QUAKQ: Quantum knot invariants and quivers

Project funded by Fundação para a Ciência e a Tecnologia, I.P. (FCT) (Concurso para Projetos de Investigação de caráter Exploratório em Todos os Domínios Científicos 2024), grant 2024.16612.PEX. Funded amount: EUR 59,994, as stated by the source. Runs 2026-02-01 to 2027-07-31. Keywords: Khovanov homology, categorification, BPS invariants, Donaldson-Thomas invariants, Exact sciences. Source: OpenAIRE Graph, from the funder's project data (collected by OpenAIRE on 2026-03-24); national funding data, not CORDIS. Abstract given by the source: This project focuses on the interplay between homological knot invariants, Donaldson-Thomas invariants of quivers, quantum groups and their categorifications, as well as relationships with string theory, and applications in combinatorics. The main goal of this project is to study the knots-quivers correspondence and its implications. In particular, the plan is to determine precisely its origin, by finding the intrinsic definition of the correspondence, and to determine precisely how the categorification of knot invariants and quantization process of A-polynomials enter in this correspondence. The key novelties to be employed in this project include the recent discoveries of generalized knots-quivers correspondence with the usage of quivers with higher level generators, as well as the direct relationship between HOMFLY-PT homologies of torus knots and generalized Schröder paths, both done by team members. Furthermore, this proposal aims to exploit consequences of knots-quivers correspondence in different fields, including low-dimensional topology, categorified invariants of knots and quivers, enumerative combinatorics and integrality properties, by explicit computations and using the complete sets of knots and quivers invariants involved. Related tasks of this proposal include the rigorous definition of (colored) HOMFLY-PT homologies of as well as the rigorous constructions and proofs of some novel properties in the classical Khovanov and sl(n) knot homologies that are motivated by the results on knots-quivers correspondence and structural properties of colored HOMFLY-PT homologies. The knots-quivers correspondence that we have discovered, postulates a deep relationship between quantum invariants of a knot, and motivic Donaldson-Thomas invariants of the corresponding quiver. This intriguing connection between two distinct invariants was motivated by quantization of A-polynomials, structural invariants of homological invariants of knots, and string theory insights on [shortened; the full text is on the OpenAIRE page]

Original source.

Source: OpenAIRE Graph: projects of national funders, OpenAIRE, from the project data of Fundação para a Ciência e a Tecnologia, I.P. (FCT). Retrieved 2026-10-28. Licence: Creative Commons Attribution 4.0 (OpenAIRE Graph). Selected metadata, adapted presentation; the publisher's record is authoritative. No endorsement by the source is implied. Licence: Creative Commons Attribution 4.0 (CC BY 4.0).

AI-assisted summary: The project "QUAKQ: Quantum knot invariants and quivers" is funded by FCT with a grant of EUR 59,994, running from 2026-02-01 to 2027-07-31. It aims to explore the relationship between homological knot invariants and quivers, focusing on their categorification and implications. Suggested technology pillar: enabling. Generated by AI from the public source text; it may contain errors and the original source is authoritative.