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Quantum fields and knot homologies

Objective

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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Principal Investigator

Piotr Sulkowski (Dr.)

Host institution

UNIWERSYTET WARSZAWSKI

Address

Krakowskie Przedmiescie 26/28
00 927 Warszawa

Poland

Activity type

Higher or Secondary Education Establishments

EU Contribution

€ 1 176 480

Principal Investigator

Piotr Sulkowski (Dr.)

Administrative Contact

Magdalena Kleszczewska (Ms.)

Beneficiaries (4)

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UNIWERSYTET WARSZAWSKI

Poland

EU Contribution

€ 1 176 480

INSTITUTE FOR ADVANCED STUDY - LOUIS BAMBERGER AND MRS FELIX FULD FOUNDATION CORPORATION

United States

EU Contribution

€ 20 313,43

ASSOCIACAO DO INSTITUTO SUPERIOR TECNICO PARA A INVESTIGACAO E DESENVOLVIMENTO

Portugal

EU Contribution

€ 96 000

THE REGENTS OF THE UNIVERSITY OF CALIFORNIA

United States

EU Contribution

€ 52 286,57

Project information

Grant agreement ID: 335739

Status

Closed project

  • Start date

    1 December 2013

  • End date

    30 November 2018

Funded under:

FP7-IDEAS-ERC

  • Overall budget:

    € 1 345 080

  • EU contribution

    € 1 345 080

Hosted by:

UNIWERSYTET WARSZAWSKI

Poland