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

Projektinformationen

MACOLAB

ID Finanzhilfevereinbarung: 747555

DOI

10.3030/747555

Das Projekt endete am 1 August 2018

EK-Unterschriftsdatum 16 Februar 2017

Startdatum 1 August 2017

Enddatum 31 Juli 2019

Finanziert unter

• EXCELLENT SCIENCE - Marie Skłodowska-Curie Actions

Gesamtkosten

€ 165 598,80

EU-Beitrag

€ 165 598,80

Koordiniert durch

UNIVERSITEIT UTRECHT
Netherlands

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

Berichtszeitraum: 2017-08-01 bis 2019-07-31

Zusammenfassung vom Kontext und den Gesamtzielen des Projekts

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.

Arbeit, die ab Beginn des Projekts bis zum Ende des durch den Bericht erfassten Berichtszeitraums geleistet wurde, und die wichtigsten bis dahin erzielten Ergebnisse

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.

Fortschritte, die über den aktuellen Stand der Technik hinausgehen und voraussichtliche potenzielle Auswirkungen (einschließlich der bis dato erzielten sozioökonomischen Auswirkungen und weiter gefassten gesellschaftlichen Auswirkungen des Projekts)

"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