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

Informacje na temat projektu

MACOLAB

Identyfikator umowy o grant: 747555

DOI

10.3030/747555

Realizacja projektu zakończyła się 1 Sierpnia 2018

Data podpisania przez KE 16 Lutego 2017

Data rozpoczęcia 1 Sierpnia 2017

Data zakończenia 31 Lipca 2019

Finansowanie w ramach

• EXCELLENT SCIENCE - Marie Skłodowska-Curie Actions

Koszt całkowity

€ 165 598,80

Wkład UE

€ 165 598,80

Koordynowany przez

UNIVERSITEIT UTRECHT
Netherlands

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

Okres sprawozdawczy: 2017-08-01 do 2019-07-31

Podsumowanie kontekstu i ogólnych celów projektu

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.

Prace wykonane od początku projektu do końca okresu sprawozdawczego oraz najważniejsze dotychczasowe rezultaty

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.

Innowacyjność oraz oczekiwany potencjalny wpływ (w tym dotychczasowe znaczenie społeczno-gospodarcze i szersze implikacje społeczne projektu)

"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