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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.

Field of science

  • /natural sciences/physical sciences/quantum physics/quantum field theory
  • /natural sciences/mathematics/pure mathematics/topology/knot theory
  • /natural sciences/mathematics

Call for proposal

ERC-2013-StG
See other projects for this call

Funding Scheme

ERC-SG - ERC Starting Grant

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)

UNIWERSYTET WARSZAWSKI
Poland
EU contribution
€ 1 176 480
Address
Krakowskie Przedmiescie 26/28
00 927 Warszawa
Activity type
Higher or Secondary Education Establishments
Principal investigator
Piotr Sulkowski (Dr.)
Administrative Contact
Magdalena Kleszczewska (Ms.)
INSTITUTE FOR ADVANCED STUDY - LOUIS BAMBERGER AND MRS FELIX FULD FOUNDATION CORPORATION

Participation ended

United States
EU contribution
€ 20 313,43
Address
Einstein Drive
08540 Princeton
Activity type
Higher or Secondary Education Establishments
Administrative Contact
Roxanne Bridger (Ms.)
ASSOCIACAO DO INSTITUTO SUPERIOR TECNICO PARA A INVESTIGACAO E DESENVOLVIMENTO
Portugal
EU contribution
€ 96 000
Address
Avenida Rovisco Pais 1
1049 001 Lisboa
Activity type
Research Organisations
Administrative Contact
Teresa Malhoa (Dr.)
THE REGENTS OF THE UNIVERSITY OF CALIFORNIA
United States
EU contribution
€ 52 286,57
Address
Franklin Street 1111, 12 Floor
94607 Oakland Ca
Activity type
Higher or Secondary Education Establishments
Administrative Contact
James Ringo (Mr.)