Towards a mathematical conjecture for the Landau-Ginzburg/conformal field theory correspondence and beyond

Información del proyecto

MACOLAB

Identificador del acuerdo de subvención: 747555

DOI

10.3030/747555

Proyecto finalizado el 1 Agosto 2018

Fecha de la firma de la CE 16 Febrero 2017

Fecha de inicio 1 Agosto 2017

Fecha de finalización 31 Julio 2019

Financiado con arreglo a

• EXCELLENT SCIENCE - Marie Skłodowska-Curie Actions

Coste total

€ 165 598,80

Aportación de la UE

€ 165 598,80

Coordinado por

UNIVERSITEIT UTRECHT
Netherlands

Periodic Reporting for period 1 - MACOLAB (Towards a mathematical conjecture for the Landau-Ginzburg/conformal field theory correspondence and beyond)

Período documentado: 2017-08-01 hasta 2019-07-31

Resumen del contexto y de los objetivos generales del proyecto

What is the problem/issue being addressed?

The project aims to get a deeper understanding of the relation (suggested by physics, that we will call LG/CFT) between two apparently very different mathematical entities: matrix factorizations (MFs) and representations of vertex operator algebras (VOAs).

Why is it important for society?

This is a project within pure mathematics, and has little relevance for society.

What are the overall objectives?
1) Obtain more equivalences (\mathbb{C}-linear and tensor) between categories of MFs and categories of representations of VOAs,
2) Study further properties shared between these two,
3) Attempt to construct a higher categorical framework where to embed all these equivalences.

Trabajo realizado desde el comienzo del proyecto hasta el final del período abarcado por el informe y los principales resultados hasta la fecha

Research output in the period August 2017-May 2018: 3 preprints in preparation,
- 1 on spectral flows and conjugation morphisms in categories of MFs,
- 1 on algorithmic approaches to orbifold equivalence of potentials, and
- 1 on higher categorical structures within LG/CFT.

Avances que van más allá del estado de la técnica e impacto potencial esperado (incluida la repercusión socioeconómica y las implicaciones sociales más amplias del proyecto hasta la fecha)

"I have found interesting results implying the existence of structures (""spectral flows"") predicted by physics in categories of matrix factorizations. Jointly with my PhD student, I have developed an algorithmic approach that will help finding further equivalences in this setting. Last but not least, I also have made progress towards getting a clear understanding of the higher categorical structures lying behind this correspondence."

EU