QuantumG: Irregular connections on algebraic curves and Quantum Field Theory

Project funded by Fundação para a Ciência e a Tecnologia, I.P. (FCT) (Concurso para Financiamento de Projetos de Investigação Científica e Desenvolvimento Tecnológico em Todos os Domínios Ci), grant PTDC/MAT-PUR/30234/2017. Funded amount: EUR 222,556, as stated by the source. Runs 2018-09-16 to 2022-09-15. Keywords: Irregular connections (opers), Quantum Field Theory, Higgs bundles, Random matrices, Exact sciences. Source: OpenAIRE Graph, from the funder's project data (collected by OpenAIRE on 2026-07-23); national funding data, not CORDIS. Abstract given by the source: Geometry traditionally plays a central role in the mathematical formalism of physics. This relationship received a great impetus from the discovery of the integrability phenomenon in classical field theory, since soliton equations were linearized on the Jacobian variety of an algebraic curve and this led to the solution of celebrated problems in algebraic and enumerative geometry. It has recently emerged that principal and vector bundles on algebraic curves play a central role -albeit not yet properly understood- also in the case of quantum integrable systems. Remarkably, quantum field theories are mostly associated with irregular connections/bundles/fields. For example: The g-Quantum Korteweg- de Vries (KdV) model is a Conformal Field Theory built on any affine Kac Moody algebra g. The surprising but conjectural ODE/IM (Ordinary Differential Equations/Integrable Models) correspondence shows that the physical observables of the theory can be computed as Stokes multipliers of irregular opers with values in the Langlands dual algebra of 'g'. The hyperkaehler metric on the moduli space of stable Higgs bundles can be computed via the Thermodynamic Bethe Ansatz equation of a massive deformation of quantum KdV. The massless limit corresponds to restriction of the moduli space to the opers-subvariety. Random matrices have also appeared on the scene in relation with Painleve equations, the string equations of hermitian and unitary matrix models of 2D gravity are the consistency conditions for isomonodromic deformation of an equation with an irregular singularity, and three dimensional gauge theories, in particular Chern-Simons theory. The general aim of the project is to create a fertile research and training environment for senior and junior scientists working in the fields of Geometry, Mathematical Physics, and Theoretical Physics. The scientific questions we plan to address are mainly two: 1. We plan to achieve a complete analytic and geometric understanding of the [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 "QuantumG" focuses on irregular connections on algebraic curves and quantum field theory, funded by FCT with a grant of EUR 222,556 from 2018-09-16 to 2022-09-15. It explores the role of geometry in physics, particularly in quantum integrable systems. Suggested technology pillar: enabling. Generated by AI from the public source text; it may contain errors and the original source is authoritative.