this, Kontsevich formulated his famous homological mirror symmetry conjecture for categories. In this conjecture, the A-model is the Fukaya category of X, and the B-model is the derived category of coherent sheaves of X^. Cluster algebras were introduced in the early 2000s to provide a combinatorial framework for dual canonical bases. Many new ideas in representation theory have their origin in cluster algebras, bringing together category theory, particularly Calabi-Yau categories, combinatorics and the geometry of Riemann surfaces. In exciting recent developments cluster theory and homological mirror symmetry have been linked through scattering diagrams, opening up both theories.

In this project, I will study the connections between cluster combinatorics and scattering diagrams through Calabi-Yau algebras, which appear in a natural way in cluster theory and mirror symmetry. I will develop geometric models for the representation theory of Calabi-Yau algebras encoding, in particular, their (co)homology. This will lead to a complete understanding of these algebras and their role in the mirror symmetry program. Dimer models are intrinsically linked to both cluster algebras and mirror symmetry. As part of my project, I will generalize dimer models to the general setting of special multiserial algebras. Both Calabi-Yau algebras and special multiserial algebras are of wild representation type and my geometric models will lead the way to an understanding of stability conditions for wild algebras.

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The information about "STABREP" are provided by the European Opendata Portal: CORDIS opendata.