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

Informazioni relative al progetto

MACOLAB

ID dell’accordo di sovvenzione: 747555

DOI

10.3030/747555

Progetto concluso il 1 Agosto 2018

Data della firma CE 16 Febbraio 2017

Data di avvio 1 Agosto 2017

Data di completamento 31 Luglio 2019

Finanziato da

• EXCELLENT SCIENCE - Marie Skłodowska-Curie Actions

Costo totale

€ 165 598,80

Contributo UE

€ 165 598,80

Coordinato da

UNIVERSITEIT UTRECHT
Netherlands

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

Periodo di rendicontazione: 2017-08-01 al 2019-07-31

Sintesi del contesto e degli obiettivi generali del progetto

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.

Lavoro eseguito dall’inizio del progetto fino alla fine del periodo coperto dalla relazione e principali risultati finora ottenuti

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.

Progressi oltre lo stato dell’arte e potenziale impatto previsto (incluso l’impatto socioeconomico e le implicazioni sociali più ampie del progetto fino ad ora)

"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