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FIELDS-KNOTS

Financiado

Cerrado

Quantum fields and knot homologies

This project is concerned with fundamental problems arising at the interface of quantum field theory, knot theory, and the theory of random matrices. The main aim of the project is to understand two of the most profound phenomena... ver más

30/11/2018

UNIWARSAW

1M€

Presupuesto del proyecto: 1M€

Líder del proyecto

UNIWERSYTET WARSZAWSKI No se ha especificado una descripción o un objeto social para esta compañía.

TRL 4-5

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Financiación concedida El organismo FP7 notifico la concesión del proyecto el día 2018-11-30 No tenemos la información de la convocatoria

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4 Participantes

UNIWARSAW

0.00€ | Lider

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Líder del proyecto

UNIWERSYTET WARSZAWSKI No se ha especificado una descripción o un objeto social para esta compañía.

TRL 4-5

Presupuesto del proyecto 1M€

Fecha límite de participación Sin fecha límite de participación.

Descripción del proyecto This project is concerned with fundamental problems arising at the interface of quantum field theory, knot theory, and the theory of random matrices. The main aim of the project is to understand two of the most profound phenomena in physics and mathematics, namely quantization and categorification, and to establish an explicit and rigorous framework where they come into play in an interrelated fashion. The project and its aims focus on the following areas: - Knot homologies and superpolynomials. The aim of the project in this area is to determine homological knot invariants and to derive an explicit form of colored superpolynomials for a large class of knots and links. - Super-A-polynomial. The aim of the project in this area is to develop a theory of the super-A-polynomial, to find an explicit form of the super-A-polynomial for a large class of knots, and to understand its properties. - Three-dimensional supersymmetric N=2 theories. This project aims to find and understand dualities between theories in this class, in particular theories related to knots by 3d-3d duality, and to generalize this duality to the level of homological knot invariants. - Topological recursion and quantization. The project aims to develop a quantization procedure based on the topological recursion, to demonstrate its consistency with knot-theoretic quantization of A-polynomials, and to generalize this quantization scheme to super-A-polynomials. All these research areas are connected via remarkable dualities unraveled very recently by physicists and mathematicians. The project is interdisciplinary and aims to reach the above goals by taking advantage of these dualities, and through simultaneous and complementary development in quantum field theory, knot theory, and random matrix theory, in collaboration with renowned experts in each of those fields.

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